A critical stress model for cell motility

Abstract

A detailed theoretical model that combines the conventional viscoelastic continuum description of cell motion with a dynamic active stress is presented. The model describes the ameboid cells movement comprising of protrusion and adhesion of the front edge followed by detachment and movement of the tail. Unlike the previous viscoelastic descriptions in which the cell movement is steady, the presented model describes the “walking” of the cell in response to specific active stress components acting separately on the front and rear of the cell. In this locomotive model first the tail of the cell is attached to the substrate and active stress is applied to the front of the cell. Consequently, the stress in the tail increases. When the stress in the tail exceeds a critical value, namely critical stress, the conditions are updated so that the front is fixed and the tail of the cell is detached from the substrate and moves towards the front. Consequently, the stress in the tail decreases. When the stress goes to zero, the starting conditions become active and the process continues. At start the cell is stretched and its length is increased as the front of cell migrates more than the rear. However, after several steps the front and rear move equally and the cell length stays constant during the movement. In this manuscript we analyzed such cell dynamics including the length variation and moving velocity. Finally, by considering this fact that at the single-cell level, interactions with the extracellular environment occur on a nanometer length scale, the value of critical stress was estimated.