Curvature-Driven Molecular Flow on Membrane Surface

Abstract

This work presents a mathematical model for the localization of multiple species of diffusion molecules on membrane surfaces. Morphological change of bilayer membrane in vivo is generally modulated by proteins. Most of these modulations are associated with the localization of related proteins in the crowded lipid environments. We start with the energetic description of the distributions of molecules on curved membrane surface, and define the spontaneous curvature of bilayer membrane as a function of the molecule concentrations on membrane surfaces. A drift-diffusion equation governs the gradient flow of the surface molecule concentrations. We recast the energetic formulation and the related governing equations by using an Eulerian phase field description to define membrane morphology. Computational simulations with the proposed mathematical model and related numerical techniques predict (i) the molecular localization on static membrane surfaces at locations with preferred mean curvatures, and (ii) the generation of preferred mean curvature which in turn drives the molecular localization.

Transport phenomena in fluid films with curvature elasticity

“…The advection–diffusion equation (2.23) in our model is also similar to (13) of Mietke et al. (2019), (3.27) of Mikucki & Zhou (2017), (2.12) of Nitschke, Voigt & Wensch (2012) and (4) of Gera & Salac (2017). These studies, however, did not include the strong coupling between bending and diffusion in (2.23), which results from the curvature inducing property of the membrane proteins.…”

“…(2019), the coupling between bending and diffusion occurs through an active tension induced by the proteins. Mikucki & Zhou (2017) calculated the phase field of protein density in an inviscid framework, Nitschke et al. (2012) solved the coupled in place flow and higher-order diffusion equation on a convective surface, while Gera & Salac (2017) solved a Cahn–Hilliard equation on a pre-existing curved surface.…”

“…In the model presented by Mietke et al (2019), the coupling between bending and diffusion occurs through an active tension induced by the proteins. Mikucki & Zhou (2017)…”

Simulation of Multiscale Hydrophobic Lipid Dynamics via Efficient Integral Equation Methods

“…Under hydrophobic attraction and excluded volume repulsion, the particle mixture segregates into two bilayers of more uniform composition. Diffusive interface and level-set approaches have dealt with the problem of mixtures by defining transport equations for each lipid species density [49,55,25].…”

On Curvature Driven Rotational Diffusion of Proteins on Membrane Surfaces

“…While quantitative determination of this dependence using the first principle still remains a grand challenge for biophysicists and mathematicians, geometrical characterization is possible by relating the membrane curvature induced by a single protein to the membrane composition in specific solvation environment and applying this intrinsic curvature of the protein to a distribution of proteins in membrane. The intrinsic mean curvature of the protein is recently defined and used along with the intrinsic mean curvature of lipids to define the intrinsic mean curvature of the lipid-protein complex with varying lipid composition and protein coverage [17]. When the membrane curvature around a protein is different from protein intrinsic curvature, the membrane will deform and the protein will displaced, leading to a dynamic coupling between membrane morphology and protein localization.…”