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Doctoral Thesis

Numerical homogenization of subcellular cytoskeletal processesto reveal novel mechanisms of Rho/Rac dependent adhesion

Author(s): Loosli, Yannick

Publication Date: 2012

Permanent Link: https://doi.org/10.3929/ethz-a-007619561

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Diss. ETH No. 20533

Numerical homogenization of subcellular cytoskeletal

processes to reveal novel mechanisms of Rho/Rac

dependent adhesion

A dissertation submitted to the

ETH Zürich

For the degree of

Doctor of Science

Presented by

Yannick Loosli

Dipl. Masch-Ing. ETH

Born 31th August, 1979

Citizen of Sumiswald, BE

Accepted on the recommendation of

Prof. Dr. Jess G. Snedeker

Dr. Alexander Verkhovsky

Dr. Reto Luginbühl

2012

How simplification highlights hidden mechanism

“Everything should be made as simple as possible, but not

simpler", A. Einstein

iii Preface

Table of Contents

Aknowledgement ............................................................................................................................... vi

Summary .......................................................................................................................................... viii

Résumé .............................................................................................................................................. xi

................................................................................................ 15 Chapter 1 : Motivation and aims

Abstract ............................................................................................................................................. 17

Introduction ...................................................................................................................................... 18

Detailed research plan ...................................................................................................................... 19

Reference .......................................................................................................................................... 21

................................................. 23 Chapter 2 : Background to the top-down theoretical framework

Abstract ............................................................................................................................................. 25

Introduction ...................................................................................................................................... 26

Biological Underpinnings .................................................................................................................. 27

Spreading ...................................................................................................................................... 27

Controlled cell spreading .............................................................................................................. 28

Cellular adhesion and focal adhesion plaques .............................................................................. 29

Actin machinery ............................................................................................................................ 31

Single cell spreading models ............................................................................................................. 32

Kinetics of spreading ..................................................................................................................... 33

Cell reinforcement models ............................................................................................................ 34

Discrete spreading model using divided medium ......................................................................... 34

A Novel Predictive Model of Cytoskeleton Reorganization .............................................................. 35

Algorithm description ................................................................................................................... 35

Initial comparison between “in-vitro” and “in-silico” experiments.............................................. 39

Discussion.......................................................................................................................................... 40

Conclusion and Outlook for integrated Multi-scale simulations ...................................................... 41

Reference .......................................................................................................................................... 43

................................................................... 49 Chapter 3 : Description of the numerical framework

Abstract ............................................................................................................................................. 51

Introduction ...................................................................................................................................... 52

Aknowledgement

The Model ......................................................................................................................................... 53

General description of the spreading algorithm ........................................................................... 55

The motility functions: lamellipodia and filopodia ....................................................................... 57

Combining filopodia and lamellipodia motility functions through spatiotemporal rules of

interaction ..................................................................................................................................... 57

Computational Detail .................................................................................................................... 60

Results ............................................................................................................................................... 61

Lamellipodia are the principal drivers of cell spreading on highly constrained adhesive islands 61

Filopodial spreading dominates cell flattening on arrays of squares ........................................... 63

Cell spreading on parallel adhesive stripes is characterized by a mixed spreading mode ........... 64

Remote force gathering is essential to achieve realistic focal adhesion and actin bundle

organizations ................................................................................................................................. 66

Discussion: ........................................................................................................................................ 68

The model successfully predicts cells spreading on micro-patterned adhesive substrates that

elicit a dominant motility function ............................................................................................... 68

Simplifications in the modeling framework: Limitations and potential consequences ................ 69

Novel insight to the formation and evolution of focal adhesions – the central role of remote

force gathering according to actin bundle length......................................................................... 70

Conclusion ......................................................................................................................................... 71

Supplementary Material ................................................................................................................... 72

Reference .......................................................................................................................................... 73

...................................................... 77 Chapter 4 : An actin length threshold regulates cell adhesion

Abstract ............................................................................................................................................. 78

Introduction ...................................................................................................................................... 79

Method ............................................................................................................................................. 82

Pattern microfabrication ............................................................................................................... 82

Cell culture .................................................................................................................................... 83

Results ............................................................................................................................................... 84

The length threshold maturation creates actin bridges spanning non-adhesive gaps ................. 84

Statistical quantification of the length threshold maturation ...................................................... 87

Discussion.......................................................................................................................................... 90

LTM, myosin and contractility under the scope ........................................................................... 92

Decoupling the effect of pattern geometry and LTM-base process ............................................. 92

Actin bridges, transverse arcs and cell morphological integrity ................................................... 93

Length threshold maturation and the lamellipodium/lamellum hypothesis ............................... 94

v Preface

Conclusion ......................................................................................................................................... 94

Supplementary material ................................................................................................................... 95

References ........................................................................................................................................ 97

............................................................................ 99 Chapter 5 : How Rho/Rac regulates cell shape

Abstract ........................................................................................................................................... 101

Introduction .................................................................................................................................... 102

Methods .......................................................................................................................................... 103

Spreading algorithm ................................................................................................................... 104

Parametric investigation ............................................................................................................. 106

Results ............................................................................................................................................. 107

Cell roundness and membrane activity are dominated by the maturation threshold length and

the variability in lamellipodial velocity, whereas spreading kinetics mostly rely on protrusion

speed ........................................................................................................................................... 107

Specific combinations of parameters are required to mimic the isotropic-anisotropic transition

.................................................................................................................................................... 109

Discussion........................................................................................................................................ 112

The length dependent loading of the actin bundles delineating the lamellum/lamellipodium

interface ...................................................................................................................................... 113

Lamellipodium inhibition can be regulated by a subtle shift in Rho and Rac protein interaction

affecting focal adhesion maturation ........................................................................................... 113

How Rho/Rac signaling cooperate to trigger transition between isotropic and anisotropic

spreading modes ......................................................................................................................... 114

Conclusion ....................................................................................................................................... 116

References ...................................................................................................................................... 117

................................................................................................................ 121 Chapter 6 : Synthesis

Retrospective .................................................................................................................................. 122

Limitations ...................................................................................................................................... 125

Outlook ........................................................................................................................................... 127

Conclusion ....................................................................................................................................... 127

Reference ........................................................................................................................................ 129

Curriculum Vitae ...................................................................................................................... 131

Aknowledgement

Aknowledgement

I am now happy to write the acknowledgement section of the thesis for two reasons. It means that I

am getting really close to achieve my thesis and, of course, for the opportunity to thank the many

people who have supported me both humanly and scientifically during the accomplishment of my

PhD. While reading these lines keep in mind my high decibels flourish English with its charming

“pointe” of French accent. This will add some relief to the following lines.

A PhD is definitively a long journey, where the role of the supervisor is central. An ideal supervisor

gives you sufficient liberty to move forward in your own way without forgetting to keep you on the

right track. Prof. Jess Snedeker did so and definitively much more. It is simply not possible here to list

everything since it ranges from science to “life”. Furthermore it would be presumptuous since Prof.

Snedeker might have better memories of some social activities than me. Besides the supervisor, one

has the chance to meet people that help moving more efficiently forward. Dr. Verkhosky is one of

them. All over the course of my PhD I have had the opportunity to discuss and develop some

fundamental ideas of my work with Dr. Verkhovsky. I am furthermore really glad that Dr. Verkhosky

accepted to join my committee. The third member of my committee, Dr. Luginbuehl, is the one who

support me from the very beginning at the RMS Foundation. He helps me to bring concepts together

and to draw the first proposal. He then stays along during the whole journey with advices and

scientifical help. Not to forget is the whole not professional part, which I enjoyed very much.

Therefore Dr. Luginbuehl deserves definitively very special thanks.

This brings me to RMS Foundation, where I have spent 6 great years. I have learned a lot there since

my master. Robert Mathys and Beat Gasser have made the PhD possible by arranging my schedule at

the RMS and supporting me with the required funding. Leätitia, Josi, Jorge, Rainer, Marc, André and

many others have provided me with advices and scientific expertise or have, simply, lent me an

attentive ears.

Before going further, I would like to acknowledge Benoit Vianay and Céline Labouesse, two gifted

and passionate scientists form the LCB (EPFL). We had elaborate together research projects and

challenge our opinions on cell biology during endlessly conversations. Their help has been key to the

success of my thesis. Obviously we also had other center of interests that we have deepen outside

the labs.

During a PhD, you spend quite a bit of time in your Lab and in its logical “follow ups”. A Lab is made

of people, who I want to thanks for their scientific help but not only… Yufei, I really appreciated your

unexpected and incisive retorts during lunch breaks. I would like to thank Xiang, who had helped me

to prepare a journey to Xinjiang that will unfortunately not occur this year. But all the tips are not

lost… I will go to China! Marco and Jen. I enjoyed a lot talking with you about mountains and travels.

Keep on going with such great experiences! And many thanks to Jen for revising the conclusion

manuscript. Gion, I really appreciated having long conversations with you especially about more

than science. Having you around as only Swiss German PhD student in and out the lab was really fun.

I like to thank a really gifted artist whose peculiar drawings have remained long around my office

even after his departure. Speaking French with Philippe about orthopedics, products from Valais or

what inspired his drawing, was always fun. I am looking forward for each of his new piece of art! I

vii Preface

hope that Philippe will pass his passion to both his sons (of course with the Carole’s agreement).

Italy is well-known, among others, for wines, fashion, food culture and so on. In our Lab, it is known

as the country of origin of a colleague as loud as myself, Guido. I appreciated how Guido fought

courageously four years long against a matter of fact: France is cooler (e.g. better) than Italy…. We

had this conversation in many different locations, often not in the lab. It was really AUSOM to have

this Mediterranean colleague and more important, a friend. Thanks Guido!

To conclude I would like to thanks my friends from Zürich and Bienne. They were at any time

motivated (not too early) for some activities essential to relax: Thomas, Romain, Fab, Rob and many

others in Zürich and the Anklin brothers from Bienne. I am really happy that my parents have

encouraged me to continue to study rather than opting for an apprentice at Crossair and support me

all along my definitively “long” studies. Congratulations to my brother as well who will soon follow

up with writing the acknowledgements for his PhD. One last line to thank my wife, Samuela, simply

for being here every day.

Yannick

Summary

Summary From the early beginning of humanity, humans have had to fight against injuries and diseases.

Consequently a wide range of treatment strategies have been empirically developed during these

past three thousand years. Without any knowledge of the existence of cells, five centuries B.C.,

Hyppocrates and his contemporaries have successfully established mechanical and chemical

methods that modify cellular behaviors to achieve healing. For instance, they resorted to plant

based medications to alter biochemical pathways, which today are known as intra- and extra-cellular

communication means. Cells respond to these stimuli and produce proteins, which, for instance,

inhibit pain receptors or act against inflammation. Similarly, local mechanical constraining of limbs

favors fracture healing by providing cells with an ideal environment for healing.

Current medical science aims at more specificity and efficiency by triggering a targeted adaptation of

the cellular behavior. This is only achievable by enhancing our knowledge of the interactions both

within cells and between cells and their environment. Although long underestimated, the ability of

cells to dynamically sense their mechanical environment has emerged as a major vector that

influences cellular behavior. For instance, cells respond to periodic deformations of their

environment by adapting their internal structural organization. Another illustration is how

mesenchymal stem cells differentiate toward bone-like or neuron-like cells depending on the

stiffness of their surroundings. These are examples of mechanobiology, an interdisciplinary field

dedicated to the survey of the processes employed by cells to sense, transduce and response to

mechanical stimuli. The coming section gives a broad overview of the some underpinnings of

mechanobiology, in which adhesions sites and actin cytoskeleton plays a central role.

Adhesion sites are clusters of proteins organized around a transmembrane protein connected to the

cell “muscle”. Cells generate contractile and protruding forces with their actin cytoskeleton (a

network of filamentous bio-polymers) and myosin (a molecular motor). Besides force generation,

contractility plays a second role. According to recent investigations, contractility is a major

mechanism for cells to sense their environment. This occurs by a subtle dynamic balance of the cell

endogenous forces and the extra-cellular forces at adhesion sites. A consequence, on a short time

scale (hour), is the maturation of the adhesion sites along with their anchoring actin bundles. While

maturating, adhesion sites grow by recruiting further proteins. Consequently mechanical stability

increases, endogenous force rises and an adhesion signaling is modified. Adhesion sites that have

undergone the whole maturation process (focal adhesions) last for hours, whereas small nascent

adhesions lifetime only spans minutes. Similarly actin bundles thicken, while maturating, by

recruiting further actin filaments and certainly cross-linking proteins. In their final stage myosin

colocalizes and enables high contraction forces. How adhesions sites and actin bundles mature is of

paramount importance for cellular behavior such as adhesion, motility or modification of cells fate. A

deeper understanding of adhesion site and actin bundle maturation processes will certainly bring

essential clues on cancer circumvention, wound healing promotion, orthopedic implant design, etc.

As established by recent studies, cellular behavior is the result of the coordination of numerous

meso-cellular processes (process occurring at an intermediate scale between cell and molecular

length scale), which themselves involve a multitude of molecular events. Current methods of cell

biology have revealed key aspects of all these underlying subcellular processes. However,

deciphering how these processes interact one with each other on various time and length scales is

extremely challenging with classical techniques.

ix Preface

In the first part of this thesis, we elaborate a method to alleviate the aforementioned limitation. We

develop a stochastic numerical top-down framework beyond current state of the art, where meso-

scale processes are, in contrast to the classic analytical approach, geometrically modeled to

principally focus on their interactions and not on their own underlying mechanisms. We resort to the

top-down approach to decipher how motility functions, the principal meso-scale processes driving

cell motion, interact with actin bundles and adhesion sites to achieve cell spreading. Cell spreading is

common behavior for cells that contact a 2D substrate (surface) they can interact with. During

spreading, cells initiate specific anchorage locations (adhesion sites) and heavily reorganize their

actin cytoskeleton. For the numerical outcomes to reproduce with fidelity published data of cell

spreading on geometrically constraining substrates (substrate with well-defined regions on which

cells can attach to), we had to elaborate an additional interaction rule to complete the one derived

from the literature. This novel rule describes how lamellar contractility (centripetal forces generated

within the cell body) is gathered by cells to trigger the stabilization of the adhesion sites and actin

bundles. To support the existence of this innovative mechanism called “the length threshold

maturation process”, we subjected it to tailored experiments of cell spreading on constraining

adhesive regions. The aim is to provide the cells with the ideal boundary conditions supposed to

trigger the length threshold maturation process. In agreement with our expectations we observed

actin bundles having the spatial characteristics inherent to the length threshold maturation process,

which strongly supports the existence of the length threshold maturation process. We were

furthermore able to obtain quantitative insight that corroborated in-silico predictions.

In the second part of the thesis, we successfully attempt to explore the mechanism by which cells

integrate intra-cellular biomechemical signaling into morphology adaptation with our thoroughly

validated top-down numerical approach. It was experimentally established that cells adopt either

circular or polygonal shapes depending of the constituents of their culture media. The numerical

top-down approach successfully reproduces this observation by adequately varying the parameters

describing the motility function dynamics and the length threshold maturation process. We were

able to relate this parameter variation to the activation of two signaling proteins, Rho and Rac.

Scientists already suspected Rho and Rac to be upstream from cell morphology regulation. However

the outcomes presented in this thesis go one step further by describing a mechanism by which cells

transform a molecular biochemical signal (Rho/Rac activity) into an alteration of the global cell

mechanical and structural behavior (cell morphology).

Refocusing on medical science, this thesis brings interesting pieces to the picture though the puzzle

is far from completion. Knowing how to regulate these adhesion sites and actin bundles during

spreading, which are essential for cellular contractility, provides critical insight to design cell-

instructive biomaterials with enhanced cellular adherence and optimized controlled on cell fate.

Orthopaedic devices manufactured out of such biomaterials are expected to perform better than

current ones. The second major finding is the mechanism by which cell morphology responds to the

variation of the Rho/Rac balance. This finding could eventually assist to find a point of attack to fight

against metastatic invasion, which resorts to shape and actin cytoskeleton alteration to invade the

organism.

In conclusion, in this thesis, we elaborated and validated an efficient novel innovative numerical

approach to investigate how cells orchestrate sub-cellular processes. By applying this strategy to cell

spreading, we predicted the downstream consequences of geometrically constraining a cell

Summary

regarding to adhesion sites and actin bundle layout. We further revealed how cells integrate

changing molecular signaling in cell morphology modification via lamellar contraction and the length

threshold maturation process. Conjugating multi-scale aspects and detailed explanation of the

underpinnings render this thesis complete.

xi Preface

Résumé Depuis ses origines, l’humanité essaie de se soigner. L’humain a appris à se battre contre différentes

maladies et blessures en développant diverses solutions empiriques durant plus de trois mille ans.

Cinq siècles avant J.C., Hyppocrate et ses contemporains ont posé les fondements de la médecine

moderne sans même connaitre l’existence des cellules. Ils ont réussi à modifier le comportement

cellulaire pour permettre la guérison. Pour ce faire, ils ont altéré les voies de communications des

cellules par des moyens chimiques, grâces à des médicaments dérivés de plantes. Les cellules ont

répondu en conséquence en produisant des protéines qui inhibent la douleur ou agissent contre

l’inflammation. De manière similaire, une immobilisation d’un membre cassé favorise la

régénération osseuse en fournissant aux cellules un environnement idéal pour permettre la

guérison.

De nos jours, les techniques médicales tendent vers l’efficacité et la spécificité ce qui est

envisageable en induisant des changements ciblés du comportement cellulaire. La meilleure

stratégie pour atteindre cet objectif est d’approfondir notre compréhension actuelle des interactions

entre les cellules et leur environnement. Longtemps négligée, la capacité des cellules à percevoir

dynamiquement leur environnement mécanique est acceptée, aujourd’hui, comme un des

principaux vecteurs influençant le comportement cellulaire. Un exemple est la réorganisation des

composants internes de la cellule lorsque son environnement est sujet à des déformations

périodiques. De la même manière, les cellules souches se différencient en cellules osseuses ou en

neurones suivant la rigidité de leur environnement. Ces deux exemples sont tirés de la mécano-

biologie, une science interdisciplinaire dédiée aux processus utilisés par les cellules pour percevoir,

convertir le signal et réagir aux stimuli mécaniques. Le paragraphe suivant décrit quelques

mécanismes de mécano-biologie dans lesquels les sites d’adhésion entre une cellule et son substrat

(2D environnement) ainsi que le cytosquelette jouent un rôle primordial.

Les sites d’adhésion sont des agrégats de protéines organisés autour d’une protéine

transmembranaire. Ces régions adhésives lient le cytosquelette de la cellule à l’extérieur. Ce

cytosquelette, qui est un réseau de bio-polymère, permet aux cellules de générer des forces dites de

contraction et de protrusion. La contractilité n’a pas que des effets mécaniques. En effet, de

récentes études ont établi que la contractilité est au centre du processus de perception mécanique

de la cellule. Ceci est possible par un subtil changement de l’équilibre entre les forces intra- et extra-

cellulaires. A court terme (quelques heures), les cellules intègrent ces stimuli en déclenchant la

maturation des sites d’adhésion ainsi que des câbles d’actine pour les stabiliser. La maturation des

sites d’adhésion est caractérisée par un recrutement de nouvelles protéines ce qui permet

d’augmenter la stabilité mécanique des adhésions. En conséquence, de plus grandes forces intra-

cellulaires peuvent agir dessus ce qui modifie les signaux émis par les sites d’adhésion. Les sites

d’adhésion qui ont entièrement subi le processus de maturation, les adhésion focales, sont stables

pour plusieurs heures. En revanche les sites d’adhésion qui ne maturent pas ont une espérance de

vie de quelques minutes. De manière similaire, les câbles d’actine s’épaississent pendant le

processus de maturation en recrutant de nouveaux filaments d’actine qui sont interconnectés par

des protéines dites de «réticulation». A la fin de leur maturation, les câbles d’actine se lient à des

myosines. Ces complexes peuvent générer d’importantes forces contractiles. L’importance des sites

d’adhésion et des câbles d’actine pour la détermination de comportements cellulaires tels que

l’adhésion, la motilité et même, en fin de compte, le sort de cellules est aujourd’hui clairement

Résumé

acceptée par les scientifiques. Néanmoins, notre compréhension de ces phénomènes est toujours

limitée. Etendre notre entendement de ces processus aurait un impact indiscutable sur la médicine

en amenant des éléments pour, entre autres, améliorer le traitement de cancers, favoriser la

guérison des plaies ou améliorer le design des implants orthopédiques.

Les comportements cellulaires sont le résultat de la coordination de nombreux « méso-processus »

(processus ayant une taille typiquement comprise entre l’échelle de la cellule et celle des

molécules), qui sont, eux-mêmes, engendrés par une multitude de processus moléculaires. La

biologie cellulaire d’aujourd’hui a mis en évidence les mécanismes qui régulent les processus sub-

cellulaires. En revanche notre compréhension des interactions qui existent entre ces processus,

couvrant plusieurs échelles temporelles et spatiales, reste limitée principalement à cause des

approches classiques utilisées pour les étudier. En effet ces dernières ne sont pas réellement

adaptées.

Dans la première partie de cette thèse, nous introduisons une nouvelle méthode permettant de

réduire cette limitation. Nous avons développé une approche numérique non-déterministique

clairement innovante. Contrairement aux modèles classiques, qui sont généralement analytiques,

notre approche est fonctionnelle ce qui permet de mettre en exergue l’étude des interactions entre

méso-processus et non pas leur propre fonctionnement. Nous avons appliqué cette approche pour

explorer comment les fonctions motiles, qui sont les principaux méso-processus de la motilité

cellulaire, interagissent avec les câbles d’actine et les sites d’adhésion pour permettre le

déploiement cellulaire. Presque toutes les cellules touchant un substrat adhésif régissent en

« s’aplatissant » dessus. Ce phénomène est appelé le déploiement cellulaire. Pendant le

déploiement cellulaire, les cellules établisses des points d’ancrage spécifiques, les sites d’adhésion,

et le cytosquelette d’actine subit une importante modification de sa configuration spatiale. Pour

simuler les résultats publiés de cellules se déployant sur des surfaces adhésives comportant des

micro-motifs (substrat ayant des zones adhésives définies très exactement), nous avons mis à jour

un nouveau mécanisme qui régit les interactions entre les cellules et leur substrat. Cette loi décrit

comment les contractions de la lamella (force centripètes générées dans le corps de la cellule) sont

cumulées pour déclencher la stabilisation des sites d’adhésion et des câble d’actine, en d’autres

termes leur maturation. Pour vérifier l’existence de ce phénomène, nous avons l’avons testé

expérimentalement. Pour ce faire, nous avons élaboré des micro-motifs supposés fournir aux

cellules des conditions de bords (géométriques) idéales pour déclencher le processus de maturation.

En accord avec nos prédictions, nous avons observé la formation de câbles d’actine ayant toutes les

caractéristiques spatiales inhérentes au processus de maturation décrit ci-avant. Ces faits nous

apportent des appuis tangibles concernant l’existence de processus de maturation. De plus, la

quantification expérimentale du processus corrobore nos prédictions numériques.

Dans le deuxième partie de la thèse, nous avons réussi à comprendre par quel mécanisme les

cellules intègrent des signaux bio-chimiques pour changer leur morphologie. Pour ce faire, nous

avons utilisé notre approche innovante décrite précédemment. Des expériences ont permis

d’observer des cellules modifiant leur forme de circulaire à polygonale suivant les constituants de

leur solution de culture. Cette altération est certainement due à des modifications des signaux intra-

cellulaires pertinents pour la coordination du cytosquelette d’actine. Notre modèle peut reproduire

avec exactitude ces observations en modifiant convenablement les paramètres décrivant les

xiii Preface

fonctions motiles et celui régulant le processus de maturation décrit ci-avant. Nous avons réussi à

interpréter ces résultats en termes activation de deux protéines de signalisations, Rho et Rac.

D’autres groupes de recherche ont déjà établi une corrélation entre la signalisation de Rho/Rac et la

forme des cellules. Néanmoins nous sommes allés plus loin dans cette thèse en décrivant un

mécanisme par lequel les cellules transforment un signal biochimique (activité de Rho/Rac) en une

réponse structurelle de la cellule (morphologie de la cellule).

Pour revenir aux techniques médicales, cette thèse apporte quelques pièces fort intéressantes mais

le puzzle est néanmoins loin d’être complété. En effet comprendre comment les cellules régulent

leurs sites d’adhésion et leurs câbles d’actine est essentiel pour prédire la contractilité cellulaire et

apporter des éléments nécessaires au design de biomatériau ayant une capacité accrue d’adhésion

et une augmentation du contrôle du sort cellulaire. La seconde découverte de cette thèse est

l’isolation d’un des mécanismes qui est à l’origine des modifications morphologiques des cellules. Ce

point va permettre de claires avancées dans notre compréhension du contrôle morphologique des

cellules ce qui a un large spectre d’applications.

Pour conclure, dans cette thèse, nous avons développé et validé une nouvelle approche numérique,

innovante et efficace pour étudier comment les cellules orchestrent leur processus sub-cellulaires.

En l’appliquant au déploiement cellulaire, nous avons été capables de prédire les conséquences

d’une restriction géométrique sur l’organisation des sites d’adhésion et des câbles d’actine. De plus

nous avons mis à jour un processus par lequel les cellules intègrent des signaux bio-chimiques pour

modifier leur forme par le biais de la contraction de la lamella. Ces avancées sont détaillées au long

de la thèse et leur aspect « multi-échelles » est discuté dans la synthèse.

Chapter 1

Motivation and Aims

17 Background

Abstract

Aim: Describe major interactions between relevant cellular sub-functions of cell spreading within

a theoretical framework to explore adhesion turnover and actin dynamic and their upstream

signaling pathways.

Motivation: Cell motility is an essential aspect of developmental biology, wound healing and many

form of cancer development. This cellular process initiated, by spreading, relies on numerous sub-

cellular events, which are generally widely investigated. However mechanistic interpretation and

integration of these events into a comprehensive framework describing global cellular behavior is

still largely missing. This prevents, among others, the elaboration of target drugs enhancing

wound healing or enabling an early action on congenital diseases or cancer as well as optimized

orthopedic implants structures and surfaces.

Strategy: Instead of applying a traditional reconstructive approach to decipher the spatiotemporal

integration of sub-cellular processes, we propose a radically different method, where

homogenized sub-cellular events are investigated through a numerical top-down approach

describing their interactions. This strategy is applied to cell spreading, a process where cells

initiate adhesions and contractile acto-myosin bundles. The so uncovered mechanisms are then

experimentally verified. Finally upstream adhesion based signaling is explored by an extensive

parametrical study.

Introduction

Introduction Cell spreading and migration are driven by highly coordinated but stochastic molecular processes

like actin polymerization and acto-myosin contractility (Welf and Haugh, 2010). In the case of

migration, these coordinated processes respectively protrude the leading edge of the cell and retract

its rear (Lauffenburger and Horwitz, 1996; Mogilner and Keren, 2009; Small and Resch, 2005). In cell

spreading, the spatiotemporal interactions between the actin machinery and cell/substrate

adhesions coordinate a rapid increase in interface area between a cell and its substrate after first

contact (Cuvelier et al., 2007; Döbereiner et al., 2004; Giannone et al., 2004). To achieve such goals,

a cell must synchronize numerous and complex “cellular subfunctions” in both space and time.

These subfunctions manifest at the mesoscale, with effective outcomes acting above the molecular

length scales (e.g. protein signaling or actin retrograde flow) but below the scale of the whole cell

(e.g. cell morphology, cell-cell contact). In cell motility and spreading, the key mesoscale

subfunctions include the actions of the lamellipodia and filopodia, and the formation and maturation

of substrate adhesions. This PhD explores the biophysical interdependencies of these processes

that act to govern focal adhesion dynamics and collectively enable cell to spread.

While extensive molecular investigations of cell movement have elucidated many key mechanisms

(e.g. molecular mechanics; signaling), understanding signaling cross-talk across spatiotemporally

interrelated cellular subfunctions is extremely complex, and remains a major challenge in cell biology

and cell biophysics (Fletcher and Mullins, 2010). We propose to introduce a novel theoretical

framework (and numerical implementation) that overcomes some aspects of this complexity to

probe possible spatiotemporal coordination mechanisms that govern focal adhesion dynamics.

Theoretical derived insight will enable identification of plausible spatiotemporal interactions for

further in-vitro investigation.

To understand how mesoscale processes integrate to a functional, whole-cell behavior, two distinct

and often complementary strategies have emerged. A bottom-up approach attempts to define the

essential molecular components and their interactions by reconstituting complex cell behaviors

using isolated molecules and/or cell extracts (Liu and Fletcher, 2009). This approach can yield

elegant experimental designs that provide clear insight into how cells integrate molecular events

within the larger (mesoscale) processes that coordinate cell behavior. However, bottom-up

approaches are generally limited to relatively simplified processes that can be investigated using

purified components and cell-extracts. Further, the use of numerous molecular compounds and/or

cell extracts permits mechanisms to enter an experiment that are only phenomenologically

understood. Thus applying this strategy to elaborate highly complex regulation of processes like

focal adhesion dynamics may be intractable; Our current knowledge of focal adhesion regulation

involves at least 180 interacting proteins (Zaidel-Bar, 2009; Zaidel-Bar and Geiger, 2010; Zaidel-Bar

et al., 2007).

Complementary “top-down” strategies can be used in an attempt to overcome some of the detailed

complexity that will inevitably bog-down a bottom-up approach. We describe here how this may be

achieved by homogenizing complex molecular interactions into phenomenological descriptions of

cellular subprocesses (subfunctions) that are defined in terms of functional inputs and outputs. For

dynamic cell behaviors like cell spreading, the inputs and outputs can be defined in spatiotemporal

terms: the advance of the lamellipodium; the dynamics of filopodial protrusion; the formation of

mature focal adhesions and acto-myosin bundles. We will demonstrate that by dictating rules of

19 Background

interaction between such mesoscale cell subprocesses, we can gain insight into cellular coordination

of these processes, and quantitatively elucidate key details involved in the mechanisms. In this work

we will focus on cell spreading, using the model to elaborate potential mechanisms behind how focal

adhesions form, mature, and eventually dictate spread cell morphology.

Detailed research plan Aim 1 Development of a novel numerical method to investigate cell spreading by integrating

cellular subfunctions: How a top-down numerical approach helps to decipher interplay between

sub-cellular processes.

Our assumption: Cellular processes are generally ruled by numerous redundant molecular events that

are difficult to isolate and to individually understand. As a consequence, simulating independently

every molecular event and their consequences on cell behavior is extremely difficult if not impossible.

An alternative approach to such reconstruction method is requested. By assuming that numerous

events act together toward a single objective, one can use a top-down method to model whole cell

behavior. In other words a single functional rule is sufficient to capture diverse molecular events

aiming at a single downstream consequence.

Our strategy is to develop an initial coarse numerical model of spreading cells to ensure the

feasibility of this top-down approach. For this purpose an extensive literature review of the

processes governing spreading is mandatory to determine the most important ones. Then these

processes are translated into rules that are numerically implementable. To control model ability to

mimic experimental data, in-silico outcomes are compared against in-vitro results of cell spreading

on two dimensional highly constraining adhesive micro-patterned substrates as illustrated by Théry

and co-workers (Théry et al., 2006).

