The Effects of Intra-membrane Viscosity on Lipid Membrane Morphology: Complete Analytical Solution

Mahdi Zeidi,Chun Il Kim

doi:10.1038/s41598-018-31251-6

Abstract

We present a linear theory of lipid membranes which accommodates the effects of intra-membrane viscosity into the model of deformations. Within the Monge parameterization, a linearized version of the shape equation describing membrane morphology is derived. Admissible boundary conditions are taken from the existing non-linear model but reformulated and adopted to the present framework. We obtain a complete analytical expression illustrating the deformations of lipid membrane subjected to the influences of intra-membrane viscosity. The result predicts wrinkle phenomena in the event of membrane-substrate interactions. Finally, we mention that the obtained solutions reduce to those from the classical shape equation when the viscosity effects are removed.

Highlights

In the present work, we reformulate the non-linear governing equations of membranes directly from the membrane free-energy density function within the frame work of tensor analysis of surfaces
Effects when a rectangular portion of membranes is subjected to intra-membrane viscous flow
The result is aligned with the numerical study conducted under the compatible settings9

Summary

Viscosity on Lipid Membrane

We present a linear theory of lipid membranes which accommodates the effects of intra-membrane viscosity into the model of deformations. Due to the delicate and complex nature of lipid membranes, the study of the various mechanical responses of lipid bilayers can be, most often, practiced with the use of an artificial ‘model’ This includes the development of continuum-based models in the description of the behavior of lipid bilayers, typically based on the Cosserat theory of elastic surfaces (see, and the reference therein). Within this context, the work in reveals that intra-membrane viscosity has considerable effects on the deformation of lipid membranes. While Eq [25] remains and [20], we find intact

From the incompressibility condition

Monge Representation and Superposed Incremental Deformations

4Aν k and

Cm sin mθ

Additional Information