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Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Published online by Cambridge University Press:  01 July 2011

Frank L. H. Brown*
Affiliation:
Department of Chemistry and Biochemistry and Department of Physics, University of California, Santa Barbara, CA 93106, USA
*
*Author for correspondence: Frank L. H. Brown, Department of Chemistry and Biochemistry and Department of Physics, University of California, Santa Barbara, CA 93106, USA. Email: [email protected]

Abstract

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

Type
Review Article
Copyright
Copyright © Cambridge University Press 2011

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References

9. References

Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K. & Watson, J. (1994). Molecular Biology of the Cell. 3rd edn.New York: Garland Publishing.Google Scholar
Alexander, J. C., Bernoff, A. J., Mann, E. K., Mann, J. A. Jr., Wintersmith, J. R. & Zou, L. (2007). Domain relaxation in langmuir films. Journal of Fluid Mechanics 571, 191219.CrossRefGoogle Scholar
Allen, M. P. & Tildesley, D. J. (1996). Computer Simulation of Liquids. New York: Oxford University Press.Google Scholar
Ashcroft, N. W. & Mermin, N. D. (1976). Solid State Physics. New York: Holt, Rinehart and Winston.Google Scholar
Atilgan, E., Wirtz, D. & Sun, S. X. (2006). Mechanics and dynamics of actin-driven thin membrane protrusions. Biophysical Journal 90, 6576.CrossRefGoogle ScholarPubMed
Atkins, P. W. (1990). Physical Chemistry. 4th edn.New York: W. H. Freeman and Co.Google Scholar
Baxter, R. (1982). Exactly Solved Models in Statistical Mechanics. New York: Academic Press.Google Scholar
Berkowitz, M. L. (2009). Detailed molecular dynamics simulations of model biological membranes containing cholesterol. Biochimica et Biophysica Acta 1788, 8696.CrossRefGoogle ScholarPubMed
Blood, P. D. & Voth, G. A. (2006). Direct observation of bin/amphiphysin/rvs (bar) domain-induced membrane curvature by means of molecular dynamics simulations. Proceedings of the National Academy of Sciences, USA 103, 1506815072.CrossRefGoogle ScholarPubMed
Boal, D. (2002). Mechanics of the Cell. Cambridge: Cambridge University Press.Google Scholar
Brannigan, G. & Brown, F. L. H. (2006). A consistent model for thermal fluctuations and protein induced deformations in lipid bilayers. Biophysical Journal 90, 15011520.CrossRefGoogle ScholarPubMed
Brannigan, G. & Brown, F. L. H. (2007). Contributions of gaussian curvature and non-constant lipid volume to protein deformation of lipid bilayers. Biophysical Journal 92, 864876.CrossRefGoogle Scholar
Brannigan, G., Lin, L. C.-L. & Brown, F. L. H. (2006). Implicit solvent simulation models for biomembranes. European Biophysical Journal 35, 104124.CrossRefGoogle ScholarPubMed
Bray, A. J. (1994). Theory of phase-ordering kinetics. Advances in Physics 43, 357.CrossRefGoogle Scholar
Brochard, F. & Lennon, J. F. (1975). Frequency spectrum of the flicker phenomenon in erythrocytes. Journal de Physique (Paris) 36, 10351047.CrossRefGoogle Scholar
Brochard, F., de Gennes, P. G. & Pfeuty, P. (1976). Surface tension and deformations of membrane structures: relation to two-dimensional phase transitions. Journal de Physique (Paris) 37, 10991104.CrossRefGoogle Scholar
Brown, F. L. H. (2003). Regulation of protein mobility via thermal membrane undulations. Biophysical Journal 84, 842853.CrossRefGoogle ScholarPubMed
Brown, F. L. H. (2008). Elastic modeling of biomembranes and lipid bilayers. Annual Review of Physical Chemistry 59, 685712.CrossRefGoogle ScholarPubMed
Callen, H. B. (1961). Thermodynamics. New York: John Wiley and Sons.Google Scholar
Camley, B. A. & Brown, F. L. H. (2010). Dynamic simulations of multicomponent lipid membranes over long length and time scales. Physical Review Letters 105, 148102.CrossRefGoogle ScholarPubMed
Camley, B. A. & Brown, F. L. H. (in press). Dynamic scaling in phase separation kinetics for quasi-two-dimensional membranes. Submitted.Google Scholar
