BA

E F G H

JIK

Y

Y

1 µm

X

4T3T

16(6,6)

15(6,4)

14(6,2)

13(6,1)

12(4,6)

11(4,4)

10(4,2)

9(4,1)

8(2,6)

7(2,4)

6(2,2)

5(2,1)

4(1,6)

3(1,4)

2(1,2)

1(1,1)

C Da

8(8)

7(7)

6(6)

5(5)

4(4)

3(3)

2(2)

1(1)

1 µm

1 µm

2T1T (X,Y) in µm

(T) in µm

0102030405060708090

100

1.1

1.2

1.4

1.6

2.1

2.2

2.4

2.6

4.1

4.2

4.4

4.6

6.1

6.2

6.4

6.6

Con

trol

d

Re

lativ

e m

ine

ra

liza

tio

n

Z=1.6 µmZ=2.4 µm

Shar

kski

n

Mineralization Height 1.6 µmc

Mineralization Height 2.4 µm

Serie

s A,

C,E

,I(2

,3,1

5,16

)Se

ries

B,D

,G,J

(2,3

,15,

16)

Serie

s F,

H(2

,3,1

5,16

)C

ontro

lK

1-8

Serie

s A,

C,E

,I(2

,3,1

5,16

)Se

ries

B,D

,G,J

(2,3

,15,

16)

Serie

s F,

H(2

,3,1

5,16

)C

ontro

lK

1-8

A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13

A14 A15 A16 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10

B11 B12 B13 B14 B15 B16 C1 C2 C3 C4 C5 C6 C7

C8 C9 C10 C11 C12 C13 C14 C15 C16 D1 D2 D3 D4

D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 E1

E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14

E15 E16 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10

F11 F12 F13 F14 F15 F16 G1 G2 G3 G4 G5 G6 G7

G8 G9 G10 G11G12 G13 G14 G15 G16 H1 H2 H3 H4

H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 I1

I2 I3 I4 I5 I6 I7 I8 I9 I10 I11 I12 I13 I14

I15 I16 J1 J2 J3 J4 J5 J6 J7 J8 J9 J10 J11

J12 J13 J14 J15 J16 K1 K2 K3 K4 K5 K6 K7 K8

Z = 0.6 µm

Z = 1.6 µm Z = 2.4 µm

b

J. Lovmand et al. / Biomaterials xxx (2009) 1–82

ARTICLE IN PRESS

Please cite this article in press as: Lovmand J et al., The use of combinatorial topographical libraries for the screening of enhanced osteogenicexpression and mineralization, Biomaterials (2009), doi:10.1016/j.biomaterials.2008.12.081

¿QUÉ HACEMOS NOSOTROS?

Desarrollo algorítmicoSimulacionesAnálisis estadísticoModelado matemáticoOptimización

The use of combinatorial topographical libraries for the screening of enhancedosteogenic expression and mineralization

Jette Lovmand a,b, Jeannette Justesen a,b, Morten Foss a, Rune Hoff Lauridsen a,b, Michael Lovmand c,Charlotte Modin a,b, Flemming Besenbacher a,c, Finn Skou Pedersen a,b,*, Mogens Duch a,b

a Interdisciplinary Nanoscience Center (iNANO), Aarhus University, DK-8000 Aarhus C, DenmarkbDepartment of Molecular Biology, Aarhus University, DK-8000 Aarhus C, DenmarkcDepartment of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark

a r t i c l e i n f o

Article history:Received 17 November 2008Accepted 26 December 2008Available online xxx

Keywords:BiocompatibilityCell cultureMicrostructureSurface topography

a b s t r a c t

Nano- and microstructured surfaces are known to impact on the binding and differentiation of cells, butthe detailed basic understanding of the underlying regulatory mechanisms is still scarce, which impedesthe rational design of smart biomaterials. Towards a comprehensive analysis of the interplay betweentopographical parameters such as feature design and lateral and vertical dimensions we here report ona combinatorial screening approach, BioSurface Structure Array (BSSA) of test squares each witha distinct topography. Using such BSSA libraries of 504 topographically distinct surface structures, wehave identified combinations of size, gap and height of structures which enhance mineralization as wellas the expression of osteogenic markers of a preosteoblastic murine cell line. This generic BSSA screeningplatform is a versatile technology for the systematic identification of surfaces with specific biologicalproperties, and it may for example be useful for optimizing the design of biomaterials for regulatingcellular behaviour.

