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One of the most important cellular behaviors is crawling migration. It is observed in many cellular systems both in culture and in vivo and involved in many essential physiological or pathological processes (wound healing, embryonic development, cancer metastasis etc.). Recent studies indicate that cell migration can be achieved without adhesion in confining three-dimensional environments. Increasing levels of confinement seem to favor adhesion-independent migration in many cell types and can trigger transitions from adhesion-based towards low-adhesive migration modes. If in the last decade adhesion-independent migration has emerged as a possibly common migration mode, the mechanisms of cell propulsion in this case are still poorly understood.
We construct a 2-dimensional mathematical model for cells migrating without adhesion capabilities. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. We carry out an existence analysis by adapting ideas from the theory of gradient flows. Numerical simulations showthat these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.
Collaborations
M. Sixt, A. Reversat, G. Jankowiak, C. Schmeiser
Publications
G. Jankowiak , D. Peurichard , A. Reversat , C. Schmeiser , M. Sixt, Modelling adhesion-independent cell migration, Mathematical Models and Methods in Applied Sciences (2020) Vol. 30 (3): 513-537, lien arXiv
Top: Leukocyte (in red) migrating from left to right in a ratchet channel. The channelhas three sections with wavelengths 6m, 12m, and, respectively, 24m. Example of asimulation with our mathematical model using the setting of the experiment.
Numerical simulation of a cell in a ratchet channel of minimal width 1.4 m,amplitude 2.7 m, and variable wave lengths (3.9, 7.6, and 11.7 m), for h 0:1. Bottomleft: initial condition. Top: at time 2h. Bottom right: Speed of the center of gravity vs. time
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