New methods to study motile phenomena
A progress report
Topics
The challenge of understanding cell migration
Use of photoactivation & CALI to perturb cell migration
CMAP, a systems biology tool
How do we approach a quantitativeHow do we approach a quantitativeunderstanding of cell movement?understanding of cell movement?
Build up from Build up from molecularmolecular
mechanisms mechanisms
Top down modeling ofTop down modeling ofintegration of collectiveintegration of collectivemolecular mechanisms molecular mechanisms
e.g. protrusion, contraction etc.e.g. protrusion, contraction etc.
“Up close the paintings of Renoir & Monet look like ‘daubs of paint’, nothing more. Yet when we step back from the canvases, we see
fields of flowers”
From Davidson’s review of A Different Universe by Robert Laughlin-NYTimes 6/19/05
Philosophy of quantitative modeling
• Use model to simulate behavior & compare to experiment
• Revise model until concrete insight gained into key factors determining migration
• Test alternate models• Overarching goal: Quantitatively organize
information & ideas on migration mechanisms
Advantages of Simple-shaped Cells for Biophysical Studies
• Amenable to modeling
• Simple shape & migratory pattern: easy to see results of perturbation
• Simple, symmetric net traction stress pattern
Gliding Fish Keratocyte
In the keratocyte, protrusion & retraction smoothly coordinated
QuickTime™ and aH.264 decompressor
are needed to see this picture.
Keratocyte Doing the LimboKeratocyte Doing the Limbo
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Magnitudes of cell forces
Type of force Force (pN)
Single actomyosin interaction ~ 1
Estimated actin polymerization force
per filament
~ 4
Tension on neurite during growth
cone advance
< 6000
Stall force for keratocyte ~ 50,000
Estimated maximum traction force
exerted by fibroblasts
~200,000
Gliding Fish Keratocyte
In the keratocyte, protrusion & retraction smoothly coordinated
QuickTime™ and aH.264 decompressor
are needed to see this picture.
MyosinII F-actin
Dynamic Network Contraction
Rxn-diffusion sub-model (simplified)
polymn
depolyncofilin PF-ADPactin
PF-ATPactin TB4-ATPactin
A virtual keratocyte--A. Mogilner et al, UC-Davis[Front-dendritic nucleation; rear-dynamic network contraction]
Density of f-actin plotted
Rubenstein et al SIAM J. 3:413 (2005)
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Test robustness of in silico models of Test robustness of in silico models of migration i.e. do we have the rules of migration i.e. do we have the rules of
integration of protrusion, retraction and integration of protrusion, retraction and adhesion correct?adhesion correct?
Use light-directed methods to perturb molecular activities in single migrating cells in a spatially & temporally defined way--complement to genetic perturbations
Concentration of players as numerical input to
Mogilner model
G, F-actin, T4, profilin etc.
1 3
2
Release or inactivate at
different points in cell
Provide simultaneous traction & network
dynamics maps with photoactivation/CALI
operation
Photoactivate or laser inactivate different ABP
polymn PF-ATPactin TB4-ATPactin
capping protein
Experimental Perturbation
Local ACTIVATIONof molecule:
photoactivation
Local INACTIVATIONof molecule:CALI, photoactivation
Thymosin -4
Cofilin
FAK peptides
-actininConnexinsAurora B kinaseMenaCapping Capping proteinprotein
CALI: Chromophore Assisted Laser Inactivation
[Dan Jay]
Chromophore Assisted Laser Inactivation (CALI)
High spatial resolution – Subcellular inactivation– High selectivity
High temporal resolution– Instantaneous inactivation– Eliminates genetic/molecular compensation
Light-mediated loss-of-function tool
CALI Mechanism
Cell
proteinChr
Laser
Protein damage
x-x-
Reactive oxygen species
Loss of function
• Chromophore excitation leads to production of free radicals• Free radicals are highly destructive, causing protein damage - short half-life (nm destruction radius)• Potential for local, instantaneous inactivation of adjacent protein
EGFP as a CALI Chromophore
• Advantages– Genetically encoded– Covalent linkage to protein of
interest insures specificity– Widely used
• Disadvantages– Photostable
Ineffective ROS generator– 200-1000X less efficient than
other dyes
Photostability may also be an advantage in that there are separate regimes for imaging and inactivation
EGFP
CALI of EGFP-Capping Protein
Eric Vitriol, Andrea Utrecht & Jim Bear
Mena, Capping Protein, and the Regulation of Actin Structure
Mejillano et al. 2004
CPß Knockdown exhibits more filopodia: can CALI reproduce this
phenotype?