Aim 2 Actin cytoskeleton and adhesive footprint organization during cell spreading under a

numerical scope: How the maturation threshold, a geometrical criterion, controls adhesions and

actin-bundles maturation.

Our assumption: Cells uses large proteins complexes to anchor themselves on the underlying

substrate. These structures are highly dynamic and evolve from small dot-like nascent adhesions to

large elongated mature focal adhesions through different sequential steps. Here we assume that the

last adhesion maturation step is ruled by a geometrical process referred as the maturation

threshold: If the distance separating consecutive adhesions overcomes the maturation threshold,

the corresponding adhesions and related actin bundle mature further into long lasting entities.

Our strategy is to refine the numerical top-down cell spreading model developed in aim 1 by

introducing further key spreading processes. The paradigm is reformulated to render with higher

fidelity time dependent events. The so enhanced simulation tool is then expected to be able

mimicking spreading on various micro-patterned adhesive substrates. Comparing in-silico outcomes

with in-vitro data of cell spreading on different constraining substrates enables a systematic

validation of numerical algorithm (Lehnert et al., 2004; Théry et al., 2006; Zimerman et al., 2004). As

a consequence the novel proposed maturation rule, the maturation threshold, becomes a candidate

to explain focal complexes evolution toward focal adhesions.

Detailed research plan

Aim 3 Experimental investigation of the maturation threshold. How to observe the maturation

threshold with tailored cell spreading experiments

Our assumption: The maturation being a geometrical criterion, as originally established in aim 2, one

is able to switch on/off this process with smartly defined micro-patterned adhesive substrates. We

assume that cells, spreading on adhesive discs with radial non-adhesive gaps of constant width,

exhibit or not mature focal adhesions along the edges depending on the gap width.

Our strategy: Current micro-patterning techniques allow producing substrate with adhesive islands

with two micrometers resolution (Vianay et al., 2010). This last enables the creation of a set of

substrate with adhesive discs having non-adhesive gap of width ranging from 4 to 12 m. Once the

gap overpasses the maturation threshold, actin filaments ended by adhesion are detected by life

imaging of transfected cells for fluorescent actin and mature adhesion proteins (Wang et al., 2008).

These investigations are repeated for different cell phenotype to ensure verify the universality of the

maturation threshold.

Aim 4 Determine how adhesion signaling coordinate spreading. How Rho/Rac small GTpases

influence spreading

Our assumption: As most of the subcellular processes, the maturation threshold investigated in aim 2

and 3 is controlled by molecular dynamic. We suggest that the Rho/Rac activity coordinate the

processes essential for spreading.

Our strategy: Experimental evidences demonstrate that cells, spreading on homogenous substrate,

have the ability to modify their morphology while spreading (Dubin-Thaler et al., 2004). Live

characterization of the leading edge motion provides precise and reliable clues on morphology

dynamic (Dubin-Thaler et al., 2004; Machacek and Danuser, 2006). To reproduce these results, input

parameters of the numerical model, which are directly related to Rho/Rac activity, are systematically

varied to determine the impact of the maturation threshold and the lamellipodia dynamic on cell

morphology and membrane activity.

21 Background

Reference Cuvelier, D., Théry, M., Chu, Y.S., Dufour, S., Thiéry, J.P., Bornens, M., Nassoy, P., and Mahadevan, L. (2007). The Universal Dynamics of Cell Spreading. Curr Biol 17, 694-699. Döbereiner, H.G., Dubin-Thaler, B., Giannone, G., Xenias, H.S., and Sheetz, M.P. (2004). Dynamic phase transitions in cell spreading. Phys Rev Lett 93. Dubin-Thaler, B.J., Giannone, G., Döbereiner, H.G., and Sheetz, M.P. (2004). Nanometer Analysis of Cell Spreading on Matrix-Coated Surfaces Reveals Two Distinct Cell States and STEPs. Biophys J 86, 1794-1806. Fletcher, D.A., and Mullins, R.D. (2010). Cell mechanics and the cytoskeleton. Nature 463, 485-492. Giannone, G., Dubin-Thaler, B.J., DÃ¶bereiner, H.G., Kieffer, N., Bresnick, A.R., and Sheetz, M.P. (2004). Periodic lamellipodial contractions correlate with rearward actin waves. Cell 116, 431-443. Lauffenburger, D.A., and Horwitz, A.F. (1996). Cell migration: A physically integrated molecular process. Cell 84, 359-369. Lehnert, D., Wehrle-Haller, B., David, C., Weiland, U., Ballestrem, C., Imhof, B.A., and Bastmeyer, M. (2004). Cell behaviour on micropatterned substrata: Limits of extracellular matrix geometry for spreading and adhesion. J Cell Sci 117, 41-52. Liu, A.P., and Fletcher, D.A. (2009). Biology under construction: In vitro reconstitution of cellular function. Nat Rev Mol Cell Biol 10, 644-650. Machacek, M., and Danuser, G. (2006). Morphodynamic profiling of protrusion phenotypes. Biophys J 90, 1439-1452. Mogilner, A., and Keren, K. (2009). The Shape of Motile Cells. Curr Biol 19. Small, J.V., and Resch, G.P. (2005). The comings and goings of actin: Coupling protrusion and retraction in cell motility. Curr Opin Cell Biol 17, 517-523. Théry, M., Pépin, A., Dressaire, E., Chen, Y., and Bornens, M. (2006). Cell distribution of stress fibres in response to the geometry of the adhesive environment. Cell Motil Cytoskeleton 63, 341-355. Vianay, B., Kafer, J., Planus, E., Block, M., Graner, F., and Guillou, H. (2010). Single cells spreading on a protein lattice adopt an energy minimizing shape. Physical Review Letters 105, 128101. Wang, Y.X., Shyy, J.Y.J., and Chien, S. (2008). Fluorescence proteins, live-cell imaging, and mechanobiology: Seeing is believing. Annual Review of Biomedical Engineering 10, 1-38. Welf, E.S., and Haugh, J.M. (2010). Stochastic dynamics of membrane protrusion mediated by the DOCK180/Rac pathway in migrating cells. Cellular and Molecular Bioengineering 3, 30-39. Zaidel-Bar, R. (2009). Evolution of complexity in the integrin adhesome. J Cell Biol 186, 317-321. Zaidel-Bar, R., and Geiger, B. (2010). The switchable integrin adhesome. J Cell Sci 123, 1385-1388. Zaidel-Bar, R., Itzkovitz, S., Ma'ayan, A., Iyengar, R., and Geiger, B. (2007). Functional atlas of the integrin adhesome. Nat Cell Biol 9, 858-867. Zimerman, B., Arnold, M., Ulmer, J., Blümmel, J., Besser, A., Spatz, J.P., and Geiger, B. (2004). Formation of focal adhesion-stress fibre complexes coordinated by adhesive and non-adhesive surface domains. IEE Proceedings Nanobiotechnology 151, 62-66.

Chapter 2

Background to the top-down theoretical framework

25 Background

Cytoskeleton reorganization of spreading cells on

micro-patterned islands: A functional model

Loosli Y.1,2,3, Luginbuehl R.3 and Snedeker J.G.1,2

1 Laboratory for Orthopedic Research, Department of Orthopedics, University of Zurich, 8008

Balgrist, Switzerland

2Institute of Biomechanics, Department of Mechanical Engineering, ETH Zurich, 8093 Zurich,

Switzerland

3RMS Foundation, 2544 Bettlach, Switzerland

Published in Philo. Trans.R. S. A. 368, 2629-2652 (2010).

Abstract

Predictive numerical models of cellular response to biophysical cues have emerged as a useful

quantitative tool for cell biology research. Cellular experiments “in silico” can augment in vitro and in

vivo investigations by filling gaps in what is possible to achieve through “wet work”. Biophysics-

based numerical models can be used to verify the plausibility of mechanisms regulating tissue

homeostasis derived from experiments. They can also be used to explore potential targets for

therapeutic intervention. In this perspective article we introduce a single cell model developed

toward the design of novel biomaterials to elicit a regenerative cellular response for the repair of

diseased tissues.

The model is governed by basic mechanisms of cell spreading (lamellipodial and filopodial extension,

formation of cell-matrix adhesions, actin reinforcement) and is developed in the context of cellular

interaction with functionalized substrates that present defined points of potential adhesion. To

provide adequate context, we first review the biophysical underpinnings of the model as well as

reviewing existing cell spreading models. We then present preliminary benchmarking of the model

against published experiments of cell spreading on micro-patterned substrates. Initial results

indicate that our mechanistic model may represent a potentially useful approach in a better

understanding of cell interactions with the extracellular matrix.

Introduction

Introduction Since cellular mechanisms involve processes at the molecular level that render them unobservable in

live cell experiments with most analytical techniques, numerous key aspects of cell behavior remain

unknown. Biophysics-based numerical models provide a tool to simulate subcellular processes and

can be used to systematically probe mechanisms that underlie tissue and organ homeostasis or

human disease (Mogilner et al., 2006). The work focuses on a subset of these mechanisms that

regard interaction between cells and the extra-cellular matrix (ECM). While the reliance of a cell on

matrix cues to guide its behavior is by now widely appreciated, many of the basic mechanisms that

govern this information exchange are yet to be elucidated.

In vivo, cells depend on the extra-cellular matrix (ECM) to provide both biochemical cues (e.g.

cytokines) and biomechanical cues (e.g. anchorage dependent mechanical stress) to guide their

behavior. Given the wide range and complexity of potential cues that the ECM can present to a cell,

a similarly wide range of scientific disciplines is required to understand cell-matrix interactions.

Biochemistry dictates the reactions between cellular receptors and substrate bound ligands that

enable anchorage of the cell (Hynes, 1987, 2002); Polymer physics underlie cytoskeletal modeling

and remodeling (Deng et al., 2006; Peskin et al., 1993); Biomechanical principles govern cell and

matrix deformation in response to endogenous and exogenous mechanical stimuli (Addae-Mensah

and Wikswo, 2008; Broussard et al., 2008; Chicurel et al., 1998). This last class of cellular cues,

mechanical signals, has received increasing attention as it has steadily become clear that mechanical

signals play a central role not only in enabling cell behaviors like migration and mitosis, but also in

integrating contextual information and triggering state changes like cellular differentiation or

apoptosis. The following sections briefly outline some key aspects of mechanical forces (and force

transduction) as they relate to cell behavior.

As early as the 19th century, Wolff proposed that bone tissue adapts its geometrical structure

according to the loads that are placed on it. One hundred years later Perren and Pawel (Perren,

1979) hypothesized that cells mediate bone healing according to fluid flow and hydrostatic pressure.

Bringing this theory forward, Carter (Carter et al., 1998), Prendergast (Prendergast et al., 1997), and

their respective co-workers proposed quantitative models that predicted progenitor cell

differentiation as functions of the nature of applied mechanical stimulus. Today it is well accepted

that processes of mechanical signal transduction (mechanotransduction) are critical to a wide range

of specific biological responses, yet elucidation of the underlying mechanisms is still ongoing (Allori

et al., 2008; McMahon et al., 2008; Shieh et al., 2006; Waldman et al., 2007).

Cells contain many proteins that are potentially involved in translating mechanical stimulation into

biochemical signals that induce downstream processes. For example “stretch-activated ion

channels” are large trans-membrane proteins that regulate ion flow and consequently intra-cellular

ion concentration in response to applied load. The classic examples of which are the hair cells of the

inner ear which transduce mechanical vibrations to a neural signal. Many less intensively studied

mechanotransductive proteins are associated to adhesion sites and/or the cytoskeleton. Among

other mechanisms, such proteins posses specific cryptic receptor binding sites which activate or

release signaling enzymes in response to mechanical load (Vogel and Sheetz, 2006).

Given that key top-level cellular behaviors like differentiation likely rely on cytoskeletal arrangement

(focal adhesion and actin distribution, cytoskeleton pretension), identifying the rules that govern

27 Background

focal adhesion (FA) formation and actin distribution of the cytoskeleton (CSK) is essential. The

complexity of these processes is daunting, and our understanding of them is still in its infancy (Gieni

and Hendzel, 2008). Nonetheless, relentless advancement in available engineering techniques and

cell biology methods allow for improving our ability to postulate and test proposed mechanisms of

cell behavior (Discher et al., 2009).

Among other things, this review discusses how new methods combining molecular biology and cell

imaging with techniques such as micro-fabrication and nano-patterning have allowed

unprecedented insight into CSK mechanobiology. In the following sections, we will introduce and

discuss one such experimental approach: “controlled cell spreading” on microfabricated adhesive

substrates. Controlled cell spreading experiments offer unique insights into the evolution of cellular

adhesions and cytoskeletal elements, and with the help of models that can mimic such experiments

we hope to advance in understanding the rules that govern these central processes.

Biological Underpinnings

Spreading

Cells change their shape from a spherical to a more flattened disc-like appearance when coming into

contact with a solid quasi two-dimensional surface. This process is called spreading. As spreading

cells adhere to a substrate, signaling is initiated that affects various physiological functions such as

cell migration (Lauffenburger and Horwitz, 1996; Woodhouse et al., 1997), morphogenesis

(Gumbiner, 1996), differentiation (McBeath et al., 2004), growth (Folkman and Moscona, 1978), or

tumor metastasis (Woodhouse et al., 1997). Initial spreading is accompanied by formation of cellular

adhesions and small actin bundles that are later remodeled into mature FAs and reinforced stress

fibers (SF). These phenomena are to some extent dictated by the “spreading history” or time-

dependent sequence of initial adhesion formation and maturation (Théry et al., 2006; Zimerman et

al., 2004). In addition to FA formation, spreading is characterized by increased area of the cell/ECM

interface, which is regulated by, among other factors, the matrix or surface stiffness (Discher et al.,

2005; Engler et al., 2004; Yeung et al., 2005). For instance fibroblasts adopt a more spread

configuration on stiffer substrates, e.g. a 25% increase in projected surface area was observed as

substrate modulus increased from 14kPa to 30kPa (Lo et al., 2000a), or disconnect from the matrix

and enter apoptosis if the substrate is too soft (Ingber and Folkman, 1988).

Maximum spreading is reached after a cell has passed through a number of intermediate spreading

steps. Based on observations of fibroblasts, Döbereiner and co-authors recently described three

distinct spreading phases with rapid inter-phase transitions as depicted in Figure 2-1 (Döbereiner et

al., 2004; Döbereiner et al., 2006; Dubin-Thaler et al., 2008): (i) early spreading, cells flatten until

they reach a similar cross sectional area as in its initial spherical shape, (ii) intermediate spreading,

cells rapidly increase their contact surface and initiate contractile forces, and (iii) late spreading, cells

optimize their surface with increased adhesion and contractile cytoskeletal pre-tension. Various

theories attribute the early spreading phase to different driving mechanisms. For instance, non-

specific spreading mechanisms have been proposed for which the process is dictated by

force/energy imbalances between cell-substrate binding and deformation of a weakened cortical

shell (Cuvelier et al., 2007). Other groups have proposed that this phase is driven by active CSK

remodeling with a breakdown of cortical actin that reduces cell stiffness combined with local

polymerization of protruding actin filaments near the cell/ECM interface (Cai et al., 2006; Chamaraux


et al., 2008). Transition to the intermediate phase of spreading has been associated with the

activation of focal adhesion kinase (FAK). FAKs co-localize with APR 2/3, a protein that initiates actin

meshwork polymerization and contractile forces, the engines of the characteristic cellular surface

increase that is associated with this phase (Serrels et al., 2007). In the intermediate phase, cells

initiate specific adhesions (particularly underneath lamellipodia and filopodia) that facilitate its own

anchorage and, eventually, provide stability for the molecular motors. These motors initiate local

contractile forces within the lamellipodia that are possibly powered by non-sarcomeric contraction

(Verkhovsky and Borisy, 1993). The late phase is characterized by a global reinforcement of the

cytoskeleton and its anchors to the substrate. As will be discussed in later sections, contractile forces

are apparently necessary for the recruitment of proteins crucial to the maturation of the adhesive

anchors; Cells recruit actin bundles to form SFs, contractile forces are generated in the SFs via

molecular motors associated to actin bundles (Reinhart-King et al., 2005), and this in turn results in

increased size of the anchoring adhesion. The process is driven by imbalances between the extra-

cellular forces (e.g. ECM/substrate deformation) and intra-cellar forces (e.g. CSK pretension). It is

disputed which cellular objectives rule the tuning of the balance (Ghibaudo et al., 2008): specifically

whether cells seek to maintain a constant deformation or a constant tension. Regardless,

experiments have shown that cell area decreases in the absence of contractile forces (Wakatsuki et

al., 2003), implying that actin polymerization alone, without contractile forces, is not sufficient to

ensure spreading.

Figure 2-1: Schematic of the evolution of cell spreading from a non-contacting state through to post spreading activity (here migration). a) Early spreading: cell flattens and initiates non specific contact. b) Intermediate spreading: cell generates adhesions and long actin bundles are formed. c) Late spreading: cell reinforcement through rearranging adhesions and actin bundles configuration. d) Migration: one possible process that follows spreading.

Controlled cell spreading

In vivo, cells reach the late spreading phase and an eventual equilibrium with a consistent

morphology and cytoskeletal organization depending on their phenotype (Gumbiner, 1996). In

contrast, cells spreading in vitro on material surfaces are not static even if the materials are coated

homogenously with sufficient ligands to saturate cell receptors. After termination of the final

spreading phase, cells start to orient themselves by generating robust, mature SFs which align to

29 Background

bring the cell into a polarized configuration (cell spatial segregation). Polarization may be

subsequently followed by either migration associated with a constantly remodeling CSK that

systematically alters cell morphology and drives the cell forward, or alternatively cells continue in

their cycle (e.g. G1 phase), which also results in a constant reorganization of the CSK (Assoian and

Klein, 2008). If the substrate is not homogenous or continuous, however, and cells are confined to

micro-patterned islands (from 600 to 1400 m2), they adopt reproducible shapes and yield a “steady

state” behavior (Singhvi et al., 1994). Controlled spreading provides the ability to systematically and

reproducibly characterize CSK evolution at discrete time points, and micro-patterned surfaces have

thus been used to study attainment of cell morphology and the basic mechanisms of CSK

organization (Chen et al., 2003; Cuvelier et al., 2003; Kevin Parker et al., 2002). Théry and co-workers

further advanced this principle by strategic investigation of SF and FA configuration using human

epithelial cells spreading on concave and convex curvatures (Théry et al., 2006). They engineered

geometries with thin adhesives areas in T, U, Y, or V shapes as depicted in Figure 2-2. After staining

actin and vinculin (adhesion proteins), they observed a common behavior of cellular FA distribution

and SF orientation: the highest vinculin concentrations were found along the periphery of adhesive

areas, and actin bundles were concentrated along non-adherent edges of concave-shaped areas.

These useful results have since been used in recent modeling studies and these are later discussed in

more detail.

Cellular adhesion and focal adhesion plaques

Cell adhesion molecules (CAMs) are central to mechanotransduction, connecting the internal cell

skeleton to the cell surroundings. Most CAMs are trans-membranous proteins and belong to the

immunoglobulin superfamily, integrins, cadherins, lectin like CAMs, or homing like receptors

(Albelda and Buck, 1990; Hynes, 1987, 2002). Integrins act as receptors to ECM ligands (collagen,

firbronectin, laminin, etc.) on the extra-cellular side, and on the cytoplasmic side they interact with

numerous proteins (paxillin, actinin, talin etc.) that in turn bind directly or indirectly to the CSK

(Zaidel-Bar et al., 2007). The adhesion process is a highly dynamic assembly that typically evolves

from a single point of adhesion into a large mature adhesion area by sequentially recruiting proteins.

How cells orchestrate this process is only partially understood. For example, Talin is an actin-binding

protein that is part of this process and that is known to be important with regard to

mechanotransduction. Talin attaches to the cytoplasmic domains of integrins that recruit other

proteins such as paxillin, actinin, tensin and zyxin (Giannone et al., 2003). In tension, talin also

changes its conformation exposing a binding site for vinculin, which induces the reorganization of

the cytoskeleton (Del Rio et al., 2009). Such changes in molecular conformational are enabled

through cell contractility mainly powered by the actin machinery.


Figure 2-2: Experimental images of hTERT-RPE1 cells plated on V-, T-, Y-, U-shaped ligand micro-patterns. Actin filaments and vinculin spots are stained in red and green respectively. All images are similarly scaled,

with the length of the V being 46m. Adapted with permission from (Théry et al., 2006). Copyright © John Wiley and Son, Ltd.

The bridging of integrins and the actin meshwork is a key step in promoting focal adhesion

maturation (Frame and Norman, 2008) with tensile force at the FA being well known to increase FA

size to maintain a constant stress at the adhesion (5.5 nN/m2) (Balaban et al., 2001). Prior to

maturation, nascent adhesions (focal complexes) with length smaller than 1 m are generally

localized in the membrane underneath filopodia and lamellipodia, (actin based membrane

protrusions that will be discussed later in more detail). The focal complexes located beneath

lamellipodia have a limited life time (on the order of minutes, the time required by the

lamellipodium to move forward), while those in filopodia have higher likelihood of evolving into

longer-lived mature FAs (Schäfer et al., 2009; Zaidel-Bar et al., 2003). Focal complexes are made of

hundreds molecular components linked together by many more interconnections (Zaidel-Bar et al.,

2007). They can reach lengths of 10m, and are generally positioned at the inner rim of lamellipodia

to provide anchorage to contractile SFs (Goffin et al., 2006; Nobes and Hall, 1995; Schäfer et al.,

2009; Zamir and Geiger, 2001). FAs are active assemblies; they not only assure the mechanical link

between the CSK and the ECM, but they also sense and translate local mechanical stimuli (Giancotti

and Ruoslahti, 1999; Gumbiner, 1996; Hynes, 2002). Such pathways regulate crosstalk between FA

31 Background

and actin mediated signaling and are important to mechanotransduction (Chen, 2008; Geiger et al.,

2009).

Actin machinery

Actin-based elements are central to cellular motility and affect both intra- and inter-cellular

processes. Rheological properties of the whole cell are regulated by tuning intra-cellular tension of

actin bundles (Trepat et al., 2007) and the stiffness of the actin cortex (Van Citters et al., 2006). On

the inter-cellular level, actin is involved in processes from embryonic development, to tissue

organization and remodeling, to apoptosis (Burridge and Chrzanowska-Wodnicka, 1996; Pollard and

Borisy, 2003).

Actin is present in cells in its globular form (G-actin) and in its filamentanous form (F-actin). It is

assumed that G-actin generates protrusive forces when it polymerizes against the membrane and

that these forces deform the lipid layer (i.e. the “ratchet” mechanism (Peskin et al., 1993; Pollard

and Borisy, 2003)). Polymerization occurs, among other places, at the leading edge of the cell

(section of the membrane undergoing directed protrusion). Here G-actin is polymerized at the

growing tip of an actin filament while depolymerization occurs at the opposite end of the filament

that is embedded within a dense actin meshwork (lamellipodia). The availability of G-actin for new

filament formation at the leading edge is ensured by the so-called process of “treadmilling” in which

depolymerzing F-actin feeds a monomer flow from the rear of the lamellipodia toward the front of

the cell where the filament grows (Small et al., 1993).

Lamellipodia and filopodia

Lamellipodia are wide flat protrusions (1-5m breadth and only 0.2m thick) formed by an actin

network, whereas filopodia are fingerlike extensions of the membrane powered by tight, parallel F-

actin bundles with a width of 0.1-0.3 m and lengths up to 10m (Mattila and Lappalainen, 2008;

Small et al., 2002). Two potential (and complementary) mechanisms underlie formation of filopodia,

which are used by the cell to explore the environment (Gupton and Gertler, 2007; Wood and Martin,

2002). The first one is based on filopodia being issued from the lamellipodium whereas in the second

filopodia generally nucleate at tips of previous entities (Mattila and Lappalainen, 2008). If

mechanical and chemical properties of ECM or a solid surface are satisfactory, focal complexes form

near the tip of a filopodium (Schäfer et al., 2009). Once a lamellipodium has reached these nascent

adhesions, they generally mature into stable FAs (Schäfer et al., 2009). Thus the purpose of such

filopodia is to guide and anchor the lamellipodia as they advance. If a filopodium is not stabilized by

FAs it will eventually buckle and fold laterally to form actin bundle contractile bridges (Nemethova et

al., 2008). These bundles, or so-called transverse arcs, are not anchored in the ECM and are either

moved toward the cell center before eventual depolymerization or alternatively can be involved in

the formation of mature SFs if the cell sends an appropriate polarization signal (Hotulainen and

Lappalainen, 2006; Senju and Miyata, 2009).

In contrast to filopodia, lamellipodia occupy a zone spanning only few micrometers behind the

leading edge, where most F-actin is polymerized into a dense meshwork stabilized by other

molecules (Arp 2/3, -actinin and filamin) (Small et al., 2002). This network provides the required

anchoring to resist protrusive forces that allow a quasi-continuous extension of the leading edge.

Single cell spreading models

Stress fibers

SFs are the third major actin based component in addition to the actin-mesh powered lamellipodia

and the protruding actin-bundle filopodia (Ridley et al., 2003). SFs are large bundles of ten to thirty

actin filaments held together by -actinin and cross-linked by myosin, which uses ATP as an energy

supply to move directionally on the SFs to induce sliding between actin filaments (Pellegrin and

Mellor, 2007). This motion results in filament length changes that in turn generate contractile force

on SFs with anchored extremities. SFs are generally divided into three groups (Hotulainen and

Lappalainen, 2006; Naumanen et al., 2008): (i) SFs that are connected at both extremities to FAs -

these are known as ventral SFs (vSF) and are essential to cell contractility; (ii) Dorsal SFs (dSF) are

linked to a transverse arc at one end and to a FA at the other; (iii) Transverse SFs (tSF) are located

under lamellipodia and connected to FAs via dorsal SFs. Senju and Miyata proposed that interplay

between dSFs and transverse arcs is at the origin of vSFs (Senju and Miyata, 2009). The common

action of vSF and actin myosin exerts contractile forces that have been measured in the range of

25nN-50nN for fibroblasts and 150nN for myofibroblast (Balaban et al., 2001; Goffin et al., 2006). A

recent study by Deguchi and coworkers investigated the mechanical properties of isolated single SFs

and described a maximum tensile strain of 2.0% (+/- 0.6%), an averaged ultimate force of 380nN (+/-

210nN), and an elastic modulus of 1.45 MPa (Deguchi et al., 2006). Furthermore, they observed that

vSFs are subjected to a substantial pre-tension with lengths decreasing to 83%+/-11% of the initial

length after detachment of one end. However, more recent in vivo investigation of SFs estimated

elastic moduli to be substantially lower (230 kPa) than the isolated fibers (Lu et al., 2008). The large

difference in these reported values is typical and indicates the difficultly in measuring mechanical

properties of biopolymers. Therefore such results must be considered with due caution.

Limitations of current experimental methods

While observations from experimental cell biology and biophysics can offer valuable insight into

fundamental cellular processes, modern experimental setups allow “top-level” behaviors to be

observed but often leave the underlying driving principles and mechanisms to only be hypothesized.

As a tool for testing the validity of such hypotheses numerical models can play an important role in

understanding and explaining experimental outcomes. The following sections focus on mechanically

based single cell models to describe cell spreading and cytoskeletal reinforcement.

Single cell spreading models Many numerical (and/or theoretical) models of single cell rheology have been developed to describe

the constitutive behavior of cells regarding their “flow” in response to applied boundary conditions.

For instance in the finite element model of Guilak and Mow, the cell was represented as a biphasic,

two dimensional structure (Guilak and Mow, 2000). Other rheological models have incorporated

quasi-dynamic processes in an attempt to capture aspects of living cells (Ingber, 1997; Trepat et al.,

2007). These models are useful in describing the passive/pseudo-active rheological behavior of cells,

and have been thoroughly reviewed elsewhere (Lim et al., 2006; Stamenović, 2008; Vaziri and

Gopinath, 2008). The present article rather focuses on models that have been introduced to

represent initial cell/substrate interaction and cytoskeletal organization which is likely to be a key

function of downstream cell behaviors. First, we introduce cell spreading kinetics models, where cell

surface is described as a function of time. We then examine biochemical-biomechanical models of

cytoskeletal architecture and reinforcement in response to mechanical stress induced by cell

33 Background

contractility. Finally we present our own functional model of cell spreading, which is based on

biophysical rules governing actin dynamics and FA modeling/remodeling.

Kinetics of spreading

Over three decades ago, a first attempt to describe cell spreading was performed by modeling time

evolution of cell area (Bardsley and Aplin, 1983). Bardsley and Aplin tried to relate the spreading

dynamics of a cell population to the laws of chemical kinetics but without notable success. Twenty

years later, Frisch and Thoumine compared initial cell spreading with surface wetting of liquid drops

(Frisch and Thoumine, 2002). Such phenomena were already extensively investigated and simulated

(Leger and Joanny, 1992; Tanner, 1979) incorporating the critical parameters of liquid viscosity,

surface tension and substrate adhesion. Considering cells as viscous droplets surrounded by a

membrane under tension and neglecting a nuclear contribution, Frisch and Thoumine computed cell

radius as a function of time and compared their predictions with experimental data. Comparison

showed an underestimation of spreading velocity at early time points (up to one hour) followed by

an overestimation of the velocity in later stages. The authors attempted to model the whole

spreading process with a single set of equations, despite the markedly different mechanisms

involved in each spreading step. Using a similar model (a membrane–bound viscous cortical shell and

membrane that encloses a fluid cytoplasm) but opting for a direct computation of the contact

diameter (circular contact assumption), Cuvelier and co-workers predicted initial spreading by

balancing adhesive energy with viscous dissipation, (Cuvelier et al., 2007). They further proposed

two mechanisms of viscous dissipation, depending upon the stage of the spreading phase. Early

damping that determines the kinetics of cell spreading is attributed to viscous flow in the cortical

shell. Later, whole cell rheology dominates dissipation (Cuvelier et al., 2007). Common to all these

passive paradigms the main parameters that regulate spreading are that the properties of the

cortical actin (thickness and cortical-shell viscosity) with actin (de)polymerization being assumed to

have a negligible effect on both the spreading kinetics and adhesive energy. Treating actin processes

to be time independent is perhaps an oversimplification since it is known that adhesion initiation

triggers a breakdown of the cortical actin and cortical structures (Döbereiner et al., 2005). Despite

this simplification, the overall agreement of the model with experimental data is fairly good, and

makes possible an estimation of initial spreading kinetics with a simple model at extremely low

computational cost. The Cuvelier model focuses mainly on the initial phase of spreading and claims

to demonstrate that substrate adhesion starts with a non-specific binding phase that is dominated

neither by actin polymerization nor diffusion of adhesive receptor through the membrane. Thus it is

not dependent on either cell type or substrate (as long as non-specific binding is possible).

Although modeling a cell as a passive entity that lacks both actin activity and specific binding can

successfully mimic initial spreading of isotropic cells, these assumptions seem to be inappropriate

for later isotropic spreading phase or anisotropic cell spreading. Chamaraux and co-authors focused

on ameobian cells with podosome-like adhesions (blebs extensions) at the leading edge that result in

an anisotropic spreading process (Chamaraux et al., 2008; Chamaraux et al., 2005). Such membrane

protrusions are different from either filopodia or lamellipodia extensions. Blebs extensions are

created by local weakening of the connection between the lipid-membrane and the actin cortex.

