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Transport phenomena in fluid films with curvature elasticity

Published online by Cambridge University Press:  23 October 2020

Arijit Mahapatra Open the ORCID record for Arijit Mahapatra [Opens in a new window] ,
David Saintillan Open the ORCID record for David Saintillan [Opens in a new window]  and
Padmini Rangamani Open the ORCID record for Padmini Rangamani [Opens in a new window]
Arijit Mahapatra
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA
David Saintillan
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA
Padmini Rangamani*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA92093, USA
*
†Email address for correspondence: prangamani@ucsd.edu
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Abstract

Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins and elastic deformation of lipid bilayers. The proteins in the membrane are modelled such that they influence membrane bending by inducing a spontaneous curvature. We formulate the free energy of the membrane with a Helfrich-like curvature elastic energy density function modified to account for the chemical potential energy of proteins. We derive the conservation laws and equations of motion for this system. Finally, we present results from dimensional analysis and numerical simulations and demonstrate the effect of coupled transport processes in governing the dynamics of membrane bending and protein diffusion.

JFM classification

Biological Fluid Dynamics: Membranes Interfacial Flows (free surface): Thin films Biological Fluid Dynamics: Capsule/cell dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 905 , 25 December 2020 , A8
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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