Damped and persistent oscillations in a simple model of cell crawling

Abstract

A very simple, one-dimensional, discrete, autonomous model of cell crawling is proposed; the model involves only three or four coupled first-order differential equations. This form is sufficient to describe many general features of cell migration, including both steady forward motion and oscillatory progress. Closed-form expressions for crawling speeds and internal forces are obtained in terms of dimensionless parameters that characterize active intracellular processes and the passive mechanical properties of the cell. Two versions of the model are described: a basic cell model with simple elastic coupling between front and rear, which exhibits stable, steady forward crawling after initial transient oscillations have decayed, and a poroelastic model, which can exhibit oscillatory crawling in the steady state.

A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line

“…Hypothesis (1) ensures that this proof holds both for repulsion and lateral inhibition effects. If N ≤ 4 the statement is true thanks to hypothesis (2). If N ≥ 6 from (4.4), (4.5), and (4.6) we have Now, in order to fix the range of variability for some parameters we solve the nondimensional system (4.1) for a N -rosette with a leader in X L , setting a frame centered X L with axes passing through the center of a follower (Figure 4.1 (b)).…”

“…About alignment effects, we base our description on the seminal paper by F. Cucker and S. Smale [9], while for the attractionrepulsion effects we refer to the mechanism introduced by D'Orsogna et al [10]; both effects are considered by [1]. Finally, we introduce a damping term, proportional to the velocities, which models cell adhesion to the substrate [36,14,2].…”

Simple model of cell crawling

“…We have chosen the direction of deformation forces as eqs. (19)- (22). It is mentioned here briefly that what happens if one uses the relations (23)- (26).…”

Effects of Adhesion Dynamics and Substrate Compliance on the Shape and Motility of Crawling Cells

“…Even less established are the effects of substrate stiffness, which so far have been accounted for only in highly simplified mechanistic models [12], [13], and on the level of force-velocity relations. Due to the complexity of the cellular adhesion mechanism [14], it is obvious that specific questions like mechano-sensitivity [15], or complex motility modes like stick-slip motion occurring e.g.…”