Finite Membrane Thickness Influences Hydrodynamics on the Nanoscale

Abstract

Many lipid membrane-mediated transport processes--such as mechanically-gated channel activation and solute transport--involve structural and dynamical features on membrane thickness length scales. Most existing membrane models, however, tend to adopt (quasi-)two-dimensional descriptions that neglect thickness-dependent phenomena relevant to internal membrane mechanics, and thus do not fully account for the complex coupling of lipid membranes with their surrounding fluid media. Therefore, explicitly incorporating membrane thickness effects in lipid membrane models will enable a more accurate description of the influence of membrane/fluid coupling on transport phenomena in the vicinity of the bilayer surfaces. Here, we present a continuum model for membrane fluctuations that accounts for finite membrane thickness and resolves hydrodynamic interactions between the bilayer and its surrounding fluid. By applying linear response analysis, we observe that membrane thickness-mediated effects, such as bending-induced lipid reorientations, can generate shear flows close to the membrane surface that slow down the relaxation of nanometer scale shape fluctuations. Additionally, we reveal the emergence of pressure inversion and flow reversal near the membrane interfaces, accompanied by localized stagnation points. Among these, extensional stagnation points give rise to a novel mode of bulk dissipation, originating from bending-induced compression and expansion of the membrane surfaces and their coupling to shear stresses in the fluid. Our findings identify membrane thickness as a key factor in nanoscale hydrodynamics and suggest that its effects may be detectable in fluctuation spectra and can be relevant to interfacial processes such as solute permeability and contact with solid boundaries or other membranes.