Thread 1. Computational Methods in Biomechanics and Mechanobiology T1.1 Computational Modelling and Mechanobiology of Cells $397

Thread 1

Computational Methods in Biomechanics and Mechanobiology

T1.1 Computational Modelling and Mechanobiology of Cells 5546 Mo, 08:15-08:45 (P7) Modelling cell behaviour in compliant environments U.S. Schwarz 1 , I.B. Bischofs 2. 1Heidelberg University, Center for Modelling and Simulation in the Biosciences, Heidelberg, Germany, 2Department of Bioengineering, University of Cafifomia at Berkeley, Berkeley, CA, USA

Adhesion-dependent cells actively sense extracellular stiffness through acto- myosin contractility and mechanotransductory processes at focal adhesions. We first introduce the two-spring model which provides a simple rationale for how the build-up of actomyosin-generated force at adhesion adhesions is mod- ulated by the rigidity of the environment and how this force might be coupled to biochemical signals through the rupture dynamics of mechanically weak links in the loaded structure [1]. Then we discuss how this dynamics of focal adhesions might be related to the behaviour of fibroblast-like cells in compliant environments, which can be formulated as an extremum principle in linear elasticity theory. For single cells, we predict cell positioning and orientation for different elastic moduli, sample geometries and boundary conditions of interest [2]. For intermediate cell densities, we predict string formation due to elastic interactions between cells. Effective interactions between strings are short-ranged because cellular traction patterns screen each other [3]. For high cell densities, we predict novel phase transitions between string-like and ring- like structures as a function of Poisson ratio. In particular, we discuss the effect of noise and cell position geometry [4].

References [1] U.S. Schwarz, T. Erdmann, I.B. Bischofs. Focal adhesions as mechanosensors:

the two-spring model. Biosystems 2006; to appear. [2] I.B. Bischofs, U.S. Schwarz. Cell organization in soft media due to active

mechanosensing. Proc. Natl. Acad. Sci. USA 2003; 100: 9274-9279. [3] I.B. Bischofs, U.S. Schwarz. Effect of Poisson ratio on cellular structure forma-

tion. Phys. Rev. Lett. 2005; 95: 068102. [4] I.B. Bischofs, U.S. Schwarz. Collective effects in cellular structure formation

mediated by compliant environments: A Monte Carlo study. Acta Biomaterialia 2006; to appear.

5946 Mo, 08:45-09:00 (P7) Cell shape on micro-patterned adhesive substrates I.B. Bischofs 1 , D. Lehnert 2, R Klein 2, M. Bastmeyer 2, U.S. Schwarz 3. 1 Department of Bioengineering, University of California at Berkeley, CA, USA, 2 Karlsruhe University, Institute of Zoology I, Karlsruhe, Germany, 3Heidelberg University, Center for Modelling and Simulation in the Biosciences, INF 293, Heidelberg, Germany

Animal cells adopt their shape in response to the biochemical and physical properties of their environment. Their shape is determined mainly by the plasma membrane and the various components of the cytoskeleton. Both the plasma membrane and the actin cytoskeleton contribute to tension in the cell envelope. Indeed, cell shape often shows a clear signature of surface tension, leading to e.g. spherical shape in suspension, polyhedral shapes in close-packed tissues, arc-like shapes of cells adhering to a flat substrate and pearling in tube-like structures like axons or adhering cells after disruption of the actin cytoskeleton. Using micro-contact printing of different patterns of adhesive islands onto flat substrates, it has been shown before that cell shape is a major determinant of cell fate [1]. Here we show that this technique can also be used to analyse the physical determinants of cell shape in more detail. Cells were cultured on square arrangements of fibronectin dots with different sizes and lattice constants [2]. We found that the typical cell shape resem- bles a sequence of circular arcs composed of actin stress fibers connecting neighbouring focal adhesions localized to the fibronectin dots. Quantitative analysis of these shapes revealed a characteristic relationship between arc radius and dot distance which can be explained nicely by a micromechanical model which includes the effect of tension both in the cell envelope and in the peripheral stress fibers. This shows that tools from materials science can provide completely new insight into traditional subjects from cell biology if combined with appropriate modelling approaches.

References [1] C.S. Chen, M. Mrksich, S. Huang, G.W. Whitesides, D.E. Ingber. Geometric

control of life and death. Science1997; 276: 1425-1418.

