Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-04-30T21:40:45.853Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of hydrodynamic interactions on the tracer and gradient diffusion of integral membrane proteins in lipid bilayers

Published online by Cambridge University Press:  26 April 2006

Stuart J. Bussell ,
Daniel A. Hammer  and
Donald L. Koch
Stuart J. Bussell
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
Donald L. Koch
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Biological membranes can be considered two-dimensional fluids with suspended integral membrane proteins (IMPs). We have calculated the effect of hydrodynamic interactions on the various diffusion coefficients of IMPs in lipid bilayers. The IMPs are modelled as hard cylinders of radius a immersed in a thin sheet of viscosity μ and thickness h bounded by a fluid of low viscosity μ′. We have ensemble averaged the N-body Stokes equations to the pair level and have renormalized them following the methods of Batchelor (1972) and Hinch (1977). The lengthscale for the hydrodynamic interactions is λa = μh / μ′, Which is O (100a), and the slow decay of the interactions introduces new features in the renormalizations compared to the analogous analyses for three-dimensional suspensions of spheres.

We have calculated the asymptotic limits for the short- and long-time tracer diffusivities, Ds and Dl, respectively, and for the gradient diffusivity, Dg, for ϕ [Lt ] 1 and λ [Gt ] 1, where ϕ is the IMP area fraction and λ = μh / (μ′a). The diffusivities are \begin{eqnarray*} D_s/D_0 &=& 1-2\phi[1-(1+\ln (2)-9/32)/(\ln(\lambda)-\gamma)], D_l/D_0 &=& D_s/D_0 - 0.07/(\ln(\lambda)-\gamma), D_g/D_0 &=& 1+\phi[-7+(6\ln(2)+7/16+0.37)/(\ln(\lambda)-\gamma)], \end{eqnarray*} where D0 is the diffusivity in the limit of zero area fraction, and γ = 0.577216 is Euler's constant. The results for Dl and Ds differ only slightly. The decrease in Dg/Do as ϕ increases contrasts with the result for spheres for which Dg/Do > 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 258 , 10 January 1994 , pp. 167 - 190
Copyright
© 1994 Cambridge University Press

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

Abney, J. R., Scalettar, B. A. & Owicki, J. C. 1989a Self diffusion of interacting membrane proteins. Biophys. J. 55, 817–833.Google Scholar
Abney, J. R., Scalettar, B. A. & Owicki, J. C. 1989b Mutual diffusion of interacting membrane proteins. Biophys. J. 56, 315–326.Google Scholar
Aguirre, J. L. & Murphy, T. J. 1973 Brownian motion of N interacting particles. II. Hydrodynamical evaluation of the diffusion tensor matrix. J. Chem. Phys. 59, 1833–1840.Google Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.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
Batchelor, G. K. 1983 Diffusion in a dilute polydisperse system of interacting spheres. J. Fluid Mech. 131, 155–175.Google Scholar
Batchelor, G. K. & Wen, C.-S. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results. J. Fluid Mech. 124, 495–528.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. & 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
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
Chazotte, B. & Hackenbrock, C. R. 1988 The multicollisional, obstructed, long-range diffusional nature of mitochondrial electron transport. J. Biol. Chem. 263, 14359–14367.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
Gennis, R. B. 1989 Biomembranes: Molecular Structure and Function. Springer.
Glendinning, A. B. & Russel, W. B. 1982 A pairwise additive description of sedimentation and diffusion in concentrated suspensions of hard spheres. J. Colloid Interface Sci. 89, 124–142.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
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. & Teller, E. 1953 Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1092.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. Natl Acad. Sci. USA 79, 4317–4321.Google Scholar
Phillips, R. J., Brady, J. F. & Bossis, G. 1988 Hydrodynamic transport properties of hard-sphere dispersions. I. Suspensions of freely mobile particles. Phys. Fluids 31, 3462–3472.Google Scholar
Qian, H., Sheetz, M. P. & Elson, E. L. 1991 Single particle tracking: analysis of diffusion and flow in two-dimensional systems. Biophys. J. 60, 910–921.CrossRefGoogle Scholar
Rallison, J. M. 1988 Brownian diffusion in concentrated suspensions of interacting 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
Saxton, M. J. 1987 Lateral diffusion in an archipelago: the effect of mobile obstacles. Biophys. J. 52, 989–997.Google Scholar