Thermodynamic Modeling of the Statistics of Cell Spreading on Ligand-Coated Elastic Substrates

Biological spread cells exist in a perpetually fluctuating state and therefore cannot be described in terms of a unique deterministic system. For modeling approaches to provide novel insight and uncover new mechanisms that drive cell behavior, a framework is required that progresses from traditional deterministic methods (whereby simulation of an experiment predicts a single outcome). In this study, we implement a new, to our knowledge, modeling approach for the analysis of cell spreading on ligand-coated substrates, extending the framework for nonequilibrium thermodynamics of cells developed by Shishvan et al. to include active focal adhesion assembly. We demonstrate that the model correctly predicts the coupled influence of surface collagen density and substrate stiffness on cell spreading, as reported experimentally by Engler et al. Low surface collagen densities are shown to result in a high probability that cells will be restricted to low spread areas. Furthermore, elastic free energy induced by substrate deformation lowers the probability of observing a highly spread cell, and, consequentially, lower cell tractions affect the assembly of focal adhesions. Experimentally measurable observables such as cell spread area and aspect ratio can be directly postprocessed from the computed homeostatic ensemble of (several million) spread states. This allows for the prediction of mean and SDs of such experimental observables. This class of cell mechanics modeling presents a significant advance on conventional deterministic approaches.