! 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In the past it has been shown that when mammalian cells bindto surfaces, the detailed surface topography influences the cellbehaviour with respect to processes such as adhesion, orientation,differentiation, proliferation, changes in contact guidance, cyto-skeletal organisation, focal adhesion point organization, apoptosis,macrophage activation, and gene expression [1–11]. Several papershave indicated that phosphorylation, expression, and translocationof transcription factors are factors that play a major role in thecellular response when cells are growing on micro- and nano-structured surfaces. More specifically, it has been shown that ratcalvarial osteoblasts differentiate and mineralize on micro-structured surfaces, resulting in the phosphorylation of Src, focaladhesion kinase (FAK), and ERK1/2 concomitant with activationthrough translocation of the transcription factor Runx2 from thecytoplasm to the nucleus [12–14]. Some of these cellular responsesmay be initiated through an alteration of the cellular contact withthe microstructured surface as demonstrated for example by Biggs

and co-workers [15], who seeded primary human osteoblasts uponsubstrates with groves/ridges varying in width from 10 to 100 mmand observed distinct differences in focal adhesion complexformation. Also, for mesenchymal stem cells (MSC) it has beendemonstrated that surfaces with nanoscale features promote thedifferentiation of MSC without the use of growth factors [15–18].Furthermore, Dalby et al. [17] have observed that pathways of generegulation towards the mineralization of osteogenic cells arestrongly affected by the detailed nanostructure of surfaces.

It thus appears that although some mechanistic insights havebeen obtained into the response of cell adhesion to surfacetopography, we are still far from a level of understanding thatallows for the rational design of improved biomaterials witha predicted influence on cellular behaviour, or for the design ofsurfaces for stem cell propagation in the absence of feeder cells.Today many surfaces applied in cell adhesion studies are often stillselected from a simple trial and error approach.

Here we present a BioSurface Structure Array (BSSA) platformtechnology enabling the systematic screening of cellular responsesto a large variety of nano- and microstructured surfaces. In thepresent setting, each BSSA screening wafer was subdivided into 169squares, each of which covered 3 mm! 3 mm on the array. Witha typical cell size of 50 mm! 50 mm, each square contained up to3600 cells, which enables statistical data analysis from each

* Corresponding author. Department of Molecular Biology, Aarhus University,DK-8000 Aarhus C, Denmark.

E-mail address: fsp@mb.au.dk (F.S. Pedersen).

Contents lists available at ScienceDirect

Biomaterials

journal homepage: www.elsevier .com/locate/biomateria ls

ARTICLE IN PRESS

0142-9612/$ – see front matter ! 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.biomaterials.2008.12.081

Biomaterials xxx (2009) 1–8

Please cite this article in press as: Lovmand J et al., The use of combinatorial topographical libraries for the screening of enhanced osteogenicexpression and mineralization, Biomaterials (2009), doi:10.1016/j.biomaterials.2008.12.081

Autoajuste de parámetros

¿Cuántas iteraciones dejarás correr el algoritmo?

¿En qué momento la solución es suficientemente buena?

¿A qué valor fijas las restricciones?

Si hay más de un objetivo, ¿qué importancia relative tiene cada uno?

