Analytical Solution of a Model of Integrin-Cytoskeletal Interactions in Migrating Fibroblasts

We demonstrate that an exact analytical solution can be constructed for an intracellular directed transport model ofintegrin developed by Schmidt et al. (1994) The model attempts to mimick the experimental observation that integrin is transported intermittently, by a combination of two-dimensional diffusion and cytoskeleton-mediated convective transport, towards the cell edge In particular, the model assumes stochastic coupling and uncoupling of integrin molecules (described by first-order rate coefficients kc and ku) to a cytoskeletal element moving at a fixed velocity Vo Uncoupled integrins are assumed to undergo isotropic twodimensional diffusion with a diffusion coefficient Do We demonstrate for this model that, in the asymptotic limit of transport over large distances and long times, transport is described by parallel diffusion and convection processes with effective diffusivity D = DOKD/(1+ KD) and effective velocity V = Vo/(1+KD), where KD " ku/kc is an equilibrium constant for decoupling. At shorter times~ the mean-squared displacement cannot be described by superposing diffusion and convection; rather complicated transport arises from dynamical correlations associated with the coupled reaction, diffusion~ and convection