Diffusion of clusters of transmembrane proteins as a model of focal adhesion remodeling.

Focal adhesions play a major role in maintaining the cell shape and motility, and in regulating numerous cellular processes. Observations suggest that the functioning of focal adhesions is possible due to their dynamic nature, yet the mechanisms that govern their motion are not well understood. This study addresses the process of focal adhesion remodeling using two distinct theoretical approaches. Namely, adhesion sites are modeled as clusters of integrins that are either bound to cytoskeletal elements or dissociated and temporarily free of any attachments. In the first approach effects of cluster size and permeability on the diffusion of mobile adhesion structures are studied using Brinkman's effective medium approach. Diffusion coefficients calculated by this hydrodynamic model significantly decrease with the increase in contact area (the effective size of the focal adhesion). In the second approach focal adhesions are modeled as clusters of transmembrane proteins tightly connected to the cytoskeleton, but still capable of motion. The remodeling of these clusters is coupled to the deformation of the cytoskeleton by means of equating energies at the end states of a reversible elastodynamic interaction. Due to large uncertainty of the plasma membrane and the cytoskeleton properties, predicted diffusion coefficients vary within several orders of magnitude. However, a reasonable set of parameters for each model yields diffusion coefficients that compare favorably with those measured by single-particle tracking (SPT), fluorescence recovery after photobleaching (FRAP), and fluorescence digital imaging (FDI). The estimated Young's modulus of the stress fibers is also in good agreement with measurements. To assess the relevance of the models to focal adhesion remodeling and to improve their predictions, further data on the morphology of focal adhesions and on properties of the plasma membrane and the cytoskeleton are required.