Si hay más que un método de solución, ¿cuál usas o cómo los combinas?Casi cualquier algoritmo tiene uno o más parámetrosCasi cualquier problema tiene más de un algoritmoCasi cualquier entrada es imprecisaCasi cualquier problema en la vida real es dinámica

Cómputo evolutivo

COMPUTACIÓN INSPIRADA EN BIOLOGÍA

Algoritmos genéticos/evolutivos

Redes neuronales artificiales

Algoritmos de colonia de hormigas / abejas

Optimización por enjambres de partículas

Cómputo orgánico (sistemas inteligentes y adaptativos)

Cómputo ADN

Metaheurísticos

Búsquedas locales simples y avanzadas

Búsqueda tabú, recocido simulado, GRASP

Computación evolutiva y biológicamente motivada

Algoritmos genéticos

Algoritmos de colonias de hormigas

Optimización con enjambre de partículas

Modelado de sistemas

En términos de grafos G = (V, E).

Los elementos de V son los vértices y los de E son las aristas que conectan los vértices.

Modelado de sistemas

Aristas (conexiones)

Modelado de sistemas

Un grafo

Figure 4.12: Each cluster has its own color; the nodes have been added oneby one, with existing nodes updating their clusters after the newcomer selectsa cluster. Cluster heads are drawn with a black border. In these examples, allnodes have a fixed communication range and they do not move.

that of Ohta et al. [248], with the difference that we choose between clustercandidates by optimizing a density-based fitness function.

If we are able to produce connected clusters that have high local densitywith only few links to the rest of the network, the routing task is simplified.For intra-cluster routing, it becomes possible to use link-state algorithms,such as OLSR [76], which require dense and relatively small networks inorder to be efficient [273]. If the clusters are stable enough, this gives goodperformance. Inter-cluster routing, on the other hand, may well use on-demand routing protocols.

By optimizing Equation 4.30, we may cluster ad hoc networks withoutextra messages, since the required messages are simple enough to be pig-gybacked on link layer or routing messages. Based on our simulations, thisproduces intuitively good clusters, thereby minimizing address changes andallowing us to optimize routing traffic.

A simple protocol for clustering is the following [280]: upon arriving to anew location or waking up from sleep, a new node probes its neighborhood.All existing nodes that hear the probe, if any, send their cluster identifiertogether with three integers: the number of nodes in the cluster |C!|, theinternal degree degint (C

!) of the cluster, and the external degree degext (C!)

of the cluster. Since these values take so little space, they could be easilyembedded into existing messages.

Based on the messages the arriving node receives, it constructs a neighborlist and calculates the fitness that each of the neighboring clusters wouldobtain if it were to join that particular cluster. It is also able to deduce thecurrent fitness of each cluster, and chooses to join the cluster which “gains”the most (or “suffers” the least) due to the arrival of the new member. If anode has no neighbors or no neighboring cluster accepts it, that is, it receivesno answers to the probe, it starts its own cluster. The acceptance criteria mayfor example include a maximum cluster size or a threshold on how muchthe cluster fitness may decrease upon a new arrival. Such parameters to the

72 CHAPTER 4. CLUSTERING

Figure 4.13: Clusters selected by a method for some anomalous networkstructures.

cluster formation serve to regulate the amount of routing traffic in link-statebased routing schemes. Once the node has solved the cluster it wants to jointo, it sends a message indicating its desire. This can be implemented as arouting-protocol message, such as an OLSR HELLO message [76].

The cluster-selection protocol described above should be repeated as thenetwork evolves. The cluster memberships can be updated, for example,on regular intervals or upon the creation or loss of connections. Detectionof a new edge causes a node to re-execute the cluster-selection protocol; anode will only change its cluster if the new cluster arrangement is (much)better than the current one. This reduces the amount of routing and addressmanagement traffic.

Clearly, if a cluster splits, each node must select a new cluster, and suchinformation should propagate along the disconnected component. In orderto determine which “half” of a separated cluster should select a new clusteridentity, one node in each cluster needs to hold a “cluster head” status. Anode that has no intra-cluster paths remaining to the cluster head must re-initiate the selection protocol, hereby alerting its neighbors to check whetherthey still have a proper path to the cluster head. If a full link-state protocolis used within a cluster, routing information allows trivial partitioning detec-tion.

