DOI: 10.1017/s0022112095001674. Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins

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

10.1017/s0022112095001674

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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.

Bibliography

Dodd, T. L., Hammer, D. A., Sangani, A. S., & Koch, D. L. (1995). Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins. Journal of Fluid Mechanics, 293, 147â180.

Authors 4

Travis L. Dodd (first)
Daniel A. Hammer (additional)
Ashok S. Sangani (additional)
Donald L. Koch (additional)

References 51 Referenced 62

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Ladd, A. J. C. 1990 Hydrodynamic transport coefficients of random dispersions of hard spheres.J. Chem. Phys. 93,3484–3493.
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.
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Ladd, A. J. C. 1989 Hydrodynamic interactions and the viscosity of suspensions of freely moving spheres.J. Chem. Phys. 90,1149.
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.
Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension.J. Fluid Mech. 83,695–720.
Durlofsky, L. & Brady, J. F. 1987 Analysis of the Brinkman equation as a model for flow in porous media.Phys. Fluids 30,3329–3341.
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.
Chazotte, B. & Hackenbrock, C. R. 1988 The multicollisional, obstructed, long-range diffusional nature of mitochondrial electron transport.J. Bio. Chem. 263,14359–14367.
Abney, J. R. , Scalettar, B. A. & Owicki, J. C. 1989 Self diffusion of interacting membrane proteins.Biophys. J. 55,817–833.
Rallison, J. M. 1988 Brownian diffusion in concentrated suspensions of intracting particles.J. Fluid Mech. 186,471–500.
Sheetz, M. P. , Schindler, M. & Koppel, D. E. 1980 Lateral mobility of integral membrane proteins in increased spherocytic erythrocytes.Nature 285,510–512.
Batchelor, G. K. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory.J. Fluid Mech. 119,379–408.
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.
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.
Metzgar, H. & Kinet, J. P. 1988 How antibodies work; focus on Fc receptors.Fed. Am. Soc. Exp. Biol. J. 2,3–11.
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Brady, J. F. & Durlofsky, L. J. 1988 The sedimentation rate of disordered suspensions.Phys. Fluids 31,717–727.
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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). (10.1016/S0006-3495(95)80359-0)
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.
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics.Ann. Rev. Fluid Mech. 20,111–157.
10.1016/S0006-3495(90)82470-X
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.
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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.
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Einstein, A. 1906 A new determination of molecular dimensions.Ann. Physik 19,289–306 (and Corrections 34, 591–592 (1911)).
Scalletar, B. A. & Abney, J. R. 1991 Molecular crowding and protein diffusion in biological membranes.Comments Mol. Biophys. 7,79–107.
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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.
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Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles.Appl. Sci. Res. A1,27–34.
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Sangani, A. S. & Yao, C. 1988 Transport processes in random arrays of cylinders. II. Viscous flow.Phys. Fluids 31,2435–2444.
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Brady, J. F. 1994 The long-time self-diffusivity in concentrated colloidal dispersions.J. Fluid Mech. 272,109–134.
Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions.J. Chem. Phys. 69,1352.
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). (10.1016/S0006-3495(95)80360-7)
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Dates

Type	When
Created	19 years, 4 months ago (April 27, 2006, 3:04 p.m.)
Deposited	6 years, 2 months ago (June 7, 2019, 4:19 p.m.)
Indexed	1 month, 3 weeks ago (July 1, 2025, 6:04 a.m.)
Issued	30 years, 2 months ago (June 25, 1995)
Published	30 years, 2 months ago (June 25, 1995)
Published Online	19 years, 4 months ago (April 26, 2006)
Published Print	30 years, 2 months ago (June 25, 1995)

Funders 0

None

BibTeX

@article{Dodd_1995, title={Numerical simulations of the effect of hydrodynamic interactions on diffusivities of integral membrane proteins}, volume={293}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112095001674}, DOI={10.1017/s0022112095001674}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Dodd, Travis L. and Hammer, Daniel A. and Sangani, Ashok S. and Koch, Donald L.}, year={1995}, month=jun, pages={147–180} }

