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

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.

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https://doi.org/10.1038/s41598-018-31251-6