[2] D. Lehnert, B. Wehrle-Haller, C. David, U. Weiland, C. Ballestrem, B.A. Imhof, M. Bastmeyer. Cell behaviour on micropatterned substrata: Limits of extracellu- lar matrix geometry for spreading and adhesion. J. Cell Sci. 2003; 117: 41-52.

5779 Mo, 09:00-09:15 (P7) A continuum finite element model predicting cell motility B. Flaherty 1,2, J.P. McGarry 2, B.P. Murphy 2, RE. McHugh 1,2. 1Department of Mechanical and Biomedical Engineering, National University of Ireland, Galway, Ireland, 2National Centre of Biomedical Engineering Science, National University of Ireland, Galway, Ireland

Development of a continuum finite element (FE) model predicting cell motility will advance both our understanding of this fundamental biological process and the application of the FE method to cellular biology. With accurate FE models it is possible to explore many permutations of the same event and investigate concisely their outcome. This FE model initially focuses on a migrating cell's response to a rigidity gradient in an underlying substrate (mechanotaxis). Con- stitutive equations, used previously in purely mechanistic applications, have been adapted to replicate the major biomechanical and biochemical factors that control cell motility. These equations interface with an FE solver through user coded FORTRAN subroutines and describe lamellipodia formation, cell contraction and the interaction between the cell and substrate. With this FE model, it will be possible to elucidate the mechanisms governing cell motility and also thoroughly investigate the influence different substrate characteristics may have on a cell's performance. These substrate characteristics include both the material properties of the substrate, and also its surface topography. A cell's performance is identified by its migration speed, shape and orientation. These are all important considerations in the design o fa substrate onto which cells are seeded. It is envisaged that this work will provide cues to scientists currently working on the development of "intelligent" substrates for future biomedical applications.

4903 Mo, 09:15-09:30 (P7) A new computational approach to obtaining substrate displacement filed for determining cell traction forces J.-S. Lin, Z. Yang, J.H-C. Wang. MechaneBielegy Laboratory, Departments ef Orthopaedic Surgery, and Civil and Environmental Engineering, University of Pittsburgh, USA

We have developed a new approach for the traction force microscopy (TFM) method that determines traction forces exerted by adherent cells on a thin, elastic polyacrylamide gel embedded with fluorescent beads. In this enhanced TFM method, a pattern recognition technique is first applied to match the pair of bead images before and after deformation, which subsequently provides the displacement field of the elastic substrate. Once the displacement field is obtained, the 3-D finite element method (FEM) is used to compute cell traction forces. The new TFM procedure has been applied in studying human tendon fibroblasts. Compared to existing TFM methods, the present procedure has the following advantages: (1) its displacement field obtained is associated with microbead movements using objective criteria; (2) it considers the finite thickness of the thin polyacrylamide gel and is therefore free from the infinite half-space approximation adopted by existing TFM methods; and (3) its traction force computation procedure is well-posed and fast.

5215 Mo, 09:30-09:45 (P7) A mathematical model for analysis of retarded diffusion and receptor binding of lipid anchored ligands in the cell-bilayer contact area

J. Wu 1 , '~ Fang 1 , C. Zhu 2. 1School of Life Sciences, Sun Yat-Sen University, Guangzhou, China, 2 Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, USA

The immunological synapse is an intercellular contact area that specializes in information transfer from one immune cell to another. Its formation is regulated in part by the diffusion of adhesion and signaling molecules into, and their binding of counter-molecules in the contact area. Therefore, kinetic rates and diffusion coefficient are important determinants for the formation, maintenance, and development of the immunological synapse. Measurements of the kinetic rates and binding affinity of receptor-ligand interaction in fluid phase using soluble molecules (i.e., three dimensional kinetic rates and affinity) do not necessarily correlate with their counterparts measured when both binding part- ners are respectively anchored to two apposing surfaces (i.e., two dimensional kinetic rates and affinity), such as the case in the immunological synapse. Furthermore, two dimensional affinities measured by different methods can differ by orders of magnitude. Moreover, diffusion coefficient of molecules inside the immunological synapse may be different from that outside. Here we present a coupled diffusion-reaction model for the fluorescence recov- ery after photobleaching (FRAP) experiment previously used to demonstrate the dynamics of adhesive bonds in a model immunological synapse - the