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.
Highlights
Cell motility is based on different biological events and pathological processes
In this regard, understanding the forces between the cells and substrates responsible for cell motility allows the underlying of many pathological processes and holds promise for designing novel engineered materials for tissue engineering and regenerative medicine [1,2,3]
We present a critical stress two-step walking model for the cell motility, which is of great interest to scientists dealing with tissue engineering and nanomedicine
Summary
Cell motility is based on different biological events and pathological processes. In this regard, understanding the forces between the cells and substrates responsible for cell motility allows the underlying of many pathological processes and holds promise for designing novel engineered materials for tissue engineering and regenerative medicine [1,2,3]. According to Mitchison and Cramer [9] the motility of ameboid cells includes four different steps of protrusion, attachment to substrate, translocation of cell body, and detachment of its rear. More recently Gracheva and Othmer [16] developed a continuum model for the cell as a viscoelastic material They studied the spatial variability of elasticity and viscosity coefficients in addition to the gradient in physical characteristics of the substrate. The motility of ameboid cells includes four steps of protrusion, adhesion to substrate, cell body movement and detachment of cell tail. As it is seen in this figure, the cell front moves while the rear is attached to the substrate. By setting the strain equation, du/dx, in eq 2, and substituting eq 2 in eq 7, eq 8 and eq 9, and discretizing with finite difference method, the equation of motion becomes:
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