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Stability of MultiComponent Biological Membranes

Givli, Sefi and Giang, Ha and Bhattacharya, Kaushik (2012) Stability of MultiComponent Biological Membranes. SIAM Journal on Applied Mathematics, 72 (2). pp. 489-511. ISSN 0036-1399.

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Equilibrium equations and stability conditions are derived for a general class of multicomponent biological membranes. The analysis is based on a generalized Helfrich energy that accounts for geometry through the stretch and curvature, the composition, and the interaction between geometry and composition. The use of nonclassical differential operators and related integral theorems in conjunction with appropriate composition and mass conserving variations simplify the derivations. We show that instabilities of multicomponent membranes are significantly different from those in single component membranes, as well as those in systems undergoing spinodal decomposition in flat spaces. This is due to the intricate coupling between composition and shape as well as the nonuniform tension in the membrane. Specifically, critical modes have high frequencies unlike single component vesicles and stability depends on system size unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We show that the predictions of the analysis are in qualitative agreement with experimental observations.

Item Type:Article
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Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 2012 Society for Industrial and Applied Mathematics. Received April 18, 2011; Accepted December 28, 2011; Published online March 01, 2012. This work was supported by the U.S. National Science Foundation (DMS060667). This work began when SG held a position at the California Institute of Technology.
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Subject Keywords:stability; membrane; biological; spherical; heterogeneous
Issue or Number:2
Classification Code:AMS subject classifications: 74K25, 92C05, 49Q10
Record Number:CaltechAUTHORS:20120518-095511348
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Official Citation:Stability of MultiComponent Biological Membranes Sefi Givli, Ha Giang, and Kaushik Bhattacharya, SIAM J. Appl. Math. 72, 489 (2012), DOI:10.1137/110831301
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31535
Deposited By: Jason Perez
Deposited On:18 May 2012 21:05
Last Modified:03 Oct 2019 03:52

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