To examine what the resulting clusters look like, we have built a simulatorto visualize clusterings. Figure 4.12 shows an example of a randomly gener-ated graph and Figure 4.13 shows the clustering for some anomalous shapes.We also built an implementation [219] of the algorithm for more re-alistic experiments. Our experiments with simulation tools are promising:the clusters achieve a proper sense of locality in space and their structurecorresponds well to the intuitive global clusterings of the network.

In the simulations, we used networks with 30 nodes in a one square-kilometer area and set the minimum cluster order to be five and the max-imum to eight nodes; the simulator was very slow for larger networks. Wehad each node probe its neighborhood, within a range of 250 meters, onfive-second intervals and the cluster heads broadcasting a status message forintra-cluster flooding also on five-second intervals. A node i executing the

CHAPTER 4. CLUSTERING 73

Load !! (T ) 854 588 1,350Load !! (F ) 362 70 1,350

Avg. hop count 2.05 2.66 1.71

Figure 5.6: A small graph (on the left) with three possible spanning trees:a random one, a line, and a star topology. Below the pictures are the val-ues for two possible global load measures (using the vertex-betweenness) andthe average hop count (calculating the hop-distance for each pair of distinctvertices once).

to route the traffic: the load of an edge is proportional to the number of pathsconnecting any pair of vertices that pass through that edge; in a tree any pathfor a given pair of vertices is always the unique shortest path. The load of avertex v can either be measured as the sum of the edge-betweenness of theedges incident on it in the spanning tree or by the vertex-betweenness, whichis defined equivalently as the number of shortest paths that pass through (orbegin or end) at v; we will use the latter definition.

In the optimal situation, all vertices would have the same load — this isof special importance when the communication nodes are battery operated,as a heavy-load node runs out of power faster after which it will not be able totake part in the function of the network. One way to measure how evenly theload has been distributed is sum of squares of the load differences; denotingthe load of a vertex v by ! (v), we can use either the load over all distinctvertex pairs

"! (T ) =!

v,w!V

"

! (v) ! ! (w)#2 (5.11)

or, denoting by F the edges that are included in the spanning tree T , overonly the edges of the tree,

"! (F ) =!

v,w!V{v,w}!F

"

! (v) ! ! (w)#2

. (5.12)

As argued above, good spanning trees for communication networks arethose that use low-weight edges, have small unweighted average path length,and in which the load is uniformly spread over the network, meaning that"! (") is small. Unfortunately, these goals are often contradictory, as illus-trated in Figure 5.6, where the star topology clearly achieves the smallestaverage distance, but puts a heavy load on the central vertex.

The worst-case tree T with respect to the average hop count is a “line” of

CHAPTER 5. SEARCHING AND ROUTING 105

Figure 5.7: A 11-vertex graph G = (V, E) and two possible spanning trees;the edges shown thick have weight 1 + ! (! > 0) and the thin ones haveweight 1. The MST (with total weight 10) is a path with average path length4, whereas the other tree has unweighted average path length 2.36, weightedaverage path length 2.36 + 1.472!, and total edge weight 10 + 5!. For smallvalues of !, the latter tree is clearly better with respect to the number of hopsneeded on average to carry out communication between to vertices.

length n ! 1, for which the average path length is always

L (T ) =1

n(n ! 1)

n!

i=1

"

i!1!

j=1

j +n!i!

j=1

j

#

=1

n(n ! 1)

n!

i=1

$

i(i ! 1)

2+

(n ! i)(n ! i + 1)

2

%

=1

n(n ! 1)·n(n2 ! 1)

3=

n + 1

3,

(5.13)

where the vertices are denoted by their index i " [n], sequentially numberedfrom one end of the path to the other. It is easy to construct graphs wherethe minimum spanning tree is a path, but where there exists an alternativespanning tree with near-optimal cost and much smaller average path length;see Figure 5.7 for an example.

