A lipid membrane morphology subjected to intra-membrane viscosity and membrane thickness dilation

We study morphological transitions of lipid membrane under the presence of the intra-surface viscous flow and membrane thickness dilation using a two-dimensional-based continuum model of Helfrich type. The effects of intra-membrane viscosity and membrane distension are simultaneously formulated into the model of continuum deformation based on the dimension reduction procedure applied to three-dimensional liquid crystal theory. The admissible set of boundary conditions is taken from the existing model yet reformulated into the present context for the sake of completeness. Among other interesting features, the proposed model predicts the off-centred protrusion of the lipid membrane when it is subjected to both local inflammation and intra-surface viscous flow. In addition, the substrate-interaction force may invoke local bending effects on membrane, resulting in thickness reduction in the vicinity of the substrate. Lastly, the obtained results are cross-examined with coarse-grained molecular dynamics simulations which demonstrate reasonable consistency in the predictions of membrane morphology and thickness dilation.