https://doi.org/10.1140/epjs/s11734-023-00963-w
Regular Article
Persistent random walks: a unified theory for durotaxis and negative durotaxis
CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, CAS Center for Excellence in Complex System Mechanics, University of Science and Technology of China, 230026, Hefei, Anhui, China
Received:
30
May
2023
Accepted:
10
August
2023
Published online:
1
September
2023
Living cells display various directed motility in response to rigidity gradients of extracellular matrix. Some cells move preferentially toward stiff matrix (durotaxis), while some cells move preferentially toward soft matrix (negative durotaxis). Understanding these seemingly contradictory observations is vital to our understanding of directed cell migration. Here, we resolve this discrepancy based on persistent random walks. Using 2D stochastic simulations, we show that, regardless of the relationship between migration speed and substrate rigidity, a biphasic dependence of the persistence time of cell motion on rigidity alone is sufficient to generate both durotaxis and negative durotaxis. However, a rigidity-independent persistence time results in random cell motion, even though the migration speed is rigidity-dependent. By further developing a simple 1D continuum theory, we verify the main results of 2D stochastic simulations and show that the directed cell motility results from wavelike transport of cells on the more persistent side. Our work, thus, reconciles durotaxis and negative durotaxis into a unified theoretical framework. As persistent random walks are similar across all domains of life, this mechanism could be relevant to a large class of systems and directed motions.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjs/s11734-023-00963-w.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