Camley, B. A., Esposito, C., Baumgart, T. & Brown, F. L. H. (2010). Lipid bilayer domain fluctuations as a probe of membrane viscosity. Biophysical Journal 99, L01L03.CrossRefGoogle ScholarPubMed
Canham, P. B. (1970). The minimum energy of bending as a possible explanation of the biconcave shape of the red blood cell. Journal of Theoretical Biology 26, 6181.CrossRefGoogle ScholarPubMed
Chaikin, P. M. & Lubensky, T. C. (2000). Principles of condensed matter physics. Cambridge: Cambridge University Press.Google Scholar
Chiu, S. W., Jakobsson, E., Mashl, R. J. & Scott, H. L. (2002). Cholesterol-induced modifications in lipid bilayers: a simulation study. Biophysical Journal 83, 18421853.CrossRefGoogle ScholarPubMed
Cicuta, P., Keller, S. L. & Veatch, S. L. (2007). Diffusion of liquid domains in lipid bilayer membranes. Journal of Physical Chemistry B 111, 3328.CrossRefGoogle ScholarPubMed
Cooke, I. R., Kremer, K. & Deserno, M. (2005). Tunable generic model for fluid bilayer membranes. Physical Review E 72, 011506.CrossRefGoogle ScholarPubMed
Crawford, G. E. & Earnshaw, J. C. (1987). Viscoelastic relaxation of bilayer lipid membranes. Biophysical Journal 52, 8794.CrossRefGoogle ScholarPubMed
Deuling, H. J. & Helfrich, W. (1976). The curvature elasticity of fluid membranes: A catalogue of vesicle shapes. Journal de Physique (Paris) 37, 13351345.CrossRefGoogle Scholar
Dimova, R., Dietrich, C., Hadjiisky, A., Danov, K. & Pouligny, B. (1999). Falling ball viscosimetry of giant vesicle membranes: Finite-size effects. European Physical Journal B 12, 589.CrossRefGoogle Scholar
Discher, D. E., Boal, D. H. & Boey, S. K. (1998). Simulations of the erythrocyte cytoskeleton at large deformation II: micropipette aspiration. Biophysical Journal 75, 15841597.CrossRefGoogle ScholarPubMed
Doi, M. & Edwards, S. F. (1986). The Theory of Polymer Dynamics. Oxford: Clarendon Press.Google Scholar
Drouffe, J.-M., Maggs, A. C. & Leibler, S. (1991). Computer simulations of self-assembled membranes. Science 254, 13531356.CrossRefGoogle ScholarPubMed
Edidin, M. (2003). The state of lipid rafts: From model membranes to cells. Annual Review of Biophysics and Biomolecular Structure 32, 257.CrossRefGoogle ScholarPubMed
Ermak, D. L. & McCammon, J. A. (1978). Brownian dynamics with hydrodynamic interactions. Journal of Chemical Physics 69, 13521360.CrossRefGoogle Scholar
Esposito, C., Tian, A., Melamed, S., Johnson, C., Tee, S.-Y. & Baumgart, T. (2007). Flicker spectroscopy of thermal lipid bilayer domain boundary fluctuations. Biophysical Journal 93, 31693181.CrossRefGoogle ScholarPubMed
Evans, E. & Skalak, R. (1980). Mechanisms and Thermodynamics of Biomembranes. Boca Raton, FL: CRC Press.Google Scholar
Evans, D. F. & Wennerstrom, H. (1994). The Colloidal Domain, where Physics, Chemistry and Biology Meet. 2nd edn.New York: VCH Publishers.Google Scholar
Fan, J., Sammalkorpi, M. & Haataja, M. (2010). Lipid microdomains: structural correlations, fluctuations, and formation mechanisms. Physical Review Letters 104, 118101.CrossRefGoogle ScholarPubMed
Farago, O. & Pincus, P. (2003). The effect of thermal fluctuations on Schulman area elasticity. European Physical Journal E 11, 399408.CrossRefGoogle ScholarPubMed
Fattal, D. R. & Ben-Shaul, A. (1993). A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch. Biophysical Journal 65, 17951809.CrossRefGoogle ScholarPubMed
Feller, S. E. (2000). Molecular dynamics simulations of lipid bilayers. Current Opinion in Colloid and Interface Science 5, 217223.CrossRefGoogle Scholar
Ferry, J. D. (1980). Viscoelastic Properties of Polymers. New York: John Wiley and Sons.Google Scholar
Fischer, T. M. (2004). The drag on needles moving in a Langmuir monolayer. Journal of Fluid Mechanics 498, 123137.CrossRefGoogle Scholar
Fourner, J.-B., Ajdari, A. & Peliti, L. (2001). Effective-area elasticity and tension of micromanipulated membranes. Physical Review Letters 86, 49704973.CrossRefGoogle Scholar
Fournier, J.-B., Lacoste, D. & Raphael, E. (2004). Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size. Physical Review Letters 92, 018102.CrossRefGoogle Scholar