Mejillano et al. 2004
Control
CPß KD
LENTIVIRUS KD / RESCUE CONSTRUCT TO REPLACE ENDOGENOUS CP WITH EGFP-CP
5.0EGFP5’ LTR PromoterU6 Promoter Capping
Protein
Jim Bear + Andrea Utrecht
-select clones for good KD& rescue to physiological levels
DIC (left panels) and fluorescence of EGFP-CP (right panels) before (above) and after CALI (below)
CALI of EGFP-CPß
<--Large CALIRegion
1. DIC-pre
2. Pre-flour.
3. Post-fluor
4. Post-DIC
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F-actin & barbed end increase after CALI-induced dissociation of EGFP-CP from barbed ends of actin filaments
Phalloidin stainfor f-actin
Barbed end assay
CMAP: The Causal MapCan the cell biologist’s scheme, which organizes
elements, be transformed to a graphical model to check whether it semi-quantitatively predicts
observed behavior?
Gabriel Weinreb, Maryna Kapustina, Nancy Costigliola& Tim Elston
Cell oscillations induced by depolymerizing MT during cell spreading
depend on elevated Rho activity and cyclic Cai
2+
Pletjushkina et al, Cell Mot. & Cytoskeleton, 48 (4): 235-244 (2001).
Spreading mouse fibroblasts with depolymerized MTs
See also Paluch et al, BJ 89: 724 (2005) &Salbreux et al, Phys Biol 4:268(2007)
Note blebbing-> QuickTime™ and a
H.264 decompressorare needed to see this picture.
Quantitation of oscillatory behavior
Inactivation ofROCK [arrow] byY27632blocks oscillations
Control cellspreading
Ca2+ also oscillates with similar period as morphological oscillations
normal spreading
increment due MT depolymerization
periodic increment due to [Ca2+]i variations
time
contractility
B.
How Rho and Ca2+ may be involved in regulating oscillations
MICROTUBULE DEPOLYMERIZATION
MORPHOLOGICAL OSCILLATIONS
Substrate stiffness
External[Ca2+]
Adhesion strength
MLC-phosphataseP
MLC- ↑P
CONTRACTILITY↑
GEF
Rho↑
ROCK↑
CICR
Activate SAC
Cai2+ ↑
MLCK↑
CaM
[Ca2+]↓ byretrieval
Functional map for cell oscillations depicting necessary elements and connections between them.
A systems biology test bed:
Experimental readout:% Cells Oscillating, Amplitude, and Period
of oscillations
CMAP(semi-quantitative)
Differential Equation model(quantitative)
Fine-grained models Coarse grained models
CMAP
Complexity
Cognitive networks
Boolean networks
Petri networks●●●●●
Complexity
ODE, PDE &Stochastic Models
Causal Mapping [CMAP]
• Concepts (elements) are enclosed in boxes and embody chemicals and/or mechanics
• Causal influences are edges and enable propagation of causality
• Concepts & influences are given numerical or linguistic weights based on data and/or expert opinion
A BW AB
W BA
•A,B are elements of the map, called ‘concepts’.
•Wij are the weights (magnitudes) of causal influence of one concept on the other;[weights are in terms of lingustic variables I.e. very strong….weak that are translated to numerical intervals between -1 to 1]
•Positive weight leads to increase of the concept it is directed to (activation)
•Negative weight leads to decrease of the concept it is directed to (inhibition).
•Time evolution described by simple “transfer” functions that connect concepts &incorporate weights from one or more input concepts
Development of a CMAP for cell oscillations
Biological background:
CMAPWeinreb, Elston, and Jacobson. 2006
•Actomyosin based contractility
•Volume oscillations
•Ca2+ oscillates
•Rho pathway involved.
Microtubule depolymerization
RhoA pathway
time, sec
concept, a.u.
0.0
0.2
0.4
0.6
0.8
1.0
time, sec
0 100 200 300
concept, a.u.
0.0
0.2
0.4
0.6
0.8
1.0
A
B
MT depolym
MT depolym+ROCK inhibition
red=contractility
blue=[Ca2+]i
CMAP simulation results
Using the CMAP for hypothesis generation: how do we determine the most likely CMAPs for the phenomenon?
Weinreb et al, in preparation
What system configurations provide viable hypotheses?
W AB
A BW BA
Configuration 1:
inactivation
activation
>0
<0
A BW AB
W BA
Configuration 2:
inactivation
inactivation
<0
<0
A BW AB
W BA
Configuration 3:
inactivation
no influence
=0
<0
MLC-P
SAC
Cai2+
MLCK
CONTRACTILITY*
Membrane
Ca-CaM
Ca-pump
MLC-P-ase
MLC-P
SAC
Cai2+
MLCK
CONTRACTILITY*
Membrane
Ca-CaM
Ca-pump
MLC-P-ase
Two distinct configurations
- feedback + feedback
• Define experimentally observable criteria that characterize the phenotype:
-oscillatory behavior in [Ca] and contractility-increasing myosin light chain phosphatase damps
oscillations• Determine all possible configurations of the network, i.e. all
combinations of possible connections between the elements
• For a each configuration, use all possible combinations of weights, Ntotal, [Monte Carlo] and count those that satisfy the criteria, Ni.