This weakening allows for formation of a bubble-like protrusions driven by intra-cellular pressure

(Boulbitch et al., 2000; Paluch et al., 2005; Paluch et al., 2006; Yoshida and Soldati, 2006). This

phenomenon is essential in the Chamaraux spreading model since it assumes that intracellular

pressure pushes the membrane onto the substrate, leading to novel adhesion regions that in turn

Single cell spreading models

trigger polymerization of basal F-actin structures connected to the membrane. This model was

proposed to simulate quite specialized cells exhibiting a pseudo-pod, and is therefore not suited for

cells that spread via lamellipodia. Further, actin activity differs between these spreading

mechanisms: in blebbing cells, actin polymerization occurs underneath the cell body to support

newly covered regions, whereas lamellipodial spreading actin polymerization acts rather to deform

the membrane (Pantaloni et al., 2001).

Thus without considering actin dynamics, several different models of cell spreading kinetics have

been able to predict spreading area as a function of time. Nonetheless spreading is not only

characterized by surface increase. The CSK reorganizes constantly during spreading, even in the final

stage (reinforcement) when cell surface area is relatively stable. Hence such models offer limited

insight into the numerous signaling pathways that are related to cellular morphological changes and

the associated force exchange between the cell and its substrate (Chen, 2008; Chen et al., 2003;

Stamenović, 2008; Stamenović and Ingber, 2002).

Cell reinforcement models

Cells reinforce their CSK in the last spreading phase by dynamically rearranging SFs and FAs

(Bershadsky et al., 2006; Chen et al., 2003; Hirata et al., 2007). This phase has important implications

for mechanotransduction, and can precede key changes in cellular state (e.g. migration,

differentiation). Hence being able to understand how cells regulate this process is highly relevant

(Chen, 2008). Based on earlier works (Deshpande et al., 2006; Deshpande et al., 2008), Pathak and

co-workers (Pathak et al., 2008) developed a two-dimensional model driven by a coupling of

biochemical rules (signal propagation and integrin diffusion) and biomechanical rules (SF

contractility) that yielded realistic predictions of previously published distributions of SFs and FAs

following reinforcement of cells spread on micro-patterned islands (Théry et al., 2006). The

similarities between simulation ad experiments (averaged actin/myosin cartography) were striking:

FAs at island corners were faithfully reproduced, as was the presence of high density SF at non-

adherent edges. In contrast to experimental data, predicted adhesions were distributed nearly

homogenously along the adhesive edges. Using a similar modeling approach, SF distribution in

response to a superimposed substrate strain has also been simulated (Wei et al., 2008). Since both

models were based on a continuum approach, investigation of subcellular evolution of single SFs or

FAs (formation, growth, fusion, etc.) was not possible. Furthermore, the models employed

deterministic methods that resulted in symmetrical SF and adhesion distributions that do not

faithfully represent living cells which are driven by non-deterministic processes. Finally, these

models focused only on reinforcement, and did not account for initial phases of spreading and the

potential role that spreading history may have on end-stage CSK arrangement.

Discrete spreading model using divided medium

The divided medium strategy is based upon modeling structures as discrete “grains” whose

interactions are simulated using springs (Jean, 1999). Divided medium models have been proposed

to investigate the dynamic organization of the CSK in response to stimuli (Milan et al., 2007), and

have been employed to model active spreading in three dimensions (Maurin et al., 2008). Maurin

and co-workers modeled the whole cell with three different types of grains (membrane, cytosol and

nucleus), which were interconnected by springs with stiffness set for each CSK component. Some

membrane peripheral grains were assigned adhesive capacities to mimic integrin activity. The

authors proposed that polymerization of microtubules (relatively high bending stiffness CSK

35 Background

elements) drive spreading and that actin filaments are only involved in maintaining structural

integrity (i.e. the tensegrity theory (Ingber, 1991)). Using this model, predicted three dimensional

shape evolution was confirmed by experimental data, despite the debatable physiological

mechanism of microtubule powered spreading. While microtubules have been described to bear

contractile loads (Stamenović et al., 2002) and to influence adhesion and actin filament activity

(Deschesnes et al., 2007; Palazzo and Gundersen, 2002), there appears to be little support in the

literature for the mechanisms hypothesized by Maurin (Maurin et al., 2008). Therefore model

predictions must be considered with caution, though the methods used are interesting regarding

their potential for incorporating the concept of cellular tensegrity within simulation of CSK

remodeling.

A Novel Predictive Model of Cytoskeleton Reorganization Based on the shortcomings of the models mentioned above, we present here a novel approach for

simulating CSK evolution over the course of spreading. Our model was developed to provide a

prediction of post-spreading FA and SF distribution. The FA/SF architecture is necessary input for

eventual computation of the force balance between the cytoskeleton and the extra-cellular matrix

(not addressed in the present work). This force balance could later be implemented as feed-back for

guiding post-spreading reorganization of the CSK, for instance to gain insight into substrate

dependent CSK reinforcement. Force balance mediated at the FAs is an important vector for

transduction of mechanical stimuli to the cell (Chen, 2008) with critical downstream consequences

for top level processes (e.g. apoptosis (Ingber and Folkman, 1988), durotaxis (Lazopoulos and

Stamenović, 2008; Lo et al., 2000b), differentiation (Engler et al., 2006), etc.)). For the modeler,

predicting the consequences of tensile forces acting at FAs requires one to quantify not only tension

of each individual SF but their directions as well. Thus an accurate prediction of CSK architecture is

critical to this goal and is delivered as output by the algorithm described below. Since spreading

history appears to be an essential factor in end-stage CSK configuration, we included a sequential,

rule-based functional model that is capable of predicting CSK and adhesion formation and

remodeling in spreading cells. The next sections describe the modeling concept and compare first

results against experimental observations of spreading cells on micro-patterned islands.

Algorithm description

We propose an iterative spreading algorithm that is conceptually illustrated in Figure 2-3 and

described as pseudocode in Figure 2-4. This CSK reorganization paradigm is driven by two weakly

coupled processes that occur in parallel: continuous lamellipodial extension and local filopodial

protrusion. These membrane activities are both thought to rule CSK and adhesion reorganization

during the active spreading phase, with lamellipodial extension believed to be the dominant

spreading mechanism (Small et al., 2002). Lamellipodial extension is the result of actin meshwork

polymerization that continually pushes the membrane outward. The model adopts leading edge

protrusion velocity distributions described from prior experimental observations (Dubin-Thaler et al.,

2008), with an iteratively stochastic advance/retraction (mean +1.7m; 1m) of the leading edge

perimeter in a normal direction. In our model, the lamellipodium is defined as the surface

encompassing the substrate area bounded by the leading edge at two consecutive iterations.

Nascent (unstable) adhesions are generated beneath this area if there is a presence of binding ligand

(Choi et al., 2008; Zaidel-Bar et al., 2003).

A Novel Predictive Model of Cytoskeleton Reorganization

Figure 2-3: Schematic representation of two consecutive iterations of the predictive model of cytoskeleton reorganization. The most relevant events are depicted for cell spreading on a substrate consisting of two parallel adhesive (i.e. ECM ligand coated) bands

The main function of the algorithm is to distribute nascent focal adhesions and determine which of

these (and their associated actin filaments) should be selected for maturation/reinforcement. The

algorithm currently considers three mechanisms for focal adhesion maturation: 1) lamellipodia

retraction occurs that would otherwise leave a nascent adhesion outside the cell body (Zaidel-Bar et

al., 2003) 2) membrane tension spanning two focal adhesions exceeds a certain force threshold

(Balaban et al., 2001; Bischofs et al., 2009). 3) the cell leading edge advances until it encompasses a

nascent focal adhesion at the protruding tip of an existing filopodium (Schäfer et al., 2009).

Focal adhesion maturation induced by lamellipodial retraction has been described as a force

independent process (Zaidel-Bar et al., 2003). While experimentally well characterized, it is until now

not well understood. In contrast, the separate mechanism of tension induced adhesion maturation is

clearly force regulated, inherently involving actin stress fibers that are recruited to the focal

adhesion. Here bending stress fibers support the membrane and this is balanced by actomyosin

contractility at the anchoring focal adhesions (Bischofs et al., 2009). This mechanism is modeled in

the present algorithm by assuming that membrane tension is uniformly distributed along transverse

stress fibers that span neighboring focal adhesions at the cell leading edge. The algorithm uses an

elastic hull technique to define the outer perimeter of the focal adhesion point cloud, and

interconnects neighboring adhesions on this perimeter by line segments of defined length. When

the spanning distance exceeds a certain length (described below in more detail), the tension of the

37 Background

stress fiber is sufficient to induce maturation of the focal adhesion and reinforcement of the stress

fiber.

Thus nascent adhesions at the perimeter of the cell leading edge support the membrane through

bridging actin bundles. Such actin bundles have been experimentally observed to form by diverse

mechanisms including filopodial buckling (Nemethova et al., 2008) and non-sarcomeric actomyosin

contraction (Verkhovsky and Borisy, 1993). As mentioned above, these supporting stress fibers are

tensioned by the combined effects of the myosin induced contractility with their anchoring

adhesions, which maturation process is force regulated. The present algorithm implements force

regulated FA maturation based on experimental evidence that membrane bridges spanning more

than 5m between adhesions require counterbalancing actin bundle tension that falls above a

threshold (>10nN) sufficient to induce FA maturation (Bershadsky et al., 2006; Galbraith et al., 2002).

This force threshold is determined by the interrelationships between membrane tension, actin-

mysosin contractility, and the FA size required to anchor them (reaching areas larger than 1m2)

(Balaban et al., 2001). In the current model, we thus implemented an actin bridge length threshold

of 5m beyond which the actin bundle tension was assumed to be large enough to trigger fiber

maturation, making the actin bundle persistent, and fixing it along with its associated adhesion

(which was previously considered to be nascent or “unstable”).

Finally, the lamellipodia protrusions are complemented by secondary filopodial activity. Based on

experimental observations, we modeled filopodium formation as a stochastic process with “stable

filopodia” being defined both as those formed close (<0.5m) to a mature FA or those extending an

already existing (stable) filopodia (Bischofs et al., 2009; Nemethova et al., 2008; Schäfer et al., 2009).

Filopodium outwardly protrude (mean +10m; 2m) from the cell body and generate a non-

mature adhesion at their tip. When these nascent filopodial-formed adhesions are later overtaken

by the advancing leading edge of the cell, they then mature into stable adhesions. Additionally, an

actin filament is formed that connects the anchoring adhesions at the filopodium origin and tip

(Schäfer et al., 2009). Finally a subsequent filopodium is then nucleated from the now stable

adhesion at the tip of the previous filopodium. The process is illustrated schematically in Figure 2-3.

To summarize, the algorithm predicts cell morphology, the FAs distribution and SFs layout based on

an iterative process. This process involves force balance between the “elastic” convex hull of the

membrane and the reciprocal recruitment of SFs and FAs to support the hull. Although there is no

explicit force computation in the present form of the algorithm, force balance is indirectly

incorporated; it is assumed that any segment of the membrane perimeter that is supported by focal

adhesions spaced greater than 5µm will require a counterbalancing SF tension above a biophysical

threshold that initiates maturation of the anchoring adhesions. The algorithm also involves spatial

interactions between the advancing front of the cell leading edge and the filopodial extensions that

protrude from the actin meshwork. The model is deemed to reach a steady state (convergence)

when the cell area remains constant over ten iterations or if the cell area has reached an imposed

physical limitation (here set to 1200m2). The described algorithm was implemented in Matlab

R2009 (Mathworks Inc., Natwick MA, USA) according to the pseudo-code presented in Figure 2-4.

A Novel Predictive Model of Cytoskeleton Reorganization

Figure 2-4 : Pseudo-code describing the predictive model of cytoskeleton reorganization. Note that italicized words proceeded by “%%” represent comments, and that boldface type is used to represent variables.

39 Background

Initial comparison between “in-vitro” and “in-silico” experiments

As mentioned above, the proposed paradigm mainly focuses on cell shape, adhesion formation and

maturation, and the resultant SF/FA architecture at the end-stage of the spreading process. To

evaluate the predictive ability of the model, we employed published controlled spreading

experiments of epithelial cells seeded on micro-patterned substrates (Théry et al., 2006). This

dataset is has been used by other authors for similar purposes (Pathak et al., 2008). In the original

experiments, constraining the cell to an island forced the cells to a steady state after spreading, and

the cells were then stained to reveal adhesive proteins (vinculin) and actin. As in the experiments,

we defined geometrical ligand covered surfaces (Y- and V-shaped island) and used them as input to

the model (Figure 2-5 A and D). The model was then assessed for its ability to faithfully reproduce

the experimental arrangement of actin bundles and FAs.

Visual comparison of the model against the benchmark data revealed a close similarity in CSK

architecture (Figure 2-5 B, C, E and F). Bundles running along non-adhesive regions did not cross

each other; Distribution and clustering of adhesions was also similar, with large adhesions predicted

to reside at the corners where large fibers are supported. Small discontinuous adhesions were

successfully predicted to form along external edges (green arrows). Highly oriented adhesions on the

internal edges were also successfully predicted (blue arrows). The algorithm did fail, however, to

fully predict the preference for sparse adhesion formation at curved regions of the geometries,

indicating that this process is driven by other mechanisms that are not yet included in the algorithm

(i.e. enhanced lamellipodial activity in convex regions (James et al., 2008)). Lacking explicit

consideration of membrane induced bending of SFs, the simulated cell morphologies also did not

capture the curvature of the large actin bundles spanning non-adhesive regions of the substrate

(white arrows in Figure 2-5).

Discussion

Figure 2-5 : Experiments and simulation of controlled spreading on T shaped (A-C) and V shaped (D-F) adhesive islands. A and D represent the tested geometries (gray zones are adhesive). B and E are experimental data (actin stained in red and vinculin in green) adapted with permission from (Théry et al., 2006). C and F are the predictions obtained from numerical simulation, where red line segments corresponds to SFs, green rectangles to mature adhesions and green dots to unstable adhesions. White arrows point to non-adhesive

edges, blue and green arrows to internal and external adhesive edges respectively. Scale bar: 5 m.

Discussion We described a novel model of cell spreading driven by top-level rules that are based upon

formation of FAs and SF reinforcement dynamics. The model can apparently mimic cellular

spreading (cytoskeletal organization of SFs and FAs) on different adhesive shapes, and is based on a

limited number of biophysical parameters that have been experimentally determined. A perfect

41 Background

likeness between experiment and simulation was not expected nor observed given the stochastic

modeling approach that was employed to model lamellipodial and filopodial movements (to

simulate these similarly stochastic cellular processes). Further, the model seems to confirm that the

end-stage cytoskeletal configuration reflects earlier cell spreading history, as indicated by the non-

intersecting actin filament lattice that spans non-adhesive regions. Although the preliminary

simulations presented here do indicate the potential promise of this approach for modeling cell

spreading, the model is considered to be a prototype. Accordingly, there are limitations that must be

acknowledged.

First, the impact of filopodial spreading was limited by the relatively small dimensions of the

confining adhesive islands. To more effectively assess the effects of filopodial activity (which should

have greatest impact in spanning distances longer than 5 um), larger dimension test substrates will

have to be simulated and compared to experimental results. Experiments and simulations are

currently in progress in this regard. The model also contains a greatly simplified force balance

between membrane tension and the supporting stress fibers and adhesions. Later versions of the

model will explicitly incorporate this force balance, as well as the consequences for morphology

(curvature) of the cell membrane. Finally, the preliminary model we present must be tested with

regard to sensitivity of the model output as a function of the biophysical parameters that drive its

behavior. To this end, quantitative metrics for describing FA and SF location as a function of

substrate topology must be developed. This work is also ongoing.

Conclusion and Outlook for integrated Multi-scale simulations In the present work we have described cell spreading, and introduced selected models that have

been developed to replicate it. Our own model was built on biophysical mechanisms as interpreted

from recent experimental evidence. In contrast to some other recent cell spreading modeling

approaches, our model is based on a limited number of functional rules (such as the threshold at

which a FA becomes stable, and actin bundles thus become anchored) and takes into account active

subcellular processes (FA and SF maturation). While the model development is still in its preliminary

stages, we view the ability of the algorithm to successfully replicate CSK arrangement (size and

orientation of the actin network) as a crucial first step to providing input to later models. These

models will include an internal force balance of the cell and computation of the resultant force

acting at individual FAs. This will enable more detailed investigation of FA mediated

mechanotransduction, and eventually implementation of the model within a multi-scale framework

to predict cell-biomaterial interactions.

Models use simplifying assumptions to make a problem tractable, often with as few variables as

possible. These simplifications can be made in the interest of intuitiveness, or computational

expense. However, they often are made because the underlying mechanisms defy our

comprehension. This forces one to make a reasonable “black box” (phenomenological)

approximation of the relationships between stimulus and response. Predictive models of tissue

evolution (modeling and remodeling in growth, disease, and repair) have been no exception, with

many approximations attempting to link global tissue or organ response to chemical, electrical, and

mechanical stimuli at the cellular level (Checa and Prendergast, 2009; Isaksson et al., 2008; Isaksson

et al., 2009; Lacroix and Prendergast, 2002; McNamara et al., 1992). In contrast the model we have

described lays a foundation for more mechanistic modeling of cell response to mechanical stimuli –

by explicitly representing subcellular coupling between the single cell cytoskeleton and the ECM. We

Conclusion and Outlook for integrated Multi-scale simulations

believe this added complexity is necessary to understand (and eventually simulate) the nature of

cell-biomaterial interaction that determines the success or failure of a therapeutic biomaterial in a

healing environment. It must be noted that our single cell model itself employs simplifying

phenomenological rules to mimic subcellular behaviors like the formation and maturation of focal

adhesions. While these rules are predicated on experimental evidence and yield plausible

predictions of cell level behavior, there is a possibility to model the molecular level processes as well

(e.g. implementing a ratchet polymerization model for membrane protrusion). In any case, the

degree of model complexity one invokes need only match the complexity required to achieve a

robust and relevant predictive output.

The model we propose thus provides a framework for scalability in either metric direction with

expansion of our single cell model into three dimensions and integration within multi-scale models

of tissue differentiation that link macro-scale stimulus to cell/molecular mediated tissue level

changes. In doing so it might enable insight into the driving factors behind these processes, and for

ultimately predicting the performance of engineered biomaterials.

43 Background

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47 Background

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Chapter 3

Description of the numerical

framework

51 Description of the numerical framework

Numerically bridging Lamellipodial and Filopodial

Activity during Cell Spreading Reveals a Potentially

Novel Trigger of Focal Adhesion Maturation

Loosli Y. 1,2,3, Vianay B.4, Luginbuehl R.3, and Snedeker J.G.1,2 *

1Orthopedic Research Laboratory, University of Zurich, Balgrist, Zurich, Switzerland

2Institute for Biomechanics, ETH Zurich, Zurich,Switzerland

3RMS Foundation, Bettlach, Switzerland

4Laboratory of Cell Biophysics, Ecole Polytechnique Fédérale de Lausanne, Switzerland

Published in Integr. Biol., 4, 508-521 (2012)

Abstract We present a novel approach to modeling cell spreading, and use it to reveal a potentially central

mechanism regulating focal adhesion maturation in various cell phenotypes. Actin bundles that span

neighboring focal complexes at the lamellipodium/lamellum interface were assumed to be loaded by

intracellular forces in proportion to bundle length. We hypothesized that the length of an actin

bundle (with the corresponding accumulated force at its adhesions) may thus regulate adhesion

maturation to ensure cell mechanical stability and morphological integrity. We developed a model to

test this hypothesis, implementing a “top-down” approach to simplify certain cellular processes while

explicitly incorporating complexity of other key subcellular mechanisms. Filopodial and lamellipodial

activities were treated as modular processes with functional spatiotemporal interactions coordinated

by rules regarding focal adhesion turnover and actin bundle dynamics. This theoretical framework

was able to robustly predict temporal evolution of cell area and cytoskeletal organization as reported

from a wide range of cell spreading experiments using micropatterned substrates. We conclude that

a geometric/temporal modeling framework can capture the key functional aspects of the rapid

spreading phase and resultant cytoskeletal complexity. Hence the model is used to reveal

mechanistic insight into basic cell behavior essential for spreading. It demonstrates that actin

bundles spanning nascent focal adhesions may accumulate centripetal endogenous forces along their

length, and could thus trigger focal adhesion maturation in a force/length dependent fashion. We

suggest this mechanism could be a central “integrating” factor that effectively coordinates force-

mediated adhesion maturation at the lamellipodium/lamellum interface.

Introduction

Introduction Cell adhesion, spreading and migration are driven by highly coordinated but stochastic molecular

subfunctions including focal adhesion turnover, actin bundle assembly, and acto-myosin contractility

(Burnette et al., 2011; Welf and Haugh, 2010). In cell spreading, the spatiotemporal interactions

between the actin machinery and cell/substrate adhesions drive a rapid increase in cell area after

initial contact (Cuvelier et al., 2007; Döbereiner et al., 2004; Giannone et al., 2004; Loosli et al.,

2010). To achieve this goal, a cell must synchronize numerous complex modular processes in both

space and time. These modules are driven by molecular scale mechanisms that are functional at the

mesoscale (between the molecular and the cellular scale) and collectively enable cell motility.

Lamellipodia and filopodia are the dominant motility functions (Dubin-Thaler et al., 2008), and are

regulated by active crosstalk between the various involved molecular processes (substrate adhesion

dynamics, actin bundle turnover, myosin contractility).

Molecular investigations of cell motility have elucidated many isolated mechanisms central to cell

movement. However, signaling cross-talk and spatiotemporal coordination of cellular subfunctions is

extremely complex, and comprehensive understanding of these remains a major challenge in cell

biology and cell biophysics (Fletcher and Mullins, 2010). In the present study, we introduce a novel

theoretical framework that overcomes some aspects of this complexity to elucidate mechanisms

involved in the spatiotemporal coordination of focal adhesion and actin bundle dynamics. We

describe a non-deterministic numerical model that is able to accurately predict cytoskeletal

morphology on a wide range of micropatterned surfaces immediately after the rapid spreading phase

that corresponds to a rapid, monotonic increase in cell area during which cells initiate substrate

adhesion (Cuvelier et al., 2007; Döbereiner et al., 2004; Loosli et al., 2010). We further exploit the

model to quantitatively elucidate a geometrical parameter (“maturation threshold”) that accounts

for the centripetal forces acting along the lamellipodium/lamellum (LP/LM) interface and remotely

triggers nascent adhesion stabilization of actin bundles to enable later cell contractility and eventual

polarization as illustrated in Figure 3-1.

Two distinct and often complementary strategies have emerged to investigate how subcellular

processes integrate to a functional whole-cell behavior. First, “bottom-up” approaches have

attempted to systematically reconstitute complex cell behaviors using cell-free extracts or purified

proteins (Haviv et al., 2006; Liu and Fletcher, 2009). This approach can yield elegant experimental

designs that provide clear insight into cellular processes (functional modules) coordinating cell

behavior. Of course bottom-up approaches are also inherently limited by this simplification of

complex processes to purified components and cell-extracts. Further, even the use of cell extracts

permits unknown mechanisms to enter an experiment. Thus applying this strategy to elaborate

highly complex regulation of processes like focal adhesion turnover may be intractable. Indeed our

current knowledge of focal adhesion regulation involves at least 180 interacting proteins (Zaidel-Bar

and Geiger, 2010), and the value of bottom-up strategies in this case is likely to be limited.

Complementary “top-down” strategies can be used in an attempt to overcome some of the detailed

complexity that will inevitably bog-down a bottom-up approach. We describe here how this may be

achieved by homogenizing complex molecular interactions into phenomenological descriptions

defined


Figure 3-1: The mechanisms behind the maturation threshold. These sketches represent the formation of the lamellum/lamellipodium interface due to entanglement of actin filaments as they are driven by actin retrograde flow. Let be (A) an initial configuration, where nascent adhesions are generated beneath the lamellipodium. While the leading edges advances, some drifting actin bundles create a barrier between nascent adhesions on the outer cell perimeter (B). These actin bundles delineate a portion of the LM/LP interface, and they are subject to lamellipodial and lamellar centripetal forces. These forces are distributed over the length of an actin bundle. In the meantime the LM/LP boundary moves incrementally toward this barrier (C). Here two potential outcomes are possible. First the adhesion spacing either (l) exceeds the maturation threshold, related to a net forces sufficiently large to trigger focal adhesion maturation (C1), or (2) the focal complexes supporting this short segment of the LM/LP boundary is unstable, and eventually disappears as the boundary moves forward (C2). Thus, centripetal forces are essentially accumulated by the spanning actin bundle, with a directly proportional relationship between the adhesion separation (l) and the total force acting on these adhesion that balances the acting centripetal forces (D1 and D2).

in terms of functional inputs and outputs. For dynamic cell behaviors like rapid spreading, these can

be defined in spatiotemporal terms. As inputs, motility function complexity may be distilled to a

description of a time dependent geometric advance. As outputs, the establishment and evolution of

adhesion sites and actin bundles can also be defined in descriptive geometric terms.

Using non-deterministic models built on these principles, we observed striking similarities to in vitro

data for a wide range of experimental configurations. These results support the validity of the

modeled rules governing the spatiotemporal interaction between the considered subcellular

processes, and indicate that the model holds promise in elucidating key details involved in these

mechanisms.

The Model The cell model we present differs from classic modeling approaches that describe a system through a

set of continuous mathematical functions, with a defined objective function (often in energetic

terms) that is “optimized” to predict system behavior (Cirit et al., 2010; Pathak et al., 2008; Vianay et

al., 2010; Xiong et al., 2010). From this optimal solution, the corresponding set of model parameters

(ideally having physiological relevance) can then be examined to gain insight into the biology that

inspired the model. The current model has no objective function other than for a cell to increase its

area to a predefined maximum, if possible.

At its essence, our model geometrically describes the functional activity of the cellular actin

machinery and resultant adhesive site turnover in space and in time. The model tracks these

processes and their consequences within an iterative simulation. This iterative approach captures the

time dependent history that affects the resultant cytoskeleton (Théry et al., 2006), using a fixed time

The Model

step. Motility functions (lamellipodia and filopodia subfunctions) are weakly coupled, and these

functions further crosstalk with cytoskeletal functional modules (nascent focal adhesion formation;

focal adhesion resorption/adhesion site maturation; actin bundle recruitment). As we will show, the

interaction of these functions dictates the cytoskeletal layout at end stage spreading. How these

interactions are implemented within the model can yield insight into their biological underpinnings.

Further, as the model is challenged by varied substrate micropatterns, the range of viable model

parameters narrows until interesting (biologically relevant) threshold values begin to emerge.

Figure 3-2: Correspondence between adhesion site evolution and the rapid spreading numerical algorithm. Biological events controlling adhesion evolution from nascent adhesions to mature focal adhesions are shown (left panel, depicting adhesion turnover). The rapid spreading algorithm (right panel) illustrates the corresponding flow chart, for iteration “i”, along with the five “rules” linking lamellipodial and filopodial protrusion (appearing as shaded boxes within the flow chart). These rules are briefly elaborated in the sketches located outside the flow-chart. Direct interactions between these functions are highlighted by red arrows.

To facilitate the reading of the model description, the principal features are briefly listed here and

shown schematically in the algorithm depicted in Figure 3-2. The stochastic behavior of the two

motile functions we consider (lamellipodial advance and filopodial protrusion) are defined based

upon a broad foundation of published experimental evidence. Their interactions are regulated by five

rules that govern: (1) “nascent adhesion generation” (stochastic generation of nascent adhesions

beneath the lamellipodia and at the filopodial tips), (2) delineation of the LP/LM interface

approximated by an “elastic convex-hull” and establishment of nascent adhesions as focal

complexes, (3) maturation of focal complexes to focal adhesions anchoring actin bundles as

regulated by a novel “maturation threshold” criterion, (4) nucleation of new lamellipodia at the tips

of persistent filopodia dubbed “neo-lamellipodium nucleation” and (5) “filopodia integration” into

lamellipodium.


Following we provide first a global description of the algorithm and then describe in detail both

motility functions. In the final section the five rules above are elaborated in detail.

General description of the spreading algorithm

The model is constructed to elucidate the progression from nascent adhesion to mature adhesion

along with their corresponding actin bundles and the influence of spreading history on cell

morphology immediately after the rapid spreading phase. The model was specifically designed to

elucidate force-mediated adhesion maturation (Bershadsky et al., 2006a; Gardel et al., 2010).

Adhesion forces can result from several sources including myosin activity in the lamellipodia

(Giannone et al., 2007), contractility in the lamella (Burnette et al., 2011) and actin retrograde flow

(Alexandrova et al., 2008; Gardel et al., 2008). For purposes of the present work we do not concern

ourselves with the source of the force, only that intracellular forces are born by cell/substrate

adhesions and that these forces collectively trigger adhesion maturation as a function of cytoskeletal

geometry.

To predictively model cell spreading, we first predefine a geometric substrate ligand pattern and a

limited set of parameters characterizing lamellipodial and filopodial dynamics (Table 1). An iterative

algorithm simulates rapid spreading (Figure 3-2) from an initially assumed circular shape of 5m

radius (Cuvelier et al., 2007). Each iteration commences by advancing the lamellipodium from the

predicted cytoskeletal morphology of the previous step, and determines a “pool” of candidate points

for the formation of nascent adhesions. The lamellipodium has a variable breadth depending upon its

status after the previous iteration and an incremental advance corresponding to a stochastically

implemented lamellipodial protrusion velocity profile. Simultaneously, nascent filopodia are

stochastically distributed at the cell edges with a pre-designated filopodial density.

Nascent adhesions are established from a “pool” of candidate points if binding ligand is present,

otherwise such points are eliminated from further consideration. Lack of binding ligand similarly

induces suppression of nascent filopodia due to their inherent instability. In the absence of ligand,

lamellipodia can protrude from the lamellum to a maximal non-adhesive reach of 7 m (Zimerman et

al., 2004). Then filopodia fate is determined. Pre-existing filopodia that have been stable for 10-12

min without being overtaken by an advancing lamellipodium are allowed to initiate satellite

lamellipodium protrusions at their tips (Guillou et al., 2008). Potential points of adhesion are then

generated beneath these neo- lamellipodia. This process enables cells to establish adhesive zones

that would otherwise be beyond the reach of existing lamellipodia. Stable filopodia that are

overtaken by an advancing lamellipodium become integrated to the cell body, resulting in a

maturation of the related filopodial focal complexes and actin bundles (Schäfer et al., 2009). The

numerical output of each iteration thus consists of an indexed list of spatial coordinates representing

nascent adhesions, focal complexes, and mature focal adhesions bridged by actin bundles. This forms

the basis for the definition of the lamellipodium/lamellum interface from which the cell will advance

in the next iteration.