Frolov, V. A., Chizmadzhev, Y. A., Cohen, F. S. & Zimmberg, J. (2006). “Entropic traps” in the kinetics of phase separation in multicomponent membranes stabilize nanodomains. Biophysical Journal 91, 189.CrossRefGoogle ScholarPubMed
Funkhouser, C. M., Solis, F. J. & Thornton, K. (2007). Coupled composition-deformation phase-field method for multicomponent lipid membranes. Physical Review E 76, 011912.CrossRefGoogle ScholarPubMed
Fygenson, D. K., Marko, J. F. & Libchaber, A. (1997). Mechanics of microtubule-based membrane extension. Physical Review Letters 79, 44974500.CrossRefGoogle Scholar
Gambin, Y., Lopez-Esparza, R., Reffay, M., Sierecki, E., Gov, N. S., Genest, M., Hodges, R. S. & Urbach, W. (2006). Lateral mobility of proteins in liquid membranes revisited. Proceedings of the National Academy of Sciences, USA 103, 20982102.CrossRefGoogle ScholarPubMed
Gambin, Y., Reffay, M., Sierecki, E., Homble, F., Hodges, R. S., Gov, N. S., Taulier, N. & Urbach, W. (2010). Variation of the lateral mobility of transmembrane peptides with hydrophobic mismatch. Journal of Physical Chemistry B 114, 35593566.CrossRefGoogle ScholarPubMed
Gardiner, C. W. (1985). Handbook of Stochastic Methods. 2nd edn.Berlin: Springer-Verlag.Google Scholar
Gennis, R. B. (1989). Biomembranes: Molecular Structure and Function. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Girard, P., Prost, J. & Bassereau, P. (2005). Passive or active fluctuations in membranes containing proteins. Physical Review Letters 94, 088102.CrossRefGoogle ScholarPubMed
Goetz, R., Gompper, G. & Lipowsky, R. (1999). Mobility and elasticity of self-assembled membranes. Physical Review Letters 82, 221224.CrossRefGoogle Scholar
Goldstein, R. E. & Jackson, D. P. (1994). Domain shape relaxation and the spectrum of thermal fluctuations in Langmuir monolayers. Journal of Physical Chemistry 98, 96269636.CrossRefGoogle Scholar
Gouliaev, N. & Nagle, J. F. (1998a). Simulations of a single membrane between two walls using a Monte Carlo method. Physical Review E 58, 881888.CrossRefGoogle Scholar
Gouliaev, N. & Nagle, J. F. (1998b). Simulations of interacting membranes in the soft confinement regime. Physical Review Letters 81, 26102613.CrossRefGoogle ScholarPubMed
Goulian, M., Bruinsma, R. & Pincus, P. (1993). Long-range forces in heterogeneous fluid membranes. Europhysics Letters 22, 145150.CrossRefGoogle Scholar
Gov, N., Zilman, A. G. & Safran, S. (2003). Cytoskeleton confinement and tension of red blood cells. Physical Review Letters 90, 228101.CrossRefGoogle Scholar
Gov, N., Zilman, A. G. & Safran, S. A. (2004). Hydrodynamics of confined membranes. Physical Review E 70, 011104.CrossRefGoogle ScholarPubMed
Gov, N. (2004). Membrane undulations driven by force fluctuations of active proteins. Physical Review Letter 93, 268104.CrossRefGoogle ScholarPubMed
Gov, N. S. (2006). Diffusion in curved fluid membranes. Physical Review E 73, 041918.CrossRefGoogle ScholarPubMed
Grakoui, A., Bromley, S. K., Sumen, C., Davis, M. M., Shaw, A. S., Allen, P. M. & Dustin, M. L. (1999). The immunological synapse: a molecular machine controlling t cell activation. Science 285, 221227.CrossRefGoogle ScholarPubMed
Granek, R. & Klafter, J. (2001). Anomalous motion of membranes under a localized external potential. Europhysics Letters 56, 1521.CrossRefGoogle Scholar
Granek, R. (1997). From semi-flexible polymers to membranes: anomalous diffusion and reptation. Journal de Physique II (Paris) 7, 17611788.Google Scholar
Grossfield, A., Feller, S. E. & Pitman, M. C. (2006). A role for direct interactions in the modulation of rhodopsin by ω-3 polyunsaturated lipids. Proceedings of the National Academy of Sciences, USA 103, 48884893.CrossRefGoogle ScholarPubMed
Halle, B. & Gustafsson, S. (1997). Diffusion in a fluctuating random geometry. Physical Review E 55, 680686.CrossRefGoogle Scholar
Happel, J. & Brenner, H. (1983). Low Reynolds Number Hydrodynamics. The Hague, The Netherlands: Kluwer.CrossRefGoogle Scholar
Harland, C., Bradley, M. & Parthasarathy, R. (2011). Phospholipid bilayers are viscoelastic. Proceedings of the National Academy of Sciences, USA 107, 1914619150.CrossRefGoogle Scholar
