Transport phenomena in fluid films with curvature elasticity

Abstract

Abstract

Curvature-driven feedback on aggregation-diffusion of proteins in lipid bilayers

“…We first formulate the governing equations for coupled diffusion and aggregation of curvature-inducing proteins on a deformable viscous lipid membrane with bending elasticity, building on previous models [12,24,25]. We begin by formulating a free energy function for the membrane and apply the principle of energy minimization to derive the governing equations.…”

“…Here, H and K are mean and Gaussian curvatures of the membrane, κ andκ are the bending and Gaussian rigidities, and C is the spontaneous curvature induced by the proteins. The spontaneous curvature is assumed to depend linearly on protein density σ [12,25] as…”

“…The lipid bilayer is modeled as a two-dimensional surface, ω, in a three-dimensional space (Figure 1b). We refer the reader to [12,24,28] for details of the derivation and briefly summarize the key steps here. The surface is parametrized by a position vector r(θ α , t), where θ α are the surface coordinates, α ∈ {1, 2}.…”

“…Here, p is the normal pressure acting on the surface, ζ βα and M αβ are the elastic stress and moment tensors, and π βα is the viscous stress tensor. The elastic stress and moment tensors can be obtained from the energy density for an incompressible membrane as [12,28] ζ…”

“…In addition to protein aggregation, in-plane viscous flow of the lipid molecules has been found to dominate some of the phase-transition kinetics of vesicle shapes [11]. Recently, we showed that the interaction of membrane bending, protein diffusion, and lipid flow can lead to an aggregation-like configuration on the membrane [12].…”