The Model

The delineation of the LP/LM interface is achieved using an elastic convex hull algorithm to identify

the outermost adhesions in the pool of tracked nascent adhesions (the elastic convex hull algorithm

is described in detail later) as shown on Figure 3-2 and Figure 3-3. The elastic convex hull algorithm

determines the maturation of nascent adhesions into focal complexes, identifying the outermost

adhesions and assuming that neighboring adhesion nodes are bridged by actin bundles (as observed

De

scriptio

n

Valu

e So

urce

Type

Parameters

Motile Functions

Lame

llipo

dial p

rotru

sion

velo

city is a Gau

ssian d

istribu

tion

of th

e lamellip

od

ial velo

city alon

g cell leadin

g edge

Epith

elial and

m

elano

ma:

v = 0.8

m/s

=0.3

Fib

rob

last: v = 1.6

m

/s =0

.2

Op

timized

and

verified

A

dap

ted to

cell typ

e

Lame

llipo

diu

m re

ach rep

resen

ts the m

aximal d

istance th

at can b

e reached

by a

lamellip

od

ium

, wh

ile pro

trud

ing acro

ss a no

n-ad

hesive regio

n

7

m

(Zime

rman

et al., 2

00

4)

Co

nstan

t

Filop

od

ia len

gth is a G

aussian

distrib

utio

n o

f the filo

po

dia len

gth

7

m

=4

; O

ptim

ized an

d

verified

Stoch

astic

Rules

Time

be

fore

ne

o-n

ucle

ation

of lam

ellip

od

ia is the lag tim

e req

uired

befo

re o

bservatio

n o

f neo

-lamellip

od

ium

nu

cleation

at the tip

of a stab

le filop

od

ia

Ran

do

mly selected

in

range b

etween

: 1

0-1

2 m

in

(Gu

illou

et al., 20

08

) Sto

chastic

Time

be

fore

inte

gration

of n

eo-lam

ellip

od

ia represen

ts the

time n

eeded

by th

e cell to

inco

rpo

rate a remo

te lamellip

od

ia R

and

om

ly selected

betw

een

: 2

-4 m

in

Extracted

(Gu

illou

et al., 20

08

) Sto

chastic

Nasce

nt ad

he

sion

s de

nsity in

dicates th

e nu

mb

er of gen

erated n

ascent ad

hesio

ns p

er area u

nit b

eneath

a lamellip

od

ium

1

adh

esion

/m

2 (Zaid

el-Bar et al.,

20

03

) C

on

stant

Matu

ration

thre

sho

ld is th

e min

imal d

istance b

etween

two

con

secutive ad

hesio

ns

located

at lamellu

m/lam

ellipo

diu

m in

terface; en

able

s adh

esion

matu

ration

and

d

isables o

ccurren

ce of lam

ellipo

dia.

Epith

elial and

m

elano

ma:

7.5

m

Fibro

blast: 5

m

;

Op

timized

and

verified

(Th

éry et al., 20

06

)

Ad

apted

to

cell type

Table 3-1 The main parameters used in the model.


by Shemesh and co-workers(Shemesh et al., 2009)). At this point, focal complexes from the previous

iteration are established as mature adhesions if their bridging actin bundle is determined to span a

distance exceeding a pre-defined “maturation threshold”. As will be elaborated, this maturation

threshold is a central concept related to force-regulated adhesion maturation, and forms a key focus

of the present work.

The motility functions: lamellipodia and filopodia

We implemented a top-down approach that describes lamellipodial and filopodial function in

geometric terms. Lamellipodia are parameterized according to their width and “splay” angle. In the

model, lamellipodia are assumed only to occur on convex membrane segments (James et al., 2008;

Kevin Parker et al., 2002; Rotsch et al., 1999). Convex segments (on which active lamellipodia occur)

are observable on sections of the membrane supported by intermediate adhesions. Conversely,

longer sections of membrane whereby inward directed cell tension (membrane tension, lamellum

contractility, etc.) induces a convexity of the elastic hull, do not form lamellipodial protrusions (due

to a corresponding lack of adhesion signaling and inadequate mechanical stability)(Small et al., 2002).

The width of the lamellipodium corresponds to the incremental advance within a given time step,

and was modeled using a lamellipodia protrusion velocity distribution with mean and standard

deviations selected to approximate the experimental literature (Table 1). After an incremental

advance, if a lamellipodium advances to a region without ligand, the lamellipodial width is further

extended in subsequent time steps until it reaches a pre-designated maximal reach of 7m, before

fully retracting (Zimerman et al., 2004). On the other hand, if a lamellipodium has extended to a

ligand covered region of the substrate, nascent adhesions are generated (Choi et al., 2008; Zaidel-Bar

et al., 2003), the LP/LM interface is permitted to sequentially advance (Alexandrova et al., 2008), and

the leading edge distance from the LP/LM is reset to zero for the next increment. Finally, the splay

angles of lamellipodia, essential to ensure lateral lamellipodial substrate detection, were derived

from the local cell shape indicated by the elastic convex hull; splay angle was defined as 2/3 of the

angle formed by consecutive membrane segments. Splay angles were estimated from experimental

images (Kevin Parker et al., 2002).

Function of the filopodia was also phenomenologically described in geometric terms. Filopodia were

represented as vectors, reflecting their morphology as thin, long actin structures (0.1-0.3m wide

and up to 10m long for fibroblasts (Mattila and Lappalainen, 2008)). In the present model, only

fully mature filopodia were considered, with lengths assumed to be normally distributed (7±4 m

determined through parametric study described later). The direction of filopodial action was

implemented as a randomly chosen value between – 45° and +45° from normal to the local

membrane curvature. Lacking published experimental data, we assumed a constant filopodial density

of 0.2 filopodia/m (total active filopodia divided by cell perimeter). Filopodial density was

maintained by adding filopodia in new iterations to compensate for filopodia collapsed/embedded in

the previous iteration.

Combining filopodia and lamellipodia motility functions through spatiotemporal rules of

interaction

Five rules were used to model the key motility functions, activities, and interactions. As mentioned

above and illustrated in Figure 3-2, a rule was implemented to govern cell seeding of nascent

adhesions beneath the lamellipodia (Alexandrova et al., 2008; Choi et al., 2008; Zaidel-Bar et al.,

The Model

2003). At each iteration onset, nascent adhesions were randomly generated at a density of 1

adhesion/m2 (Alexandrova et al., 2008; Zaidel-Bar et al., 2003). These nascent adhesions below the

lamellipodia, together with any mature adhesions established in previous steps, were then

considered by the convex hull algorithm to determine the location of the LP/LM interface.

The second rule of spatiotemporal integration implemented an elastic convex hull to delineate the

LP/LM interface (Alexandrova et al., 2008; Shemesh et al., 2009). Defining this interface is crucial,

since it determines which nascent adhesions are selected to mature into focal complexes according

to their geometric predisposition (mechanical leverage) to inward directed forces. These forces may

originate from retrograde flow (Alexandrova et al., 2008), membrane tension (Théry et al., 2006),

or/and myosin II activity (Giannone et al., 2007). While the LP/LM interface has been reported to

move sequentially after a phase of quiescence (Alexandrova et al., 2008), and others suggest

movement after a phase of retraction (Giannone et al., 2007), we implemented a definition based on

the selection of outermost nascent adhesions that adequately represents both possibilities. The

elastic convex hull detects the outermost adhesions via an iterative process (Figure 3): first a classic

convex hull is applied to define an envelope of rigid segments connecting the outermost cell

adhesions; then an iterative “elastic” process is applied, where an arc is conceptually drawn between

adhesions anchoring the rigid hull segment; if the inward bending arc intersects another nascent

adhesion, this adhesion is selected as a new anchor node and the process is repeated until no new

hull nodes are selected. In bridging neighboring adhesion nodes, one of two curvatures of the hull

were applied (based upon experimental reports in the literature (Bischofs et al., 2009). If the distance

was small (less than the maturation threshold, as defined below), the LM/LP interface was treated as

“deformable”, using a higher curvature arc with a diameter of 1.1 times the distance between the

anchoring adhesion nodes. In cases where the membrane segment bridged longer distances without

support of underlying adhesions (i.e. exceeding the maturation threshold), a “less elastic” (less

curved) arc with a diameter of 1.5 times the spanning distance was implemented.

The third rule concerns the mechanism we have dubbed the “maturation threshold”. As mentioned

above, we assume that focal complexes mature to focal adhesions when the distance between two

neighboring adhesions along the LP/LM interface exceeds the maturation threshold. To apply this

rule, the inter-adhesion length is extracted from the convex hull algorithm. In vitro, the supporting

actin bundles are tensioned at their anchoring adhesions and maturation of these adhesions is force

regulated (Bershadsky et al., 2006b; Galbraith et al., 2002). Whether adhesion forces exceed this

threshold is determined by the net effects of retrograde flow, membrane tension, and/or lamellar

actomyosin contractility – all of which act transversely to the actin filaments bridging LP/LM interface

adhesions (Figure 3-1). For purposes of the present work we presume that the force on the anchoring

adhesions should act in proportion to the length of the bridging bundle. In this sense, a length-based

maturation threshold (spacing between adhesions at the LP/LM interface) effectively serves as an

upstream proxy for a force-based adhesion maturation.


Figure 3-3: Schematic illustration of the elastic convex hull algorithm within context of the rapid spreading algorithm.

The iterative convex hull process is performed at each time step of the spreading algorithm (laying between the nascent adhesions generation and the application of the maturation threshold rules) to delineate the outermost adhesions based on an elastic geometric selection criterion. Nascent adhesions are formed beneath the lamellipodium (shown here for spreading algorithm iteration “i”). In the first step (elastic convex hull process iteration k=1), outermost nascent adhesions are identified through a rigid convex hull. Then (k=2 and 3) an elastic hull is applied to these outermost nascent adhesions. Locally, the elastic hull is either highly curved (1.5 times the spanning distance between adhesions) or assumed to be reinforced (1.1 times the spanning distance between adhesions ) depending on the bridging distance. Nascent adhesions located inside the new limits are added to the “outermost adhesion pool”. This step is repeated until the “outermost adhesion pool” reaches a constant size. In the final iteration (k=4), the lamellum moves toward the newly selected nascent adhesions resulting in their maturation to focal complexes. The remaining “non-selected” nascent adhesions are resorbed.

The last two remaining rules apply to filopodia. Filopodia that buckle or retract are neglected, since

they can be assumed to have a limited influence on spreading. Although buckled filopodia probably

supply actin filaments to the lamella network (Nemethova et al., 2008), they are not thought to

affect adhesion site turnover nor contribute to the final actin bundle layout. To reflect this view, we

used a low filopodial density representing only filopodia that actively participate in

searching/spreading. Such filopodia are thought to have two possible fates, both of which were

represented in the model. First, they can be encompassed by lamellipodia as the leading edge

advances. As a result, the adhesion site located at the tip of the embedded filopodia matures into a

FA, and the actin bundles forming the filopodial shaft become persistent actomyosin fibers. The tip

The Model

then regains function and elongates to form a novel filopodium (Schäfer et al., 2009). Alternatively,

stable filopodia (that have not been overtaken by an advancing lamellipodium within 10-12 min of

their own formation) nucleate a novel lamellipodium that participates in lamellipodia driven

spreading after an imposed delay of 2-4 min, an important process well described by Guillou et al.

(Guillou et al., 2008).

Computational Detail

The modeling approach we implemented utilized a one minute interval time step. This time step

facilitated parameterization of whole and subcellular behaviors within a top-down approach. Each

iteration proceeded until one of the following criteria was reached: Limits on maximal cell area were

set to 2000m2, maximal aspect ratio (maximum cell length along a pre-designated axis divided by

the maximum width in the direction normal to this axis) could not exceed a value of 10, and maximal

allotted spreading was set to 60 minutes.

Three different type of micropatterns, schematically represented in Figure 3-4, were defined to

constrain cell spreading: : (i) Highly constraining single island substrates (Théry et al., 2006); (ii)

Discrete 9 m2 adhesive squares spaced by center to center distances of 10, 15, 20 and 25 m

(Lehnert et al., 2004); (iii) Thin adhesive stripes (2m) with various spacing (from 4 to 12m)

(Zimerman et al., 2004).

Figure 3-4 Micro-patterns used as input for the simulations. (a) Islands: The “V” and “U” are based on confined spreading experiments of Théry and co-workers (Théry et

al., 2006). The thickness of the lines are 6m. (b) Array of squares: The square patterned arrays reflect the

study of Lehnert and co-workers (Lehnert et al., 2004). Adhesive squares have a 9m 2

area and the indicated distance represent the center to center distance. (c) Stripes: The striped pattern is inspired by Zimerman and

co-authors (Zimerman et al., 2004). Stripes have a 2m thickness, with a variable distance between the

stripes (ranging from 4 to 12m). The configuration with a 10m gap is represented. Expected final cell morphologies are drawn (gray) on each pattern, as well as the anticipated dominant motility functions

(lamellipodia in red and filopodia in green). Dimensions on the figure are in m.


Results We confronted the numerically predicted cytoskeletal morphologies against experimental studies of

cell spreading on micropatterned substrate designs that elucidate the dominant spreading functions

(Figure 3-4). Ten simulations were performed on each of 11 different patterns, and the various

outcomes were averaged. Outcomes are briefly summarized in the following sections. Further, we

tested the model using extreme values of the proposed maturation threshold, effectively making it

“constitutively active” or “switched off”. These simulations were intended to demonstrate the

centrality of the maturation threshold in mediating spatiotemporally appropriate focal adhesion

maturation and the efficiency of the top-down numerical approach by achieving a realistic resultant

configuration of actin bundles and focal adhesions.

Lamellipodia are the principal drivers of cell spreading on highly constrained adhesive

islands

On large continuous islands, cell spreading was mostly powered by lamellipodial protrusion.

According to the model, the cell advanced unimpeded, overtaking and embodying extended filopodia

before new lamellipodia could nucleate at their tips. In all simulations on these substrates, cell area

reached a steady state that provoked termination of the simulation. To investigate the effect of

lamellipodial velocity distribution on the dynamics of cell spreading on “V” shaped islands, we varied

the lamellipodial velocity distribution. The time required to cover the whole island was simulated by

varying mean velocity from 0.5 to 1.5m/min and respective standard deviation from 0.1 to

1m/min (Figure 3-5A). The time required to spread was consistent for a given velocity distribution,

with small standard deviations relative to the mean (e.g. 18 +/- 2 min for the most rapid cells, or a

standard deviation of approximately 10% of the mean). A lamellipodial velocity of 0.8m±0.3m/

min was then selected for all subsequent micropattern simulations based upon robust agreement

between numerical and experimental comparisons (Figure 3-5A) and to be consistent with reported

experimental velocity distributions (ratio of standard deviation to mean) (Dubin-Thaler et al., 2004).

Using this lamellipodial velocity distribution, simulated cell spreading on ”U” shaped patterns also

required approximately 30 min to reach steady state (30.8±1.3 min). Here the time required to

spread was computed for an initial seeding position as reported in the experiments. As expected,

there was a high degree of morphometric similarity between simulation and experiment Figure

3-5B). In silico actin bundle and focal adhesion organization reflected all salient experimental

features (parallel arrangement of actin bundle on non-adhesive regions, adhesions located on

internal edges). Varying the initial position of the cell on the substrate influenced the orientation of

the actin bundles, but did not alter the characteristic cytoskeletal patterns. The main discrepancies

between simulation and experiment were a lack of focal adhesions at external pattern corners and a

low density of actin bundles on adhesive regions. A reasonable explanation for these disparities is

that the model did not include post-spreading CSK reinforcement that was likely present (to some

degree) in the experimental data.

Results

Figure 3-5 Cells spreading on highly constraining adhesive islands.

Influence of the lamellipodial velocity distribution (defined by its mean and its standard deviation) on the spreading dynamics of cells on “V” shaped adhesive islands (10 repetitions). For three characteristic distributions (i), (ii) and (iii) leading to spreading times similar to those experimentally observed (roughly 30 min; corresponding to the yellow region), the actin cytoskeleton layout is simulated. Red lines represent stable actin bundles (curvature of the elastic hulls has not been rendered for the sake of visual clarity), whereas blue lines are related to unstable bundles (lifetime of one iteration). (ii) and (iii) differ from (i) in that the stable actin filaments end close on the left arm of the “V” are anchored not on the adhesive edge but near adhesive region center. Predicted cytoskeletal morphologies after spreading (right) on “V” and “U” shaped islands (left) compared to experimental data (center). The numerical outcomes correspond to the layout after 30 min. Similarity between experiment and simulation is striking: Stable actin bundles on the non-adhesive regions are non-crossing and span from adhesive edge to adhesive edge. Red lines represent stable and long lasting actin bundles (curvature of the elastic hulls have not been rendered) anchored at mature focal adhesions, represented here by green rectangles. Yellow lines indicate stable actin bundles formed by filopodia embedment (note that the corresponding adhesions are not pictured for the sake of clarity). Unstable bundles, with a lifetime of a single iteration before drifting toward cell center, are represented by blue lines. Images from corresponding experiments are reproduced with permission of from Théry et al. (2006). Copyright © John Wiley and Sons, Ltd. Cells have been stained red for F-actin and green for vinculin.


Filopodial spreading dominates cell flattening on arrays of squares

Cell spreading on 9m2 squares with variable spacing (10, 15, 20 and 25m) was simulated to yield

insight to the filopodial functions. Indeed spreading across gaps beyond the reach of lamellipodia is

only possible through filopodia(Guillou et al., 2008), and this process (including nucleation of a new

lamellipodium at the filopodial tip) is visible both experimentally and numerically in movies provided

as supplementary material. We observed that the filopodia length distribution and dimension of the

non-adhesive gap substantially affected spreading dynamics (Figure 3-6A). An important feature of

area evolution as function of time is the characteristic “step-function”. This is a consequence of

filopodial dominancy in spreading, and we provide a typical experimental example of this feature in

the supplementary data. From the investigated filopodia length distributions, we selected a

distribution of 7±4m for our model based on qualitative agreement between experimental data and

in silico spreading dynamics. Predicted morphological features were similar to experiments (Figure

3-6B), although larger; the model overestimated spread area in accordance with the imposed upper

limit of 2000 m2 (as adapted from cell spreading studies using homogeneous substrates). In both

experiments and simulation, cells adopted a polygonal shape approximating a square. Although the

vast majority of filopodia bridged adjacent adhesive regions, in rare cases filaments spanned non-

adjacent squares. On substrates of square islands separated by 25m non-adhesive gaps, the initial

location of the cell was critical; cells initially centered on a square could not bridge to a neighboring

adhesive region, resulting in a cell covering a single square. In contrast, cells that were initially

located between adhesive regions could eventually span 3-4 adhesive regions. This explains the

highly diverse post-spreading configurations observed experimentally by Lehnert and co-workers

(Lehnert et al., 2004).

Results

Figure 3-6 Cells spreading on array composed of small adhesive squares

(A) Evolution of cell area as a function of time for in silico cells with different filopodia length distributions (10

repetitions). Five filopodia distributions are investigated (mean length and standard deviation): 7±2m (filled

diamond); 7±4m (filled circle); 10±2m (filled triangle); 10±4m (filled square); 12±4m (hollow diamond) as represented in the inserts below the graphs.

The left panel shows that cells spreading on squares arrays with a 10 m non-adhesive gap, reach their

maximum permitted area (2000m 2

) for all tested filopodial distributions. However maximal size is attained

faster for cells with longer filopodia. The right panel indicates that cells spreading on substrates with 15 m gaps require sufficiently long filopodia to fully spread. (B) Predicted cytoskeletal morphologies (right column) of cell spreading on square arrays separated by 10 (top

row) and 15 m (bottom row) having reached a size of 2000m 2. In silico outcomes are compared to

experimental data (center column). In silico, red lines represent stable and long lasting actin bundles anchored (curvature of the elastic hulls have not been rendered) at mature focal adhesions as represented here by green rectangles. Yellow lines indicate stable actin bundles formed by filopodia embedment (note that the corresponding adhesions are not pictured for the sake of clarity). Unstable bundles, with a lifetime of a single iteration before drifting toward cell center, are represented by blue lines. The dashed yellow lines represent filopodia nucleated from the membrane without adhesion at their origin. Images from corresponding experiments are reproduced with permission of from Lehnert et al. (2004). Copyright © The Company of Biologists Ltd. Here F-actin is stained in green and fibronectin in red.

Cell spreading on parallel adhesive stripes is characterized by a mixed spreading mode

In the final tested substrate, cell spreading was simulated on parallel adhesive stripes in which

dynamic lamellipodial and filopodial interplay is essential for the cell to attain its final morphology. In

this final set of in silico experiments, we implemented the above described parameters for

lamellipodial velocity and filopodial length distributions.

As in the experimental studies upon which the striped patterns were based (Zimerman et al., 2004),

predicted cell shape was strongly correlated to spacing of the adhesive bands (Figure 3-7). Defining

aspect ratio as the maximal cell length along the axis of the stripe divided by the maximal width in

the direction normal to the stripes, band spacing of 4 m and 6 m resulted in cells with fairly round

shapes (aspect ratios near 1). Larger spacing progressively resulted in more elongated cells in the

direction of the stripes, in accordance with a shift toward a mixed spreading mode: lamellipodial

extension along the stripe dominated whereas spreading across stripes occurred only through

filopodia activity.


Figure 3-7 Cells flattening on parallel arranged adhesive bands

(A) Predicted cytoskeletal morphologies (right column) of cell spreading on 2m stripes separated by 10m

(top row) and 4m (bottom row) having reached a size of 2000m2. In-silico outcomes are compared to

experimental data (center column). In silico, red lines represent stable and long lasting actin bundles (curvature of the elastic hulls have not been rendered) anchored at mature focal adhesions as represented here by green rectangles. Yellow lines indicate stable actin bundles formed by filopodia embedment (note that the corresponding adhesions are not pictured for the sake of clarity). Unstable bundles, with a lifetime of a single iteration before drifting toward cell center, are represented by blue lines. Images from corresponding experiments are reproduced with permission of from Zimerman et al. (2004). Copyright © IET Publishing. Actin is stained in green, paxillin in red and non adhesive gaps between fibronectin stripes in blue.

(B) Cell spreading on 2m stripes spaced from 4 m to 10 m (10 repetitions). The light grey bars are related

to cells modeled with a lamellipodial velocity distribution of v = 0.8 ±0.3m/s , the dark grey of v = 1.6

±0.3m/s , and the black bars correspond to published experimental outcomes (Zimerman et al., 2004).

To elucidate the interplay of lamellipodial and filopodial dynamics on cells spreading over stripes,

aspect ratios were computed for two different lamellipodia velocities (Figure 3-7A). Interestingly, on

substrates with larger spacing where filopodial activity becomes important, aspect ratios were more

affected by the lamellipodial speed. We note that while filopodial length distribution was not

parametrically varied in a systematic fashion, lower filopodial reach (and/or longer delays in the

nucleation of remote lamellipodia at the tips of bridging filopodia) for a given lamellipodial speed

yields similarly elongated cells. With regard to cytoskeletal architecture of cells spread on adhesive

stripes, the patterns of actin bundles bifurcated at 6m gap between adhesive stripes, which

corresponded to a transition from a rounded to a more elongated shape (Figure 3-7B). Actin bundle

of rounded cells were organized either tangential to the cell leading edges (formed based on

adhesion maturation related to the threshold), or with a radial orientation (formed according to

filopodial embedment by the advance lamellipodia). These crossing actin bundles resulted in a mesh-

like organization, with focal adhesions located on stripes with apparently no systematic pattern. By

reducing the applied maturation threshold from 7.5m (as set previously to optimally match the

confined island experiments) to 5m, we were able to successfully reproduce the experimentally

observed actin bundle patterns. Here the 7.5 m maturation resulted in an overly sparse

arrangement of persistent actin bundles and focal adhesion. We presume that the maturation

threshold could be cell specific (e.g. 7.5 m for epithelial cells and 5m for fibroblasts; alternatively

filopodial length distributions could be similarly phenotype dependent). With regard to other

spreading characteristics compared to Zimerman and co-workers’ experiments, our simulations failed

to render the possibility that bundles occasionally span three stripes without an intermediate

adhesion on the middle stripe. The simulations failed to render this feature since the end to end

fusion of bundles is associated with cellular reinforcement, which was not modeled here. For stripes

spaced by 8 to 10 m, the predicted organization was dramatically different. The mesh-like

Results

organization was replaced by highly organized actin bundles arranged in parallel. As in experiments,

focal adhesions were generally positioned at the edges of the stripes away from the cell body. The

simulations also featured parallel actin bundles spanning adjacent stripes, yet another feature that is

strikingly similar to experiments.

Remote force gathering is essential to achieve realistic focal adhesion and actin bundle

organizations

The in silico outcomes reported above were computed using a biologically relevant maturation

threshold of either 5 or 7.5 m as estimated from experimental data. We also investigated the

effects of setting the maturation threshold to very large values (100m) and to very small values

(2m) (Figure 3-8). The largest value corresponds to an effective “switching off” of the maturation

threshold rule since no actin bundle ever reached such a length in our simulations. On the other

hand, 2m was small enough to systematically trigger maturation of actin bundles and their

corresponding adhesions through the imposed maturation rules. While spreading dynamics seemed

not be influenced by the applied maturation threshold, cell morphology and the resulting pattern of

actin bundles and focal adhesions organization were affected to different degrees depending on the

tested adhesive substrate.

With a 100 m maturation threshold (“switched off”), cells spreading on all tested patterns exhibited

a common lack of focal adhesions and actin bundles (Figure 3-8). Indeed only adhesions formed by

the filopodia embedment by lamellipodia were present. This result is non-physiological, as evidenced

by the reference experiments (Lehnert et al., 2004; Théry et al., 2006; Zimerman et al., 2004).

Interestingly, for cells spreading on “V” shaped islands, an overly large maturation threshold

impeded the formation of the outermost actin bundles that act to close the “V” pattern. Here the

elastic convex-hull algorithm did not identify the adhesions that would anchor these actin bundles; as

implemented in the algorithm, the elastic convex-hull preferentially creates actin bundle that spans

adhesions spaced by more than the maturation threshold. This indicates the importance of the

maturation threshold in ensuring cell integrity, which increases with reinforcement of each actin

bundle larger than the maturation threshold.

The highly active maturation threshold (2µm), as expected, led to increased density of mature actin

bundles and focal adhesions. On the “V” pattern this was reflected by numerous actin bundles on

adhesive regions originating from a few focal points, an effect that is not apparent in the reference

experimental data. Aside from the designation of mature actin bundles and focal adhesions, end

stage morphology after simulated cell spreading on 10m spaced adhesive squares was not affected

by the decreased maturation threshold (Figure 3-5, Figure 3-7). This was likely due to the non-

adhesive gaps having lengths larger than the in vitro maturation thresholds (5 or 7.5µm).


Figure 3-8 Characteristic effects of extreme maturation threshold values on final spread morphology on three patterns

(“V” shaped islands, adhesive squares separated 10m, and 4m spaced stripes).

Simulations with a maturation threshold of 100m represent a “switching off” the maturation threshold rule,

whereas the 2m maturation threshold results into a quasi-constitutive maturation of focal complexes into focal adhesions. On all patterns, cells showed different density of mature actin bundles and focal adhesions

however cell morphology was only affected on the “V” island and 4m spaced stripes. In silico, red lines represent stable and long lasting actin bundles (curvature of the elastic hulls have not been rendered) anchored at mature focal adhesions as represented here by green rectangles. Yellow lines indicate stable actin bundles formed by filopodia embedment (note that the corresponding adhesions are not pictured for the sake of clarity). Unstable bundles, with a lifetime of a single iteration before drifting toward cell center, are represented by blue lines.

Cell morphology after spreading on 4m spaced adhesive bands was significantly affected by the

imposition of extreme maturation threshold values. Cells lacking an effective maturation threshold

(100m) exhibited a nearly round shape similar to both experimental data and in silico data

computed with the default maturation threshold. On the other hand, cells adopted a polygonal

morphology for the imposed maturation threshold of 2m, with actin bundles spanning numerous

adhesive bands without intermediate attachment points. The cell shape transition from round to

polygonal was seen to occur at low maturation threshold values (<5m). This finding indicates that

the maturation threshold has only a limited influence on cell shape for this experimental condition.

However morphological transitions have been experimentally observed in fibroblasts spreading on

homogenous substrates, if the culture conditions were altered (standard versus serum deprivation

experiments) (Dubin-Thaler et al., 2004). A more extensive parametric investigation is thus required

to elaborate the mechanisms and downstream effects of the maturation threshold on this aspect of

cell morphology.

Discussion:

Discussion: Complex cell functions like adhesion and spreading rely on crosstalk between loosely coupled

subcellular processes playing out across different length and time scales. Since cell spreading is above

all a time-dependent geometric process, we reasoned that this crosstalk could largely be governed by

geometric and historical information “stored” in the current state of cytoskeletal morphology. More

precisely, we hypothesized that filopodial and lamellipodial dynamics loosely interact in space and

time, and that these interactions are driven by (or at least tightly correlated to) geometric cues. On

this premise, we constructed a dynamic numerical model that predicts the formation of stable

cytoskeletal structures (focal adhesions and their associated actin bundles) based on spatiotemporal

interplay between lamellipodial and filopodial activity near the cell leading edge. With only a limited

number of descriptive parameters based on experimental observations or numerical optimization,

we demonstrated this conceptual framework to robustly predict post-spreading cytoskeletal

architecture on fully- and partly-constrained micropatterned substrates.

In essence the model represents a “top-down” approach, with the key subcellular behaviors being

modeled using phenomenological descriptions. Specifically, dynamics of an individual lamellipodium

were modeled as a stochastic process with a statistical description of velocity profile over its length.

In addition, rules were implemented to dictate where lamellipodium can occur (i.e. on convex

membrane regions, and at the extended tips of long-lived filopodia). Similarly, the formation of

nascent focal adhesions was modeled as a stochastic process. Filopodial dynamics were also

stochastically determined, with a probability distribution describing nucleation and protrusion from

the leading edge, and additional rules governing their fate.

Although the model treats these complex subcellular behaviors as “functional processes” with a

phenomenological description of their output, the model offers mechanistic insight to their potential

spatiotemporal interactions. More precisely, the intent of the modeling framework we present is to

explore the formation and evolution of focal attachments between a cell and its substrate and the

corresponding actin bundles that span them. Rules determining these interactions were mostly

derived from published evidence, but include here a proposed novel mechanism that regulates the

selection of certain focal complexes for maturation. We dub this rule “the maturation threshold”.

Through this mechanism, remote mechanical forces acting over the length of an actin bundle and

trigger maturation of the anchoring adhesions according to their spacing. By parametrically varying

lamellipodial and filopodial dynamics (velocity and length distributions, respectively) and by adapting

the maturation threshold, the model demonstrated both accuracy and sensitivity of the cytoskeletal

interaction with the tested substrate geometries. The successfully applied rule sets and

corresponding model parameters may elucidate mechanisms essential to cell spreading as detailed

below.

The model successfully predicts cells spreading on micro-patterned adhesive substrates

that elicit a dominant motility function

Micro-patterned adhesive substrates restrict cellular behavior to better isolate targeted motility

processes for experimental observation (Théry, 2010). In the present study, lamellipodial dynamics

were assessed using highly confining patterns (Théry et al., 2006), filopodial extensions were

characterized using arrays of small adhesive squares (Guillou et al., 2008; Lehnert et al., 2004), and

interactions between these motility functions were elucidated using thin stripes with variable spacing


that elicit mixed-mode spreading (Zimerman et al., 2004). Finally, importance of the maturation

threshold was demonstrated on each substrate.