Helfrich, P. & Jakobsson, E. (1990). Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels. Biophysical Journal 57, 10751084.CrossRefGoogle ScholarPubMed
Helfrich, W. (1973). Elastic properties of lipid bilayers: theory and possible experiments. Zeitschrift fur Naturforschung c 28, 693703.CrossRefGoogle ScholarPubMed
Helfrich, W. (1978). Steric interaction of fluid membranes in multilayer systems. Zeitschrift fur Naturforschung a 33, 305315.CrossRefGoogle Scholar
Helfrich, W. (1985). Effect of thermal undulations on the rigidity of fluid membranes and interfaces. Journal de Physique (Paris) 46, 12631268.CrossRefGoogle Scholar
Henle, M. L. & Levine, A. J. (2010). Hydrodynamics in curved membranes: the effect of geometry on particulate mobility. Physical Review E 81, 011905.CrossRefGoogle ScholarPubMed
Honerkamp-Smith, A. R. et al. (2008). Line tensions, correlation lengths, and critical exponents in lipid membranes near critical points. Biophysical Journal 95, 236.CrossRefGoogle ScholarPubMed
Howard, J. (2001). Mechanics of Motor Proteins and the Cytoskeleton. Sunderland, MA: Sinauer.Google Scholar
Huang, H. W. (1986). Deformation free energy of bilayer membrane and its effects on gramicidin channel lifetime. Biophysical Journal 50, 10611070.CrossRefGoogle ScholarPubMed
Hughes, B. D., Pailthorpe, B. A. & White, L. R. (1981). The translational and rotational drag on a cylinder moving in a membrane. Journal of Fluid Mechanics 110, 349.CrossRefGoogle Scholar
Immordino, M. L., Dosio, F. & Cattel, L. (2006). Stealth liposomes: review of the basic science, rationale, and clinical applications, existing and potential. International Journal of Nanomedicine 1, 297315.Google ScholarPubMed
Kaizuka, Y. & Groves, J. T. (2004). Structure and dynamics of supported intermembrane junctions. Biophysical Journal 86, 905912.CrossRefGoogle ScholarPubMed
Kaizuka, Y. & Groves, J. T. (2006). Hydrodynamic damping of membrane thermal fluctuations near surfaces imaged by fluorescence interference microscopy. Physical Review Letters 96, 118101.CrossRefGoogle ScholarPubMed
Kamien, R. D. (2002). The geometry of soft materials: a primer. Reviews in Modern Physics 74, 953971.CrossRefGoogle Scholar
Kim, S. & Karrila, S. J. (1991). Microhydrodynamics Principles and Selected Applications. Mineola, New York: Dover Publications.Google Scholar
Kim, K. S., Neu, J. & Oster, G. (1998). Curvature-mediated interactions between membrane proteins. Biophysical Journal 75, 22742291.CrossRefGoogle ScholarPubMed
Kloeden, P. E. & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. New York: Springer.CrossRefGoogle Scholar
Kloeden, P. & Platen, E. (1999). Numerical Solution of Stochastic Differential Equations. New York: Springer.Google Scholar
Koga, T. & Kawasaki, K. (1991). Spinodal decomposition in binary fluids: Effects of hydrodynamic interactions. Physical Review A 44, R817R820.CrossRefGoogle ScholarPubMed
Korlach, J., Schwille, P., Webb, W. W. & Feigenson, G. W. (1999). Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy. Proceedings of the National Academy of Sciences, USA 96, 8461.CrossRefGoogle ScholarPubMed
Krobath, H., Schutz, G. J., Lipowsky, R. & Weikl, T. R. (2007). Lateral diffusion of receptor-ligand bonds in membrane adhesion zones: effect of thermal membrane roughness. Europhysics Letters 78, 38003.CrossRefGoogle Scholar
Laradji, M. & Kumar, P. B. S. (2005). Domain growth, budding and fission in phase-separating self-assembled fluid bilayers. Journal of Chemical Physics 123, 224902.CrossRefGoogle ScholarPubMed
Laradji, M. (1999). Polymer adsorption on fluctuating surfaces. Europhysics Letters 47, 694700.CrossRefGoogle Scholar
Laradji, M. (2002). Elasticity of polymer-anchored membranes. Europhysics Letters 60, 594600.CrossRefGoogle Scholar
Laradji, M. (2004). A Monte Carlo study of fluctuating polymer-grafted membranes. Journal of Chemical Physics 121, 15911600.CrossRefGoogle ScholarPubMed
Lee, J.-H., Choi, S.-M., Doe, C., Faraone, A., Pincus, P. A. & Kline, S. R. (2010). Thermal fluctuation and elasticity of lipid vesicles interacting with pore-forming peptides. Physical Review Letters 105, 038101.CrossRefGoogle ScholarPubMed
