On Curvature Driven Rotational Diffusion of Protein on Membrane Surface
This work provides a foundational theoretical model for understanding how membrane curvature influences protein orientation, relevant to biophysics and cell biology.
The authors developed a theoretical framework coupling membrane curvature to protein rotational diffusion, deriving a generalized Smoluchowskii equation and proving existence/uniqueness of stationary solutions under biologically relevant conditions.
Morphological dynamics of bilayer membrane is intrinsically coupled to the translational and orientational localization of membrane proteins. In this paper we are concerned with the orientational localization of membrane proteins in the absence of protein interaction and correlation. Entropic energy depending on the angular distribution function and the curvature energy depending on the principal curvature vectors are introduced to assemble an energy functional for the coupled system. Application of the Onsager's variational principle gives rise to a generalized Smoluchowskii equation governing the temporal and angular variations of the protein orientation. We prove the existence of the stationary solution of the equation as fixed points of a continuous nonlinear nonlocal map, and for biologically relevant conditions we obtain the uniqueness of the solution. To approximate the stationary solution in the Fourier space we construct an efficient numerical method that reduces the expansion and relates the coefficients to the modified Bessel functions of the first kind. Existence and uniqueness of the numerical solution are justified for biologically relevant conditions.