The theoretical framework was able to successfully reproduce experimentally observed cytoskeletal

features including actin fiber length, location, and orientation. The model did fail to render the

experimentally observed density of stable actin bundles on adhesive regions. We suggest that this

difference is dependent on cellular contractility in the post-spreading reinforcement phase preceding

cell motion (Hotulainen and Lappalainen, 2006; Senju and Miyata, 2009), which was not modeled

here. With regard to predicted focal adhesion layout, the model faithfully rendered many aspects of

the experimental datasets for biologically relevant values of the maturation threshold. However, the

model did not mimic adhesion preference for regions of high curvature. In vitro, this preference is

possibly related to increased lamellipodial activity on concave surfaces and the need for focal

adhesion complexes to provide stability against lamellipodial protrusion (James et al., 2008; Kevin

Parker et al., 2002). While the model could have been refined to incorporate this behavior, the

closely spaced adhesion complexes on these surfaces would likely not be selected for maturation (i.e.

inter-adhesion spacing would be below the maturation threshold).

Simplifications in the modeling framework: Limitations and potential consequences

Top-down approaches, by design, involve a drastic reduction of systemic complexity. For instance, a

lamellipodium was described here in terms of only its spatiotemporal location and rate of advance. In

reality, lamellipodia involve extremely complex processes ranging from actin assembly (Small et al.,

2002) to integrin/adhesion clustering (Mogilner, 2006; Peskin et al., 1993). The proposed

homogenization to a geometric description distills this vast complexity to a functional outcome. In

contrast to less homogenized models, the top-down approach cannot be employed to investigate the

molecular events that underpin these processes (Inoue et al., 2011; Mogilner, 2006, 2009). However

a simple geometrical description facilitates investigation of both motility function (filopodia and

lamellipodia) and, especially, how they interact with functional elements of the cytoskeleton to

achieve a global cellular goal. We view our framework as an attempt to reassemble isolated

mechanisms that have been experimentally characterized into a functional system that yields insight

into the interactions of the components.

In the current study, a “default” filopodial length distribution of 7±4m was based on optimal

prediction of cell spreading on adhesive square arrays, and this also yielded satisfactory results on

the striped patterns. In any case, we note that this parameter selection remains somewhat arbitrary

due to a dearth of available experimental evidence according to which non-viable parameter sets

could be eliminated. Tailored, high-throughput experiments using a consistent cell phenotype and

ligand are thus required. Nonetheless, the model was able to successfully replicate spreading under

three widely different experimental conditions (also with varying cell phenotype and ligand

concentration) and this may indicate that motility mechanisms involved in the rapid spreading phase

are similar among very diverse cell phenotypes, as has been suggested elsewhere (Cuvelier et al.,

2007).

The known and highly dynamic “micro-fluctuations” inherent in lamellipodial and filopodial activity

were temporally homogenized by implementing a relatively large incremental time step (1 minute).

This effectively discounted local membrane advances and retractions that can occur several times

per minute (Dubin-Thaler et al., 2004). Although highly relevant for investigations of molecular or

Discussion:

local cellular events (Alexandrova et al., 2008; Giannone et al., 2007; Liu et al., 2009), tracking these

fluctuations over 30 min of spreading would not likely affect the resultant cell morphology. As a

consequence of this assumption, the model neglects potential maturation of nascent adhesions into

focal complexes based on local membrane retraction or ruffling (Giannone et al., 2007; Zaidel-Bar et

al., 2003). However, we note that this simplification may be of limited consequence given

experimental studies that indicate no causal relationship between local retraction and maturation

(Alexandrova et al., 2008). Similar limitations apply to our implementation of filopodia based

spreading. Within the scope of the applied top-down modeling approach, the complex machinery

that drives filopodia (actin filaments arrangement in the filopodia shaft, traction generation, force

sensing at the associated focal adhesions, etc.) were simplified to a geometric representation of a

base (anchored to a focal adhesion or nucleated at the cell edge) and a tip (nascent focal adhesion).

Nevertheless this simplification leaves the pertinent outcomes intact (neo-lamellipodium nucleation

or embedment), as the tip location represents the key functional feature.

The model further does not explicitly consider cell contractility (lamellar contractility and tension-

dependent mature actin bundle contraction), which is essential for mechanotransduction (Chen,

2008). This does not necessarily represent a limitation since the current model focused on the rapid

spreading phase where contractility remains minimal and is dominated by activity of the lamellum

(Aratyn-Schaus et al., 2011). However quantitative insight into force generation during spreading

(e.g. force transmission through adhesions) could provide interesting clues to mechanisms in

adhesion dynamics, and represents future work.

Novel insight to the formation and evolution of focal adhesions – the central role of

remote force gathering according to actin bundle length

The model demonstrates that complex remote cytoskeletal and/or membrane induced force

gathering along the LP/LM interface can be successfully integrated by spreading cells according to a

geometrically defined adhesion “maturation threshold” that triggers establishment of stable actin

bundles and focal adhesions. By switching the threshold “off” or alternatively to a constitutively

active state (as approximated using biologically non-relevant values of the threshold at 100m and

2m, respectively), this process of remote force gathering was demonstrated to be essential to

obtaining realistic cytoskeletal morphologies. In our top-down approach, we introduced this

mechanism as a functional/geometric threshold regulating the maturation of neighboring focal

complexes at the LP/LM interface according to the distance spanned between the adhesions. Other

candidate mechanisms that have been proposed to regulate adhesion maturation (Alexandrova et

al., 2008; Choi et al., 2008; Rossier et al., 2010) generally yield centripetally oriented actin

arrangements that are not consistently observed in experiments (Rossier et al., 2010; Théry et al.,

2006; Zimerman et al., 2004). Although focal complex maturation has been directly related to force

thresholds (Galbraith et al., 2002), the mechanisms that transmit dynamic centripetal forces

(oriented toward cell body) to adhesion sites located in the vicinity of the LP/LM interface and

convert them into quasi-tangential forces (locally aligned with the cell edge) are not fully understood.

While it has been shown that retrograde flow induces tractions of 100-150Pa near the LP/LM

interface (Gardel et al., 2008), it is unclear if adhesions and actin flow are sufficiently coupled to

trigger force-regulated changes in the adhesion especially for adhesion undergoing tangential forces.

Recent work further indicates a complex relationship between focal adhesion strength and local

lamellar contractility (Stricker et al., 2011).


We propose that an actin bundle bridging two focal complexes could effectively accumulate

centripetal forces (inward directed membrane tension (Théry et al., 2006), retrograde flow (Gardel et

al., 2008), non-sarcomeric actomyosin contraction within in the lamellum (Verkhovsky and Borisy,

1993) and/or “bow-tie” contractile structures (Rossier et al., 2010)) not only in the immediate vicinity

of its adhesion complexes but also over the length that the actin bundle spans. In essence, the

tangentially oriented “line force” dependent to the length of the actin filament could be generated as

detailed in Figure 3-1. For our purposes the source of these forces is much less important than the

fact that the forces, either independently or cumulatively, act in a distributed manner over the length

of the bundle. These line forces are ultimately perceived at the focal complexes that anchor the actin

filament, and could trigger their maturation if sufficiently high. Quantifying the forces associated with

maturation and direcly relating this to adhesion spacing represent the next obvious steps to confirm

the existence and importance of the maturation threshold. However this quantification will be

experimentally challenging, and will further require complex (computational) analysis to separate the

relative force contributions of actin retrograde flow (Shemesh et al., 2009) and non-sarcomeric acto-

myosin contraction (Inoue et al., 2011).

Conclusion We present a modular, “top-down” model that compartmentalizes and simplifies the complex

molecular events behind the rapid spreading phase after cell attachment to a substrate, and yields

accurate predictions of cytoskeletal morphology after adhesion on constrained and partly-

constrained micro-patterns for diverse cell phenotypes. The model provides basic insight into

lamellipodial and filopodial functions, particularly with regard to their spatiotemporal interactions.

We further elucidated a potentially central mechanism we dub the “maturation threshold” by which

remotely acting forces are gathered by actin bundles at the LM/LP interface to reliably trigger

maturation of focal adhesion complexes into appropriately located stable adhesions.

Acknowledgement

We wish to thank Dr. Alexander Verkhovsky for the fruitful conversations we had as well as for his

critical and constructive review of this manuscript.

Supplementary Material

Supplementary Material

Supplementary Figure 1

Representation of the cell area evolution in function of time measured from .


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Chapter 4

An actin length threshold regulates

cell adhesion

Abstract

An actin length threshold regulates adhesion

maturation at the lamellipodium/lamellum interface

Loosli Y. 1,2,3, Labouesse C. 4, Luginbuehl R.3 Meister J.J. 4, Snedeker J.G.1,2 and Vianay B.4





Submitted to Int. Biol.

Abstract The mechanical coupling between adherent cells and the substrate is a major driver of downstream

behavior. This coupling relies on the formation of adhesion sites and actin bundles. How cells

generate these elements remains only partly understood. A potentially important mechanism, the

length threshold maturation (LTM), has previously been proposed to regulate adhesion maturation

and actin bundle stabilization tangential to the leading edge. The LTM describes a mechanism by

which cells integrate lamellar myosin forces to trigger adhesion maturation. These forces, cumulated

over the length of an actin bundle, are balanced at the anchoring focal complexes. When bundle

length exceeds a certain threshold, the distributed lamellar forces become sufficient to trigger the

stabilization of the bundle and its adhesions. In this continuing study, we experimentally challenge

the LTM, by seeding cells on micropatterned substrates with various non-adhesive gaps designed to

selectively trigger the LTM. While stable actin bundles were observed on all patterns, their lengths

were almost exclusively above 3 µm or 4 µm depending on cell type. Furthermore, the frequency

with which gaps were bridged increased nearly as a step function with increasing gap width,

indicating a substrate dependent behavioral switch. These combined observations point strongly to a

LTM with a threshold above 3 µm (respectively 4 µm). We thus experimentally confirm with two cell

types our previous theoretical work postulating the existence of a length dependent threshold

mechanism that triggers adhesion maturation and actin bundle stabilization.

79 An actin length threshold regulates cell adhesion

Introduction Cells like fibroblasts deploy membrane protrusions to explore their environment and to establish

initial links to their substrate. These early attachment points, called nascent adhesions, are arranged

around integrins, a family of transmembrane proteins. With appropriate mechanical cues, nascent

adhesions that have been generated beneath the lamellipodium mature first into focal complexes

then into stable elongated focal adhesions by recruiting further proteins (Alexandrova et al., 2008;

Choi et al., 2008). In early stages, a complex interplay between fast actin retrograde flow of the

lamellipodium and nascent adhesions generates a boundary that delineates the lamellipodium and

the lamellum, while generating sufficient forces to trigger the maturation of nascent adhesions into

focal complexes (Alexandrova et al., 2008; Shemesh et al., 2009). This boundary is hereafter referred

to as the lamellum/lamellipodium (LM/LP) interface. For the subsequent evolution of focal

complexes into mature focal adhesions, the essential role of myosin II has been highlighted in

different studies (Choi et al., 2008; Pasapera et al., 2010). Myosin II activity generates intracellular

forces through the relative sliding of actin filaments within various structures in different manners,

including non-sarcomeric contraction in the lamellum (Verkhovsky and Borisy, 1993) and graded

contraction in stress fibers (Pellegrin and Mellor, 2007). Focal adhesions generally elongate in the

direction of the applied myosin force, betraying the direction of the underlying force transmission

(Bershadsky et al., 2006). Planar forces, such as those observed in two dimensional cell culture, can

be spatially described as being composed of a centripetal component (normal to the leading edge)

and a tangential component (aligned with the leading edge; see Figure 4-1). Since adhesions elongate

in the direction of acting forces, those oriented toward the cell center can be assumed to support

forces normal to the leading edge. Various studies have suggested that such adhesions, generally

located distally to the LM/LP interface, mature under the action of dorsal stress fibers (stress fibers

terminated only at a distal focal adhesion that is oriented toward the cell center), as reported, for

instance, by Wolfenson and co-authors (Wolfenson et al., 2009) or Alexandrova and co-workers

(Alexandrova et al., 2008). In addition to dorsal stress fiber activity, a more recent study by Oakes

and co-authors indicated the importance of lamellar actin contraction in adhesion maturation (Oakes

et al., 2012). A close visual analysis of the presented data from this study indicates that cells with

fewer dorsal stress fibers tend to orient their mature adhesions more tangentially (parallel to the

leading edge), suggesting an alternative tension-based maturation mechanism. Interestingly, such

tangentially aligned adhesions are located in the vicinity of the LM/LP interface and have been

observed in various studies (Burnette et al., 2011; Théry et al., 2006).

The tangential orientation of these adhesions is interesting since the myosin mediated forces

responsible for their maturation appear to be principally oriented in a centripetal direction (lamellar

actin retrograde flow, dorsal stress fibers). Logically, cells should therefore possess a mechanism that

enables the conversion of centripetal forces to tangential forces (thus explaining the tangential

orientation of the adhesions). Hotulainen and Lappalainen described a mechanism by which dorsal

stress fibers and actin transverse arcs interact to form ventral stress fibers (Hotulainen and

Lappalainen, 2006; Tojkander et al., 2012). The focal adhesions anchoring such ventral stress fibers

can possibly exhibit tangential orientation. However the dorsal-transverse arc reorganization into

ventral stress fibers generally occurs across the cell body (i.e. far from the LP/LM interface) and the

resulting fibers are globally oriented from the leading edge toward the cell center or the cell rear.

In earlier work we hypothesized an additional mechanism by which centripetal myosin forces are

translated into tangential forces, and dubbed this “the length threshold maturation” (LTM) (Loosli et

Introduction

al., 2010; Loosli et al., 2012). The LTM (Figure 4-1) relies on actin bundles connecting tangential

adhesions at the LM/LP interface (Loosli et al., 2012).

Figure 4-1: This schematic representation depicts actin cytoskeleton remodeling and adhesion site reorganization triggered by the length threshold maturation (LTM). Let (A) be the initial configuration, where the lamellum (sparse actin filament network with myosin II activity), the lamellipodia (dense actin filament network beneath which nascent adhesions are generated), the actin arcs and dorsal stress fibers are visible. Here drifting actin filaments in the lamellipodium (retrograde flow represented by black arrows and dashed red lines) interact with nascent adhesions to elicit a shift of the LM/LP interface toward the leading edge. Along with the LM/LP interface shift, actin filaments and adhesion sites reorganize as shown in (B). A novel LP protrudes distally from this new limit, whereas proximally myosin II cross links with actin filaments in the lamellum. The focal complexes that earlier formed the LM/LP interfaces are now dissolved and the actin bundles linking the focal complexes migrate toward the cell center as forming actin arcs. The blue arrows indicate segments of the LM/LP interface that link two focal complexes. Due to local inhomogeneity in the lamellipodial protrusions, the nascent adhesions anchoring this bundle are separated by a distance larger than a “maturation length”. As a consequence the terminating focal complexes mature into focal adhesions that stabilize the interconnecting bundles and locally arrest lamellipodial activity. Such a mature bundle is visible in the lamellum on (C). Note the coordinate system defining the tangential direction (locally aligned with the leading edge) and the centripetal direction (orthogonal to the tangential direction).

Here the LTM governs the maturation of the adhesion sites anchoring the actin bundle that spans

them. The required mechanical force to initiate adhesion maturation is “collected” by the bundle as

it is loaded by centripetal forces in proportion to the bundle length. When the length of an actin

bundle (with the corresponding accumulated force at its adhesions) exceeds a certain threshold (i.e.

the “length threshold maturation”), the terminating focal complexes mature into stable, elongated

focal adhesions. This force-based process is possibly powered by non-sarcomeric contraction of the

lamellum actin network, which is attached point-wise to the actin bundle delineating the LM/LP

interface. The centripetally oriented forces thus are converted to tangential forces pulling the

adhesion parallel to the direction of the LM/LP interface, and are thus aligned with the leading edge

(Figure 4-1). Consequently, the resulting stable actin bundles terminated by matured focal adhesions

are oriented tangentially as observed by Théry and co-workers (Théry et al., 2006). Alternatively, if

the distance between two focal complexes is smaller than the maturation threshold, the nascent

adhesions are resorbed and the actin filaments drift towards the cell center where they may

eventually form actin arcs as reported elsewhere (Burnette et al., 2011; Hotulainen and Lappalainen,

2006). Recent work by Prager-Khoutorsky and co-workers postulated a similar force threshold

mechanism, and provided evidence of this mechanism in polarizing cells (Prager-Khoutorsky et al.,


2011). However, in contrast to the mechanism described by Prager-Khoutorsky and co-authors, we

propose that the LTM already occurs during spreading (within the first two hours after cell seeding) –

a phase of cell-substrate interaction that precedes polarization (Zemel et al., 2010). In addition, the

LTM provides insight to local actin and adhesion modeling and remodeling processes that occur near

the cell leading edge, differing from those involving long actin bundles crossing the body of a

polarizing cell.

Although our theoretical work was based upon experimental observations (Loosli et al., 2010; Loosli

et al., 2012), direct experimental testing of the mechanism is required to verify the validity and the

potential importance of this paradigm. The two principal features of the LTM are first: the tangential

orientation of the anchored actin bundles and, second: the “thresholding” aspect of bundle length on

adhesion maturation. In the present work, we investigated both these features using two fibroblast

lines to demonstrate the existence of the LTM: 3T3 fibroblasts and primary subcutaneous fibroblasts

(SCF). We employed micro-patterned substrates to constrain possible focal complex distributions and

to directly probe the length dependence of the LTM. Micro-patterns allow the precise definition of

adhesive regions on cellular substrates (Guillou et al., 2008; Théry, 2010). Consequently, actin

cytoskeleton organization is highly reproducible as a response to the external adhesive/non adhesive

geometry(Vianay et al., 2010). For purpose of testing the LTM, we engineered circular micro-

patterns displaying 8 rectangular non-adhesive gaps (widths ranging from 2 to 10 µm depending on

the pattern) as depicted in Figure 4-2. For these substrates, two characteristic adhesion site

distributions and actin filament layouts were expected depending upon whether or not the

maturation threshold length was exceeded by the non-adhesive gap (Figure 4-2). In support of the

LTM, we demonstrate that actin bundles terminated by two adhesions with a tangential orientation

become more systematic in fibroblasts seeded on micro-patterns with increasing gap width. More

precisely, close analysis of these actin bridges revealed that only bundles longer than 4.5 µm in 3T3

and longer than 3.1 µm in more contractile SCF cells were observed, indicating a characteristic

“threshold” associated with the LTM.

Method

Figure 4-2 : Hypothesized actin bundles organization on a 2 m and 10 m micropattern. According to the LTM, we hypothesized that cells would exhibit different actin organizations depending on

the non-adhesive gap width of the micropattern. This transition was expected to occur between 5 and 7.5m

according to previous numerical investigations (Loosli et al., 2012). The cell on the left, seeded on a 2m pattern, represents the predicted homogenous mesh like organization of the actin bundles along with a continuous lamellipodium, occurring if the non-adhesive gap is narrow. On the other hand, the cell on the right side represents the predicted outmesh like organization (on adhesive regions) and actin bridges terminated by stable adhesions (across non-adhesive regions). This configuration was predicted to occur when the non-adhesive gap width exceeds threshold length. White regions correspond to adhesive zones, black regions to non-adhesive zones. Actin filaments are

presented in red, adhesion site in green and lamellipodia in blue. Bar 8m.

Method

Pattern microfabrication

Pattern microfabrication was performed as detailed elsewhere(Guillou et al., 2008). Briefly,

micropatterned substrates were fabricated using a standard UV-photolithography process. Glass

coverslips, first functionalized with OctadecylTrichloroSilane (SIGMA-ALDRICH, St-Louis, MO, USA),

were coated with S1805 positive photoresist (CTS, Antony, FRANCE), and insolated through a chrome

mask by UV light. After development of the insolated resist using CD26 developer (CTS, Antony,

FRANCE), human plasma fibronectin (MILLIPORE, Zug, Switzerland) was adsorbed on the patterned

surface (concentration 5µg/ml) for 1h30 at 37°C. Fibrinogen conjugated with Alexa Fluor 647

(MOLECULAR PROBES, Eugene, OR, USA) was added to the solution to mark the pattern

fluorescently. The remaining resist was stripped in ethanol, and the surface was backfilled with anti-

adhesive 2% Pluronic, diluted in water (SIGMA-ALDRICH, St-Louis, MO, USA) for 2h at 37°C or

equivalently at room temperature overnight, then extensively washed with PBS. Patterns with

different total areas, ranging from 1000 µm² to 4000 µm², were designed to adapt the adhesive

constraint to each cell type. The results presented here were obtained for 3T3 on 1000 µm² and 2000

µm² patterns, and SCF on 3000 and 4000 µm² patterns since these pattern sizes and cell type pairs

correspond to fully spread single cell coverage per pattern. The non-adhesive gaps were given a


width of 2, 4, 6, 8 or 10 µm. Figure 4-3 shows an example of a 2000 µm2 circular micro-pattern

containing 8 non-adhesive gaps (gap width of 8 µm). Patterns geometries are further detailed in

Supporting Material (Table S1). To improve the manuscript readability, the adhesive micropatterns

with a 2 µm gaps are called “2 µm patterns”. This definition is as well applied to the other designs.

Cell culture

3T3 fibroblasts and primary rat subcutaneous fibroblasts (SCF) were cultured in Dulbecco's Modified

Eagle Medium (GIBCO, Grand Island, NY, USA) supplemented with 1% penicillin, streptomycin,

glutamine, and 10% Fetal Calf Serum (GIBCO, Grand Island, NY, USA). SCF were extracted as

previously described(Hinz et al., 2001). For fixed cell experiments, cells were detached with trypsin

(GIBCO, Grand Island, NY, USA), and seeded on the patterned coverslips. A concentration of 50,000

cells/coverslip gave an optimal number of patterns occupied by a single cell. 3T3 were left to spread

for 1.5 to 2 hours, SCF up to 4 hours. In both cases the extent of spreading was assessed regularly by

observing with a 10x objective. Fixation was performed once the individual island coverage and

spreading was sufficient, yet prior to the cellular reinforcement phase. Cells were fixed with

Paraformaldehyde 3% and rinsed with PBS. For fluorescence imaging, cells were permeabilized with

Triton 0.2% in PBS, then incubated with vinculin primary antibody (SIGMA, St-Louis, MO, USA), rinsed

and incubated with Alexa Fluor 488 and Phalloidin Alexa-Fluor 568 (MOLECULAR PROBES, Eugene,

OR, USA).

For live experiments, SCF were seeded in 12-well plates (~50,000 cells/well) and cultured 24 hours to

reach ~60% confluence. They were then transfected 48 hours prior to the experiment with LifeAct

EGFP (IBIDI, Martinsried, Germany) using Fugene HD (PROMEGA, Madison, WI, USA) and cultured in

antibiotic-free medium.

Imaging

Fluorescence imaging was done on a widefield OLYMPUS IX81 system with a 60x magnification (oil

immersion, NA=1.4) and on a Zeiss Axiovert with a 63x magnification (oil immersion, NA=1.4). Images

were acquired either with a Hamamatsu ORCA ER B7W, with an ANDOR iXon3-885, or a Photometrics

Coolsnap HQ2 camera. Live imaging was done with controlled temperature (37°C) and CO2 (5%)

conditions. Acquisition times were of the order of 250 ms, and fluorescence was verified to be stable

over several hours, with acquisition rate of 1 frame per minute. Image quality is enhanced with

ImageJ to facilitate manual detection of the actin bundles and their related focal adhesions.

Image and data analysis

The aim of image analysis was to identify actin bridges as distinct from others actin structures. A four

step process utilizing information from all three fluorescence image channels was structured as

follows: (i) manual identification of tangential actin bundles, (ii) selection of bundles spanning non-

adhesive regions of the substrate, (iii) bundles terminated by a single adhesion (vinculin only

colocalized at one extremity of the actin bundle) were discarded and finally (iv) in the case of parallel

aligned actin bundles, only the most distal bridging bundle was considered (yielding a maximal

number of 1 bridge per substrate gap, thus maximally 8 bridged gaps per cell).

Once the number of actin bridges per cell was assessed, the number of non-adhesive gaps effectively

bridged by the cell was used to compute the “bridging ratio”. The bridging ratio, calculated for each

Results

cell, was defined as the ratio between the number of actin bridges per cell and the total number of

gaps covered by the cell body. For instance, a bridging ratio of 1 indicates an actin bridge across each

non-adhesive gap. By definition the bridging ratio was always less than or equal to one.

Bridging ratio distributions for each group were compared using a Kruskal-Wallis test assuming

independent samples with different variances. Each cell was regarded as an independent

measurement assuming the inter-pattern distance (100 µm²) was sufficient to provide a single cell

experiment. Significant differences were identified for a p-value less than 0.01, after applying

Bonferroni correction to compensate for multiple comparisons. Statistical analysis was performed

with MATLAB 7.12 (The Mathworks Inc., Natick, MA, USA).

Distances between the terminating focal adhesions of actin bridges were measured using ImageJ

(NIH). Error in localization of the actin bundle ends was generally less than 2 pixels (approximately

0.25 µm). This inexactitude corresponds to a maximal inaccuracy of 0.5 µm in the assessment of

adhesion site spacing (and corresponding bundle length).

Results

Evidence obtained from the single cell experiments supported the length threshold maturation as a

central checkpoint for tangential focal adhesion maturation in spreading cells. For both cell types

(3T3 and SCF), analysis of these data revealed systematic actin bridging on micro-patterns with gaps

of 6 µm and larger. Consistent with this observation, a thorough analysis of detectable actin bridges

formed on 2, 4 and 6 µm gap width micro-patterns indicated lengths of actin bundles almost

exclusively above 4 µm for 3T3 and 3 µm for SCF. These values reflect the length threshold

maturation for each respective cell type.

The length threshold maturation creates actin bridges spanning non-adhesive gaps

According to the LTM, we hypothesized that actin bundles would be aligned with the cell edge and

correspondingly terminated by two tangentially elongated focal adhesions. These bundles (actin

bridges) should occur if the distance between both adhesions exceeds the length threshold, with

tangential orientation of actin bridges formed by the LTM as a distinctive feature. Analysis of the

actin and vinculin staining of spread cells revealed adhesions localized in the vicinity of the LM/LP

interface that were oriented either centripetally or tangentially (Figure 4-3). As expected according to

the LTM, tangentially oriented adhesions were generally mirrored in pairs connected by an actin

bundle (seen in yellow on Figure 4-3). The latter corresponds to the definition of an “actin bridge”

since they spanned non-adhesive substrate gaps. In contrast, more centripetally oriented adhesions

were attached to an actin filament directed towards the cell center, forming a dorsal stress fiber

(seen in red on Figure 4-3). Centripetal adhesions were thus apparently elongated under forces

induced by dorsal stress fibers, whereas tangentially oriented adhesions appear to have been

generated by the LTM.


Figure 4-3 : Typical cell spread on 8m micropattern exhibiting distinct actin bundle and adhesion orientation due to the length threshold maturation. On (A) a picture of a manufactured micro-pattern covered by fibronectin labeled with Alexa647 including height 8 um non adhesive gaps is presented. Actin (B) and vinculin (C) visualisation allow identifying actin bridges (yellow dashed lines) from the other actin bundles (red dashed line). Focus on the actin channel (B) enables to distinct the most peripheral spanning actin bundle to the others. The vinculin channel (C) permits the localization of the ending adhesions (yellow and red ovals) and therefore distinguishing dorsal stress fiber with a single ending adhesion to the actin brides.

Images were deconvolved using the Huygens Software. Bar 10 m.

Characteristic actin network organization shifted its appearance on patterns with gap widths above 6

µm; actin bridges spanned non-adhesive regions whereas a mesh like organization dominated

adhesive zones, as generally observed for cells spreading on homogenous substrates (Small et al.,

2002) (Figure 4-4). On the other hand, cells spread on 2 µm patterns displayed a distal actin mesh

that was apparently not influenced by the non-adhesive regions (Figure 4-4). The 4 µm patterns

produced an intermediate effect, as the gap width fell close to the length threshold maturation

distance. Taken together, observations on the 2 µm and 6 µm patterns support the “thresholding”

aspect of the LTM, since smaller gaps did not create sufficient adhesive discontinuity to

systematically trigger actin bundle stabilization by the LTM.

To supplement these observations taken at discrete time points, and to verify that cell morphological

anisotropy in fact triggered the LTM, a temporal analysis of incremental cell spreading on a non-

adhesive gap of 8 µm was performed (Figure 4-5). In a first step, there appeared two distinct

lamellipodia on neighboring adhesive regions adjacent to their shared gap – with one protruding

lamellipodium and the other being stabilized. After 9 minutes, diffuse actin filaments initiated a

LM/LP interface as already suggested elsewhere (Alexandrova et al., 2008; Shemesh et al., 2009). The

bundle delineating the LM/LP interface was then reinforced, creating an actin bridge. During the next

40 minutes, this bridge advanced from the cell center toward the outside of the pattern while staying

stably anchored at its ends to the adhesive surface. This mechanism appeared to be sequential, and

as originally suggested in our previous theoretical work (Loosli et al., 2010; Loosli et al., 2012), was

likely due to the sequential advance of the LM/LP interface. This concept is further supported by the

occasionally observed presence of accumulated parallel actin bridges that were consistently and

locally aligned parallel the LP/LM interface (Figure 4-5).

Results

Figure 4-4 : Non-adhesive gap width influences the local actin organization.

Actin channel of 3T3 (A-C) and SCF (D-F) spread on 2, 6 and 10 µm micropatterns respectively in panels (A,D),

(B,E) and (C,F) (overlays delimit the adhesive patterns). While cells on the 2 µm pattern showed a mesh-like

actin organization not influenced by non-adhesive regions (A), cells on 10 µm patterns were dominated by

strong bundles distally delimitating the cell (C). Cells seeded on the 6 µm pattern exhibited a mixed mode: on

adhesive regions the actin network was similar to the mesh-like organization observed on the 2 µm pattern,

whereas non-adhesive regions were bridged by actin bundles. Images were deconvolved using the Huygens

Software. Dotted frames indicate the zoomed-in regions. Pattern sizes are 2000 µm2 for 3T3 and 4000 µm

2

for SCF. Bars are 10 µm and 5 µm in insets.

These data, obtained on both 3T3 and SCF, thus provided experimental evidence of the existence of

the LTM and supported our assumption that sufficiently large adhesive discontinuities in a cell

substrate would trigger the LTM. We next concentrated on quantitatively characterizing the

systematic establishment of bridges across non-adhesive substrate gaps.