Leitenberger, S. M., Reister-Gottfried, E. & Seifert, U. (2008). Curvature coupling dependence of membrane protein diffusion coefficient. Langmuir 24, 12541261.CrossRefGoogle Scholar
Levine, A. J. & MacKintosh, F. C. (2002). Dynamics of viscoelastic membranes. Physical Review E 66, 061606.CrossRefGoogle ScholarPubMed
Lim, H. W. G., Wortis, M. & Mukhopadhyay, R. (2002). Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: evidence for the bilayer-couple hypothesis from membrane mechanics. Proceedings of the National Academy of Sciences, USA 99, 1676616769.CrossRefGoogle Scholar
Lin, L. C.-L. & Brown, F. L. H. (2004a). Brownian dynamics in fourier space: Membrane simulations over long length and time scales. Physical Review Letters 93, 256001.CrossRefGoogle ScholarPubMed
Lin, L. C.-L. & Brown, F. L. H. (2004b). Dynamics of pinned membranes with application to protein diffusion on the surface of red blood cells. Biophysical Journal 86, 764780.CrossRefGoogle ScholarPubMed
Lin, L. C.-L. & Brown, F. L. H. (2005). Dynamic simulations of membranes with cytoskeletal interactions. Physical Review E 72, 011910.CrossRefGoogle ScholarPubMed
Lin, L. C.-L. & Brown, F. L. H. (2006). Simulating membrane dynamics in nonhomogeneous hydrodynamic environments. Journal of Chemical Theory and Computation 2, 472483.CrossRefGoogle ScholarPubMed
Lin, L. C.-L., Gov, N. & Brown, F. L. H. (2006a). Nonequilibrium membrane fluctuations driven by active proteins. Journal of Chemical Physics 124, 074903.CrossRefGoogle ScholarPubMed
Lin, L. C.-L., Groves, J. T. & Brown, F. L. H. (2006b). Shape, fluctuations and dynamics of intermembrane junctions: a simulation study. Biophysical Journal 91, 36003606.CrossRefGoogle Scholar
Lipowsky, R. & Zielenska, B. (1989). Binding and unbinding of lipid membranes: a monte carlo study. Physical Review Letters 62, 15721575.CrossRefGoogle ScholarPubMed
Lipowsky, R. & Sackmann, E. (1995). Structure and Dynamics of Membranes. Amsterdam: Elsevier Science.Google Scholar
Lipowsky, R. (1991). The conformation of membranes. Nature 349, 475481.CrossRefGoogle ScholarPubMed
Lodish, H., Baltimore, D., Berk, A., Zipursky, S. L., Matsudaira, P. & Darnell, J. (1995). Molecular Cell Biology. 3rd edn.New York: Scientific American Books.Google Scholar
Lubensky, D. K. & Goldstein, R. E. (1996). Hydrodynamics of monolayer domains at the air–water interface. Physics of Fluids 8, 843854.CrossRefGoogle Scholar
Mann, E. K., Hénon, S., Langevin, D., Meunier, J. & Léger, L. (1995). Hydrodynamics of domain relaxation in a polymer monolayer. Physical Review E 51, 5708.CrossRefGoogle Scholar
Marčelja, S. (1976). Lipid-mediated protein interaction in membranes. Biochimica et Biophysica Acta 455, 17.CrossRefGoogle ScholarPubMed
Marrink, S.-J., Berkowitz, M. & Berendsen, H. J. C. (1993). Molecular dynamics simulation of a membrane/water interface: the ordering of water and its relation to the hydration force. Langmuir 9, 31223131.CrossRefGoogle Scholar
McConnell, H. M. & Vrljic, M. (2003). Liquid–liquid immiscibility in membranes. Annual Review of Biophysics and Biomolecular Structure 32, 469492.CrossRefGoogle ScholarPubMed
McConnell, H. (2005). Complexes in ternary cholesterol-phospholipid mixtures. Biophysical Journal 88, L23.CrossRefGoogle ScholarPubMed
McQuarrie, D. A. (1976). Statistical Mechanics. New York: Harper Collins.Google Scholar
McWhirter, J. L., Ayton, G. S. & Voth, G. A. (2004). Coupling field theory with mesoscopic dynamical simulations of multicomponent lipid bilayers. Biophysical Journal 87, 32423263.CrossRefGoogle ScholarPubMed
Merath, R.-J. & Seifert, U. (2006). Nonmonotonic fluctuation spectra of membranes pinned or tethered discretely to a substrate. Physical Review E 73, 010401.CrossRefGoogle ScholarPubMed
Miao, L., Fourcade, B., Rao, M., Wortis, M. & Zia, R. K. P. (1991). Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles. Physical Review A 43, 68436856.CrossRefGoogle ScholarPubMed
Miao, L., Seifert, U., Wortis, M. & Döbereiner, H. (1994). Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity. Physical Review E 49, 53895407.CrossRefGoogle ScholarPubMed