• Calculate the fitness index as a ratio fi=Ni/Ntotal in order to rank hypotheses [a zero fitness configuation is not a viable hypothesis]
Algorithm for hypotheses generation
MLC-P
SAC
Cai2+
MLCK
CONTRACTILITY*
Membrane
Ca-CaM
Ca-pump
MLC-P-ase
MLC-P
SAC
Cai2+
MLCK
CONTRACTILITY*
Membrane
Ca-CaM
Ca-pump
MLC-P-ase
HI FITNESS ZERO FITNESS
How can the competing, high fitness hypotheses be
experimentally distinguished?
• Identify on the CMAP a causal influence (weight) which can be experimentally manipulated. e.g. titration of an inhibitor .
• Vary the CMAP weight corresponding to the experimental manipulation keeping all other weights in the ensemble of hypotheses (Ni) unchanged.
• Examine how system responds to varying the weight of interest.
• Compare experimental outcome to prediction of CMAP for different hypotheses. Look for major qualitative differences.
Protocol (under development)
MLC- P
SAC
Cai2+
MLCK
CONTRACTILITY
Membrane tension
Ca-CaM
Ca-pump
MLC-phosphatase
A CMAP for cell oscillations
no buffering0.3 uM Kd buffer
Hypothesis 5Hypothesis 4
mean=4124
0
5000
10000
15000
20000
25000
30000
Period, a.u.
0 2000 4000 6000 8000 10000
counts
0
5000
10000
15000
20000
25000
30000
mean=4125
Experiment
mean=1517
0
200
400
600
800
1000
1200
1400
1600
1800
Period, a.u.
0 1000 2000 3000 4000 5000
counts
0
200
400
600
800
1000
1200
1400
1600
1800
mean=1800
Comparison of experiment & CMAP predictions
Single cell behaviorin both experiment &CMAP predictions canalso be compared
An ODE model for cell oscillations based on a likely
CMAP produces cell oscillations
Kapustina et al BJ, in press (2008)
Evidence for a linear oscillation mode
SEM (3700x) of spreading cell with colcemid
50s 70s 90s 120s
180s150s 200s220s
40s
Frames from video record
ODE model using literature parameters describes linear oscillation mode
Ca2+
contraction
Ca2+
contraction
Volume equilibration
cyt mem contract
dRF F F
dtγ = − −
R
Fcyt Fcontract
Fmem
1
2
Kapustina et al BJ epub (2008); see also Salbreux et al, Phys Biol 4:268(2007)
Fmem = force resulting from
elasticity of membrane
Fcyt = constant force generated
by pressure inside cell
Fcontract= actomyosin generated
contractile force
R
Assume contractile force is proportional to p-MLC-->kinetic model of calcium dynamics as it relates to MLCK activation
200 300 400 5000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0
10
20
30
40
50
60
[Ca],
μM
time, s
[ _ ] ( )MLC P contractility
Oscillations of [Ca2+] and [MLC_P]
CONCLUSIONS
Model reproduces the experimentally observed cortical oscillations with only 2 free parameters out of a total of 34 [proportionality constants between p-MLC and contractility and that characterizing cytoplasmic pressure].
Mechanism responsible for the oscillations is a negative feedback loop from contractility to stretch activated channels.
Oscillations only result when the level of myosin light chain phosphatase falls within a certain range
Model predicts that buffering intracellular calcium increases the period and decreases the amplitude of cortical oscillations (preliminary data supports this)
References:1. Pletjushkina O, Rajfur Z, Pomorski , Oliver T, Vasiliev J, Jacobson K. 2001. Induction of cortical oscillations in
spreading cells by depolymerization of microtubules. Cell Motility&Cytoskeleton 48:235–2442. Weinreb G, Elston T, Jacobson K. Causal Mapping as a Tool to Mechanistically Interpret Phenomena in
Cell Motility: Application to Cortical Oscillations in Spreading Cells. Cell Motility& Cytoskeleton Sep;63(9):523-32
3. Kapustina M, Weinreb G, Costigliola N, Rajfur Z, Jacobson K, Elston T. Mechanical and biochemical modeling of cortical oscillations in spreading cells. Biophysical Journal, in press..
Conclusions• CMAPs have potential value as a check of a cell biological mechanism;
does the scheme actually do what it is supposed to?
• CMAPs permit incorporation [without having exact knowledge their values] of different elements (mechanical, chemical); they can point to missing elements or superfluous ones.
• Hypotheses generated using the CMAP approach can be qualitatively checked for consistency with experiment.
• The coarse-grained CMAP prescription leads to successful ODE mechanochemical model; such differential equation models generate quantitative predictions that can be experimentally tested.
Acknowledgements- NIH Cell Migration Consortium
Photomanipulation
Partha Roy, now at Univ. of Pittsburgh
Zenon RajfurDave Humphrey, now at US Patent Office
Barbara Imperiali, MIT
Eric Vitrol &Andrea Utrecht
Jim Bear, UNC
Gerard Marriott-UW
Alex Mogilner-UC-Davis & CMC
CMAP-- all at UNC
Gabriel Weinreb
Tim Elston
Maryna Kapustina
Nancy Costigliola
Traction Experiments & Analysis
Zenon Rajfur
Micah Dembo-Boston Univ.
Xavier Trepat-HMS
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