Effect of integral proteins in the phase stability of a lipid bilayer: Application to raft formation in cell membranes

We investigate diffusion-limited reactions between a diffusing particle and a target site on a semiflexible polymer, a key factor determining the kinetics of DNA-protein binding and polymerization of cytoskeletal filaments. Our theory focuses on two competing effects: polymer shape fluctuations, which speed up association, and the hydrodynamic coupling between the diffusing particle and the chain, which slows down association. Polymer bending fluctuations are described using a mean field dynamical theory, while the hydrodynamic coupling between polymer and particle is incorporated through a simple heuristic approximation. We validate both of these through comparison to Brownian dynamics simulations. Neither of the effects has been fully considered before in the biophysical context and we show they are necessary to form accurate estimates of reaction processes. The association rate depends on the stiffness of the polymer and the particle size, exhibiting a maximum for intermediate persistence length and a minimum for intermediate particle radius. In the parameter range relevant to DNA-protein binding, the rate increase is up to 100% compared with the Smoluchowski result for simple center-of-mass motion. The quantitative predictions made by the theory can be tested experimentally.