Milner, S. T. & Safran, S. A. (1987). Dynamical fluctuations of droplet microemulsions and vesicles. Physical Review A 36, 43714379.CrossRefGoogle ScholarPubMed
Mukhopadhyay, R., Lim, H. W. G. & Wortis, M. (2002). Echinocyte shapes: Bending, stretching, and shear determine spicule shape and spacing. Biophysical Journal 82, 17561772.CrossRefGoogle ScholarPubMed
Nagao, M. (2009). Observation of local thickness fluctuations in surfactant membranes using neutron spin echo. Physical Review E 80, 031606.CrossRefGoogle ScholarPubMed
Nagle, J. F. (1980). Theory of the main lipid bilayer phase transition. Annual Review of Physical Chemistry 31, 157195.CrossRefGoogle Scholar
Naji, A. & Brown, F. L. H. (2007). Diffusion on ruffled membrane surfaces. Journal of Chemical Physics 126, 235103.CrossRefGoogle ScholarPubMed
Naji, A., Atzberger, P. & Brown, F. L. H. (2009). Hybrid elastic and discrete-particle approach to biomembrane dynamics with application to the mobility of curved integral membrane proteins. Physical Review Letters 102, 138102.CrossRefGoogle Scholar
Nelson, D., Piran, T. & Weinberg, S. (2004). Statistical Mechanics of Membranes and Surfaces. 2nd edn.New Jersey: World Scientific.CrossRefGoogle Scholar
Nelson, P. (2008). Biological Physics Energy, Information, Life. Updated 1st edn.New York: W. H. Freeman and Co.Google Scholar
Nielsen, C., Goulian, M. & Andersen, O. S. (1998). Energetics of inclusion-induced bilayer deformations. Biophysical Journal 74, 19661983.CrossRefGoogle ScholarPubMed
Oppenheimer, N. & Diamant, H. (2009). Correlated diffusion of membrane proteins and their effect on membrane viscosity. Biophysical Journal 96, 3041.CrossRefGoogle ScholarPubMed
Oppenheimer, N. & Diamant, H. (2010). Correlated dynamics of inclusions in a supported membrane. Physical Review E 82, 041912.CrossRefGoogle Scholar
Partenskii, M. B. & Jordan, P. C. (2002). Membrane deformation and the elastic energy of insertion: perturbation of membrane elastic constants to due peptide insertion. Journal of Chemical Physics 117, 1076810776.CrossRefGoogle Scholar
Pastor, R. W. (1994). Molecular-dynamics and Monte-Carlo simulations of lipid bilayers. Current Opinion in Structural Biology 4, 486492.CrossRefGoogle Scholar
Peliti, L. & Leibler, S. (1985). Effects of thermal fluctuations on systems with small surface tension. Physical Review Letters 54, 16901693.CrossRefGoogle ScholarPubMed
Peskin, C. S. (2002). The immersed boundary method. Acta Numerica 11, 139.CrossRefGoogle Scholar
Peter, B. J., Kent, H. M., Mills, I. G., Vallis, Y., Butler, P. J. G., Evans, P. R. & McMahon, H. T. (2004). Bar domains as sensors of membrane curvature: The amphiphysin bar structure. Science 303, 495499.CrossRefGoogle ScholarPubMed
Petrov, E. P. & Schwille, P. (2009). Translational diffusion in lipid membranes beyond the Saffmann–Delbruck approximation. Biophysical Journal 94, L41.CrossRefGoogle Scholar
Pitman, M. C., Grossfield, A., Suits, F. & Feller, S. E. (2005). Role of cholesterol and polyunsaturated chains in lipid–protein interactions: Molecular dynamics simulation of rhodopsin in arealistic membrane environment. Journal of the American Chemical Society 127, 45764577.CrossRefGoogle ScholarPubMed
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. (1994). Numerical Recipes in C. Cambridge: Cambridge University Press.Google Scholar
Prost, J. & Bruinsma, R. (1996). Shape fluctuations of active membranes. Europhysics Letters 33, 321326.CrossRefGoogle Scholar
Prost, J., Manneville, J.-B. & Bruinsma, R. (1998). Fluctuation–magnification of non-equilibrium membranes near a wall. European Physical Journal B 1, 465480.CrossRefGoogle Scholar
Purcell, E. M. (1977). Life at low Reynolds number. American Journal of Physics 45, 310.CrossRefGoogle Scholar
Qi, S. Y., Groves, J. T. & Chakraborty, A. K. (2001). Synaptic pattern formation during cellular recognition. Proceedings of the National Academy of Sciences, USA 98, 65486553.CrossRefGoogle ScholarPubMed
Ramachandran, S., Komura, S. & Gompper, G. (2010). Effects of an embedding bulk fluid on phase separation dynamics in a thin liquid film. Europhysics Letters 89, 56001.CrossRefGoogle Scholar
