Diffusion and swelling in a bio-elastic cylinder.

An analysis is presented of the equilibrium response of a radially deformed cylinder of isotropic, incompressible bio-elastic material swollen by an infused liquid satisfying a static diffusive balance law.

Small scale membrane mechanics.

Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or 'tilt', as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5-6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.

Interaction between surface shape and intra-surface viscous flow on lipid membranes.

The theory of intra-surface viscous flow on lipid bilayers is developed by combining the equations for flow on a curved surface with those that describe the elastic resistance of the bilayer to flexure. The model is derived directly from balance laws and augments an alternative formulation based on a variational principle. Conditions holding along an edge of the membrane are emphasized, and the coupling between flow and membrane shape is simulated numerically.

Modeling protein-mediated morphology in biomembranes.

The equilibrium theory for lipid membranes is used to describe the structure of nuclear pores and the membrane shapes accompanying endocytosis. The commonly used variant of the theory contains a fixed parameter called the spontaneous curvature which accounts for asymmetry in the bending response of the membrane. This is replaced here by a variable distribution of spontaneous curvature representing the influence of attached proteins. The required adjustments to the standard theory are described and the resulting model is applied to the study of membrane morphology at the cites of protein-assisted nuclear pore formation and endocytosis.