Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-23T16:16:02.222Z Has data issue: false hasContentIssue false
  • English
  • Français

Measuring the Spontaneous Curvature of Bilayer Membranes by Molecular Dynamics Simulations

Published online by Cambridge University Press:  03 June 2015

Han Wang ,
Dan Hu  and
Pingwen Zhang
Han Wang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China Institute for Mathematics, Freie Universität Berlin, Berlin, Germany
Dan Hu*
Affiliation:
Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, P.R. China
Pingwen Zhang*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing, P.R. China
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

We propose a mathematically rigorous method to measure the spontaneous curvature of a bilayer membrane by molecular dynamics (MD) simulation, which provides description of the molecular mechanisms that cause the spontaneous curvature. As a main result, for the membrane setup investigated, the spontaneous curvature is proved to be a constant plus twice the mean curvature of the membrane in its tensionless ground state. The spontaneous curvature due to the built-in transbilayer asymmetry of the membrane in terms of lipid shape is studied by the proposed method. A linear dependence of the spontaneous curvature with respect to the head-bead diameter difference and the lipid mixing ratio is discovered. The consistency with the theoretical results provides evidence supporting the validity of our method.

Keywords

87.16.D-82.70.UvBilayer membraneHelfrich free energyspontaneous curvaturemolecular dynamics simulation
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 4 , April 2013 , pp. 1093 - 1106
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Helfrich, W.Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch [C], 28(11):693–703,1973.CrossRefGoogle ScholarPubMed
[2]Steigmann, D.J.On the relationship between the cosserat and kirchhoff-love theories of elastic shells. Mathematics and Mechanics of Solids, 4(3):275–288,1999.Google Scholar
[3]Capovilla, R., Guven, J., and Santiago, J.A.Deformations of the geometry of lipid vesicles. Journal of Physics A: Mathematical and General, 36:6281–6295,2003.Google Scholar
[4]Hu, D., Zhang, P., and W.E. Continuum theory of a moving membrane. Physical Review E, 75(4):41605,2007.CrossRefGoogle ScholarPubMed
[5]Brochard, F. and J.Lennon, F.Frequency spectrum of the flicker phenomenon in erythrocytes. Journal de Physique, 36(11):1035–1047,1975.Google Scholar
[6]Faucon, J.F., Mitov, M.D., Meleard, P., Bivas, I., and Bothorel, P.Bending elasticity and thermal fluctuations of lipid membranes. theoretical and experimental requirements. Journal de Physique, 50(17):2389–2414,1989.Google Scholar
[7]Evans, E. and Rawicz, W.Entropy-driven tension and bending elasticity in condensed-fluid membranes. Physical Review Letters, 64(17):2094–2097,1990.CrossRefGoogle ScholarPubMed
[8]Rawicz, W., Olbrich, K.C., McIntosh, T., Needham, D., and Evans, E.Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophysical Journal, 79(1):328–339,2000.Google Scholar
[9]Cuvelier, D., Derenyi, I., Bassereau, P., and Nassoy, P.Coalescence of membrane tethers: experiments, theory, and applications. Biophysical Journal, 88(4):2714–2726,2005.Google Scholar
[10]Cooke, I.R. and Deserno, M.Solvent-free model for self-assembling fluid bilayer membranes: Stabilization of the fluid phase based on broad attractive tail potentials. The Journal of Chemical Physics, 123:224710,2005.Google Scholar
[11]Goetz, R., Gompper, G., and Lipowsky, R.Mobility and elasticity of self-assembled membranes. Physical Review Letters, 82(1):221–224,1999.Google Scholar
[12]Harmandaris, V.A. and Deserno, M.A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers. The Journal of Chemical Physics, 125:204905, 2006.Google Scholar
[13]Lindahl, E. and Edholm, O.Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophysical Journal, 79(1):426–433,2000.Google Scholar
[14]Marrink, S.J. and Mark, A.E.Effect of undulations on surface tension in simulated bilayers. Journal of Physical Chemistry B, 105(26):6122–6127,2001.CrossRefGoogle Scholar
[15]McMahon, H.T. and Gallop, J.L.Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature, 438:590–596,2005.Google Scholar
[16]Zimmerberg, J. and Kozlov, M.M.How proteins produce cellular membrane curvature. Nature Reviews Molecular Cell Biology, 7(1):9–19,2005.Google Scholar
[17]Frost, A., Unger, V.M., and Camilli, P. DeThe bar domain superfamily: membrane-molding macromolecules. Cell, 137(2):191–196,2009.Google Scholar
[18]Kozlov, M.M.Biophysics: Joint effort bends membrane. Nature, 463(7280):439,2010.CrossRefGoogle ScholarPubMed
