Ruprecht Karls Universität Heidelberg


Forces and elasticity in cell adhesion

Forces at focal adhesions Cell organization in soft media
Calculation of forces at focal adhesions from elastic substrate data. Forces (red) exerted by an adhering fibroblast at sites of focal adhesions (white) which are fluorescently marked by GFP-vinculin. The inset shows a phase contrast image of the deformation of the micro-patterned elastic substrate (green), from which the force pattern has been calculated. Balaban et al., Nature Cell Biology 2001. Predicted cell organization in soft media due to active mechanosensing. In some situations, mechanical input signals can be as important for cellular decision making as biochemical input signals. Cells actively sense the elastic properties of their environment and strengthen contacts and cytoskeleton in the direction of large effective stiffness. Therefore they orient (a) perpendicular to clamped boundaries, (b) parallel to free boundaries, (c) perpendicular and parallel on the soft and stiff sides of a rigidity gradient, respectively, and (d) in parallel in and on a homogeneous medium. Bischofs and Schwarz, PNAS 2003.

Force is ubiquitous in biological systems. Many cellular programs like cell division, cell adhesion and cell locomotion involve the generation of physical force. Just imagine that there are many cells which move inside you while you read this text: eg leukocytes circle your body using the blood flow on their search for sites of inflammation; rolling adhesion on the vessel walls allows them to survey it for signs of inflammation, and has to function under large shear forces; on encountering certain signals, leukocytes leave the blood stream by squeezing through the vessel wall; in the surrounding tissue, they crawl by pulling themselves along fibers. Or think of fibroblasts which structure the connective tissue (which fills the space between organs and tissues in the body) and close your wounds by strongly pulling on their surrouding. More examples for cellular forces and cell movements come from embryogenesis, morphogenesis, and from malignent tumors, when cells do not respond to inhibiting signals to crawling.

For cells adhering to flat rigid surfaces, cellular force is generated mainly by actomyosin contractility and transmitted to the substrate through sites of so-called focal adhesion. Focal adhesions have both structural and signalling functions. From a structural point of view, they provide the pinning sites needed by the cell in order to spread out on the surface. From a signalling point of view, focal adhesions trigger different signalling pathways which signal successful adhesion to the cell; lack of these signals can in fact lead to programmed cell death. During my postdoctoral work at the Weizmann Institute, I became involved in a collaboration with experimentalists in the Department of Cell Biology which succeeded in measuring cellular forces at the level of focal adhesions for the first time (Nature Cell Biology 2001, Biophysical Journal 2002). The experimental technique combined the use of microstructured elastic substrates and fluorescense marking of focal adhesions proteins. The theoretical part consisted in calculating the force pattern from the displacement pattern, which numerically amounts to solving an ill-posed inverse problem. We were able to show that size and direction of forces acting at focal adhesions correlate strongly with size and elongation of the adhesion plaques as monitored by GFP-vinculin (for fibroblasts, typical forces at focal adhesions are 10 nN, with a stress constant around 5.5 nN / micron^2). Thus force and protein assembly (which in turn correlates with signalling) are intimately linked at focal adhesions. However, the details of the molecular mechanisms which cause the correlations between force, protein assembly and signalling at focal adhesions are still elusive.

Recently we have improved the workflow required to measure cellular traction patterns. Our improvements in traction force microscopy include simultaneous use of several kinds of fluorescent markers, advances in image processing and filtering, and flexible use of different force reconstruction algorithms, eventually leading to a spatial resolution of one micrometer (Sabass et al., Biophysical Journal 2008). We then applied this technique to correlate for the first time traction force with retrograde flow, which is a crucial element in cell migration and can be measured with speckle fluorescence microscopy. Combining it with traction force microscopy allowed us to identify a biphasic relation between flow and force (Gardel et al., Journal of Cell Biology 2008). In detail, we found that actin speed is inversely related to traction stress near the cell edge, indicating that the flow is increasingly impeded as the actin becomes increasingly engaged to the adhesions. In contrast, larger FAs where the actin speed is low are marked by a direct relationship between actin speed and traction stress. The crossover between these two regimes occurs at at threshold flow of around 10 nm/s, independent of many possible determinants like actin polymerization or myosin activity. Thus it appears that actin speed is a fundamental regulator of traction force at FAs during cell migration.

