Abstract
Several experimental studies demonstrate that controlled substrate micro-patterning has a significant impact on cell behaviour. Several experiments reveal cell spread area is dependent on both substrate rigidity and ligand density. The biomechanisms underlying such observations are not fully understood. We demonstrate that a thermodynamically consistent statistical mechanics model explains several of the key phenomena observed experimentally. We implement a steady-state thermodynamically consistent framework for stress-fibre formation and focal adhesion assembly. A Markov chain Monte-Carlo (MCMC) methodology is used to compute the distribution of cell spread states for a given substrate ligand density and stiffness. Several million spread states are considered by imposing a sequence of random trial moves on the cell. For each spread state, we compute quantities such as the cytoskeletal protein distribution, SF orientation, and FA distribution via a mixed finite element/boundary element method scheme. The free energy of all accepted states averaged equates to the homeostatic free energy. Following completion of the MCMC scheme we can construct the probability distribution for an observable of interest. For cells on a rigid substrate both the mean spread area and SD increase as the collagen density increases. A peak spread area is observed at a collagen density of 300 ng.cm-2, with an area A/A0≅2.7. Further increases in collagen density lead to a reduction in cell area, motivated by focal adhesion free energy. On a compliant elastic substrate, lower spread areas are observed (peak A/A0≅1.8). Our computed dependence of spread area on substrate stiffness and ligand density has been observed experimentally.
