Correlating Simulation and Experimental Data of Traction and Cell Speed as Functions of Substrate Stiffness

The mechanical interactions between cells and the extra cellular matrix (ECM) play important roles in many biological processes, including cell proliferation, migration, and differentiation. The cells can probe the stiffness of the ECM and alter their own function accordingly. The objective of this study was to investigate the applicability of a mathematical model by comparing the simulation results generated by the model with published experimental results for the migration of fibroblast, smooth muscle, and glioma cells on substrates. Cell -- substrate traction was assumed to be a nonlinear function of the Young´s modulus of the substrate. Simulation parameters were determined so that the tractions and cell speeds agreed with the experimental results. It was shown that the mathematical model could predict the fibroblast migration speed by increasing the Young´s modulus of the cell with that of the substrate. Simulation results showed that the smooth muscle cell speed exhibited a biphasic relationship with respect to the substrate stiffness for two fibronectin concentrations, where the limit of elasticity sensing decreased as the fibronectin concentration increased. The numerical results also predicted that the glioma cell migration speed increased with the substrate stiffness. This mathematical model could be used to predict the experimental data for the migration of these different cell types, and is particularly suited for modeling the smooth muscle and glioma cells.