Modeling shapes and traction forces of steady moving and perturbed cells
Final Report Abstract
The substrate-based crawling motion of eukaryotic cells is essential for many biological functions, both during development and in the mature organism, and its dysfunction is involved in several pathologies. Although cell motility obviously relies on biological and biochemical processes, distinct features fall in the realm of nonequilibrium soft matter physics: force creation by chemically driven polymerization of actin filaments against the cell membrane, force transmission to the substrate via adhesion molecules, and molecular motors generating contractile stresses. The main goal of the original proposal was hence to develop a physical model – simple, but including all key physical aspects – being able to describe the persistent, steadystate motion of simple cells like keratocytes on a flat substrate. The focus was laid on the overall self-organized shape of the cell and the traction forces it exerts on the substrate during motion, which both reflect the physical force balance on the global and local level, respectively. Indeed the developed model, accounting for spatially resolved traction forces, allows for a wide diversity of cell shapes, force patterns and overall dynamics. In addition, we improved the description of the cell membrane by including its tension, which as a global force regulator counteracts actin polymerization and modulates cell shape and velocity. Finally, inspired by the recent interest in collective motion, we generalized the model to multiple cells and could successfully describe several scenarios of collective cell motility. Building on this progress, the follow-up proposal aimed to broaden the perspective to non-steady situations, as occurring at the onset of motion, i.e. when the cell polarizes and breaks its symmetry, and for the relaxation of shape and traction forces upon external perturbations of moving cells. We found that our model framework can indeed capture the spontaneous rotational states prior to the motility and polarization onset recently found for keratocyte cells by two experimental groups independently, and interpreted them as nonlinear shape deformation waves. Concerning cellular perturbations, our external collaborator A. Verkhovsky carried out experimental studies on keratocyte encounters. They showed a very broad range of outcomes, including disassembly of lamellipodia (contact inhibition) and lamellipodia of two cells going over each other. Though intriguing, these scenarios go far beyond the current modeling. In search of more well-defined perturbations on the cellular scale, and considering the plethora of studies on sterically confined cells, we decided to generalize our modeling approach to threedimensions and – in principle – arbitrarily shaped surroundings. Doing so, we were able to study the cellular response in several well-defined scenarios, such as: the motion on curved substrates, systematically varying the substrate’s curvature (from cells on thin fibers to the movement inside capillaries); motion under vertical confinement between two plates; as well as motion on topographically structured substrates. The found, purely physical, guiding principles for motile cells should help discerning effects from truly specific biochemical cues and/or regulatory activity from the cell itself. The model developments within this project now allow to describe many generic aspects of steady and time-dependent cell motion, its onset, as well as motion in inhomogeneous environments (chemically, mechanically, or topographically/sterically). Both the multi-cell, and the three-dimensional model are only first steps and may pave the way for future studies on the motion of cells and other, biological or artificial, driven soft systems.
Publications
- Modeling crawling cell movement on soft engineered substrates, Soft Matt. 10, 1365 (2014)
J. Löber, F. Ziebert and I. S. Aranson
(See online at https://doi.org/10.1039/c3sm51597d) - Modular approach for modeling cell motility, Eur. Phys. J. Special Topics 223, 1265 (2014)
F. Ziebert and I. S. Aranson
(See online at https://doi.org/10.1140/epjst/e2014-02190-2) - Collisions of deformable cells lead to collective migration, Sci. Rep. 5, 9172 (2015)
J. Löber, F. Ziebert and I. S. Aranson
(See online at https://doi.org/10.1038/srep09172) - Computational approaches to substrate-based cell motility, npj Computational Materials 2, 16019 (2016)
F. Ziebert and I. S. Aranson
(See online at https://doi.org/10.1038/npjcompumats.2016.19) - Macroscopic model of substrate-based cell motility, in Physical Models of Cell Motility, I. S. Aranson, Ed.; Springer series - Biological and Medical Physics, Biomedical Engineering, 2016, pp. 1-67
F. Ziebert, J. Löber and I. S. Aranson
(See online at https://dx.doi.org/10.1007/978-3-319-24448-8 1) - Membrane tension feedback on shape and motility of eukaryotic cells, Physica D 318-319, 26 (2016)
B. Winkler, I. S. Aranson and F. Ziebert
(See online at https://doi.org/10.1016/j.physd.2015.09.011)
