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Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins

Published online by Cambridge University Press:  26 April 2006

Travis L. Dodd ,
Daniel A. Hammer ,
Ashok S. Sangani  and
Donald L. Koch
Travis L. Dodd
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
Daniel A. Hammer
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
Ashok S. Sangani
Affiliation:
Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244, USA
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

Proteins in a biological membrane can be idealized as disks suspended in a thin viscous sheet surrounded by a fluid of lower viscosity (Saffman 1976). To determine the effect of hydrodynamic interactions on protein diffusivities in non-dilute suspensions, we numerically solve the Stokes equations of motion for a system of disks in a bounded periodic two-dimensional fluid using a multipole expansion technique. We consider both free suspensions, in which all the proteins are mobile, and fixed beds, in which a fraction of the proteins are fixed. For free suspensions, we determine both translational and rotational short-time self-diffusivities and the gradient diffusivity as a function of the area fraction of the disks. The translational self- and gradient diffusivities computed in this way grow logarithmically with the number of disks owing to Stokes paradox; to obtain finite values, we renormalize our simulation results by treating long-range interactions in terms of a membrane with an enhanced viscosity in contact with a low-viscosity three-dimensional fluid. The diffusivities in fixed beds require no such adjustment because, at non-dilute area fractions of disks, the Brinkman screening of hydrodynamic interactions is more important that the viscous drag due to the surrounding three-dimensional fluid in limiting the range of hydrodynamic interactions. The diffusivities are determined as functions of the area fractions of both mobile and fixed proteins. We compare our results for diffusivities with experimental measurements of long-time protein self-diffusivity after adjusting our short-time diffusivities calculations in an approximate way to account for effects of hindered diffusion due to volume exclusion, and find very good agreement between the two.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 293 , 25 June 1995 , pp. 147 - 180
Copyright
© 1995 Cambridge University Press

