Shape dynamics and lipid hydrodynamics of bilayer membranes: modeling, simulation and experiments
Authors:   , Rahmi Mohammad 
Published: October 2023

Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. The dynamics of lipid membranes are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, the rearrangement of the lipid molecules, and their interactions with adjacent structures. The main goal of the present work is to understand the dynamical shape deformations and reorganizations of lipid bilayers, including lipid hydrodynamics, and the mechanical shaping and stabilization of highly curved membrane structures. Towards this goal, we develop theory, simulation methods, and perform experiments.
We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its mid-surface and by a lipid density field for each monolayer. In this model, the viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the intermonolayer friction and the membrane interfacial shear viscosity. In contrast with previous studies, our numerical approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We apply our model to describe the dynamics of biologically relevant experimental observations, which are insufficiently understood through simpler models introducing geometrical and physical simplifications. We study the dynamical formation of membrane tubes, followed by pearling instabilities, as a consequence of a localized density asymmetry, the tubular lipid transport between cells, the dynamics of bud absorption, and the very recently observed protrusions out of planar confined bilayers. The passive formation of stable highly curved protrusions in confined bilayers suggests that mechanics plays a role in the morphogenesis and homeostasis of complex organelles (e.g., endoplasmic reticulum, or mitochondrial cristae), in addition to the widely accepted role of proteins and the regulation of lipid composition. We also study experimentally and theoretically the shape transformations and membrane reorganizations of model membranes upon the adsorption of cholesterol, a ubiquitous constituent of biomembranes, which regulates their structural and mechanical properties. Our observations offer new insights into the reorganizations of macrophages and the formation of foam cells as a consequence of the cholesterol elevation in vessel walls.
In this thesis, we have payed particular attention to the membrane fluidity and the influence of the membrane viscosity in the bilayer dynamics. The role of the membrane interfacial viscosity is often ignored due to its minor role in the linearized equations about planar states. We challenge this assumption, show theoretically that membrane viscosity plays an important role in the presence of high curvature, and show its effect on the membrane fluctuations of quasi-spherical vesicles and tubular membranes.