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      "unstructured": "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\u2013514."
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      "unstructured": "Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interactions.J. Fluid Mech. 74,1\u201329."
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      "unstructured": "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\u2013286."
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      "key": "S0022112095001674_ref024",
      "unstructured": "Hinch, E. J. 1977 An averaged-equation approach to particle interactions in a fluid suspension.J. Fluid Mech. 83,695\u2013720."
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      "unstructured": "Durlofsky, L. & Brady, J. F. 1987 Analysis of the Brinkman equation as a model for flow in porous media.Phys. Fluids 30,3329\u20133341."
    },
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      "key": "S0022112095001674_ref011",
      "unstructured": "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\u2013190."
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    {
      "key": "S0022112095001674_ref015",
      "unstructured": "Chazotte, B. & Hackenbrock, C. R. 1988 The multicollisional, obstructed, long-range diffusional nature of mitochondrial electron transport.J. Bio. Chem. 263,14359\u201314367."
    },
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      "key": "S0022112095001674_ref001",
      "unstructured": "Abney, J. R. , Scalettar, B. A. & Owicki, J. C. 1989 Self diffusion of interacting membrane proteins.Biophys. J. 55,817\u2013833."
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      "unstructured": "Rallison, J. M. 1988 Brownian diffusion in concentrated suspensions of intracting particles.J. Fluid Mech. 186,471\u2013500."
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      "key": "S0022112095001674_ref048",
      "unstructured": "Sheetz, M. P. , Schindler, M. & Koppel, D. E. 1980 Lateral mobility of integral membrane proteins in increased spherocytic erythrocytes.Nature 285,510\u2013512."
    },
    {
      "key": "S0022112095001674_ref004",
      "unstructured": "Batchelor, G. K. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory.J. Fluid Mech. 119,379\u2013408."
    },
    {
      "key": "S0022112095001674_ref023",
      "unstructured": "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\u2013201."
    },
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      "key": "S0022112095001674_ref002",
      "unstructured": "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\u20131069."
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    {
      "key": "S0022112095001674_ref034",
      "unstructured": "Metzgar, H. & Kinet, J. P. 1988 How antibodies work; focus on Fc receptors.Fed. Am. Soc. Exp. Biol. J. 2,3\u201311."
    },
    {
      "key": "S0022112095001674_ref014",
      "unstructured": "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\u20131589."
    },
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      "key": "S0022112095001674_ref008",
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      "unstructured": "Saffman, P. G. & Delbr\u00fcck, M. 1975 Brownian motion in biological membranes.Proc. Natn Acad. Sci. USA 72,3111\u20133113."
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      "DOI": "10.1016/S0006-3495(95)80359-0"
    },
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      "key": "S0022112095001674_ref026",
      "unstructured": "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."
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      "key": "S0022112095001674_ref007",
      "unstructured": "Brady, J. F. & Bossis, G. 1988 Stokesian dynamics.Ann. Rev. Fluid Mech. 20,111\u2013157."
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    },
    {
      "key": "S0022112095001674_ref005",
      "unstructured": "Brady, J. F. 1984 The Einstein viscosity correction in n dimensions.Intl J. Multiphase Flow 10,113\u2013114."
    },
    {
      "key": "S0022112095001674_ref025",
      "unstructured": "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\u2013475."
    },
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      "key": "S0022112095001674_ref035",
      "unstructured": "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\u20131652."
    },
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      "key": "S0022112095001674_ref018",
      "unstructured": "Einstein, A. 1906 A new determination of molecular dimensions.Ann. Physik 19,289\u2013306 (and Corrections 34, 591\u2013592 (1911))."
    },
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      "key": "S0022112095001674_ref047",
      "unstructured": "Scalletar, B. A. & Abney, J. R. 1991 Molecular crowding and protein diffusion in biological membranes.Comments Mol. Biophys. 7,79\u2013107."
    },
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      "key": "S0022112095001674_ref039",
      "unstructured": "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\u2013346."
    },
    {
      "key": "S0022112095001674_ref037",
      "unstructured": "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\u20134321."
    },
    {
      "key": "S0022112095001674_ref010",
      "unstructured": "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\u2013697."
    },
    {
      "key": "S0022112095001674_ref009",
      "unstructured": "Brinkman, H. C. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles.Appl. Sci. Res. A1,27\u201334."
    },
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      "unstructured": "Sangani, A. S. & Mo, G. 1994 Inclusion of lubrication forces in dynamic simulations.Phys. Fluids 6,1653\u20131662."
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    },
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      "key": "S0022112095001674_ref038",
      "unstructured": "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\u20133472."
    },
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      "key": "S0022112095001674_ref049",
      "unstructured": "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\u2013539."
    },
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      "unstructured": "Sangani, A. S. & Yao, C. 1988 Transport processes in random arrays of cylinders. II. Viscous flow.Phys. Fluids 31,2435\u20132444."
    },
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      "key": "S0022112095001674_ref051",
      "unstructured": "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\u20134401."
    },
    {
      "key": "S0022112095001674_ref006",
      "unstructured": "Brady, J. F. 1994 The long-time self-diffusivity in concentrated colloidal dispersions.J. Fluid Mech. 272,109\u2013134."
    },
    {
      "key": "S0022112095001674_ref019",
      "unstructured": "Ermak, D. L. & McCammon, J. A. 1978 Brownian dynamics with hydrodynamic interactions.J. Chem. Phys. 69,1352."
    },
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      "key": "S0022112095001674_ref013",
      "doi-asserted-by": "crossref",
      "unstructured": "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).",
      "DOI": "10.1016/S0006-3495(95)80360-7"
    },
    {
      "key": "S0022112095001674_ref021",
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