Ramadurai, S., Holt, A., Krasnikov, V., van den Bogaart, G., Killian, J. A. & Poolman, B. (2009). Lateral diffusion of membrane proteins. Journal of the American Chemical Society 131, 1265012656.CrossRefGoogle ScholarPubMed
Ramadurai, S., Holt, A., Schafer, L. V., Krasnikov, V. V., Rijkers, D. T. S., Marrink, S. J., Killian, J. A. & Poolman, B. (2010a). Influence of hydrophobic mismatch and amino acid composition on the lateral diffusion of transmembrane peptides. Biophysical Journal 99, 14471454.CrossRefGoogle ScholarPubMed
Ramadurai, S., Duurkens, R., Krasnikov, V. V. & Poolman, B. (2010b). Lateral diffusion of membrane proteins: consequences of hydrophobic mismatch and lipid composition. Biophysical Journal 99, 14821489.CrossRefGoogle ScholarPubMed
Reigada, R., Buceta, J., Gomez, J., Sagues, F. & Lindenberg, K. (2008). Phase separation in three-component lipid membranes: From Monte Carlo simulations to Ginzburg–Landau equations. Journal of Chemical Physics 128, 025102.CrossRefGoogle ScholarPubMed
Reister, E. & Seifert, U. (2005). Lateral diffusion of a protein on a fluctuating membrane. Europhysics Letters 71, 859865.CrossRefGoogle Scholar
Reister-Gottfried, E., Leitenberger, S. M. & Seifert, U. (2007). Hybrid simulations of lateral diffusion in fluctuating membranes. Physical Review E 75, 011908.CrossRefGoogle ScholarPubMed
Reister-Gottfried, E., Leitenberger, S. M. & Seifert, U. (2010). Diffusing proteins on a fluctuating membrane: Analytical theory and simulations. Physical Review E 81, 031903.CrossRefGoogle Scholar
Saffman, P. G. (1976). Brownian motion in thin sheets of viscous fluid. Journal of Fluid Mechanics 73, 593602.CrossRefGoogle Scholar
Saffman, P. G. & Delbrück, M. (1975). Brownian motion in biological membranes. Proceedings of the National Academy of Sciences, USA 72, 3111.CrossRefGoogle ScholarPubMed
Safran, S. A. (1994). Statistical Thermodynamics of Surfaces, Interfaces and Membranes. Boulder, CO: Westview Press.Google Scholar
Sakuma, Y., Imai, M., Urakami, N., Nagao, M., Komura, S. & Kawakatsu, T. (2010). Diffusion of nano-meter-sized domains on a vesicle. Biophysical Journal 98, 220a.CrossRefGoogle Scholar
Saxton, M. J. & Jacobson, K. (1997). Single particle tracking: applications to membrane dynamics. Annual Review of Biophysics and Biomolecular Structure 26, 373399.CrossRefGoogle ScholarPubMed
Schulten, K. & Kosztin, I. (2000). Lectures in Theoretical Biophysics. http://www.ks.uiuc.edu/Services/Class/NSM.pdfGoogle Scholar
Seifert, U. (1994). Dynamics of a bound membrane. Physical Review E 49, 31243127.CrossRefGoogle ScholarPubMed
Seifert, U. & Langer, S. A. (1993). Viscous modes of fluid bilayer membranes. Europhysics Letters 23, 7176.CrossRefGoogle Scholar
Seifert, U. & Lipowsky, R. (1995). Morphology of vesicles. In Structure and Dynamics of Membranes, Volume 1 (eds. Lipowsky, R. & Sackmann, E.), pp. 403464. Amsterdam: Elsevier Science.Google Scholar
Seifert, U., Berndl, K. & Lipowsky, R. (1991). Shape transformations of vesicles: Phase diagram for spontaneous-curvature and bilayer-coupling models. Physical Review A 44, 11821202.CrossRefGoogle ScholarPubMed
Shinozaki, A. & Oono, Y. (1993). Spinodal decomposition in 3-space. Physical Review E 48, 26222654.CrossRefGoogle ScholarPubMed
Shkulipa, S. A., den Otter, W. K. & Briels, W. J. (2006). Thermal undulations of lipid bilayers relax by intermonolayer friction at submicrometer length scales. Physical Review Letters 96, 178302.CrossRefGoogle ScholarPubMed
Simons, K. & Vaz, W. L. C. (2004a). Model systems, lipid rafts, and cell membranes. Annual Review of Biophysics and Biomolecular Structure 33, 259.CrossRefGoogle ScholarPubMed
Simons, K. & Vaz, W. L. C. (2004b). Model systems, lipid rafts, and cell membranes. Annual Review of Biophysics and Biomolecular Structure 33, 269295.CrossRefGoogle ScholarPubMed
Singer, S. J. & Nicolson, G. L. (1972). The fluid mosaic model of the structure of cell membranes. Science 175, 720731.CrossRefGoogle ScholarPubMed
Smondyrev, A. M. & Berkowitz, M. L. (1999). Structure of dipalmitoylphosphatidylcholine/cholesterol bilayer at low and high cholesterol concentrations: Molecular dynamics simulation. Biophysical Journal 77, 20752089.CrossRefGoogle ScholarPubMed
