A model explaining environmental stiffness-dependent migration of fibroblasts with a focus on maturation of intracellular structures

Cell migration is fundamental to many biological processes, while it remains elusive how cells modulate their migration upon different environmental stiffness. In this work, we focus on the structural maturity of actin stress fibers to explain the substrate stiffness-dependent emergence of different cell migration velocity. We demonstrate that fibroblasts migrate longer distances on softer elastic substrates, and the distance is increased by lowering the myosin-driven contractile force. Stress fibers, the major intracellular structure to generate and sustain contractile forces, were found to be less mature in structure on soft substrate than on stiff substrate. Based on these experimental results, we present a minimal mathematical model to capture the salient features of how the substrate stiffness alters the migration velocity. Specifically, the ability of cells to generate large contractile forces is limited on soft substrate according to the Hookes law. The inverse relationship between the cellular force and migration velocity is described by the Hills muscle equation. These mathematical descriptions suggest that the migration velocity is raised on softer substrate where cells exert a lower magnitude of contractile forces. Cells undergoing faster movement make stress fibers less mature in structure as mathematically described by the maturation model, thereby limiting the ability to sustain the force and in turn allowing for consistent increase in cell migration velocity on soft substrate again according to the Hookes law and Hills muscle equation, respectively. Thus, our model, reproducing the basic trend of the experimental results, provides insights into the mechanisms of environmental cue-dependent migratory behavior of cells.