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References

Abney, J. R., Scalettar, B. A. & Owicki, J. C. 1989 Self diffusion of interacting membrane proteins. Biophys. J. 55, 817–833.Google Scholar
Axelrod, D., Koppel, D. E., Schlessinger, J., Elson, E. & Webb, W. W. 1976 Mobility measurements by analysis of fluorescence photobleaching recovery kinetics. Biophys. J. 16, 1055–1069.Google Scholar
Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interactions. J. Fluid Mech. 74, 1–29.Google Scholar
Batchelor, G. K. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory. J. Fluid Mech. 119, 379–408.Google Scholar
Brady, J. F. 1984 The Einstein viscosity correction in n dimensions. Intl J. Multiphase Flow 10, 113–114.Google Scholar
Brady, J. F. 1994 The long-time self-diffusivity in concentrated colloidal dispersions. J. Fluid Mech. 272, 109–134.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157.Google Scholar
Brady, J. F. & Durlofsky, L. J. 1988 The sedimentation rate of disordered suspensions. Phys. Fluids 31, 717–727.Google Scholar
Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27–34.Google Scholar
Bussell, S. J., Koch, D. L. & Hammer, D. A. 1992 The resistivity and mobility functions for a model system of two equal-sized proteins in a lipid bilayer. J. Fluid Mech. 243, 679–697.Google Scholar
Bussell, S. J., Koch, D. L. & Hammer, D. A. 1994 The effect of hydrodynamic interactions on the tracer and gradient diffusion of integral membrane proteins in lipid bilayers. J. Fluid Mech. 258, 167–190.Google Scholar
Bussell, S. J., Koch, D. L. & Hammer, D. A. 1995a The effect of hydrodynamic interactions on the diffusion of integral membrane proteins: tracer diffusion in organelle and reconstituted membranes. Biophys. J. (in press).Google Scholar
Bussell, S. J., Koch, D. L. & Hammer, D. A. 1995b The effect of hydrodynamic interactions on the diffusion of integral membrane proteins: diffusion in plasma membranes. Biophys. J. (in press).Google Scholar
Chae, D. G., Ree, F. H. & Ree, T. 1969 Radial distribution functions and equation of state of the hard-disk fluid. J. Chem. Phys. 50, 1581–1589.Google Scholar
Chazotte, B. & Hackenbrock, C. R. 1988 The multicollisional, obstructed, long-range diffusional nature of mitochondrial electron transport. J. Bio. Chem. 263, 14359–14367.Google Scholar
Deatherage, J. F., Henderson, R. & Capaldi, R. A. 1982 Relationship between membrane and cytoplasmic domains in cytochrome c oxidase by electron microscopy in media of different density. J. Mol. Biol. 158, 501–514.Google Scholar
Durlofsky, L. & Brady, J. F. 1987 Analysis of the Brinkman equation as a model for flow in porous media. Phys. Fluids 30, 3329–3341.Google Scholar
Einstein, A. 1906 A new determination of molecular dimensions. Ann. Physik 19, 289–306 (and Corrections 34, 591–592 (1911)).Google Scholar
Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions. J. Chem. Phys. 69, 1352.Google Scholar
Hasimoto, H. 1959 On the periodic fundamental solution of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317–328.CrossRefGoogle Scholar
Henderson, R. & Unwin, P. N. T. 1975 Three-dimensional model of purple membrane obtained by electron microscopy. Nature 257, 28–32.Google Scholar
Henis, Y.I. & Elson, E. L. 1981a Inhibition of the mobility of mouse lymphocyte surface immunoglobins by locally bound concanavalin A. Proc. Natl Acad. Sci. USA 78, 1072–1076.Google Scholar
Henis, Y. I. & Elson, E. L. 1981b Differences in the response of several cell types to inhibition of surface receptor mobility by local concanavalin A binding. Exp. Cell Res. 136, 189–201.Google Scholar
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension. J. Fluid Mech. 83, 695–720.Google Scholar
Howells, I. D. 1974 Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed objects. J. Fluid Mech. 64, 449–475.Google Scholar
Kops-Werkhoven, M. M. & Fijnaut, H. M. 1981 Dynamic light scattering and sedimentation experiments on silica dispersions at finite concentrations. J. Chem. Phys. 74, 1618.Google Scholar
Kops-Werkhoven, M. M., Vrij, A. & Lekkerkerker, H. N. W. 1983 On the relation between diffusion, sedimentation, and friction. J. Chem. Phys. 78, 2760.Google Scholar
Ladd, A. J. C. 1988 Hydrodynamic interactions in suspensions of spherical particles. J. Chem. Phys. 88, 5051.Google Scholar
Ladd, A. J. C. 1989 Hydrodynamic interactions and the viscosity of suspensions of freely moving spheres. J. Chem. Phys. 90, 1149.Google Scholar
Ladd, A. J. C. 1990 Hydrodynamic transport coefficients of random dispersions of hard spheres. J. Chem. Phys. 93, 3484–3493.Google Scholar
Leonard, K., Haiker, H. & Weiss, H. 1987 Three-dimensional structure of NADH: ubiquinone reductase (complex I) from Neoropora mitochondria determined by electron microscopy of membrane crystals. J. Mol. Biol. 194, 277–286.Google Scholar
McCloskey, M. A., Liu, Z-y. & Poo, M.-y. 1984 Lateral electromigration and diffusion of Fce receptors on rat basophilic leukemia cells: effect of IgG binding. J. Cell Biol. 99, 778–787.Google Scholar
Medina-Noyala, M. 1988 Long-time self-diffusion in concentrated colloidal dispersions. Phys. Rev. Lett. 60, 2705–2708.Google Scholar
Metzgar, H. & Kinet, J. P. 1988 How antibodies work; focus on Fc receptors. Fed. Am. Soc. Exp. Biol. J. 2, 3–11.Google Scholar
Mo, G. & Sangani, A. S. 1994 A method of computing Stokes flow interactions among spherical objects and its application to suspensions of drops and porous particles. Phys. Fluids 6, 1637–1652.Google Scholar
Myers, J. N., Holowka, D. & Baird, B. 1992 Rotational motion of monomeric and dimeric immunoglobulin E-receptor complexes. Biochemist 31, 567–575.Google Scholar
Peters, R. & Cherry, R. J. 1982 Lateral and rotational diffusion of bacteriorhodopsin in lipid bilayers: experimental test of the Saffman-Delbruck equations. Proc. Natn Acad. Sci. USA 79, 4317–4321.Google Scholar
Phillips, R. J., Brady, J. F. & Bossis, G. 1988 Hydrodynamic transport properties of hardsphere dispersions. I. Suspensions of freely mobile particles. Phys. Fluids 31, 3462–3472.Google Scholar
Rahman, N. A., Pecht, I., Roess, D. A. & Barisas, B. G. 1992 Rotational dynamics of type I Fce receptors on individually-selected rat mast cells studied by polarized fluorescence depletion. Biophys. J. 61, 334–346.Google Scholar
Rallison, J. M. 1988 Brownian diffusion in concentrated suspensions of intracting particles. J. Fluid Mech. 186, 471–500.Google Scholar
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73, 593–602.Google Scholar
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natn Acad. Sci. USA 72, 3111–3113.Google Scholar
Sangani, A. S. & Mo, G. 1994 Inclusion of lubrication forces in dynamic simulations. Phys. Fluids 6, 1653–1662.Google Scholar
Sangani, A. S. & Yao, C. 1988 Transport processes in random arrays of cylinders. II. Viscous flow. Phys. Fluids 31, 2435–2444.Google Scholar
Saxton, M. J. 1987 Lateral diffusion in an archipelago: the effect of mobile obstacles. Biophys. J. 52, 989–997.Google Scholar
Saxton, M. J. 1990 Lateral diffusion in a mixture of mobile and immobile particles: a monte carlo study. Biophys. J. 58, 1303–1306.CrossRefGoogle Scholar
Scalletar, B. A. & Abney, J. R. 1991 Molecular crowding and protein diffusion in biological membranes. Comments Mol. Biophys. 7, 79–107.Google Scholar
Sheetz, M. P., Schindler, M. & Koppel, D. E. 1980 Lateral mobility of integral membrane proteins in increased spherocytic erythrocytes. Nature 285, 510–512.Google Scholar
Young, S. H., McCloskey, M. & Poo, M.-m. 1984 Migration of cell surface receptors induced by extracellular electric fields: Theory and applications. The Receptors 1, 511–539.Google Scholar
Zagyansky, Y. A. & Jard, S. 1979 Does lectin-receptor complex formation produce zones of restricted mobility within the membranes? Nature 280, 591.Google Scholar
Zidovetzski, R., Bartholdi, M., Arndt-Jovin, D. & Jovin, T. M. 1986 Rotational dynamics of Fc receptor for immunoglobulin E on histamin-releasing rat basophilic leukemia cells. Biochemist 25, 4397–4401.Google Scholar