Figure 4-5 : (A) Image sequence of a cell transfected with LifeActEGFP spreading on a 8m gap pattern. The importance of asymmetrical lamellipodial protrusions in actin bridge formation can be clearly seen. Asynchronous protrusion of two lamellipodium (indicated by red arrows) on two distinct adhesive regions is shown in 1min frame. These two lamellipodia eventually merge (5min) and give rise to a new LP/LM interface over the non-adhesive gap. The actin bundle bridging the gap is indicated by the cyan arrow (frames from 9min to 51min). After 27 min, the same process is observed on the right non-adhesive gap, giving rise to an actin bridge (right cyan arrow, frames 31min to 51min). The position of the arrows are the same throughout the frames, showing the great stability of the bridges over more than 30 minutes, corresponding to many protrusion/Retraction cycles of the leading edge (novel LP protrusions marked by red arrows). At 23min (middle adhesive area) and 35min (right adhesive area), the initiation of dorsal SF oriented towards the cell

center is seen. The yellow overlay delineates the pattern. Scale bar in frame A is 10m. (B) Actin bridge accumulation Actin (red) and vinculin (green) channels representing a cell with actin bridges arranged in parallel that span non-adhesive gaps of 6µm width. The adhesive pattern is shown in yellow overlay. The dotted frame shows the zoomed-in region in inset. Bars are 10µm (full frame) and 5µm (inset) respectively.

Statistical quantification of the length threshold maturation

With a view to providing more robust test of the LTM mechanism, we statistically analyzed the

“bridging ratio”. This ratio was computed for each cell as the number of actin bridges divided by the

total number of spanned gaps. We performed statistical comparisons between cells on patterns with

the same non-adhesive gap but different sizes (either 1000 or 2000 µm2 for 3T3 and 3000 or 4000

µm2 for SCF), which were regarded as individual measures at first. No significant differences in the

bridging ratios among cells of identical type on the various patterns area were revealed (Tables S2-S3

and Figure S1). This confirmed that the gap width was the dominant independent variable. We also

determined that the adhesive density (fraction of adhesive area in the pattern) did not influence

bridge formation: bridging ratios of SCF spread on identical pattern areas but with different numbers

of gaps (4 or 8) presented no significant difference in outcome (Figure S1). Consequently, we pooled

data from patterns having different areas, focusing on comparing cell response to varying gap width

and cell type.

Cumulatively, analysis of 3T3 fibroblasts comprised 89 spanned gaps (from 14 cells) on 2 µm

patterns, 156 spanned gaps on 4 µm patterns (25 cells) and 103 spanned gaps on 6 µm patterns (17

cells). On 8 and 10 µm patterns, 32 gaps were spanned (from 4 cells of each respective

configuration). Experiments on SCFs yielded 257 gaps on 2 µm patterns (37 cells), 238 on 4 µm

patterns (32 cells), 340 on 6 µm patterns (49 cells), 290 on 8 µm patterns (39 cells) and finally 168 on

10 µm patterns (27 cells).

Results

Figure 4-6 : Quantitative analysis of actin bridging establishes a relationship between non-adhesive gap width and onset

of bridging. A significant behavioral switch appears to occur between a 4 and 6 m gap width. The box represents the interquartile range (region between the 25

th and the 75

th percentiles), the bars

represent the 5th and the 95th percentile. The median value is indicated by the line crossing the box, whereas the square indicates mean values. Maxima and minima are located by crosses. Light grey and dark grey boxes represent the groups that are significantly different according to a Kruskal-Wallis test (p<0.01).

We then focused on the 2 µm gap substrates (where we expected no triggering of the LTM) and 6 µm

gap patterns (where we expected systematic triggering of the LTM) in line with our previous work

predicting a threshold value of 5 µm for REF cells(Loosli et al., 2012). We further verified these

outcomes by additional analysis of intermediate gap width (4 µm) and extreme gap width (8 and 10

µm) configurations. Bridging ratio distributions were characterized according to their median and

relevant percentile values (5th, 25th, 75th, 95th) Figure 4-6. Unexpectedly, the median bridging ratio

was found to be non-zero on 2 and 4 µm patterns. For 3T3, these values were of 0.29 and 0.38. They

were, however, significantly lower (p<0.01) than the bridging ratios on larger gap patterns: on 6 µm

patterns, bridging occurred nearly systematically (median bridging ratio of 1; 5Th percentile of 0.63),

and became systematic on 8 µm and 10 µm gaps as expected (bridging ratio of 1 for all cells on both

patterns). For SCF, the median bridging ratio on 2 µm gaps was of 0.25. This was also significantly

lower (p<0.01) than those on larger gap patterns of 6, 8 and 10 µm, where median bridging ratios

were 1 in all cases, and 5th percentiles of 0.88, 0.75 and 0.83 respectively. Only on 4 µm gaps was the

distribution of bridging ratios very large, with a median of 0.63, making them an intermediate

category, where the behavioral variability reflects proximity to the length threshold. Nonetheless, for

both cell types, the bridging ratio increased with increasing gap width in a statistically significant

manner, highlighting the relationship between the LTM and spreading asymmetry induced by local

adhesive discontinuity of the micropattern. Indeed this spreading asymmetry was the fundamental

difference between the tested patterns. The smaller gap width of the 2 and 4 µm did not fully

preclude the development of spreading asymmetry, as evidenced by the sporadic presence of

mature actin bundles terminated by two adhesions. The increasing likelihood that spreading

asymmetry would occur such as to trigger the LTM was evidenced by decreased bridging ratio

variability with increasing gap size Figure 4-6. Interestingly, for 3T3 and SCF, the bridging ratio

variability was maximal on the 4 µm patterns, suggesting a potentially important behavioral switch as

the distance between adhesions linking the bridge exceeds 4 µm.

To further investigate the unexpected presence of actin bridges across 2 µm and 4 µm gaps, the

distance separating both adhesions of these actin bridges were assessed. Outcomes are reflected in

the cumulative distributions displayed in Figure 4-6 (histogram distributions in Figure S2). In the 3T3


pool, from 27 detected actin bridges on 2 µm patterns, the smallest measured inter-adhesion

distance was 3.9 µm and the largest was 26.8 µm. For SCF, the minimal and maximal measured

distances are 3.1 and 40.3 µm for 67 detected bridges on 2 µm patterns. For both cell types the

smallest actin bridges were thus longer than the width of the smallest non-adhesive gap. It seems

likely that aside from the imposed non-adhesive gaps, these patterns permitted other sources of cell

spreading anisotropy that could ostensibly trigger the LTM, with resulting bridges above 4 µm for 3T3

and 3 µm for SCF. Regardless, the central outcome of these experiments is that the minimal actin

bridge length, on small gap patterns also lay slightly above 4 µm for 3T3 (respectively 3 µm for SCF),

fully consistent with observations on the larger gap substrates that more clearly demonstrated the

“thresholding” aspect of the LTM. To highlight this, the distributions of bridge lengths were plotted

as cumulative curves in Figure 4-6. Taking a closer look at the smaller bridges, it is clear that the

curves for 2 µm and 4 µm gaps overlap for the 3T3, illustrating the thresholding behavior discussed

above. For SCF on 2 µm gaps, the initial increase of the number of bridges at a length of 3 µm is an

indicator of a LTM value lower than for 3T3 cells.

Based on these results and the framework of the LTM with a length threshold maturation value

ranging between 4 and 5 µm for 3T3, we would expect cells on the 6 µm patterns to exhibit

systematic bridging. While this was largely the case, the 25th percentile of the bridging ratio for 6 µm

gaps was 0.88 for 3T3 Figure 4-6. For those gaps that were not bridged by a LTM-derived actin

bundle, there was usually no single distinct peripheral bridge. In some cases, several bundles were

involved, possibly being cross-linked. Although tangentially aligned, the so obtained bundles

exhibited a variable curvature, bringing into question their classification as an actin bridge. Bundles

with “kinks” were not counted as bridges because most probably they were connected to other

stress fibers, complicating the manner in which force would be distributed along the bundle.

Alternatively, we suspect that cell-assembled fibronectin matrix may have effectively reduced the

substrate gap, potentially explaining the presence of actin bridges as small as 5.4 µm measured for

3T3 spread on the 6 µm patterns. While focusing on SCF, one observed non-systematic bridging on 4

and 6 µm patterns. Although both these non-adhesive gaps were above the estimated threshold

length for SCF (slightly more than 3 µm), we also suspect that self-assembled fibronectin on both

sides of the gap may have played a role in this outcome.

Discussion

Discussion

In 2006, Hotulainen and Lappalainen published a breakthrough study revealing some of the

mechanisms in the generation of large actin bundles (Hotulainen and Lappalainen, 2006). They

suggested that ventral stress fibers (stress fibers crossing the cell body and terminated by two

mature focal adhesions) originate from two mechanisms: (i) end to end fusion of dorsal stress fibers

and (ii) recombination of dorsal stress fibers and transverse arcs. More recently, tropomyosin

incorporation along actin filaments was suggested to promote myosin II recruitment during these

processes (Tojkander et al., 2011) providing additional insight into this actin bundle recombination

process (Tojkander et al., 2012). However both these mechanisms fail to explain the formation of

actin bundles located immediately behind the lamellipodium that are aligned with the leading edge

and that are terminated by two adhesions. These have been observed in cells constrained on

discontinuous micropatterns such as those used in the present study, the work of Théry and co-

workers (Théry et al., 2006), and as well in cells spreading on homogeneous substrates (Burnette et

al., 2011; Oakes et al., 2012; Prager-Khoutorsky et al., 2011). Such bundles are certainly formed by

local actin reorganization processes, whereas most of the current models provide insight in global

actin bundle turnover (Hotulainen and Lappalainen, 2006; Prager-Khoutorsky et al., 2011; Senju and

Miyata, 2009). Along the lines of a recent experimental study (Burnette et al., 2011), we focus on a

numerically derived mechanism, the length threshold maturation process, that describes actin

bundle fate in the vicinity of the lamellipodium/lamellum interface (Loosli et al., 2010; Loosli et al.,

2012).

Figure 4-7 : Schematic representation summarizing actin bundles organization and adhesion layout as experimentally observed.

Bridging occurred on all tested patterns, becoming frequent on 4 m patterns and systematic above 8 m. Interestingly, cells did not systematically cover the patterns. White regions correspond to adhesive zones, black regions to non-adhesive zones. Actin filaments are

presented in red, adhesion site in green and lamellipodia in blue. Bar 8 m.

In this study, we provide experimental evidence that strongly supports the existence of the LTM. As

the formation of bundles according to the LTM is driven by distance between focal complexes, we

employed micropatterned substrates to investigate the formation of actin bundles bridging non-

adhesive substrate regions (Figure 4-7). Using such substrates we demonstrated that cells spreading

over non-adhesive gaps broader than 6 µm systematically bridge this gap with an actin bundle

anchored by two tangentially elongated focal adhesions (actin bridges). We further observed actin

bridges that were longer than a spanned non-adhesive gap, suggesting that cellular adhesion


anisotropy also comes from sources other than substrate geometry (Figure 4-7). These elements

highlight the key characteristic of the LTM: a given threshold length between two consecutive

adhesions is required to trigger the adhesion maturation process. Our observations of the dynamics

of actin bridge formation (Figure 4-5) further highlight the critical importance of lamellipodial

protrusions in the bridging of non-adhesive gaps. This definitively demonstrates different

underpinnings behind actin bundle formation according to the LTM in contrast to currently

established “polarization” models. Furthermore these considerations generalize the LTM by

explaining why structures similar to tangentially oriented actin bridges are also visible in cells spread

on homogenous substrates (Burnette et al., 2011; Oakes et al., 2012; Prager-Khoutorsky et al., 2011),

where sufficient adhesive anisotropy to trigger the LTM can be caused by the considerable temporal

and spatial variability of lamellipodial advance (Dubin-Thaler et al., 2004) and associated cellular

adhesions (Choi et al., 2008; Zaidel-Bar et al., 2003).

The tendency for tangential orientation of adhesions near the lamellipodium/lamellum interface

suggests in turn that the forces acting on them are also tangential. Yet intracellular forces in the

vicinity of the LP/LM interface are mostly oriented toward the cell center. Recently, we hypothesized

that actin filaments delineating the LM/LP interfaces accumulate centripetal forces along their length

and convert these to tangential forces that act on focal complexes as they resist to the centripetal

contraction by crosslinking together and triggering maturation of the terminating adhesions. If the

focal complexes are sufficiently spaced, the bundle of actin filaments connecting them stabilizes

along with the adhesions. According to our classification, this defines an actin bridge, as shown on

Figure 4-1. In the current study, we analyzed the lengths of over 1100 individual actin bridges formed

by two different cell types on an array of different substrates. While a clear transition of gap bridging

behavior was seen between 4 and 6 µm gap substrates (indicating a maturation threshold in this

range), cells seeded on micro-patterns having non adhesive gaps of 4 µm and smaller also exhibited

some actin bridges - possibly reflecting the irregular lamellipodial advance mentioned above.

However most of these bridges were longer than 4 µm for 3T3 and 3 µm for SCF. A single bridge in a

3T3 (resp. SCF) assessed at 3.9 µm (3.1 µm), within the range of measurement inaccuracy, was the

lone exclusion. This lower limit on observed actin bridge length leads us to narrow our estimation of

the maturation threshold length to approximately 4 µm for 3T3 and 3 µm for SCF. As an aside, and as

will be discussed later, we interpret the difference between 3T3 and SCF maturation threshold length

to reflect differences in cell contractility (myosin activity), thus supporting the basic mechanisms

underpinning the LTM. In any case cells were able to establish bridges despite substrate gap widths

below the LTM distance, and this may have been due to uneven lamellipodial advance as well as the

fact that the distance between adhesions was evaluated without taking into account the bundle

curvature. This latter fact possibly resulted in an underestimation of the maturation threshold length.

However such a bias is difficult to quantify since bridges exhibited various curvatures and the exact

relationship between bridge length, bridge curvature and accumulated force remains somewhat

unclear. Nevertheless the similarity of our experiments to our previous theoretical predictions (based

on a composite of the experimental literature) is striking, where the maturation threshold length was

estimated at 5 µm for REF52 fibroblasts (Loosli et al., 2012). However some of the downstream

consequences of the LTM we proposed in our theoretical work still require further investigation.

Indeed, we supposed that the LTM would locally inhibit lamellipodial occurrence, a prediction that

was generally not supported by the time-lapse imaging we performed in the present study (Figure

4-5). It is possible that lamellipodia generated on both sides of the bridge can fuse together.

Discussion

Alternatively, two unique thresholding lengths could possibly regulate adhesion maturation and

lamellipodial inhibition. Further investigation focusing solely on this is required to resolve this issue.

LTM, myosin and contractility under the scope

Myosin II activity and the LTM are inextricable. We propose that myosin II activity in the lamellum

provides sufficient forces to trigger actin bundle stabilization along with maturation of the anchoring

adhesions. While lamellar contraction appears to be essential, alternative sources of forces that are

consistent with the LTM are also possible. Burnette and co-workers have observed the necessity of

myosin II activity for the formation and maintenance of transverse arcs in lamellipodium and

lamellum (Burnette et al., 2011). This suggests a potential early colocalization of myosin II at the

LM/LP interface capable of providing another source of tangential force. Even if this were the

dominant intracellular source of tangential forces, the thresholding aspect of the LTM remains

pertinent since force generation of mechanically isolated sarcomeres also depends on filament

length (Herzog et al., 2010). To address this issue and open new perspectives on myosin II activity,

assessing myosin II localization and activity in the LM/LP interface region is essential. Another

consequence of the myosin II dependent formation of transverse arcs in the lamellipodium is that

controlled myosin activity modification has not only consequences on the lamellar contractility but

on the establishment of an actin bundle delineating the LM/LP interface as well. Therefore such

experiments aiming at investigating consequences of myosin II on the LTM have to be taken with

extreme care since isolating the effects of both phenomena is extremely challenging. Nevertheless

the characteristic differences in LTM for the investigated cells (3T3 vs. SCF) provide some support to

the assumption that myosin II induced contractility drives the LTM. We indeed observed that

threshold length regulating the LTM is smaller for the highly contractile SCF compared to 3T3 cells

(Hinz et al., 2001).

Along these lines, another argument concerning the LM/LP interface may arise. Based upon

experimental evidence (Alexandrova et al., 2008), we presume that the LM/LP interface is generated

according to mechanical interactions between actin retrograde flow and cellular adhesion sites.

Nevertheless an alternative mechanism involving fusion of aligned nascent dorsal stress fibers could

generate bundles oriented along cell edge with two terminal adhesions. Oakes et al. have established

that dorsal stress fibers are not mandatory for the stable formation of tangential actin bundles

(Oakes et al., 2012). To further analyze this issue, Atn-1 knockdown cells and/or Dia1 knockdown

cells seeded on micro-patterns similar to ones used in the present study could be performed. This is

however out of the scope of the present study.

Decoupling the effect of pattern geometry and LTM-base process

Adhesive substrate geometry is known to influence cell behavior (Théry, 2010). Cells on square

substrates tend to assemble adhesion sites and stress fibers principally at their corners, resulting in

high local concentration of traction forces at the square vertices (Parker et al., 2002). In the present

experiments, all patterns exhibited 16 corners (two per gap) covered by cells with similar external

morphology on the adhesive zone. However actin filament reorganization (transitioning from a

continuous mesh to bridge-like structures) seemed to be principally influenced by the width of the

non-adhesive gap between the corners. This behavior was in agreement with the LTM. This suggests

that along with global cell morphology (effectively held constant in our study) and local ligand layout

(e.g. corners), lamellar contractility (via the LTM) controls actin bundle organization.


It has been shown that micropattern area and adhesive density (fraction of adhesive area in the

pattern) can also modulate cell spreading (Han et al., 2012; Lehnert et al., 2004). Local adhesive

constraints onto a mostly non adhesive substrate, such as spots arrays, forces cells to exhibit a

reproducible actin cytoskeleton organization of long, stable actin bundles (Vianay et al., 2010). In the

current study, the dominantly adhesive surface area in comparison to the non-adhesive area (all

adhesive ratios exceed 50%) allowed cells to spread as if on a homogeneous coated substrate, while

still allowing the leading edge to encounter non-adhesive gaps of variable width. Thus, our data

indicates that the LTM-based formation of actin bridges appears not to be dependent on global

parameter such as pattern size or adhesive density. Indeed pattern size did not appear to influence

the observed bridging characteristics of either cell type on the tested patterns (Figure S1). Our results

suggest that the dominant factors in the LTM are local geometric factors rather than global. In this

study, the local alternation of adhesive and non-adhesive region clearly differs from adhesive spots

arrays often used to investigate differences in adhesive ratios (Han et al., 2012; Lehnert et al., 2004).

We hypothesize that on our pattern geometries, the adhesive zones were sufficient to reproduce

local cytoskeletal configurations similar to those observed on homogeneous substrates where the

actin cytoskeletal organization includes dorsal stress fibers and transverse arcs (Figure 4-3, Figure 4-4

and Figure 4-5).

It is however extremely challenging to isolate single downstream consequences of pattern geometry

and adhesive density since all these processes (cell morphology, cell adhesion and contractility) are

tightly interwoven. We believe that combining microprinting and traction force microscopy, which is

currently technically challenging (Tseng et al., 2012), is essential to further disentangle the influence

of these factors. Furthermore, live traction force microscopy of cell spreading on elastic micro-

patterned substrate might widen the spectrum of contractility based phenomena that possibly

influence cell behavior by tracking the effect of cell spreading memory on cell behavior.

Actin bridges, transverse arcs and cell morphological integrity

The fate of actin filaments that delineate the LM/LP interface and which do not reach the LTM

remains unclear. We suggest that such filaments may drift toward the cell center while fusing with

others, thus forming transverse actin arcs. This would explain why actin transverse arcs are typically

observed in isotropic cells (Senju and Miyata, 2009), since such cells exhibit homogeneous peripheral

adhesion distributions that would limit the formation of stable anchored transverse actin bundles

according to the LTM. In this case, we suppose that transverse arcs provide morphological integrity

(Cai et al., 2010). While “floating” (non-anchored) transverse-arcs may be sufficient to withstand

limited inward directed forces, they are not sufficiently robust to sustain the observed concavity of

long non-active leading edges. Based on our spatiotemporal observations of anisotropic spreading,

we offer an alternative mechanism to cell preservation of shape integrity. In contrast to cells

spreading on homogeneous substrates, cells spreading on micropatterned substrates exhibit

localized lamellipodia and a heightened potential for morphological concavity as demonstrated in the

present study and elsewhere (James et al., 2008; Théry et al., 2006). For instance, Théry and

colleagues report that cells seeded on “V” shaped islands generally exhibit an advancing

lamellipodium on each arm of the “V”. These move along with a cell edge linking both lamellipodia

that has a nearly constant curvature and thus limits cell concavity (Théry et al., 2006). We

hypothesize that cells resort to actin bridges formed by the LTM to stabilize this curvature during

spreading, a concept that is corroborated by a recent study suggesting that stress fibers stabilize the

lamellar actin network (Oakes et al., 2012). The dynamic aspect of spreading would then explain the

Conclusion

existence of the parallel arranged actin bridges observed by Théry and co-workers, and this is

replicated in this study. This mechanism thus provides anisotropic cells an efficient tool to withstand

concavity and ensure cell morphological integrity.

Length threshold maturation and the lamellipodium/lamellum hypothesis

The LTM is based on the existence of actin bundles forming segments that delineate the LM/LP

interface which transmit and convert centripetal forces to more tangential forces acting at an

adhesion. It has been shown experimentally (Alexandrova et al., 2008; Vallotton and Small, 2009) and

numerically (Shemesh et al., 2009) that such a distinct frontier delimits the lamellipodium and the

lamellum. It has also been suggested that the lamellum pulls the lamellipodium from the rear,

indicative of a mechanical coupling between actin network (Giannone et al., 2007). However this

standard model (along with the level of coupling thought to be mediated by actin filament exchange

and mechanical force) has been challenged by the “lamella hypothesis”. The latter framework is

based on fluorescent speckle microscopy, with Ponti and co-workers suggesting that the lamella and

the lamellipodia are overlapping but kinetically and molecularly distinct (Danuser, 2009; Ponti et al.,

2004). Thus a question arises: could the LTM and the “lamella hypothesis” be compatible? In the

lamella hypothesis, a sparse lamellar network is possibly present beneath the lamellipodium with no

supposed actin exchange between these networks. This lack of exchange would seem to preclude the

formation of actin bridges spanning focal complexes formed by a drifting actin bundle from the

lamellipodium entanglement, as assumed for the standard model (Alexandrova et al., 2008). Under

the “lamella hypothesis” an alternative mechanism would thus be required to explain the formation

of bundles linking two focal complexes. Since the lamella is located beneath the lamellipodia and

adhesion sites are not localized immediately at the front of the lamella but more proximally to the

LM/LP transition (Ponti et al., 2004), one could propose that actin filaments of the lamella itself may

entangle. So despite a possible presence of a sparse lamellar network within the lamellipodium, the

LTM occurs locally. It is therefore interesting that the LTM should be compatible with both models.

Conclusion

This study provides quantitative experimental evidence of the existence of a length dependent

threshold for actin bundle and adhesion maturation driven by centripetally acting lamellar myosin II

activity that is effectively converted to more tangential force. This mechanism strengthens our

current understanding of adhesion maturation and formation of persistent actin bundles. We further

provide a first estimate for a fibroblastic threshold length of approximately 4 µm for 3T3 and 3 µm

for SCF. Finally we discuss how the length threshold maturation may be a reliable and efficient

geometry-based means to guarantee cellular morphological integrity of a spreading cell.

Acknowledgement

The authors acknowledge Gion Fessel for the fruitful conversations on bio-statistic and Josiane Smith

for her help with the cell cultures. We thank as well the Center for Micronanotechnology (CMI) and

the BioImaging and Optics Platform (BIOP) at EPFL for the use of their equipment for micropattern

fabrication and imaging, respectively.


Supplementary material

Figure S1

Dependency of bridging ratios on the adhesive pattern

We verified that the area of the adhesive pattern did not change the distributions of bridging ratios by doing a kruskal-wallis test, with a significance value p<0.01. For each gap width, we checked that the data from smaller patterns (1000 µm² for 3T3 and 3000 µm² for SCF) could be pooled with data on the larger patterns (2000 µm² for 3T3 and 4000 µm² for SCF). The results showed no significant difference. We had the same approach to compare SCF on patterns with 8 non-adhesive branches of 2 µm wide and only 4 non-adhesive branches of same width to see if the adhesive area density could change our results. As discussed in the main text, for our geometry of patterns, adhesive density had no significant impact. Figure S1 shows separately the bridging ratios of cells for all patterns considered in this study, curly braces indicate those that were pooled for the analysis. Box, box whiskers, and dashes correspond respectively to the 25th-75th percentiles, the 5th and 95th percentiles and the extrema values. The median is indicated by a line, the mean by a square. The legend details the pattern category: number of non-adhesive branches, total pattern area, gap width. For example "8b-1000-g2" is a 1000 µm² pattern with 8 non-adhesive gaps of 2 µm wide.

Supplementary material

Figure S2

Distribution of actin bridges' lengths

Histogram distribution of the lengths of actin bridges on 2 µm (A), 4 µm (B) and 6 µm(C) gaps. In each plot the bridges' lengths for each cell type are compared. Bin width is 1 µm. Whereas there is clearly a difference on the smaller gaps between 3T3 and SCF, since the latter extend bridges over distances as small as 3 µm, the distributions for 4 µm and 6 µm gaps are similar, the gaps being at least as large as the LTM both for 3T3 and SCF.


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99 How Rho/Rac regulates cell shape

Chapter 5

How Rho/Rac regulates cell shape


Rho/Rac morphology control of spreading cells – simulation

based elucidation of underlying mechanisms

Loosli Y. 1,2,3, Vianay B.4, Luginbuehl R.3, and Snedeker J.G.1,2 *





Abstract

Cell morphology is widely used to characterize cell phenotype, and is known to affect cell fate.

Morphology is defined by the spatial distribution of cytoskeletal structures and substrate adhesions,

and depends on a complex coordination of processes occurring over a range of spatial and temporal

scales. While regulation of individual elements is beginning to be understood, the collective

interaction of these manifold processes remains largely obscure. In this study we explore how

cellular machinery related to membrane protrusion and lamellar contraction are orchestrated to

regulate cell morphology during spreading. To this end, we exploit a recently developed numerical

framework that homogenizes the molecular complexity of these sub-cellular processes according to

their collective function. We then focus on the cooperative interaction of these processes in cell

spreading. Previous parametric studies using this numerical model revealed the central importance

of lamellipodial protrusion dynamics in focal adhesion maturation. This earlier work demonstrated

that adhesion maturation is robustly predicted by a “maturation threshold length”, a parameter

referring to the length of actin bridges between anchoring focal complexes at the

lamellum/lamellipodium interface. This threshold corresponds to the ability of a cell to collect

distributed lamellar myosin contractile forces, concentrate these forces at focal complexes, and thus

regulate adhesion maturation. In the present work we demonstrate that by varying the length

threshold within a physiological range one can qualitatively and quantitatively reproduce the

transition between isotropic and anisotropic spreading modes that can be experimentally observed.

Close analysis of these in-silico results taken together with related upstream signaling controlling

lamellipodia protrusion and lamellar contractility point to a “biomechanical pathway” by which cells

can plausibly employ relative Rho/Rac activity to regulate their resulting morphology. More

specifically, a shift of the Rho/Rac balance toward Rho seems to favor cellular anisotropy by

redistributing lamellipodial activity with locally increased adhesion, a phenomenon that plausibly

could rely on the maturation threshold length mechanism.

Introduction

Introduction Analysis of cell morphology has long been a cornerstone in cell biology research because it not only

reflects the current state of cell behavior, but can also drive it. For instance, seminal work has

demonstrated how cell shape can switch behavior from growth to apoptosis (Chen et al., 1997). Later

research established that cell shape locally influences membrane protrusion dynamics and

contractility (Parker et al., 2002). This critical link between cell shape and cytoskeletal dynamics has

been subsequently supported and elucidated in numerous shape dependency studies (Guillou et al.,

2008; James et al., 2008; Sero et al., 2011; Théry et al., 2006; Vianay et al., 2010).

Post-spreading cytoskeletal morphology depends on a complex integration of subcellular processes

including membrane protrusion and adhesion turnover – functions that are tightly related to Rho/Rac

activity (Nobes and Hall, 1995). Stochastic protrusion of the cell membrane, myosin II driven cell

contractility, and focal adhesion turnover are widely viewed as requiring a close synchronization to

enable proper cell movement: while the broad strokes of adhesion and motility have been

appreciated for over a decade (Lauffenburger and Horwitz, 1996; Ridley et al., 2003), the mechanistic

coordination among the involved sub-cellular processes are still obscure (Keren et al., 2008). Even

the earliest stages of cell-substrate interaction remain unclear (cell adhesion and spreading), despite

the fact that spreading cells exhibit less polarized behavior and simplified adhesion dynamics

compared to motile cells (Loosli et al., 2010). While it has remained largely unclear why

experimentally “identical” cells do (or do not) adopt variable post spreading morphologies depending

on their culture conditions (Dubin-Thaler et al., 2004), there has been some progress in unraveling

the underpinning signaling processes. More than a decade ago Sander and co-workers suggested that

the intracellular balance between the small GTPases Rho and Rac may control cell shape (Sander et

al., 1999). Since then, it has become increasingly clear that Rho/Rac regulation of integrin mediated

adhesion plays a central role in driving cell morphology, both affecting lamellipodia dynamics

(Machacek and Danuser, 2006) and regulating myosin activity via the Rho-ROCK pathway (Cai et al.,

2010). However the orchestrating mechanisms by which a cell consolidates Rho/Rac biochemical

signaling into a structural adaption (e.g. altering its shape) remain unclear.

Membrane protrusion and adhesion dynamics involve various length and time scales, and although

certain individual elements are well characterized their collective interaction remains poorly

understood (Keren et al., 2008; Parsons et al., 2010). While experimental “bottom-up” approaches

show promise for deciphering the integration of molecular events into cellular behaviors (Liu and

Fletcher, 2009; Smith, 2010), such cellular “reconstruction” studies have been limited to fairly

simplified systems (Giraldo, 2010; Haviv et al., 2006). In our own work, we have introduced a

complementary approach in the form of “top-down” numerical frameworks that synthesize the

results of such “bottom-up” studies, and bridge the gaps between them. We have demonstrated the

utility of such in silico approaches in not only accurately predicting cell morphology and cytoskeletal

layout on a wide range of adhesive substrates (Loosli et al., 2010; Loosli et al., 2012), but also for

extracting mechanistic understanding of how morphology is coordinated by the cell in space and

time. Our initial modeling studies focused on how cellular structural integrity is related to (and likely

drives) adhesion site and actin bundle distribution.

In the current work we probed Rho/Rac control of cell morphology by extending these models. The

balance of Rho/Rac signaling and related effects on contractility and lamellipodial dynamic were

integrated within the numerical framework by linking increased Rho signaling with the so-called


“length threshold for maturation” (LTM). This link effectively relates lamellar contractility to focal

adhesion maturation (Balaban et al., 2001; Stricker et al., 2011) and a shape-based local inhibition of

lamellipodial activity (James et al., 2008). A shift in Rho/Rac signaling balance toward Rac was

implemented by correspondingly adjusting the lamellipodial protrusion velocity distribution. This

assumption, in agreement with our top-down approach, simplifies our current knowledge of small

GTPases effects on lamellipodia protrusion that are summarized elsewhere (Ridley, 2011). In this

fashion, we parametrically exploited the numerical model to characterize model sensitivity, and

identify parameter combinations that could provoke a transition from an isotropic to an anisotropic

spreading mode. Such transitions have been reported experimentally (Dubin-Thaler et al., 2004;

Giannone et al., 2004; Lam Hui et al., 2012). Very generally, we observed that by shifting the

modeled Rho/Rac balance towards Rho, we could drive the model toward an anisotropic spreading

mode Figure 5-1, a finding consistent with the experimental literature. We conclude that the model

demonstrates a plausible mechanism by which Rho/Rac signaling can act along a “biomechanically”

regulated pathway to coordinate cell shape.

