Simple model of cell crawling

Abstract

Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of the cell on a substrate. For time-independent forces we show that not only a stationary motion but also a limit cycle oscillation of the migration velocity and the shape occurs as a result of nonlinear coupling between different deformation modes. Time-dependent forces are generated in a stochastic manner by utilizing the so-called coherence resonance of an excitable system. The present coarse-grained model has a flexibility that it can be applied, e.g., both to keratocyte cells and to Dictyostelium cells, which exhibit quite different dynamics from each other. The key factors for the motile behavior inherent in each cell type are identified in our model

Control of cell colony growth by contact inhibition

“…It is now understood that the shape of cells can be highly variable and has a strong influence on their collective behavior [36,[60][61][62][63][64][65]. In our previous work, we showed that the present model exhibits an alignment transition in coherent migration as a function of cell shape [47].…”

Physical models of collective cell motility: from cell to tissue

“…This is perhaps most explicitly modeled in the minimal approach of Ohta et al [122], who study the dynamics of a deformable self-propelled particle, and have later extended this to describing the dynamics of Dictyostelium cells [123]. In the simplest version of their model, cells are described by a velocity v and a single tensor variable S ij indicating the cell’s shape deformation from a circle [122]; the most general equations of motion coupling v and S ij to a given order can then be written down.…”

Swinging motion of active deformable particles in Poiseuille flow

“…For this purpose, we replace eqs. (20) and (22) by constant values for the active velocity and shape deformation, as explained shortly. In order to highlight the effect of the Poiseuille flow, we do not consider the interaction with the boundary explicitly in this section.…”

“…The other is the time-derivative term of the active velocity in eq. (20). Note that this inertia-like term is also derived from the Stokes equation for an active droplet on the interface of which a chemical reaction takes place to change the local surface tension [91,92].…”

“…There also exist deformable ones, whose shape changes in time. In particular, such shape deformation is of great importance for the migration and the proliferation of eukaryotic cells [14][15][16][17][18][19][20]. Synthetic deformable active particles are also realized such as self-propelled liquid droplets [21][22][23][24][25][26][27][28][29] and active vesicles [30][31][32][33].…”