Superposition of Substrate Deformation Fields Induced by Molecular Clutches Explains Cell Spatial Sensing of Ligands

Cells can sense the physical properties of the extracellular matrices (ECMs), such as stiffness and ligand density, through cell adhesions to actively regulate their behaviors. Recent studies have shown that varying ligand spacing of ECMs can influence adhesion size, cell spreading, and even stem cell differentiation, indicating that cells have the spatial sensing ability of ECM ligands. However, the mechanism of the cells' spatial sensing remains unclear. In this study, we have developed a lattice-spring motor-clutch model by integrating cell membrane deformation, the talin unfolding mechanism, and the lattice spring for substrate ligand distribution to explore how the spatial distribution of integrin ligands and substrate stiffness influence cell spreading and adhesion dynamics. By applying the Gillespie algorithm, we found that large ligand spacing reduces the superposition effect of the substrate's displacement fields generated by pulling force from motor-clutch units, increasing the effective stiffness probed by the force-sensitive receptors; this finding explains a series of previous experiments. Furthermore, using the mean-field theory, we obtain the effective stiffness sensed by bound clutches analytically; our analysis shows that the bound clutch number and ligand spacing are the two key factors that affect the superposition effects of deformation fields and, hence, the effective stiffness. Overall, our study reveals the mechanism of cells' spatial sensing, i.e., ligand spacing changes the effective stiffness sensed by cells due to the superposition effect of deformation fields, which provides a physical clue for designing and developing biological materials that effectively control cell behavior and function.