Figure 5-1: Hypothesized downstream effects of Rho Rac on spreading mode. An increased Rho activity is supposed to enhance myosin II activity and to reduce lamellipodial protrusion velocity. In turn, short segments of the LP/LM interface mature, resulting into cells spreading anisotropic with focal adhesions obtained through the length maturation threshold process as well as through the conjugated effect of transverse arc and dorsal stress fibers. On the other hand dominant Rac spreading, contractility is reduced (decreased myosin light chain phosphorylation). Thus only few bundles delineating the LP/LM interface reinforced consequently lamellipodia occurs nearly all over cell perimeter what is characteristic of isotropic spreading. Furthermore lamellipodial protrusions are wide and focal adhesions maturation is triggered by the combined action of transverse arc and dorsal stress fibers.

Methods We implement a previously described, “top-down”, numerical approach to investigate the spatio-

temporal interaction of subcellular processes related to motility and cytoskeletal reinforcement

during spreading (Loosli et al., 2012). This iterative framework can be used to probe the underlying

cellular orchestration of these complex cellular machineries. As described in the following section,

Methods

this strategy aims at predicting the evolution of adhesion sites and actin bundle layout (i.e. cell

morphology) based on a dynamic and non-deterministic algorithm.

Spreading algorithm

A paradigm for simulating cell spreading was applied as described in detail elsewhere (Loosli et al.,

2012). In brief, cells were modeled as initially circular with a 5m radius (Cuvelier et al., 2007) having

neither focal complexes nor ventral actin bundles. This configuration corresponds to typical cell

geometry and cytoskeletal layout after a passive and non-specific phase of initial adhesion (Loosli et

al., 2010). From this initial configuration, an iterative spreading process begins, incrementally

predicting the evolution of adhesion site distribution, actin bundle layout and cell morphology. The

main events within a given iteration are briefly summarized as follows: First, lamellipodial

protrusions are simulated using nodes to define the leading edge. These nodes are displaced from

their location in the previous iteration according to a stochastic implementation of the leading edge

velocity (v ± v) and an assumed fixed time step (1 minute) that results in a “wavy” edge protrusion.

Nascent adhesions are then homogenously generated beneath the incrementally advanced

lamellipodia with an areal density of 1 adhesion m-2 (Zaidel-Bar et al., 2003). The lamellipodium/

lamellum (LP/LM) interface movements are modeled using a geometric criteria we refer to as an

elastic convex-hull (Loosli et al., 2012), that defines this boundary by selecting the outermost nascent

adhesions. These selected nascent adhesions are designated for maturation into focal complexes. At

this stage, focal complexes at the LP/LM interface mature into focal adhesions (along with their

associated actin bundles) according to an actin length threshold maturation (LTM) process. The LTM

directly relates to myosin driven contraction of the lamellum, a process that triggers focal complex

maturation to focal adhesions (Oakes et al., 2012) and that results in long lasting (reinforced) actin

bundles that are nearly aligned with the cell edge . The LTM is based upon the accumulation of

sufficient centripetally directed force to trigger adhesion maturation; this occurs when the distance

between consecutive focal complexes supporting an LP/LM actin bundle exceed a given threshold

length “T”. This geometrical selection criteria is effective if the LP/LM bundle is loaded by

homogeneously distributed point loads due to lamellar contraction, as suggested by electron

microscopy (Shemesh et al., 2009).

Reinforcement of an actin bundle, along with its terminating adhesion sites, creates a localized

convexity due to inward bending of the cell edge. A key element of the model with regard to

spreading is local inhibition of lamellipodial activity on convex regions of the cell perimeter (James et

al., 2008). This shape-based suppression of lamellipodial activity is then carried over to the next

iteration of the algorithm along with other boundary conditions (focal adhesion distribution,

reinforced actin bundle location, current state of cell geometry, and location of active lamellipodia

protrusions). Convergence is reached once the cell area exceeds 1300m2, corresponding to typical

experimentally measured values for fibroblasts (Dubin-Thaler et al., 2004).


Figure 5-2: How to use the top-down numerical framework of spreading cells to parametrically investigate the iso/anisotropic transition. The right panel described the hypothesis of the present investigation: variation the maturation threshold along with the lamellipodia protrusion velocity distribution is sufficient to alter cell morphology after

spreading (TIRF microscopy of the spreading of transiently transfected GFP -actinin-labeled cells are extracted from Dubin-Thaler and co-worker study (Dubin-Thaler et al., 2004)). For this purpose a top-down numerical framework dedicated to cell spreading is applied. A concise version of the rapid spreading algorithm (central panel) is illustrated in the flow chart, for iteration “i”, along with the five “rules” linking lamellipodial and filopodial protrusion (appearing as shaded boxes within the flow chart). These rules are briefly elaborated in the sketches located outside the flow-chart. Direct interactions between these functions are highlighted by red arrows. Finally the left panel shows how the parameters study integrates the spreading algorithm to survey the iso/anisotropic transition.

The cell spreading model we implemented included a filopodial module and related rules governing

filopodial behavior (Loosli et al., 2012). However filopodial relevance was limited in the present

investigation due to the assumption of a homogeneous culture substrate; filopodial activity primarily

comes into play on adhesive geometries with spatial discontinuities near or beyond the limit of

lamellipodial reach (Loosli et al., 2012). Given the insensitivity of the simulation outcomes to

filopodial activity, we applied a single set of parameters that sufficiently describe their behavior

(Loosli et al., 2012). Briefly, filopodia were assumed to be distributed on the leading edge with a

density of 0.2 m-1, and “instantaneously” protruded to a stochastically determined length within a

normal distribution (7±4m). In cases for which a generated filopodium was not overtaken by the

advancing cell body within 10-12 minutes after its nucleation, a neo-lamellipodia was created at its

tip (Guillou et al., 2008).

Methods

Parametric investigation

As previously mentioned, spreading was principally regulated by three parameters: T, v and v (actin

length threshold for adhesion maturation, mean and standard deviation of the lamellipodia velocity

distribution). Before detailing the parametric investigation, it is interesting to briefly highlight how

these three parameters are related to Rho/Rac activity. Rac activated Arp2/3 is essential for the

formation, spatial coordination and maintenance of lamellipodial width (Burridge and Wennerberg,

2004; Nobes and Hall, 1995; Sero et al., 2011). Based on these studies, we simulated cellular

modulation of Rac activity by adjusting lamellipodia mean protrusion velocity. Specifically, we

assumed that low v is related to a decay in Rac activity, whereas large v mimics enhanced Rac

activity. Rho is known to increase cellular contractility by favoring myosin II light chain

phosphorylation through ROCK (Burridge and Wennerberg, 2004; Nobes and Hall, 1995). This effect

is localized (among other places) in the lamella. Enhanced lamellar contractility results in large forces

acting on actin bundles spanning focal complexes, consequently resulting in a smaller T. In other

words, to gather sufficient net force required to trigger adhesion site maturation, the required length

(T) of the bridging actin bundle becomes smaller with increasing lamellar contractility. Thus one may

model an increase of Rho activity by reducing T. Another effect of Rho induced myosin II activity is

the increase of the actin retrograde flow within the lamellipodia. A consequence is the decrease of v,

which correspond to the protrusion rate minus the retrograde flow. In summary, by parametrically

varying v, v and T we can capture the effects of competing regulation by Rho and Rac, and the

downstream consequences of the Rho/Rac balance on the cell morphology after spreading.

Here we suggest that differential Rho/Rac balance can induce a transition from an isotropic to an

anisotropic spreading mode, and the model was parametrically explored to elucidate potential

mechanisms behind this transition. The lamellipodial parameters driven by Rac (v, v) and the

contractility driven focal adhesion maturation driven by Rho (T) were systematically varied and

model outcomes were quantitatively assessed (Figure 5-2). Cell morphology was primarily quantified

by determining cell roundness (deviation of cell morphology from a circular shape). To obtain this

measure, points of the cell perimeters were best-fit to a parameterized circle (center and radius)

(Taubin, 1991). Roundness was then defined as one minus the mean of normalized distance

separating the cell perimeter points and the circle. A large roundness value (e.g. >0.95) corresponds

to round, isotropic cells, whereas lower values (e.g. <0.9) reflect anisotropic, polygonal cells. Besides

cell morphology, the area increase rate (AIR) was applied to characterize spreading dynamics, which

are known to vary between isotropic and anisotropic cells (Dubin-Thaler et al., 2004). Finally, we

calculated the relative percentage of cell perimeter with active lamellipodia in an effort to

quantitatively characterize differentially distributed lamellipodial activity as a function of cell

geometry (Parker et al., 2002). Here we assessed relative lamellipodial activity using the ratio

between the sum of non-reinforced segment lengths (defined in the algorithm as the only segments

where lamellipodia were allowed to occur) and the total perimeter of the cell. Roundness, AIR, and

activity were thus deemed to be sufficient criteria to assess whether cells exhibited isotropic or

anisotropic spreading modes.

The three parameters were varied over broad ranges spanning values reported in the experimental

literature. The maturation threshold, the mean and the standard deviation of the lamellipodia

protrusion velocity distribution were parametrically investigated with T varied between 3m and

10m (Loosli et al., 2012), v ranging from 1m/min to 6m/min (Dubin-Thaler et al., 2004) and v

from 0.1 to 2 (Dubin-Thaler et al., 2004). Lamellipodial velocity distributions were limited to positive


values and were kept smaller than 10m/min. Due to the non-deterministic nature of the model;

fifty (50) simulations were performed for each set of identical parameters, providing sufficient

statistical power to reasonably compare the effects of parameter variation.

Results The top-down numerical framework was parametrically exploited to assess the downstream effects

of Rho/Rac on cell spreading. To this end, the lamellipodial dynamic (v ± v) and the maturation

threshold length (T) were systematically varied. To determine cell behavior three criteria were closely

analyzed: First cell morphology via the roundness, secondly cell ability to generated lamellipodia with

the activity and finally the spreading dynamic with the area increase rate (AIR). The coming sections

detail the relationship between the model parameters and the spreading criteria.

Cell roundness and membrane activity are dominated by the maturation threshold length

and the variability in lamellipodial velocity, whereas spreading kinetics mostly rely on

protrusion speed

Before being able detailing consequences of combined parameter variation on spreading behavior,

we first describe the individual impact of each parameter on the spreading characterization criteria.

To determine relative parameter dominancy, a contour plot was created with each criterion plotted

against two parameters to be compared (the third parameter was kept constant in each of these).

Within these plots, dominancy is first qualitatively estimated by observing isocline orientation.

Isoclines aligned with an axis indicate a small gradient, thus a weak dependency of the model output

on the parameter reported on the axis. This method enables one to efficiently assess local

dominancy. To obtain more global insight, normalized-gradients in each direction were computed.

Here, gradient distributions (computed over the whole studied range) were then compared using a T-

test assuming unequal variance (hypothesis is accepted for a significance level of 0.01). Both these

methods are limited to a bilateral comparison (T-v, T-v andv-v).

Cell morphology varied from polygonal to nearly round (0.80<roundness<0.99) in accordance with

increasing the maturation threshold length, (2m<T<10 m) and narrowing the width of the

lamellipodia protrusion velocity distribution 2.0m/min<v<0.1m/min(Figure 5-3)This was

established at a constant averaged lamellipodia protrusion velocity (v = 3m/min). This relationship

was also valid for other values of v, since v has only a limited influence on the roundness; in both T-v

andv-v graphs, the gradient in the v-direction was significantly smaller than that in the T- or v-

direction. On the other hand, T and v affected roundness to a similar extent (no significant

differences in the normalized-gradient in either direction). However a more local assessment of these

curves reveals three distinct modes: (i) in the lower region (v<0.5m/min), v is clearly dominant

(isoclines were nearly aligned with the T-axis) and cells remained isotropic regardless of the applied

value of T; (ii) in the upper left zone, diminished roundness indicated anisotropic spreading and

indicating a heavy dependence on T (isoclines were nearly aligned with the v -axis for v>0.5m/min

and T<6m); (iii) finally, in the upper right region both parameters appeared to be equally important

(with isoclines exhibiting an approximately 45° slope).

Results

Figure 5-3: Relative effect of model parameters (T, v and v) on the spreading criteria (roundness, membrane activity an area increase rate) computed with the top-down numerical framework. The contour plots describes the dependency of the roundness, the activity and area increase rate in function of two parameters the third being constant. The displayed results are the mean values for each criteria based

on 50 repetitions. In T-v and T-v , v was fixed to v=3m/min and for v-v, T is 4m. Histograms complete the contour plots to assess quantitatively the dominant parameters all over the studied intervals. They show that

both T andv influences equally the roundness, whereas T dominated the computation of the activity and v the derivation of the AIR. The light gray bar being the averaged value of the abscises and the dark grey of the ordinates. Note that the stars point the cases devoted of statistical differences between the gradient in both direction (T-test with p>0.01).

As with reduced roundness, reduced lamellipodial activity is characteristic of anisotropically spread

cells, and membrane activity was similarly dependent on the tested parameters. Specifically, there

was only limited sensitivity of membrane activity to v but a dominant effect due to v, and a less

pronounced (but still significant) dominance of T. This is demonstrated by the normalized-gradient in

T direction and by asymptotic behavior along the v-axis (except in a small region located in the

lower-right corner; v<0.25m/min and T>7m) (Figure 5-3). Varying T from 2m to 10m yielded a

broad range of membrane activity from values above 0.9 (i.e. more than 90% of the cell edge

exhibiting lamellipodia) to smaller than 0.5. However to achieve smaller values (below 0.3), it was

necessary to set v sufficiently high (>1 m/min, for v=3m/min)

Finally, the clear alignment of cell area increase rate isoclines with the v-axis reveals an unambiguous

dominance on v (Figure 5-3). Here AIR increases from 50m2/min to nearly 450m2/min over the

tested parameter range. To reach values above 500 m2/min, a high v is required (>1.8 m/min).

This aspect is further supported by the comparison of the normalized gradient. These results were

computed with a constant T (T = 4m).


Figure 5-4: Required evolution of the model parameters (T, v and v) to reproduce the iso/anisotropic transition based on an analysis of the spreading criteria (roundness, membrane activity an area increase rate).

Here the increase of the roundness (A) and the activity (B) in function of T is detailed for different values of v

(0.1, 0.25, 1.35, 1.75 and 2 m/min) and a constant v=3m/min. Similarly, the relation between the AIR and v

(C) is exposed for the same range of v. To help to reader to visualize the characteristic values of each criteria for both the spreading mode, a yellow region indicates the isotropic spreading mode related values, whereas a grey zone designates the criteria observed for the anisotropic spreading mode.

Specific combinations of parameters are required to mimic the isotropic-anisotropic

transition

In a final step, we explored parameter interactions and their effects on the assessed criteria

(roundness, activity and AIR). We were particularly interested identify model configurations yielding

outcomes similar to experimentally reported transitions between iso/anisotropic spreading (Dubin-

Thaler et al., 2004). Simulation outcomes from this parametric study are reported in Figure 5-4, as

are analogous values extracted from the reference study (Dubin-Thaler et al, 2004). This study

reported that lamellipodia activity was heavily reduced in anisotropically spreading cells, with

isotropic cells exhibiting lamellipodia on nearly three fourth of their perimeters (activity of 0.76±0.20,

n=40 cells), whereas lamellipodia occurrence was limited for anisotropic cells (activity of 0.34±0.16,

n=40 cells). Finally spreading dynamics was reported to be strongly diminished in anisotropic

spreading modes, with isotropic cells flattening more than twice as fast when quantified by the AIR

Results

(340±101 vs. 126±60 m2/min n=40 cells each). While roundness was not assessed in the

experimental study, we performed a limited morphological analysis of reported images, determining

that the iso/anisotropic transition corresponded to a decrease in roundness from 0.97 for an

isotropic cell to a value of 0.87 for an anisotropic cell, indicating that the roundness metric we

applied could adequately characterize morphological differences between iso/anisotropically spread

cells.

Of course roundness and relative lamellipodial activity are interrelated, with deviation from a

rounded shape occurring when spreading is dominated by uneven distributions of local membrane

protrusion. We modeled the tendency of lamellipodial activity to be locally inhibited on inward

bending regions of the membrane (James et al., 2008) by exploiting the maturation threshold length;

a local concavity results after adhesion reinforcement and lamellipodial protrusion on the segment of

the membrane between these adhesions is suppressed by the algorithm. Thus when the value of T is

increased (analogous to lower lamellar contractility in experiments), lamellipodia stay active on a

larger proportion of the cell perimeter. In turn, the roundness of the cell increases as lamellipodia

occurrence is more homogeneous. However, it is interesting to note that the relationship between

activity and roundness differed substantially when the maturation threshold length was set to small

values (e.g. T = 2m) along with narrowly distributed lamellipodia protrusion velocities (v0.1

m/min). In such cases, cell were predicted to remain round even though lamellipodia were active

on less than half of the cells perimeter (Figure 5-4A-B). This behavior can be attributed to the fact

that the active and inactive regions were homogenously interspersed. This “cytoskeletal coherence”

ensures cell morphological integrity (Cai et al., 2010) by limiting the presence of large, local

invaginations of the membrane and may explain the counterintuitive fact that limited lamellipodial

activity could also be found on round cells.

In simulations, a transition from isotropic to anisotropic spreading was provoked as values of T were

decreased (Figure 5-3B). Roundness roughly decreased from 0.96 to 0.86 and activity from 0.8 to

0.3. The predicted lamellipodial activity for isotropic cells (0.82±0.4) considerably exceeded values

reported by Dubin-Thaler (0.76±0.2), although predicted roundness corresponded well with the

limited experimental morphology data that was presented in the benchmark study. The discrepancy

in lamellipodial activity reflects the likelihood that factors apart from local membrane geometry can

regulate membrane activity, and may expose a limitation to our assumption that membrane

convexity alone is sufficient to suppress lamellipodial activity. The discrepancy could also possibly

indicate that the maturation threshold length is not tightly strictly coupled with the corresponding

membrane segment over which local lamellipodial protrusions are inhibited (the actual zone could be

larger, for instance). Finally, while we note that the model yielded better matched membrane activity

when higher values of v were applied, this was only achieved using nearly non-physiological values

of v , and with a corresponding loss of cell roundness compared to experiments (Dubin-Thaler et al.,

2004; Giannone et al., 2004).

The simulated area increase rate (AIR) was mainly dominated by v (Figure 5-4C). Across the range of

tested (physiological) values of v, the AIR varied quasi linearly from roughly 140 to 340m/min, as

the average protrusion velocity increased from 1 to 5 m/min. Though having limited impact on

predicted cell morphology, decreasing values of v from 4± 1.7 to 2.1±1 m/min was essential to

mimic the increasing AIR that have been experimentally associated with the iso/anisotropic

transition. Further considering the variability in the area increase rates, both in-silico and in-vitro


data are well in agreement. Nevertheless in vitro measured AIR seems to be less sensitive to v than

predicted by the model, possibly due to cellular mechanisms that were neglected or insufficiently

weighted in the algorithm.

Figure 5-5: Qualitative and quantitative confrontation of the spreading criteria (roundness, membrane activity an area

increase rate) obtained by in-silico and in-vitro means demonstrating the ability of the model to

iso/anisotropic transition.

The three histograms demonstrate the quantitative similarity for both spreading modes between in-vitro

(dark grey) and in-silico (light grey) data for roundness, membrane activity and AIR. T= 8 m, v=4 m/min and

v=1.35 m/min for the isotropic spreading and with T= 3 m, v=2 m/min and v=1.35 m/min for the

anisotropic spreading mode. In-silico data stem from 20 different experiments, whereas activity and AIR of the

experimental data are derived from 40 cells. Only the experimental roundness was determined from a single

cell. Experimental and numerical single cell experiences are then qualitatively and quantitatively confronted

revealing striking similarities for both spreading modus. TIRF microscopy of the spreading of transiently

transfected GFP -actinin-labeled cells are extracted from Dubin-Tahler and co-authors work (Dubin-Thaler et

al., 2004) and compared with numerical outcomes obtained with the parameter mention hereinbefore The in

silico figure only depict the most relevant actin structures and adhesion site for the present study: the green

dot correspond to the nascent adhesion formed bellow the lamellipodia, the red lined to the stabilized actin

bundle and the yellow line to the unstable actin bundle. Bar is 5 m

Finally, we used the model to demonstrate how relative Rho/Rac signaling may mechanistically drive

the transition from isotropic to anisotropic spreading. We selected two parameter sets, one

representing Rho-dominated signaling (increased contractility reflected in a lower T value), and one

Discussion

representing Rac dominated signaling (increased lamellipodial velocity, v). We hypothesized that

setting the Rac dominated parameters (T= 8 m, v=4 m/min,v=1.35 m/min) and Rho dominated

parameters (T= 3 m, v=2 m/min ,v=1.35 m/min) on this rationale would reproduce the

iso/anisotropic transition that has been reported in the literature (Dubin-Thaler et al., 2004;

Giannone et al., 2004; Lam Hui et al., 2012). In fact, when results from forty simulations were

compared against analogous in-vitro data, morphological similarity was striking (Figure 5-5).

Quantitatively, agreement was also quite good, although with membrane activity in isotropically

spreading cells being slightly overestimated and roundedness slightly underestimated, and AIR in

anisotropic cells being marginally underestimated. The model performance thus confirmed that the

modeling framework was not only adequate to simulate both isotropic and anisotropic spreading

modes, but also yielded a plausible mechanistic insight to how increased contractility (Rho) and

decreased lamellipodial velocity (Rac) concur to yield anisotropic morphology.

Discussion Suspended cells generally adopt a spherical shape that rapidly changes upon initial adhesion to a

substrate (Galli et al., 2005). To accomplish this morphological change, cells coordinate a variety of

complex mechanisms that drive physical (mechanical) interactions with their substrate via focal

adhesions (Smith, 2010). In previous work, we established a top-down numerical framework that

captures the key functional interactions between force generating filamentous actin structures and

adhesion sites during early adhesion (Loosli et al., 2012). This model was able to predict the evolution

of cell morphology during the spreading process by explicitly accounting for lamellipodial and

filopodial motile functions, and how they interact with the cytoskeleton to regulate focal adhesion

maturation. Our top down framework homogenizes certain subcellular behaviors to permit an

accurate prediction of spreading using a limited number of descriptive parameters. These seven

descriptive parameters are spatio-temporal in nature, all have physiological relevance, and all but

one was directly derived from experimental studies.

The single parameter that could not be extracted from the literature is an actin bundle length

threshold that governs focal adhesion maturation (T). This length threshold was discovered in our

earlier work (Loosli et al., 2012) as being key to consistently and accurately predicting the spatial

distribution of mature focal adhesions in a spreading cell. More recently, we experimentally

confirmed the existence and relevance of this threshold (Chapter 4). Although mechanistic details of

the threshold remain to be elucidated, particularly the precise relationship between the length of

transverse actin bundles and the forces acting on their anchoring adhesions, it can be used as a proxy

manner to mimic increased cellular contractility; A more highly contractile cell (e.g. increased Rho

signaling) diminishes the required actin bundle length (i.e. lower T) to accumulate forces at a focal

adhesion sufficient to trigger its maturation (Wolfenson et al., 2011).

In the present study, we harnessed the model to focus on upstream signaling (Rho/Rac) that may

control cell morphology. Here we considered cells spreading on homogenous substrates, a behavior

dominated by lamellipodial activity (Loosli et al., 2012) and lamellar contractility (Cai et al., 2010). In

the scope of the top-down approach, we utilized the parameters related to lamellipodial protrusion

(v±σv) to capture the principal effects of the Rho/Rac signaling balance shift (Ridley, 2011). By

simultaneously varying T and v within a physiological range, we obtained two clearly distinct post

spreading cell groups. In isotropically spread cells, cells were circular with broad lamellipodia that

facilitated rapid spreading. The anisotropic group was composed of polygonal cells with more


limited, localized lamellipodial activity associated with slower spreading rates. These distinct

spreading modes have been experimentally observed and reported elsewhere (Dubin-Thaler et al.,

2004; Giannone et al., 2004; Lam Hui et al., 2012).

Among all parameters we evaluated, the spreading outcome (isotropic vs. anisotropic) was most

sensitive to the length threshold maturation process regulated by T. The reason for model sensitivity

to this parameter was two-fold. First, the morphological delineation of the lamellipodium/lamellum

interface was driven by the setting of T. Perhaps more importantly, lower values of T strongly

predispose the formation of mature focal adhesions and actin bundles at the cell perimeter that then

immediately inhibit lamellipodial activity along that segment of the leading edge.

The length dependent loading of the actin bundles delineating the

lamellum/lamellipodium interface

Lamellar contraction powered by myosin II activity is an important source of cellular contractility

(Aratyn-Schaus et al., 2011). These contractile forces mediate, at least in part, the maturation of

focal complexes to focal adhesions (Balaban et al., 2001; Stricker et al., 2011) and are transmitted to

adhesions by various mechanisms (Gardel et al., 2010; Loosli et al., 2012). According to the actin

length threshold maturation (LTM) mechanism, centripetal forces acting transverse to actin-bundles

aligned with the cell leading edge “collect” these forces in proportion to the bundle lengths. Once

sufficient force is accumulated, the (two) adhesion sites that anchor the bundle are triggered toward

maturation. In this sense, focal adhesion maturation depends on both the length of the actin bundle

and the lamellar contraction intensity. In other words, assuming that a focal adhesion matures at a

given stress threshold, cells with little lamellar contractility require a longer actin bundle (larger T) to

accumulate sufficient force to trigger maturation. On the other hand, more contractile cells require

shorter bundles (smaller T) to trigger adhesion maturation. In this sense, by adjusting the value of T

required to trigger maturation within the model, we can effectively capture the effect that

increased/decreased contractility would have on the resulting cell morphology.

We exploit this feature of the model to mimic the influence of Rho signaling on lamellar contractility.

Such contractility acts via ROCK activation and the consequent phosphorylation of myosin II light

chain (Burridge and Chrzanowska-Wodnicka, 1996). We thus demonstrate that the LTM provides a

mechanism by which Rho mediated non-sarcomeric contraction (Verkhovsky and Borisy, 1993) could

potentially direct end stage morphology via force-based maturation of focal adhesion sites. Although

we did not explore this in the model, this mechanism could be further reinforced by a simultaneous

Rho mediated increase in coupling efficiency between the cytoskeleton and the substrate (Gardel et

al., 2008).

Lamellipodium inhibition can be regulated by a subtle shift in Rho and Rac protein

interaction affecting focal adhesion maturation

The model highlights what is perhaps the most critical aspect in driving a transition between isotropic

and anisotropic spreading modes: how does a cell regulate the suppression of local lamellipodial

activity? To regulate this within the model, the algorithm suppressed lamellipodial activity on

segments of the LM/LP interface as long as they are reinforced according to the LTM.

This algorithmic rule regulating lamellipodia inhibition was based on observations in the literature,

which we interpreted using both mechanical and geometrical rationale. Mechanically, membrane

protrusions require a sufficient mechanical foundation (anchorage) that is provided by adhesion sites

Discussion

(DeMali and Burridge, 2003). On the other hand, lamellipodial extensions appear to only occur on

geometrically convex regions of the cell perimeter (James et al., 2008). Once the adhesions

supporting the lamellipodial protrusions at the cell perimeter have matured along with a peripheral

actin bundle (i.e. according to the LTM) centriptally acting forces (lamellar contractility, retrograde

flow, etc) cause these peripheral actin bundles to arc inwardly, thus becoming concave (Théry et al.,

2006). On this basis, we algorithmically suppressed lamellipodial activity on subregions of the cell

edge that were reinforced according to the LTM. We thus suppose that lamellipodial inhibition is

tightly coupled with focal complex maturation and actin bundle stabilization. While the precise

mechanisms behind this coupling remain to be elucidated, myosin II force driven focal complex

maturation is accompanied by an increased protein turnover at the adhesion sites (Kuo et al., 2011)

and adhesive protein activation state switching (Gardel et al., 2010) that could reasonably drive

lamellipodial activity vie re-regulation of the small GTPases (Choi et al., 2008; Nayal et al., 2006).

Tailored experiments are nonetheless required to clarify whether both adhesion maturation and

lamellipodia inhibition are driven in lockstep according to the length maturation threshold T. In any

case, even if adhesion maturation and lamellipodia suppression occur at different lengths, we expect

the model behavior to shift in a manner such that the character of the model predictions will remain

unaffected, leaving our model-based conclusions intact.

How Rho/Rac signaling cooperate to trigger transition between isotropic and anisotropic

spreading modes

Cell shape is an important precursor to downstream behaviors including polarization, migration,

proliferation, and differentiation. When spreading after first contact with an adhesion-permissive

substrate, it is clear that cells can and do direct their morphology based upon their perceived local

environment (Paluch and Heisenberg, 2009). Such shape changes are achieved by modifying the

balance of intra- and extra-cellular forces. The model we present demonstrates how differential

Rho/Rac signaling could potentially drive the morphology of a spreading cell towards certain post-

spreading morphologies.

Intra-cellular forces are primarily generated by two actin based mechanisms. First, actin

polymerization at the leading edge drives lamellipodial membrane protrusion (Mogilner, 2006).

Lamellipodia protrusion velocity distribution is regulated by two different Rho/Rac pathways. Rho

being a upstream signaling of myosin light chain phosphorylation, a modification of Rho signaling

could be at the origin of periodic myosin II contraction of the lamellipodia (Giannone et al., 2007),

which could eventually affect the net protrusive dynamics of the leading edge. Variability of the

lamellipodia protrusion (σv) seems to be only little affected by Rho signaling however extensive

experimental studies are required to clarify this issue. This point motivates our decision keep σv

constant while focusing on shape transition despite its potential consequnces demonstrated in th

eüpresent study (σv increase induces a drop of roundness and activity). Besides regulating

contractility, the Rho/Rac balance is essential for lamellipodial formation and localization (Brock and

Ingber, 2005; Sero et al., 2011). The Rho/Rac balance also influences lamellipodia via ARP2/3. Indeed

Rac is upstream to ARP2/3, influencing the rate at which this protein catalyzes the polymerization of

lamellipodial actin network (Nobes and Hall, 1995). In the current modeling framework, we thus

relate diminished Rac signaling to lower lamellar protrusion velocities (v) (Ridley, 2011).


