Abstract
Brownian dynamics simulations were performed to study the contribution of electric interactions between charged membrane components to their lateral distribution in a two-dimensional viscous liquid (bilayer lipid membrane). The electrostatic interaction potential was derived from an analytical solution of the linearized Poisson-Boltzmann equation for point charges in an electrolyte solution — membrane — electrolyte solution system. Equilibrium as well as dynamic quantities were investigated. The lateral organization of membrane particles, modelled by mobile cylinders in a homogeneous membrane separating two electrolyte solutions was described by spatial distribution functions, diffusion coefficients and cluster statistics. Disorder, local order and crystal-like arrangements were observed as a function of the particle charge, the closest possible distances between the charges and the particle density. The simulations revealed that the system is very sensitive to the position of the charges with respect to the electrolyte solution — membrane interface. Electrostatic interactions of charges placed directly on the membrane surface were almost negligible, whereas deeper charges demonstrated pronounced interaction. Biologically relevant parameters corresponded at most to local and transient ordering. It was found that lateral electric forces can give rise to a preferred formation of clusters with an even number of constituents provided that the closest possible charge-charge distances are small. It is concluded that lateral electrostatic interactions can account for local particle aggregations, but their impact on the global arrangement and movement of membrane components is limited.
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References
Abney JR, Owicki JC (1985) Theories of protein-lipid and protein-protein interactions in membranes. In: Watts A, DePont JJ (eds) Progress in Protein-Lipid Interactions. Elsevier Science Publishers B.V., Amsterdam, pp 1–60
Allen MP, Tildesley DJ (1987) Computer Simulation of Liquids, Clarendon Press, Oxford
Arakelian VB, Walther D, Donath E (1993) Electric potential distribution around discrete charges in a dielectric membrane — electrolyte solution system. Colloid Polym Sci 270: 268–276
Brown GC (1990) Electrostatic coupling between membrane proteins. FEBS Lett 260: 1–5
Brussel SJ, Koch DL, Hammer, DA (1995) Effect of Hydrodynamic Interactions on the Diffusion of Intergral Membrane Proteins: Tracer Diffusion in Organelle and Reconstituted Membranes. Biophys J 68: 1828–1835
Cevc G (1990) Membrane electrostatics. Biochem Biophys Acta 1031: 311–382
Clarke RJ (1993) A theoretical description of non-steady-state diffusion of hydrophobic ions across lipid vesicle membranes including effects of ion-ion interactions in the aqueous solution. Biophys Chem 46: 131–143
Clegg RM, Vaz WLC (1985) Translational diffusion of proteins and lipids in artificial lipid bilayer membranes. A comparison of experiment with theory. In: Watts A, dePont JJ (eds) Progress in Protein- Lipid Interactions. Elsevier Science Publishers B.V., Amsterdam, pp 173–229
Davis ME, Madura JD, Luty BA, McCommon A (1991) Electrostatics and diffusion of molecules in solution: simulations with the Houston Brownian dynamics program. Comp Phys Commun 62: 187–197
Edmonds DT (1988) The different screening of electric charges and dipoles near a dielectric interface. Eur Biophys J 16: 255–257
Egberts E, Marrink SJ, Berendsen HJC (1994) Molecular dynamics simulation of phospholipid membrane. Eur Biophys J 22: 423–436
Ermak DL (1975) A computer simulation of charged particles in solution.I.Technique and equilibrium properties. J Chem Phys 62: 4189–4196
Forsten KE, Kozack DA, Lauffenburger DA, Subramaniam S (1994) Numerical solution of the nonlinear Poisson-Boltzmann equation for a membrane -electrolyte system. J Phys Chem 98: 5580–5586
Frausto JN, Läuger P, Apell HJ (1992) Electrostatic coupling of ion pumps. Biophys J 61: 83–95
