Volume 62, 2018CIMPA School on Mathematical Models in Biology and Medicine
|Page(s)||56 - 67|
|Published online||17 October 2018|
A Stochastic Model For Protrusion Activity
MAP5, CNRS UMR 8145, Université Paris Descartes, 45 rue des Saints Pères 75006 Paris, France.
2 MAP5, CNRS UMR 8145, Université Paris Descartes, 45 rue des Saints Pères 75006 Paris, France.
In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics , we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration.
© EDP Sciences, SMAI 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.