The other morphology driving mechanism is the generation of cell contractility via the coupled action

of myosin II and actin filaments (Pellegrin and Mellor, 2007; Verkhovsky et al., 1995). Cell contractility

creates a cytoskeletal pre-stress that ensures necessary morphological integrity (Bischofs et al., 2008;

Cai et al., 2010; Kumar et al., 2006; Loosli et al., 2012). The two CSK structures providing this

contractility are the lamellar network and the stress fibers (Aratyn-Schaus et al., 2011). Of these, the

lamellar contractility dominates the phase of rapid spreading, with stress-fibers becoming important

only later during the reinforcement phase prior to polarization (Döbereiner et al., 2004). It is known

that lamellar contractility is increased with increasing Rho signaling (Burridge and Chrzanowska-

Wodnicka, 1996), and that Rho activity also affects cytoskeleton/ substrate coupling (Gardel et al.,

2008). As previously discussed, we relate increased Rho activity to a diminished LTM thresholding

length (T).

Figure 5-6: Flow chart describing how cell integrate Rho/Rac activity to modify their morphology while spreading. This figure summarizes the downstream effects of a Rho/Rac balance shift on cell morphology according to the theoretical framework we proposed (thin blue arrows). It further present a validation feedback from the experiments proposed by Dubin-Thaler et al. (Dubin-Thaler et al., 2004)(red arrows).

Through mutually antagonist aspects of Rho and Rac signaling (Burridge and Doughman, 2006;

Sander et al., 1999), these pathways efficiently cooperate to drive cell morphology. This interplay is

captured in our numerical top-down framework, and the implications of this cooperation are

captured our results (Figure 5-4, Figure 5-5 and Figure 5-6). Specifically, cell roundness, membrane

activity and area increase rate all decrease when the Rho/Rac balance shifts toward Rho – otherwise

describable as anisotropic spreading. Conversely, a modeled shift toward increased Rac signaling led

to rapidly spreading, round cells, with a high degree of lamellipodial activity – criteria consistent with

isotropic spreading. It is noteworthy that these states could be reliably provoked by adjusting the

model parameters within physiological ranges for the maturation threshold and lamellipodial

protrusion velocities. While existing studies have already highlighted potential relationships between

Rho activation and regulation of cell morphology (Chauhana et al., 2011; Huang et al., 2011), as well

as Rac (Obermeier et al., 1998), we believe that this study presents the first mechanistic

understanding of how these signaling changes translate to cell morphological switching.

Interestingly, Dubin-Thaler and co-worker constrained cells to spread in an isotropic mode by

resorting to serum deprived culture conditions (Dubin-Thaler et al., 2004). Serum deprivation seems

to reduce focal adhesion assembly by blocking myosin light chain phosphorylation (Dumbauld et al.,

2010), a Rho dependent event.Such experiments using serum straved cells has also linked suppressed

Rho activity to increased Rac activation (Zuluaga et al., 2007). According to our model predictions, a

shift in the balance toward Rac dominancy is a key upstream driver of isotropic spreading. The

Conclusion

predicted downstream effects of this shift toward Rac manifested in cell shapes that corresponded

very well to available experimental evidence (Dubin-Thaler et al., 2004; Giannone et al., 2004).

Conclusion In this study a numerical top-down approach was used to simplify and functionally cluster processes

related to cell motility and force-driven focal adhesion maturation. In this sense, we use the model to

reveal how molecular processes are coordinated to yield a global cell behavior. We specifically

demonstrated that cell morphology can be driven by differential regulation of lamellipodial

protrusion and focal adhesion dynamics, and we identify how these processes may plausibly be

controlled by Rho/Rac signaling. In addition to providing a mechanistic understanding of how

differential Rho/Rac signaling may drive cell morphology control, the study demonstrates the power

that top-down models offer for consolidating experimental evidence toward improved

understanding in cell biology.


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Ridley, A.J. (2011). Life at the leading edge. Cell 145, 1012-1022. Ridley, A.J., Schwartz, M.A., Burridge, K., Firtel, R.A., Ginsberg, M.H., Borisy, G., Parsons, J.T., and Horwitz, A.R. (2003). Cell Migration: Integrating Signals from Front to Back. Science 302, 1704-1709. Sander, E.E., Ten Klooster, J.P., Van Delft, S., Van Der Kammen, R.A., and Collard, J.G. (1999). Rac downregulates Rho activity: Reciprocal balance between both GTPases determines cellular morphology and migratory behavior. J Cell Biol 147, 1009-1021. Sero, J.E., Thodeti, C.K., Mammoto, A., Bakal, C., Thomas, S., and Ingber, D.E. (2011). Paxillin mediates sensing of physical cues and regulates directional cell motility by controlling lamellipodia positioning. PLoS ONE 6. Shemesh, T., Verkhovsky, A.B., Svitkina, T.M., Bershadsky, A.D., and Kozlov, M.M. (2009). Role of focal adhesions and mechanical stresses in the formation and progression of the lamellum interface. Biophys J 97, 1254-1264. Smith, A.S. (2010). Physics challenged by cells. Nature Physics 6, 726-729. Stricker, J., Aratyn-Schaus, Y., Oakes, P.W., and Gardel, M.L. (2011). Spatiotemporal constraints on the force-dependent growth of focal adhesions. Biophys J 100, 2883-2893. Taubin, G. (1991). Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 1115-1138. Théry, M., Pépin, A., Dressaire, E., Chen, Y., and Bornens, M. (2006). Cell distribution of stress fibres in response to the geometry of the adhesive environment. Cell Motil Cytoskeleton 63, 341-355. Verkhovsky, A.B., and Borisy, G.G. (1993). Non-sarcomeric mode of myosin II organization in the fibroblast lamellum. J Cell Biol 123, 637-652. Verkhovsky, A.B., Svitkina, T.M., and Borisy, G.G. (1995). Myosin II filament assemblies in the active lamella of fibroblasts: Their morphogenesis and role in the formation of actin filament bundles. J Cell Biol 131, 989-1002. Vianay, B., Kafer, J., Planus, E., Block, M., Graner, F., and Guillou, H. (2010). Single cells spreading on a protein lattice adopt an energy minimizing shape. Physical Review Letters 105, 128101. Wolfenson, H., Bershadsky, A., Henis, Y.I., and Geiger, B. (2011). Actomyosin-generated tension controls the molecular kinetics of focal adhesions. J Cell Sci 124, 1425-1432. Zaidel-Bar, R., Ballestrem, C., Kam, Z., and Geiger, B. (2003). Early molecular events in the assembly of matrix adhesions at the leading edge of migrating cells. J Cell Sci 116, 4605-4613. Zuluaga, S., Gutiérrez-Uzquiza, A., Bragado, P., Álvarez-Barrientos, A., Benito, M., Nebreda, A.R., and Porras, A. (2007). p38α MAPK can positively or negatively regulate Rac-1 activity depending on the presence of serum. FEBS Lett 581, 3819-3825.

121 Synthesis

Chapter 6

Synthesis

Retrospective

Retrospective An essential aspect of numerous medical treatments is attempting to modify interactions between

cells and their environment to elicit an adequate healing response. This modification occurs from

either chemical, or mechanical means. The chemical approach, often based on pharmaceuticals, acts

directly on molecular pathways provoking downstream responses at a cellular level and in the whole

body. For example, non-steroidal anti-inflammatory drug, such as aspirin, suppresses synthesis of

prostaglandin and thromboxane by cyclooxygenase inhibition, which increases blood flow and

diminishes transmission of pain signals to the brain and has anti-inflammatory effects (Hochberg,

1989). Here, cells modify their environment under chemical stimuli. On the other hand, orthopedic

surgeons frequently resort to mechanical stimuli to treat musculoskeletal diseases or trauma.

Stabilization is a common strategy to promote fracture healing by reducing relative micro-motion

between bone fragments. Mechanical stimuli are locally controlled to optimize cell differentiation

and extracellular matrix production (Byrne et al., 2011). Both these examples highlight how cellular

behaviors are altered, in therapeutic scenarios . Both these methods rely on an identical mechanism:

modifying the interactions between cells and their environment to obtain the desired effects. This

strategy has been employed for centuries based on empirical observations; however current

medicine aims at more targeted and efficient techniques, for which our current knowledge of cell-

environment interactions needs to be deepened. Even though long underestimated, the downstream

effects of mechanically modifying the equilibrium between cells and their surroundings are now

accepted as essential (Eyckmans et al., 2011) in regenerative medicine (Butcher et al., 2011;

Warburton et al., 2010), orthopedics (Badillo-Perona et al., 2011) or oncology (Carey et al.). It gave

birth to a novel interdisciplinary field dubbed “mechanobiology”.

A major transduction factor of mechanbiology is the cellular contractility by which cells exert forces

on their environments (Chen, 2008). Endogenous forces are generated by the actin cytoskeleton, a

network of contractile biopolymer bundles. Myosin II drives relative sliding of actin bundles and

provides force for this. This sliding occurs either in a sarcomeric manner, as in stress fibers (Pellegrin

and Mellor, 2007), or in a non-sarcomeric fashion, as in stress fibers (Verkhovsky and Borisy, 1993).

Intra-cellular forces are transmitted to the cell surroundings via adhesion sites. Adhesion sites are

molecular assemblies arranged around a trans-membrane protein called an integrin. This link is not

solely of a structural nature. Adhesion sites are central signaling junctions. Numerous pathways are

activated at adhesion sites by integrins (Giancotti and Ruoslahti, 1999), and they are the end-target

of many of them. This crosstalk between adhesions sites and forces, both intra- and extracellular,

trigger rapid reorganization of the cytoskeleton and protein turnover at adhesion sites what results

into a modification of the cell behavior (Geiger et al., 2009). A well-known pathway relies on Rho and

Rac activation (Burridge and Wennerberg, 2004; Sahai and Marshall, 2003; Sero et al., 2011). Rho and

Rac are small GTPases that function as time-dependent biological switches controlling diverse cellular

functions including cell shape and migration, cell proliferation, and gene transcription. (Burridge and

Doughman, 2006). This brief description of mechanobiology is far from exhaustive and fails to render

its real sheer complexity. For this purpose a close look in Chapter 2 is required, which surveys some

aspects of mechanobiology essential for the understanding of this thesis. Despite efforts of

numerous groups, the current understanding of the mechanobiology underpinning remains

incomplete. This is mostly due to the extremely challenging aspect of dynamically observing how

mechanobiological subprocesses spatially and temporally interact (Smith, 2010).

123 Synthesis

In this thesis, we developed a radically novel top-down numerical approach that successfully

alleviates this issue, as detailed in Chapter 3. By focusing on interactions, instead of on the individual

sub-cellular processes, the proposed top-down framework revealed an additional mechanism by

which cells regulate adhesion site maturation and actin bundle stabilization as elaborated in Chapter

3. This interaction rule is dubbed “the length threshold maturation” (LTM) process. In Chapter 4, the

LTM is successfully challenged with tailored experiments by examining fibroblast spreading on

micropatterns. Finally we resort to our top-down numerical framework to decipher how Rho/Rac

balance regulates cell spreading morphology in Chapter 5.

Despite recent advances in microscopy, the visualization of subcellular mechanisms in their whole

remains extremely challenging. Cells synchronize numerous events occurring in different time and

length scales, erecting technical barriers (Smith, 2010). In this thesis we demonstrated how cell

machinery related to spreading might cooperate to regulate adhesion maturation, actin bundle

stabilization, and cell morphology. To this end, we developed a numerical top-down framework

beyond current research trends that utilizes a geometrically based description of the cellular

functions. This original strategy, which is detailed in Chapter 3, enables one to numerically explore

mechanistic interactions that may exist between various cell sub-functions. Besides complementing

and elucidating certain interactions that have been revealed experimentally (Burnette et al., 2011;

Hotulainen and Lappalainen, 2006), the framework is used to challenge novel potential interaction

mechanisms. While the “top-down” geometric homogenization framework could be applied to

investigating a wide range of cell behaviors, we focus on cell spreading. This process is particularly

interesting to explore cell/matrix interactions. It allows to survey adhesion sites initiation and

evolution since cells are focused on attaching to the substrate and forming adhesion sites before

spreading. Similarly stress fibers, which are highly contractile structures, are not yet present,

facilitating the investigation of alternative contractile means such as the lamellar network.

The first step toward implementing the cell spreading top-down paradigm was to determinate the

most relevant apparatus involved in spreading. Lamellipodia and filopodia are the principal

cytoskeletal structures enabling cell motility. . They generate the forces required for motion and are

at the driving force for adhesion initiation and actin bundle assembly. Therefore both lamellipodia

and filopodia are modeled as the principal apparatus leading to spreading. The second step focuses

on defining how this motility functions, the adhesion turnover and the actin bundle dynamics

interact with each other to enable spreading. For this purpose we elaborated five interaction rules.

Four of them based on experimental evidences completed by a last one derived from our own

observations. This last interaction rule relies on the ability of adhesion sites to mature based on a

geometrical criteria. We demonstrated this LTM process. According to the LTM process, forces are

accumulated and transmitted to focal complexes by an actin bundle delineating the

lamellipodium/lamellum. We assumed that maturation of the terminating focal complexes only

occurs if the length of the delineating bundle exceed a given threshold length. This assumption

explains how focal complexes mature into focal adhesion once sufficient forces are gathered at

adhesion site (Wolfenson et al., 2009). This relation between the actin bundle length and the

accumulated lamellar contractile force at focal complexes is a critical aspect of the LTM.

We successfully challenged our spreading paradigm by comparing in silico outcomes to various

published experiments of cell spreading on micro-patterned adhesive substrates (Lehnert et al.,

2004; Théry et al., 2006a; Zimerman et al., 2004). This demonstrated the ability of the

Retrospective

geometric/temporal modeling framework to capture the key functional aspects of the rapid

spreading phase and resultant cytoskeletal spatial distribution complexity. Hence the mechanical

insight revealed by the model is realistic and supports the existence of the LTM. In an attempt to

further support the LTM, cell spreading experiments on specific micro-pattern were conducted as

summarized in Chapter 4.

Direct observation of the maturation threshold process is extremely challenging. Indeed one should

be able to keep track of actin bundle deflection as well as the myosin activity within the lamellum on

a sufficiently large pool of cells. An alternative would be to survey the consequences of the

maturation threshold as it enables processing a sufficient amount of cells. A primary consequence of

the LTM is the formation of stable actin bundles arranged parallel to the cell edge. Such actin

structures were only stabilized once the distance between their anchoring adhesions exceeds the

maturation threshold length. To verify this hypothesis, we geometrically constrained adhesion sites

with UV-photolithography fabricated micropatterns. The circular adhesive patterns featured

rectangular non-adhesive region with various widths. According to the LTM, only actin bundles

spanning non-adhesive regions wider than the maturation threshold were supposed to be stabilized.

Fluorescent images of 3T3 fibroblasts seeded on these micropatterns were taken, which reveal the

spatial distribution of actin (principal protein constituting the actin bundles) and vinculin (one type of

proteins present in adhesion sites). A close analysis of these data enables the detection of the actin

bundle form by the LTM. The experiments provide clear evidences supporting the length threshold

maturation process and allow a first in vitro estimation for a thresholding length of approximately

4.5m, which is in total agreement with in-silico outcomes computed in Chapter 3. With LTM being

experimentally corroborated, we further exploit the top-down numerical framework to investigate

the signalling pathways responsible for morphology alterations in spreading cell.

Cells adopt various morphologies depending on intra- and extracellular stimuli. Two spreading modes

were experimentally characterized: one isotropic and one anisotropic (Dubin-Thaler et al., 2004; Lam

Hui et al., 2012). In isotropic spreading cells wide lamellipodia protrude on nearly all the circular

perimeter, whereas anisotropic cells exhibit polygonal shapes with local lamellipodia. In Chapter 5,

we resort to our top-down numerical framework to systematically investigate morphology and

membrane activity of cells immediately after spreading. The rate of area increase is monitored as

well. These criteria were selected to compare our in-silico data with published in vitro outcomes

(Dubin-Thaler et al., 2004). We demonstrate that an adequate variation of both the lamellipodia

protrusion dynamic (mean and standard deviation of the protrusion distribution) and of the

maturation threshold length is sufficient to mimic both spreading modes. Decreasing the maturation

threshold and the mean lamellipodial velocity leads to cells that progressively modify their spreading

mode from isotropic to anisotropic. The Rho/Rac controlled integrin pathways are upstream to this

parameter shift because of their established regulating activities on cytoskeleton dynamics (Burridge

and Wennerberg, 2004; Nobes and Hall, 1995).

Rho and Rac crosstalk antagonizes each other’s activities so the downstream effects are easily

distinguishable: While Rho/Rac balance dominated by Rac promotes lamellipodia and inhibits stress

fibers, a Rho dominancy enhances contractility, stress fibers formation and adhesion protein

clustering. (Burridge and Doughman, 2006). The shift from Rho dominant to Rac dominant signaling

was introduced in our numerical top-down approach by adequately varying three parameters:

lamellipodia protrusion velocity distribution mean and standard deviation as well as the LTM

125 Synthesis

thresholding lnegth. Rac dominancy is rendered by an increased lamellipodia protrusion velocity and

a raised LTM thresholding length. The relation between the lamellipodia protrusion velocity and Rac

is clearly visible. On the other hand, how Rac influences the LTM thresholding length is less evident.

The LTM accumulates lamellar contractile forces along an actin bundle in relation to its length in

order to trigger adhesion maturation. Contractility decreases under Rac dominancy, since this

antagonizes Rho which is known to trigger contractility. While reducing contractility, forces have to

be gathered on a longer distance by the LTM to transmit a sufficient amount of force at focal

adhesions to trigger maturation. Therefore a Rho/Rac balance shift towards Rac is modeled by an

increased LTM thresholding distance and a rise of the mean lamellipodial protrusion velocity. A Rho

dominancy has the opposite effects: slower lamellipodial protrusion and a reduced thresholding

length. Interestingly the effects of Rho/Rac shift toward Rho correspond to a modification in the

paradigm parameters (thresholding length and lamellipodia velocity) that to model the transition

between the isotropic and the anisotropic modes. Based on these evidences, we hypothesized that

the Rho/Rac balance is an upstream stimulus controlling morphology of a spreading cell.

Furthermore we are the first to provide a “biomechanical” mechanism to explain how cells integrate

Rho/Rac activity into shape modification.

Limitations Numerical, as well as experimental, investigations of cellular subprocesses require models. Inherent

to models, which abstract reality, are their limitations. However the potential outcomes of models

relying on judicious simplifications clearly overcome the downside induces by these limitations. It is

essential to clearly understand the limitation and their consequences to provide base elements for

follow-up studies aiming at alleviating or at least dampening their consequences to sharpen model

results.

The principal strength of our top-down numerical framework is paradoxically one of its limitations.

The geometrical description of processes (like lamellipodia or filopodia) enables to focus on their

interaction. For example we described lamellipodia protrusion as stochastic protrusions distributed

normally. Thus in agreement with literature (Dubin-Thaler et al., 2008), it fails to render such

phenomena as lateral wave of leading edge (Giannone et al., 2004) or membranes ruffles, which are

supposed to be taken into account in the averaged protrusion speed. Following the same line, we

decided to neglect blebs, an established membrane protrusion mode active in motility (Charras and

Paluch, 2008). Despite these issues, our spreading model replicated reliably cytoskeletal layout,

adhesions distribution and shape of cells spreading on various adhesive substrates patterns within

the chosen time step of 1 minute. To our beliefs, this support our geometrical and temporal

homogenization strategy as well as the selection of the most relevant processes for cell spreading.

Cell phenotype has dramatic consequences on the adhesion site layout, cytoskeletal organization and

cell morphology. In this thesis, we successfully confirmed our paradigm to fibroblast, epithelial cells

and melanoma cells by adequately adjusting the membrane protrusion dynamics related parameters

and the maturation threshold length. It is however not sufficient to claim the universal aspect of the

spreading of the model despite the currently trend stating the universality of the rapid spreading

(Cuvelier et al., 2007). Other motility functions and/or interaction rules, presently not included in the

model, might be dominant in the spreading process of some cell types. Consequently a simple

parameter adjustment is not sufficient to render properly their adhesion initiation. Typically neurons,

with their peculiar dendritic organization might, certainly require to further develop the descriptions

Limitations

and the rules relative to the filopodial activity. To settle this issue, live imaging of a large pool of

spreading cells with various phenotypes is required. It would provide sufficient time dependent data

to verify whether our lamellipodia/filopodia powered model is universal or not. Also essential

elements to implement novel motility functions will certainly emerge, which enables developments

of our model.

Chapters 3 and 4 support the length thresholding aspect of the LTM both numerically and

experimentally. However the correspondence between the lamellar contractility, which is the

supposed underlying source of force, and the LTM is only buttress by indirect evidence obtained

from the current literature. To definitively demonstrate that the LTM is driven by the lamellar

contractility, surveying cells with chemically and/or genetically altered myosin activity (Cai et al.,

2010; Choi et al., 2008) seeded on similar micropatterns, as described in the Chapter 4, is certainly an

adequate strategy. For instance, one expects a rise of the maturation threshold length for cells with

artificially decrease in myosin II activity. It is however essential to mention that cells treated to alter

their myosin activity might modify their actin filament bundle organization, since myosin bundles

cross-link them. This could influence the pointwise connection between the lamellar network and the

actin bundle supposed to gather the centripetal forces. In turn the relation between the length of the

bundle and the force collected at the adhesion might be altered.

A clear limitation of the present numerical investigation is the lack of quantitative insight relative to

the force cumulated at the adhesion sites. Despite hypotheses about the underpinning of the LTM,

alleviating this limitation is of paramount difficulty. Semesh and co-workers proposed a numerical

approach to quantify the stresses occurring at adhesions due to lamellipodial retrograde flow

(Shemesh et al., 2009). However, we view it as difficult to predict whether this has a dominant effect

on the maturation threshold, without first knowing the degree of coupling between the lamella and

the lamellipodial retrograde flow. We know of no experimental or numerical study attempting to

quantify this coupling. Other factors (centripetal forces) potentially affecting the maturation

threshold could include membrane tension, and certainly more importantly, non-sarcomeric

contractions (Verkhovsky and Borisy, 1993), for which explicit modeling is possible but

computationally expensive (Inoue et al., 2011). This represents important grounds for future work to

better understand the maturation threshold and more generally cell contractility.

Finally, we would like to discuss the local lamellipodia inhibition by the LTM described in Chapter 5.

We currently assumed that the same process, the LTM, triggers simultaneously adhesion site

maturation, actin bundle stabilization and lamellipodia inhibition. The relation between adhesion site

maturation and actin bundle stabilization was already experimentally established in Chapter 4.

However the link between LTM and lamellipodia protrusion remains to be discussed. In Chapters 3 to

5, we resort on literature to relate adhesion maturation, signaling, local curvature and lamellipodia

inhibition. We however failed to find clear evidences that inhibition occurs at the very same length as

maturation does. Indeed the distance between two focal complexes at the lamellipodia/lamella

interface might be sufficient to trigger adhesion sites maturations without sufficiently impeding

signaling proteins diffusion essential for lamellipodial protrusions. Consequently the maturation

threshold might be different to the threshold length inhibiting lamellipodia. For this issue to be

clarified further experiments on micropatterned substrates are required, where the occurrence of

actin bundles and adhesion sites maturation are surveyed along with lamellipodia. This issue might

127 Synthesis

shift the curves that relate cell roundness to the thresholding length, which are presented in Chapter

5. However the conclusions drawn along this thesis should remain unaffected.

Outlook By nature our top-down numerical framework allows modeling of other cellular behaviors than the

rapid spreading phase. Following the rapid spreading, cells reorganize their actin cytoskeleton along

with their adhesion site distribution under the action of strong ventral stress fibers. This phase

generally precedes polarization, which eventually leads to motility. Here cell resorts to mechanisms

described elsewhere to reorganize their internal structures (Hotulainen and Lappalainen, 2006; Senju

and Miyata, 2009; Théry et al., 2006b). It is however unclear if this mechanisms list is exhaustive.

Furthermore the interactions of the sub-cellular processes, involved in the reorganization step,

remain only poorly understood. Applying the top-down framework to the reinforcement is a

challenging task that will certainly reveal some novel insights in this force-based cellular behavior. To

use our framework, one has first to extract the major sub-processes and then establish interaction

rules. With this exercise current mechanisms will be systematically tested and certainly novel

phenomenon will emerge.

Combining our current rapid spreading algorithm with reinforcement and ideally a polarization

paradigm opens an exciting research direction: cytoskeletal memory. For nearly a decade scientists

have established that constraining cell on micro-patterned adhesive substrate modify cellular

behavior an eventually cell commitment (Kilian et al., 2010; McBeath et al., 2004). A major question

remains however unanswered: is the cellular behavioral switch induced by the final cell morphology

or by the spreading and reinforcement modification alteration induced by the micropatterns?

Reformulate the impact of this question is clearly broader: Are cells able to store information

gathered by the cytoskeleton? A possible approach to tackle this issue is the earlier top-down

approach focusing on spreading, reinforcement and reorganization. As elaborated in Chapters 2 and

3, the proposed top-down algorithm is based on the “historical” aspect of cell spreading suggested

by Thréry et al. (Théry et al., 2006a). It is therefore reasonable to assume that reinforcement and

polarization have a “historical” component as well. Such a numerical approach enables a systematic

variation of the initial spreading condition (e.g. cell spatial constraining) and a tracking of the actin

cytoskeleton organization what could bring some key element to decipher the probable cytoskeleton

memory underpinning.

In Chapter 5, we identify Rho/Rac signaling pathways as critical for cell morphology and proposed

potential integration mechanisms. Other pathways certainly influence cell spreading as well. The top-

down numerical framework is not restricted to decipher “physical” processes. This approach is

certainly suitable to model “biochemical” processes, such as signaling pathways, and their

interactions. And the integration mechanisms of this lasts are nothing else but coupling vector with a

“physical” framework, as the one presented in this thesis. Such coupled numerical approaches could

be great tools to further increase the overlapping between biophysic and biochemistry essential to

open new research horizon in cell biology.

To conclude this section and to dramatically extend it, a simple question. What about 3D?

Conclusion This thesis focused on the interactions between adhesion sites and actin bundle formation during the

initial adhesion phases dominated by both lamellipodia and filopodia, which is currently a central

Conclusion

topic in biophysics (Burnette et al., 2011; Levayer and Lecuit, 2012; Oakes et al., 2012; Rottner and

Stradal, 2011). Nevertheless the lack of insight in sub-process interactions is still striking especially on

a cell level from what is certainly due to technical hurdles. One of the principal findings of this thesis

is of methodic nature. We developed a novel approach to tackle such complex problems involving

multiple processes by geometrical and temporally homogenizing them and focusing on their principal

interactions. While focusing on cell spreading we identify a mechanism, by which cells stabilize

transverse actin bundles in the back of the lamellipodia and trigger focal complexes maturation into

focal adhesions. This phenomenon, dubbed the length threshold maturation process, is supported by

recent literature by others (Burnette et al., 2011; Oakes et al., 2012). After experimentally

challenging the maturation threshold process, we demonstrate its implication in cell morphology

regulation what has simultaneously revealed novel insight on the spatio-temporal coordination of

some small GTPases in cell spreading, bringing novel sight in the integration of molecular events into

cell behavior modification.

To conclude, I want to thanks the brave readers, who have persisted up to the end of the manuscript

(assuming they started from the beginning ;-)), and I hope they have enjoyed this multi-scale journey

in cellular adhesion and actin cytoskeleton organization.

129 Synthesis

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Curriculum Vitae

Loosli Yannick Born in Meyrin (GE), August 31 1979 Swiss and French Married

Professional experience

Sine 9.2012 DepuySynthes CMF, Oberdorf, Switzerland Product Manager

10.2005 – 7-2012 RMS Foundation, Bettlach, Switzerland Collaborator in charge of computational biomechanics Technical consulting (technical programming and FEA for R&D and regulatory issues, experimental

testing) for international groups (Synthes, Mathys AG)

Invited presentations (Zwick GmbH, Altair GmbH and CADFEM AG)

Orthopaedic clinical research (published papers and congress abstracts; grants reviewing)

Patent co-inventor: “implant device”

4.2005 - 7.2005 Institute for Biochemistry, ETHZ, Zürich, Switzerland Research Assistant Modelling of growth factor effects on cellular proliferation

9.2004 - 2.2005 Institute for Mechanical System, ETHZ, Zürich, Switzerland Research Assistant Integration of a poroelastic model into the soft-tissue measurement device

1.2001 - 7.2001 2C3D, Lausanne, Switzerland Trainee Accuracy enhancement of a mechanical navigation device for orthopaedic surgery

Education

10.2008-7.2012 Institute for Biomechanics, ETHZ, Zürich, Switzerland PhD Candidate Development of a radical novel numerical approach to reveal mechanisms ruling complex cellular

processes such as motility

3 awards in national and international conferences

Establishment of international and national collaborations (EPFL and University of Kyoto)

Students supervising

Teaching assistant of “Mechanik in Biologie und Medizin” (150 students)

4.2011 – 9.2011 Biomechanics Lab, Institute of Frontier Medical Science, Kyoto University, Kyoto, Japan Visiting Scientist Numerical investigation of the cellular contraction

9.2003 - 3.2004 Laboratory of Computational Cell Biology, The Scripps Research Institute, La Jolla, CA, USA Master’s project A ratchet model to simulate microtubule force generation during yeast mitosis

9.2000 - 6.2003 ETHZ, Zürich, Switzerland Master in Mechanical Engineering Major in biomedical engineering and particle technology

9.1998 - 8.2000 EPFL, Lausanne, Switzerland Bachelor in Mechanical Engineering

9.1995 – 7.1998 Lycée International de Ferney-Voltaire, Ferney-Voltaire, France Baccalauréat

Reference

Awards

Best Student Oral Presentation Swiss Society of Biomaterials (2012), August, Zürich, Switzerland

CCMX Matlife Student Travel Award

Biointerface Science Gordon Research Conference (2010), September, Les Diableret, Switzerland

Student Poster Prize

By the Swiss Society of Biomaterials, at the European Society of Biomaterials Congress (2009), September, Lausanne, Switzerland.

Publications

Yachouh, J., Domergue, Horau S., Loosli, Y. Goudot, P. (2012), Brit. J Oral Max. Surg, in press. Loosli Y, Vianay B, Luginbuehl, R., Snedeker, J.G. (2012), Integr. Biol., 4, 508-521. Bartalena G, Loosli Y, Zambelli T, Snedeker JG. (2012), Soft Matter, 8, 673-81. Yachouh, J., Domergue, S., Loosli, Y. Goudot, P. (2011), J. Craniofac. Surg. 22, 1893-1897. Bohner, M., Loosli, Y., Baroud, G. Lacroix, D. (2011), Acta Biomater,. 7, 478-484.

Sague J., Honold S., Loosli Y., Vogt J., Luginbuehl R. (2010).

Eur. Cells Mater 20, 61. Loosli, Y., Luginbuehl, R., Snedeker, J.G. (2010), Philo. Trans.R. S. A.368, 2629-2652. Hartel, M.J., Loosli, Y., Gralla, J., Kohl, S., Hoppe, S., Röder, C., Eggli, S. (2009), The Knee 16, 452-457 Benneker L.M., Haenni M., Loosli Y., Heini P.F. (2008). Eur.

Cells Mater. 16, 27.

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Transcript of Rights / License: Research Collection In Copyright - Non … · 2020-01-31 · Diss. ETH No. 20533...