Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

Abstract

We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

Topological and geometrical quantities in active cellular structures

“…The multi phase field approach is a valuable framework that can incorporate a broad range of submodels, in our case an active polar gel model. Other possibilities are couplings with biochemistry 49,50 or hydrodynamics 25 .…”

Mechanisms of cell polarization

“…A recent work describes the formation of special cell appendages, regulated by a balance of Rac Arp2/3 pathway (promotes the formation of “fin-like” structures) and Rho pathways that promote formin-based actin assembly and myosin-based blebbing behavior [141]. Several modeling studies have explored the connections between the shape of a cell and the dynamics of its intracellular signaling for polarity [5,97,142–144], but these have largely focused on 2D cell projections. The computational issues associated with simulating dynamic intracellular signaling inside a deforming 3D cell are still daunting, but developments of new methods is ongoing by several groups (see, e.g.…”

Higher-order accurate diffuse-domain methods for partial differential equations with Dirichlet boundary conditions in complex, evolving geometries

“…Later, in [48] and [49] alternate derivations of diffuse-domain methods for such problems were presented. Diffuse-domain methods have been applied to a wide variety of problems that arise, for example, in biology (e.g., [42,50,51,52,53,54,55,56,57,58]), in fluid dynamics (e.g., [59,60,61,62,63]) and in materials science (e.g., [64,55,65,66,67]), just to name a few, and have been implemented using a wide spectrum of methods including in-house finitedifference, finite-element and pseudo-spectral algorithms and software packages such as Matlab, AMDiS [68], MRAG [69], and BSAM [70].…”