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Cell Shape and Durotaxis Follow from Mechanical Cell-Substrate Reciprocity and Focal Adhesion Dynamics: A Unifying Mathematical Model

49 Pages Posted: 9 Apr 2020 Sneak Peek Status: Under Review

See all articles by Elisabeth G. Rens

Elisabeth G. Rens

University of British Columbia (UBC) - Department of Mathematics

Roeland M. H. Merks

Leiden University - Institute of Biology

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Abstract

Many cells assume small, rounded shapes when cultured on soft extracellular matrices (ECM), elongate on stiffer ECMs, and flatten out on hard ECMs. Also, cells tend to move up stiffness gradients, a phenomenon known as durotaxis.  It is well established that such behavior can be explained from the dynamics of focal adhesions (FAs), but current mathematical models cannot explain the full range of behaviors in unison. Here we unify the three phenomena into a novel multiscale computational model, based on the following observations: (1) cells apply forces onto the ECM through FAs; (2) the FAs grow and stabilize due to these forces; (3) within a given time-interval, the force that the FAs experience is lower on soft ECMs than on stiffer ECMs; and (4) smaller FAs are pulled from the ECM more easily than larger FAs. We show that these assumptions suffice for stiffness-dependent cell spreading, cell elongation, and durotaxis.

Keywords: cell shape, cell spreading, Cell migration, extracellular matrix, mechanobiology, durotaxis, focal adhesions, cell-based modeling, Cellular Potts Model

Suggested Citation

Rens, Elisabeth G. and Merks, Roeland M. H., Cell Shape and Durotaxis Follow from Mechanical Cell-Substrate Reciprocity and Focal Adhesion Dynamics: A Unifying Mathematical Model. ISCIENCE-D-20-00471. Available at SSRN: https://ssrn.com/abstract=3569534 or http://dx.doi.org/10.2139/ssrn.3569534
This is a paper under consideration at Cell Press and has not been peer-reviewed.

Elisabeth G. Rens

University of British Columbia (UBC) - Department of Mathematics ( email )

1984 Mathematics Road
Vancouver, British Columbia V6T 1Z2
Canada

Roeland M. H. Merks (Contact Author)

Leiden University - Institute of Biology ( email )

Sylvius Laboratory, Sylviusweg 72
Leiden, 2333 BE
Netherlands

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