Stability of MultiComponent Biological Membranes

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.

[1]  P. Sluijs,et al.  How proteins move lipids and lipids move proteins , 2001, Nature Reviews Molecular Cell Biology.

[2]  W. Helfrich.  Elastic Properties of Lipid Bilayers: Theory and Possible Experiments , 1973, Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie.

[3]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[4]  E. Zeidler.  Nonlinear functional analysis and its applications , 1988 .

[5]  殷雅俊.  Integral Theorems Based on a New Gradient Operator Derived from Biomembranes （Part I）： Fundamentals , 2005 .

[6]  M. Sheetz,et al.  Local force and geometry sensing regulate cell functions , 2006, Nature Reviews Molecular Cell Biology.

[7]  Axel Voigt,et al.  Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Yajun Yin,et al.  The Second Gradient Operator and Integral Theorems for Tensor Fields on Curved Surfaces , 2007 .

[9]  Sarah L Veatch,et al.  Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. , 2003, Biophysical journal.

[10]  Dynamics of shape fluctuations of quasi-spherical vesicles revisited , 2002, The European physical journal. E, Soft matter.

[11]  Lin Ma,et al.  Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics , 2007, J. Comput. Phys..

[12]  Yajun Yin,et al.  Shape equations and curvature bifurcations induced by inhomogeneous rigidities in cell membranes. , 2005, Journal of biomechanics.

[13]  R. Lipowsky,et al.  Domain-induced budding of vesicles. , 1993, Physical review letters.

[14]  David Andelman,et al.  Equilibrium shape of two-component unilamellar membranes and vesicles , 1992 .

[15]  L. Freund,et al.  Growth and shape stability of a biological membrane adhesion complex in the diffusion-mediated regime. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Rob Phillips,et al.  Membrane-protein interactions in mechanosensitive channels. , 2004, Biophysical journal.

[17]  W. Helfrich,et al.  Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. , 1989, Physical review. A, General physics.

[18]  Eduardo Perozo,et al.  Structure and mechanism in prokaryotic mechanosensitive channels. , 2003, Current opinion in structural biology.

[19]  D. Boal.  Mechanics of the Cell: Membranes , 2012 .

[20]  D. Ingber,et al.  Cellular mechanotransduction: putting all the pieces together again , 2006, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[21]  Paul A. Wiggins,et al.  Emerging roles for lipids in shaping membrane-protein function , 2009, Nature.

[22]  Donald E. Ingber,et al.  Tensegrity-based mechanosensing from macro to micro. , 2008, Progress in biophysics and molecular biology.

[23]  R Skalak,et al.  Mechanics and thermodynamics of biomembranes: part 1. , 1979, CRC critical reviews in bioengineering.

[24]  D Stamenović,et al.  Invited review: engineering approaches to cytoskeletal mechanics. , 2000, Journal of applied physiology.

[25]  James H. Davis,et al.  Phase equilibria of cholesterol/dipalmitoylphosphatidylcholine mixtures: 2H nuclear magnetic resonance and differential scanning calorimetry. , 1990, Biochemistry.

[26]  Grischa R. Meyer,et al.  Mechanosensitive channel of large conductance. , 2008, The international journal of biochemistry & cell biology.

[27]  Naito,et al.  Preferred equilibrium structures of a smectic-A phase grown from an isotropic phase: Origin of focal conic domains. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Petra Schwille,et al.  Probing Lipid Mobility of Raft-exhibiting Model Membranes by Fluorescence Correlation Spectroscopy* , 2003, Journal of Biological Chemistry.

[29]  J. Stoker.  Differential Geometry: Stoker/Differential , 1988 .

[30]  General Mathematical Frame for Open or Closed Biomembranes: Stability Theory Based on Differential Operators , 2007 .

[31]  M. Coroneo,et al.  Stretch‐activated channels: a mini‐review. Are stretch‐activated channels an ocular barometer? , 2005, Clinical & experimental ophthalmology.

[32]  Udo Seifert,et al.  Configurations of fluid membranes and vesicles , 1997 .

[33]  A. Boulbitch.  Equations of heterophase equilibrium of a biomembrane , 1999 .

[34]  C Zhu,et al.  Cell mechanics: mechanical response, cell adhesion, and molecular deformation. , 2000, Annual review of biomedical engineering.

[35]  W. Webb,et al.  Membrane elasticity in giant vesicles with fluid phase coexistence. , 2005, Biophysical journal.

[36]  Frederick Sachs,et al.  Energetic and Spatial Parameters for Gating of the Bacterial Large Conductance Mechanosensitive Channel, MscL , 1999, The Journal of general physiology.

[37]  Yajun Yin,et al.  General Mathematical Frame for Open or Closed Biomembranes (Part I): Equilibrium Theory and Geometrically Constraint Equation , 2005, Journal of mathematical biology.

[38]  Feng Feng,et al.  Finite element modeling of lipid bilayer membranes , 2006, J. Comput. Phys..

[39]  D. Engelman.  Membranes are more mosaic than fluid , 2005, Nature.

[40]  Charles M. Elliott,et al.  A Surface Phase Field Model for Two-Phase Biological Membranes , 2010, SIAM J. Appl. Math..

[41]  Watt W. Webb,et al.  Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension , 2003, Nature.

[42]  S. Leibler,et al.  Curvature instability in membranes , 1986 .

[43]  Nir S Gov,et al.  Phase transitions of the coupled membrane-cytoskeleton modify cellular shape. , 2007, Biophysical journal.

[44]  Q. Du,et al.  A phase field approach in the numerical study of the elastic bending energy for vesicle membranes , 2004 .

[45]  Mechanical stability of micropipet-aspirated giant vesicles with fluid phase coexistence. , 2008, The journal of physical chemistry. B.

[46]  P. Sens,et al.  Biophysical approaches to protein-induced membrane deformations in trafficking. , 2008, Current opinion in cell biology.

[47]  Seifert,et al.  Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models. , 1991, Physical review. A, Atomic, molecular, and optical physics.