Coupling actin flow, adhesion, and morphology in a computational cell motility model

Abstract

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-...

Cell motility in confinement: a computational model for the shape of the cell

“…To do so we use the simplified model, where we arbitrarily set the polymerized actin density to a fixed value near the plasmic membrane, forgetting every detail of actin dynamics. This assumption, in agreement with the results of the experiments performed in [23], decouples the effect of the protrusion at the membrane from other mechanisms. In the end, this will allow to calibrate the intensity of the protrusion in the complete model.…”

“…This model inspired by [23] takes into account the lamellipodium immersed in the fluid fulfilling the micro-channel, the polymerization of the actin network, the adhesion of the lamellipodium to the walls and the membrane forces which are here limited to the surface tension. Moreover, it describes the actin dynamics inside the lamellipodia.…”

On a poroviscoelastic model for cell crawling

“…It is typically computationally cheaper than tracking many individual constitutive parts of a cell and allows the modeller to formulate constitutive laws that can be tested against observations at an observable spatial scale. Such models may describe the cell as a viscous fluid (Alt and Tranquillo, 1995;Shao et al, 2012), or a viscoelastic material (Gracheva and Othmer, 2004;Larripa and Mogilner, 2006;Rubinstein et al, 2009;Sarvestani and Jabbari, 2009;Sakamoto et al, 2011;Hodge and Papadopoulos, 2012), typically with additional terms to model the active nature of the cytoskeleton. Both Shao et al (2012) and Gracheva and Othmer (2004) have been able to demonstrate the experimentally observed bell-shaped dependence on adhesion strength.…”

“…Such models may describe the cell as a viscous fluid (Alt and Tranquillo, 1995;Shao et al, 2012), or a viscoelastic material (Gracheva and Othmer, 2004;Larripa and Mogilner, 2006;Rubinstein et al, 2009;Sarvestani and Jabbari, 2009;Sakamoto et al, 2011;Hodge and Papadopoulos, 2012), typically with additional terms to model the active nature of the cytoskeleton. Both Shao et al (2012) and Gracheva and Othmer (2004) have been able to demonstrate the experimentally observed bell-shaped dependence on adhesion strength. Larripa and Mogilner (2006) present a one-dimensional model which exhibits a travelling wave solution with qualitatively plausible distributions of actin and myosin, but much of the shape of the distribution is prescribed by the boundary conditions.…”

Computational Phase‐Field Modeling

“…Among these problems, we include the interaction of a large number of cracks in three-dimensional solids of complicated geometry (Borden et al, 2014), fully three-dimensional air-water flows with surface tension (Ceniceros et al, 2010), liquid-vapor phase transitions and cavitation (Liu et al, 2013), nucleate and film boiling (Liu et al, 2015), phase-change-driven implosion of thin structures (Bueno et al, 2014), cellular migration (Shao et al, 2012) and tumor growth (Hawkins-Daarud et al, 2012;Vilanova et al, 2013Vilanova et al, , 2014Vilanova et al, , 2012Xu et al, 2015;Lorenzo et al, 2015) and others Juanes, 2012, 2014;Gomez et al, 2013). However, even though the last few years witnessed very significant advances in the area, there are still many challenges ahead.…”