In this work we do not propose algorithms for load balancing, but ratheruse measures of the evenness of the load to evaluate spanning trees generatedby optimizing other criteria. Our goal is to find methods that construct non-minimal spanning trees with respect to the edge weights, but with desirableproperties such as those of the leftmost tree in Figure 5.6 and the rightmostone in Figure 5.7: moderate load, near-optimal total edge weight, and a smallaverage hop length.

5.2.2 Centralized tree-construction algorithms

In order to gain a better understanding of the problem at hand, we first dis-cuss optimizing each of the properties — total edge weight and average pathlength — separately with a centralized algorithm. The standard minimumspanning tree algorithms [157, 162, 179, 260] solve efficiently the weightedMST problem, always finding the optimal solution.

For minimizing the average hop count, we propose the following simpleheuristic that produces a spanning tree T = (V, F ) for a given connected

106 CHAPTER 5. SEARCHING AND ROUTING

w

v

Figure 3.1: A grid with randomly placed edges and an open path from v tow.

where !k =!

n!1k

"pk(1!p)(n!1)!k and r is any fixed integer. Also E["] = p, as

E[m] = p!

n2

"and " = m/

!n2

", and the density of any subgraph of order h has

expected value p, as within the subgraph, each of the!

h2

"edges is included

with probability p.

3.1.2 Percolation

In this section we briefly review the concept of percolation for further ref-erence. For a thorough view on percolation, we recommend the work ofGeoffrey Grimmett, see e.g. [60, 61]. From our limited point of view, perco-lation is just another way of producing random graphs with plenty of knownanalytical results. The process resembles greatly that of the previous section;the main difference is that now in general, the vertex set is not limited to afixed number and edges may appear only between certain vertices instead ofall possible positions.

Consider the infinite square lattice Z2 with a possibility of placing a vertexat each “crossing” of the grid and an edge at each unit grid line. An infiniterandom graph G = (V, E) is formed by taking the set of all crossings asvertices and selecting the edge set by including each unit grid line randomlyand independently with probability p " [0, 1]. A smaller graph results if werestrict ourselves to a specified portion of Z2, usually some rectangular area.The central question in percolation theory is the following: In a randomgraph constructed on a finite portion of Z2, does an open path exist fromone boundary of the rectangle to the opposite boundary? An example of arectangular graph that contains such a path is shown in Figure 3.1.

As p is varied, the structure of the random graph begins to change. Afterreaching some critical probability pc, the infinite graph contains (with prob-ability one) an infinite cluster of connected vertices. Such a procedure ofadding edges is called bond percolation and it could of course be conductedon other structures besides the square lattice Z2. Another, somewhat lessstudied variant is site percolation, where instead of adjusting the edge pres-ence, the existence of a vertex is decided upon independently and randomlywith probability p. The edge set consists of one-unit grid lines that connecttwo vertices that are both present.

Percolation phenomena have been widely studied in physics, for exampleas models of magnetism. Also studies of epidemic spreading resort to per-colation as a mathematical model: Newman and Watts [106] have studiedsite percolation in so-called small-world networks. These results will be sum-

24 3. MATHEMATICAL NETWORK MODELS

Algoritmos genéticos

Representación de soluciones (factibles) como cromosomas

Creación de poblaciones iniciales

Evolución generacional

Cruces

Mutaciones

Selección natural

Colonias de hormigas

Ahora la población no son las soluciones, sino agentes que exploran a las soluciones

Se indica la calidad de una “zona” por rastros de feromona

Permite una coordinación implícita entre agentes

Enjambres de partículas

Aquí también son grupos de agentes

Comunican de forma explícita

Movimientos relativos a vecindades predefinidas

Preferencia al vecino con la mejor solución actual