We develop a computational model, based on the phase field method, for cell morphodynamics and apply it to fish keratocytes. Our model incorporates the membrane bending force and the surface tension and enforces a constant area. Furthermore, it implements a cross linked actin filament field and an actin bundle field that are responsible for the protrusion and retraction forces, respectively. We show that our model predicts steady state cell shapes with a wide range of aspect ratios, depending on system parameters. Furthermore, we find that the dependence of the cell speed on this aspect ratio matches experimentally observed data.

Cell migration is a pervasive process in many biology systems and involves protrusive forces generated by actin polymerization, myosin dependent contractile forces, and force transmission between the cell and the substrate through adhesion sites. Here we develop a computational model for cell motion that uses the phase-field method to solve for the moving boundary with physical membrane properties. It includes a reaction-diffusion model for the actin-myosin machinery and discrete adhesion sites which can be in a "gripping" or "slipping" mode and integrates the adhesion dynamics with the dynamics of the actin filaments, modeled as a viscous network. To test this model, we apply it to fish keratocytes, fast moving cells that maintain their morphology, and show that we are able to reproduce recent experimental results on actin flow and stress patterns. Furthermore, we explore the phase diagram of cell motility by varying myosin II activity and adhesion strength. Our model suggests that the pattern of the actin flow inside the cell, the cell velocity, and the cell morphology are determined by the integration of actin polymerization, myosin contraction, adhesion forces, and membrane forces.actin dynamics | cell adhesion | keratocyte | phase field C ell migration plays a crucial role in many biological processes, including chemotaxis, embryogenesis, and cancer metastasis. In eukaryotic cells, this migration is powered by the actin-myosin system (1): at the cell's leading edge, cross-linked actin filaments polymerize by adding actin monomers to their barbed ends, a process known as "tread-milling," while at the back of the cell, myosin II, from now on referred to as myosin, binds to the bundled actin filaments and exerts contractile stress.Recent experiments have examined cytosolic actin flow, the movement of actin network with respect to the substrate (2-6). Many of these studies were performed using fish epidermal keratocytes. These cells are ideally suited to investigate cell motion since they are able to maintain a polarized morphology and display rapid migration on the substrate (7). These studies revealed that in the front half of the cell, the actin network exhibits a small retrograde flow in the laboratory's frame of reference. In contrast, the trailing part of the cell displays anterograde actin flow at larger speed. This pattern of the actin flow, along with cell velocity and cell shape, was found to be dependent on various factors, including the rate of actin polymerization, the amount of myosin activity in the cell, and the cell-substrate adhesiveness (3,8,6).The active stresses generated by the actin-myosin system are transmitted to the substrates through adhesion sites, providing the necessary forces required for propulsion (2, 9, 10). These adhesion sites are formed near the front of the cell, grow into mature focal adhesions, and gradually disassemble as the cell advances (10-12). The force transmission between cells and the substrate is often viewed as a clutch that is either engaged or disengaged (13-...

Adaptation in signaling systems, during which the output returns to a fixed baseline after a change in the input, often involves negative feedback loops and plays a crucial role in eukaryotic chemotaxis. We determined the dynamical response to a uniform change in chemoattractant concentration of a eukaryotic chemotaxis pathway immediately downstream from G protein–coupled receptors. The response of an activated Ras showed near-perfect adaptation, leading us to attempt to fit the results using mathematical models for the two possible simple network topologies that can provide perfect adaptation. Only the incoherent feedforward network accurately described the experimental results. This analysis revealed that adaptation in this Ras pathway is achieved through the proportional activation of upstream components and not through negative feedback loops. Furthermore, these results are consistent with a local excitation, global inhibition mechanism for gradient sensing, possibly with a Ras guanosine triphosphatase–activating protein acting as a global inhibitor.