Influence of Substrate Stiffness and Thickness on Cell Traction Forces

Abstract

It is known that various cell types can sense and respond to the mechanical properties of their microenvironment. Specifically, cells have been known to spread more when cultured on stiff substrates [1-3] and are able to match their internal stiffness to that of the substrate [2, 3]. Recent works have reported on dynamics of cellular properties such as cell shape, cell spread area, and focal adhesion area, as functions of environmental properties such as substrate stiffness, thickness, and chemistry. Building on earlier models [4, 5, 6], we present mathematical models that enable us to replicate some aspects of experimentally reported time-dependent cell behavior. Our models investigate the adaptation of internal cell stiffness through increase in number of focal adhesion complexes and temporal build-up of traction force. Our models crucially invoke the ability of some cell types to adapt their internal stiffness and show that substrate stiffness and thickness can strongly assist in rapid build-up of traction forces and formation of multiple cooperative focal adhesion complexes. Further using our models we generate some mechanistic insights into why certain cell types under the influence of specific substrate properties exhibit the kind of dynamics that has been experimentally reported. We attempt to establish correlation between the mechanistic models presented here and an earlier heuristic model that we have developed [6].Reference:1. R. J. Pelham, Jr., and Y. L. Wang, Proc. Natl. Acad. Sci. USA, 94, 13661 (1997).2. J. Solon et al, Biophys. J., 93, 4453 (2007).3. S. Tee et al, Biophys. J., 100, L25 (2011).4. U. S. Schwarz et al, Biosystems, 83, 225 (2006).5. J. M. Maloney et al, Phys. Rev. E, 78, 041923 (2008).6. S. Raghavan, A. R. Rammohan, and M. Hervy, Open J. Biophys, 3, (2013).