A critical stress model for cell motility
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RESEARCH
Open Access
A critical stress model for cell motility Mehrnush Mehrayin1, Farhad Farmanzad1, Masoud Mozafari2, Daryoosh Vashaee3 and Lobat Tayebi2,4* * Correspondence: [email protected] 2 Helmerich Advanced Technology Research Center, School of Material Science and Engineering, Oklahoma State University, Tulsa, OK 74106, USA 4 School of Chemical Engineering, Oklahoma State University, Stillwater, OK 74078, USA Full list of author information is available at the end of the article
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. Keywords: Finite difference, Cell motility, Continuum model, Critical stress
Introduction 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 not only allows the underlying of many pathological processes but also holds promise for designing novel engineered materials for tissue engineering and regenerative medicine [1-3]. Migration involves different coordinated events such as protrusion of pseudopodia, formation of new adhesions, maturation of traction, and release of old adhesions [4]. To obtain suitable physiological effects, cell motility must maintain a specific speed and direction in response to environment stimuli. As a challenging issue, migration control by gradients of dissolved and surface-attached chemicals has been investigated for decades [5-8]. The motility of different cells involves
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