[19]Hamai, C., Yang, T., Kataoka, S., Cremer, P.S., and Musser, S.M.Effect of average phospholipid curvature on supported bilayer formation on glass by vesicle fusion. Biophysical Journal, 90(4):1241–1248,2006.Google Scholar
[20]Blood, P.D., Swenson, R.D., and Voth, G.A.Factors influencing local membrane curvature induction by n-bar domains as revealed by molecular dynamics simulations. Biophysical Journal, 95(4):1866–1876,2008.Google Scholar
[21]Campelo, F., McMahon, H.T., and Kozlov, M.M.The hydrophobic insertion mechanism of membrane curvature generation by proteins. Biophysical Journal, 95(5):2325–2339,2008.CrossRefGoogle ScholarPubMed
[22]Blood, P.D. and Voth, G.A.Direct observation of bin/amphiphysin/rvs (bar) domain-induced membrane curvature by means of molecular dynamics simulations. Proceedings of the National Academy of Sciences, 103(41):15068,2006.Google Scholar
[23]Arkhipov, A., Yin, Y., and Schulten, K.Four-scale description of membrane sculpting by bar domains. Biophysical Journal, 95(6):2806–2821,2008.CrossRefGoogle ScholarPubMed
[24]Arkhipov, A., Yin, Y., and Schulten, K.Membrane-bending mechanism of amphiphysin n-bar domains. Biophysical Journal, 97(10):2727–2735,2009.Google Scholar
[25]Marrink, S.J., Risselada, H.J., Yefimov, S., Tieleman, D.P., and de Vries, A.H.The martini force field: coarse grained model for biomolecular simulations. Journal of Physical Chemistry B, 111(27):7812–7824,2007.Google Scholar
[26]Ollila, O.H.S., Risselada, H.J., Louhivuori, M., Lindahl, E., Vattulainen, I., and Marrink, S.J.3D pressure field in lipid membranes and membrane-protein complexes. Physical Review Letters, 102(7):78101,2009.Google Scholar
[27]Schofield, P. and Henderson, J.R.Statistical mechanics of inhomogeneous fluids. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990), 379(1776):231–246,1982.Google Scholar
[28]Varnik, F., Baschnagel, J., and Binder, K.Molecular dynamics results on the pressure tensor of polymer films. The Journal of Chemical Physics, 113:4444,2000.CrossRefGoogle Scholar
[29]Wajnryb, E., Altenberger, A.R., and Dahler, J.S.Uniqueness of the microscopic stress tensor. Journal of Chemical Physics, 103(22):9782–9787,1995.Google Scholar
[30] A.Markvoort, J., van Santen, R.A., and Hilbers, P.A.J.Vesicle shapes from molecular dynamics simulations. Journal of Physical Chemistry B, 110(45):22780,2006.Google Scholar
[31]Rand, R.P., Fuller, N.L., Gruner, S.M., and Parsegian, V.A.Membrane curvature, lipid segregation, and structural transitions for phospholipids under dual-solvent stress. Biochemistry, 29(1):76–87,1990.CrossRefGoogle ScholarPubMed
[32]Leikin, S., Kozlov, M.M., Fuller, N.L., and Rand, R.P.Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes. Biophysical Journal, 71(5):2623–2632,1996.CrossRefGoogle ScholarPubMed
[33]Fuller, N. and Rand, R.P.The influence of lysolipids on the spontaneous curvature and bending elasticity of phospholipid membranes. Biophysical Journal, 81(1):243–254,2001.Google Scholar
[34]Kooijman, E.E., Chupin, V., de Kruijff, B., and Burger, K.N.Modulation of membrane curvature by phosphatidic acid and lysophosphatidic acid. Traffic, 4(3):162–174,2003.Google Scholar
[35]Israelachvili, J.N., Mitchell, D.J., and Ninham, B.W.Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. Journal of the Chemical Society, Faraday Transactions 2, 72:1525–1568,1976.Google Scholar
[36]Israelachvili, J.N., Mitchell, D.J., and Ninham, B.W.Theory of self-assembly of lipid bilayers and vesicles. Biochimica et Biophysica Acta, 470(2):185,1977.Google Scholar
[37]Marsh, D.Intrinsic curvature in normal and inverted lipid structures and in membranes. Biophysical Journal, 70(5):2248–2255,1996.Google Scholar
[38]Cooke, I.R. and Deserno, M.Coupling between lipid shape and membrane curvature. Biophysical Journal, 91(2):487,2006.Google Scholar
[39]Cooke, I.R., Kremer, K., and Deserno, M.Tunable generic model for fluid bilayer membranes. Physical Review E, 72(1):11506,2005.Google Scholar
[40]Alberts, B., Bray, D., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P., and Campbell, A.M.Essential Cell Biology. Garland Science New York, 2004.Google Scholar
[41]Reynwar, B.J. and Deserno, M.Membrane composition-mediated protein-protein interactions. Biointerphases, 3:FA117–FA124,2008.CrossRefGoogle ScholarPubMed
[42]Sodt, A.J. and Head-Gordon, T.An implicit solvent coarse-grained lipid model with correct stress profile. The Journal of Chemical Physics, 132:205103,2010.Google Scholar
[43]Berendsen, H.J.C., Postma, J.P.M., Van Gunsteren, W.F., DiNola, A., and Haak, J.R.Molecular dynamics with coupling to an external bath. The Journal of Chemical Physics, 81:3684,1984.Google Scholar
[44]Bussi, G., Donadio, D., and Parrinello, M.Canonical sampling through velocity rescaling. The Journal of Chemical Physics, 126:014101,2007.Google Scholar