Gennis RB (1989) Biomembranes- Molecular Structure and Function, Springer, New York
Hendrickson WA (1992) Receptor Structure: Models of Transduction. Curr Biol 2: 57–59
Honig BH, Hubell WL (1984) Stability of “salt bridges” in membrane proteins. Proc Natl Acad Sci USA 81: 5412–5416
Honig BH, Hubell WL, Flewelling RF (1986) Electrostatic interactions in membranes and proteins. Annu Rev Biophys Biophys Chem 15: 163–193
Hoppe W, Lohmann W, Markl H, Ziegler (eds) (1977) Biophysik — Ein Lehrbuch. Springer, Berlin Heidelberg New York, p 437
Jensen P, Barabdsi AL, Larralde H, Havlin Sh, Stanley E (1994) Controlling nanostructures. Nature 368: 22
Karyakin AV (1989) Simulation of protein clusterization in biological membranes (in russian). Biol Membrany 6: 218–225
Kozack RE, d'Mello MJ, Subramaniam S (1995) Computer Modelling of Electrostatic Steering and Orientational Effects in Antibody-Antigen Associations. Biophys J 68: 807–814
Lax M (1966) Classical Noise IV. Langevin methods. Rev Mol Phys 38: 541–566
Lemmon MA, Engelman DM (1992) Helix-helix interactions inside lipid bilayers. Curr Opi Struct Biol 2: 511–518
Marassi FM, MacDonald PM (1991) Response of the Headgroup of Phospahditylglycerol to Membrane Surface Charge as Studied by Deuterium and Phosphorus-31 Nuclear Magnetic Resonance. Biochem 30: 10558–10566
Marcelia S (1976) Lipid mediated protein interaction in membranes. Biochem Biophys Acta 367: 165–176
Martinez G, Sancho M (1993) Electrostatic Interactions in gramicidin channels — III. Dielectric Model. Eur Biophys J 22: 301–307
McLaughlin S (1989)The electrostatic properties of membranes. Annu Rev Biophys Biophys Chem 18: 113–136
Mouritsen OG, Bloom M (1993) Models of Lipid — Protein Interactions in Membranes. Annu Rev Biophys Bimol Struct 22: 145–171
Nelson AP, McQuarrie DA (1975) The Effect of Discrete Charges on the Electrical Properties of a Membrane. I. J Theor Biol 55: 13–27
Northrup SH, Boles JO, Reynolds JCL (1988) Brownian Dynamics of Cytochrome c and Cytochrome c Peroxidase Association. Science 241: 67–70
Pearson RP, Hui SW, Stewart TP (1979) Correlative Statistical Analysis and Computer Modelling of intramembraneous Particle Distributions in Human Erythrocyte Membranes. Biochim Biophys Acta 557: 265–282
Pink DA, Laidlaw DJ, Chisholm DM (1986) Protein lateral movement in lipid bilayers. Monte Carlo simulation studies of its dependence upon attractive protein -protein interaction. Biochem Biophys Acta: 863: 917
Sancho M, Martinez G (1991) Electrostatic modelling of dipole-ion interactions in gramicidinlike channels. Biophys J 60: 81–88
Saxton MJ (1994) Anomalous Diffusion Due to Obstacles: A Monte Carlo Study. Biophys J 66: 394–401
Schnitzer JA, Lambrakis KC (1991) Electrostatic Potential and Born Energy of Charged Molecules within Phospholipid bilayer: Calculation via 3-D Numerical Solution of the Full Poisson Equation. J Theor Biol 52: 203–222
Sitaraman V, Parajpe SA Gangal AD (1991) Charge anisotropy across biological membranes: evidence and implications. Biochem Biophys Acta 1098: 336–343
Sperotto MM, Mouritson OG (1991) Mean-field and Monte Carlo Simulation studies of the lateral distribution of proteins in membranes. Eur Biophys J 16: 369–374
Zhou HX (1993) Brownian dynamics study of the influence of electrostatic interactions and diffusion on protein-protein association kinetics. Biophys J 64: 1711–1716
Zwanzig R (1969) Langevin theory of polymer dynamics in dilute solution. Adv Chem Phys 15: 325–331
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Correspondence to: D. Walther
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Walther, D., Kuzmin, P. & Donath, E. Brownian dynamics simulation of the lateral distribution of charged membrane components. Eur Biophys J 24, 125–135 (1996). https://doi.org/10.1007/BF00180269
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DOI: https://doi.org/10.1007/BF00180269