Squires, T. M. & Mason, T. G. (2010). Fluid mechanics of microrheology. Annual Review of Fluid Mechanics 42, 413438.CrossRefGoogle Scholar
Stone, H. A. & Ajdari, A. (1998). Hydrodynamics of particles embedded in a flat surfactant layer overlaping a subphase of finite depth. Journal of Fluid Mechanics 369, 151173.CrossRefGoogle Scholar
Stone, H. A. & McConnell, H. M. (1995). Hydrodynamics of quantized shape transitions of lipid domains. Proceedings of the Royal Society of London A 448, 97111.Google Scholar
Theriot, J. A. & Mitchison, T. J. (1991). Actin microfilament dynamics in locomoting cells. Nature 352, 126131.CrossRefGoogle ScholarPubMed
Tien, H. T. & Ottova-Leitmannova, A. (2003). Planar Lipid Bilayers (BLMs) and their Applications. Amsterdam: Elsevier Science.Google Scholar
Tobias, D. J., Tu, K. C. & Klein, M. L. (1997). Atomic-scale molecular dynamics simulations of lipid membranes. Current Opinion in Colloid and Interface Science 2, 1526.CrossRefGoogle Scholar
Toyoshima, C. & Nomura, H. (2002). Structural changes in the calcium pump accompanying the dissociation of calcium. Nature 418, 605611.CrossRefGoogle ScholarPubMed
Toyoshima, C., Nakasako, M., Nomura, H. & Ogawa, H. (2000). Crystal structure of the calcium pump of sarcoplasmic reticulum at 2·6 angstrom resolution. Nature 405, 647655.CrossRefGoogle Scholar
Van Kampen, N. G. (2007). Stochastic Processes in Physics and Chemistry. 3rd edn.Amsterdam: North Holland.Google Scholar
Veatch, S. L. & Keller, S. L. (2003). Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophysical Journal 85, 3074.CrossRefGoogle Scholar
Veatch, S. L. & Keller, S. L. (2005). Seeing spots: complex phase behavior in simple membranes. Biochimica et Biophysica Acta 1746, 172185.CrossRefGoogle ScholarPubMed
Wagner, A. J. & Yeomans, J. M. (1998). Breakdown of scale invariance in the coarsening of phase-separating binary fluids. Physical Review Letters 80, 1429.CrossRefGoogle Scholar
Watson, M. C. & Brown, F. L. H. (2010). Interpreting membrane scattering at the mesoscale: the contribution of dissipation within the bilayer. Biophysical Journal 98, L09L11.CrossRefGoogle ScholarPubMed
Webb, W. W., Barak, L. S., Tank, D. W. & Wu, E. S. (1981). Molecular mobility on the cell surface. Biochemical Society Symposium 46, 191205.Google Scholar
Weikl, T. R. & Lipowsky, R. (2000). Local adhesion of membranes to striped surface domains. Langmuir 16, 93389346.CrossRefGoogle Scholar
West, B., Brown, F. L. H. & Schmid, F. (2009). Membrane-protein interactions in a generic coarse-grained model for lipid bilayers. Biophysical Journal 96, 101115.CrossRefGoogle Scholar
Wu, Y., Alexander, F. J., Lookman, T. & Chen, S. (1995). Effects of hydrodynamics on phase transition kinetics in two-dimensional binary fluids. Physical Review Letters 74, 38523855.CrossRefGoogle ScholarPubMed
Xu, K. & Klapper, I. (2007). On the correspondence between creeping flows of viscous and viscoelastic fluids. Journal of Non-Newtonian Fluid Mechanics 145, 150172.CrossRefGoogle Scholar
Yoon, H. & Deutsch, J. M. (1997). Conformation fluctuations of polymerized vesicles in the inextensible and flexible limit. Physical Review E 56, 34123420.CrossRefGoogle Scholar
Zhang, R. & Brown, F. L. H. (2008). Cytoskeleton mediated effective elastic properties in model red blood cell membranes. Journal of Chemical Physics 129, 065101.CrossRefGoogle ScholarPubMed
Zhu, Q. & Asaro, R. J. (2008). Spectrin folding versus unfolding reactions and rbc membrane stiffness. Biophysical Journal 94, 25292545.CrossRefGoogle ScholarPubMed
Zhu, J., Chen, L.-Q., Shen, J. & Tikare, V. (1999). Coarsening kinetics from a variable-mobility Cahn–Hilliard equation: application of a semi-implicit fourier spectral method. Physical Review E 60, 3564.CrossRefGoogle ScholarPubMed
Zhu, Q., Vera, C., Asaro, R. J., Sche, P. & Sung, L. A. (2007). A hybrid model for erythrocyte membrane: a single unit of protein network coupled with lipid bilayer. Biophysical Journal 93, 386400.CrossRefGoogle ScholarPubMed