Continuing our collaboration with the Gardel lab, recently we were able to demonstrate that the measurement of cell-matrix forces can also be used to infer cell-cell forces (Maruthamuthu et al., PNAS 2011). In particular, we found that cell-cell forces have a similar magnitude as do cell-matrix forces, and that they increase with increasing substrate stiffness. Our results suggest that cells balance a similar amount of tension with their environment both as single cells on a substrate and as part of a cell sheet.

In a collaboration with Julien Colombelli and Ernst Stelzer from the EMBL at Heidelberg, we were able to show that force also correlates with protein localization in stress fibers (Colombelli et al., Journal of Cell Science 2009). Using laser cutting, we were able to show that stress fibers are attached along their length to the substrate. Upon cutting, these crosslinks restrict the length over which the fiber can retract. In addition, the crosslinks become tensed and then recruit zyxin, a protein which is known to be strongly mechanosensitive. Using a theoretical model for stress distribution along stress fibers, we found that zyxin localization follows exactly the spatial distribution of force along the fiber. Therefore stress fibers act as spatially distributed mechanosensors.

In earlier work we had shown that also focal adhesions grow under the application of external force, suggesting that focal adhesions function as spatially localized mechanosensors (Riveline et al., Journal of Cell Biology 2001). Together with other experimental studies, our results demonstrate that animal cells have evolved a sophisticated apparatus which they can use to actively sense the mechanical properties of the environment. In fact it has long been known, especially in the medical and bioengineering communities, that cell organization in soft media is strongly influenced by the mechanical properties of the environment. Our experimental results now suggest that this cell organization is resulting from active processes on the level of single cells.

In order to predict and control these cellular processes (for example for applications in tissue engineering), it is essential to establish a theoretical framework for the interplay of mechanical activity of cells and mechanical properties of the surrounding matrix. We have shown that a large body of experimental observations on cell organization in soft media can be consistently explained from a relatively simple theory which describes active cell behavior by an extremum principle in linear elasticity theory (PNAS 2003, Physical Review E 2004, Physical Review Letters 2005). Our theory uses concepts which have been developed in the 70s for elastic interactions of atomic defects in crystals. In detail, we model cells as anisotropic force contraction dipoles and solve the elastic equations for elastic isotropic material with different geometries and boundary conditions (Physical Review Letters 2002). We start from the observation that cells strengthen contacts and cytoskeleton in the direction of large effective stiffness in their environment (possibly because build-up of force at focal adhesions is more efficient in a stiff environment) and show that this corresponds to a minimization of the quantity W = uij Pij, where uij is the strain tensor of the surrounding medium (including image strain in the case of finitely sized geometries) and Pij is the force dipole tensor representing the cell. From this principle, we show that cells orient in the direction of external tensile strain, that they orient parallel and normal to free and clamped surfaces, respectively, and that they interact elastically to form strings, in excellent agreement with experimental observations. We also extended this framework to deal with matrix-mediated structure formation in ensembles of cells (Acta Biomaterialia 2006).

Publications from collaborations with experimentalists:

  • N. Q. Balaban, U. S. Schwarz, D. Riveline, P. Goichberg, G. Tzur, I. Sabanay, D. Mahalu, S. Safran, A. Bershadsky, L. Addadi and B. Geiger, Force and focal adhesion assembly: a close relationship studied using elastic micro-patterned substrates, Nat. Cell Biol. 3: 466-472 (2001) (abstract, PDF)
  • D. Riveline, E. Zamir, N. Q. Balaban, U. S. Schwarz, B. Geiger, Z. Kam, A. D. Bershadsky, Focal contact as a mechanosensor: externally applied local mechanical force induces growth of focal contacts by a mDia1-dependent and ROCK-independent mechanism, J. Cell Biol.153: 1175-1185 (2001) (abstract, PDF)
  • U. S. Schwarz, N. Q. Balaban, D. Riveline, A. Bershadsky, B. Geiger, S. A. Safran, Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization, Biophys. J. 83: 1380-1394 (2002) (abstract, PDF)
  • U. S. Schwarz, N. Q. Balaban, D. Riveline, L. Addadi, A. Bershadsky, S. A. Safran, B. Geiger, Measurement of cellular forces at focal adhesions using elastic micro-patterned substrates, Mat. Sci. Eng. C 23: 387-394 (2003) (abstract, PDF)
  • C. Cesa, N. Kirchgessner, D. Meyer, U.S. Schwarz, B. Hoffmann and R. Merkel. Micropatterend silicone elastomer substrates for high resolution analysis of cellular force patterns. Rev. Sci. Instruments, 78:034301, 2007. (abstract, doi:10.1063/1.2712870, PDF)
  • B. Sabass, M. L. Gardel, C. Waterman and U. S. Schwarz. High resolution traction force microscopy based on experimental and computational advances. Biophys. J., 94:207-220, 2008. (abstract, doi:10.1529/biophysj.107.113670, PDF)
  • M. L. Gardel, B. Sabass, L. Ji, G. Danuser, U. S. Schwarz, and C. M. Waterman. Traction stress in focal adhesions correlates biphasically with actin retrograde flow speed. J. Cell Biol., 183:999-1005, 2008. (abstract, doi:10.1083/jcb.200810060, PDF)
  • Venkat Maruthamuthu, Benedikt Sabass, Ulrich S. Schwarz, and Margaret L. Gardel. Cell-ECM traction force modulates endogenous tension at cell-cell contacts. Proc. Natl. Acad. Sci. USA, 108:4708-4713, 2011. (abstract, doi:10.1073/pnas.1011123108, PDF, Supplemental material)
  • J. Colombelli, A. Besser, H. Kress, E.G. Reynaud, P. Girard, E. Caussinus, U. Haselmann, J.V. Small, U. S. Schwarz, and E.H.K. Stelzer. Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization. J. Cell Sci., 2009. (abstract, doi: 10.1242/jcs.042986, PDF)

Theoretical work on cell organization in soft media:

  • U. S. Schwarz and S. A. Safran, Elastic interactions of cells, Phys. Rev. Lett. 88: 048102 (2002) (abstract, cond-mat/0201110, PDF)
  • I. B. Bischofs and U. S. Schwarz, Cell organization in soft media due to active mechanosensing, Proc. Natl. Acad. Sci. USA 100: 9274-9279 (2003) (abstract, cond-mat/0308187, PDF)
  • I. B. Bischofs, S. A. Safran and U. S. Schwarz, Elastic interactions of active cells with soft materials, Phys. Rev. E 69: 021911 (2004) (abstract, cond-mat/0309427, DOI: 10.1103/PhysRevE.69.021911 PDF)
  • S. A. Safran, N. Gov, A. Nicolas, U. S. Schwarz and T. Tlusty, Physics of cell elasticity, shape, and adhesion, Physica A 352: 171-201 (2005) (abstract, PDF)
  • I. B. Bischofs and U. S. Schwarz, Effect of Poisson ratio on cellular structure formation, Phys. Rev. Lett. 95: 068102 (2005) (abstract, cond-mat/0504097, DOI: 10.1103/PhysRevLett.95.068102, PDF)
  • U. S. Schwarz and I. B. Bischofs. Physical determinants of cell organization in soft media. Med. Eng. Phys., 27: 763-72 (2005) (abstract, PDF)
  • U. S. Schwarz, T. Erdmann, and I. B. Bischofs. Focal adhesions as mechanosensors: the two-spring model. BioSystems, 83: 225-232 (2006) (abstract, q-bio.SC/0608006, PDF)
  • I. B. Bischofs and U. S. Schwarz. Collective effects in cellular structure formation mediated by compliant environments: a Monte Carlo study. Acta Biomaterialia, 2: 253-265, 2006. (abstract, cond-mat/0510391, doi:10.1016/j.actbio.2006.01.002, PDF)


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