Analytical and Computational Studies of Compositional Lipid Microdomains in Bilayer Membranes

Abstract

In this dissertation, we both analytically and computationally investigate several dynamic problems related to compositional lipid microdomains in model bilayer membranes. We utilize continuum diffuse-interface methods as the computational framework, and develop the corresponding sharp interface limit equations to facilitate analytical derivations. The model possesses a complicated coupling structure, which involves not only the thermodynamic and frictional coupling between the two leaflets of the membrane, but also between the membrane itself and the solvent outside.

In the compositional domain registration project, we investigate interleaflet thermodynamic and frictional coupling effects on both the recurrence of domain registration and shear flow driven domain de-registration dynamics. Analytical predictions for the approaching speed and threshold flow velocity are provided, accounting for both diffusive and advective transport mechanisms. It is proposed that these results would enable an experimental measurement of the interleaflet coupling strength.

In the compositional interface fluctuation relaxation project, we consider the frictional coupling between both the two leaflets and between the membrane and solvent outside. For symmetric membranes, a general dispersion relation between decay rate versus wavenumber is derived. Various factors are incorporated in the analysis, including diffusive and advective lipid transport processes, inertia and viscosity of both membrane and solvent, and finite thickness of solvent. All previously considered scenarios naturally emerge as limiting cases of our more general result, and two new scenarios are obtained as well, which are solvent inertia dominated and membrane viscoelasticity dominated cases, respectively. For asymmetric membranes, a new scaling behavior is derived, due to the interleaflet friction effect.

Finally, we explore the phase behaviors in spherical vesicles, under the thermodynamic coupling between membrane and inner solvent, by again employing a diffuse-interface approach. As two preliminary applications, we apply the model to numerically study the wetting transition in the system with a simple membrane coupled with a complex solvent, and phase co-localization in a system with phase-separated solvent and membrane. The numerical results qualitatively agree with experimental observations.