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The resistivity and mobility functions for a model system of two equal-sized proteins in a lipid bilayer

Published online by Cambridge University Press:  26 April 2006

Stuart J. Bussell ,
Donald L. Koch  and
Daniel A. Hammer
Stuart J. Bussell
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
Daniel A. Hammer
Affiliation:
School of Chemical Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

We have calculated the mobility and resistivity functions for two equal-sized cylinders moving in a thin viscous sheet surrounded by a lower-viscosity fluid. These functions describe the hydrodynamic interactions between proteins embedded in a lipid bilayer surrounded by an aqueous solution. For a protein of radius a embedded in a biological membrane of thickness h and viscosity μ, a key parameter λ = μh/aμ′, which characterizes the viscosity ratio between the bilayer and surounding solution, is O(100). The method of solution for the hydrodynamic interactions differs depending on the separation distance, r, between the cylinders. When r = O(a), the particles are in the near-field regime, and the solution of the Stokes equations is divided between an inner and outer domain based on the asymptotically large value of λ. The inner solution neglects the flow in the lower-viscosity fluid and is solved numerically using a bipolar expansion. The outer solution is based on the fluid flows in all phases, but the cylinders are approximated by net forces. When r [Gt ] O(a), the particles are in the far-field regime, and we use the method of reflections to solve for the hydrodynamic interactions. The uniformly valid approximations, constructed from a combination of the near-field and far-field solutions, agree with the analytic solutions obtained within the lubrication and far-field regimes. Our results show that the hydrodynamic interactions between the cylinders are long range, perarting on a lengthscale of O(λ). The range of the hydrodynamic interactions is much longer than that of non-hydrodynamic interparticle forces, suggesting that hydrodynamic interactions will be significant determinants of the structure and dynamics of biological membranes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 679 - 697
Copyright
© 1992 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
Batchelor, G. K. 1983 Diffusion in a dilute polydisperse system of interacting spheres. J. Fluid Mech. 131, 155–175.Google Scholar
Bitsanis, I., Somers, S. A., Davis, H. T. & Tirrell, M. 1990 Microscopic dynamics of flow in molecularly narrow pores. J Chem. Phys. 93, 3427–3431.Google Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157.Google Scholar
Brenner, H. & O'Neill, M. E. 1972 On the Stokes resistance of multiparticle systems in a linear shear field. Chem. Engng Sci. 27, 1421–1439.Google Scholar
Bussell, S. J. 1992 Diffusion-limited reaction rates of integral membrane proteins. Ph.D. thesis, Cornell University.
Hughes, B. D., Pailthorpe, B. A. & White, L. R. 1981 The translational and rotational drag on a cylinder moving in a membrane. J. Fluid Mech. 110, 349–372.Google Scholar
Israelachvili, J. N. & McGuiggan, P. M. 1988 Forces between surfaces in liquids. Science 241, 795–800.Google Scholar
Kim, S. & Kabrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Lorentz, H. A. 1907 Ein allgemeiner Satz, die Bewegung einer reibenden Flussigkeit betreffend, nebst einigen Anwendungen desselben (A general theorem concerning the motion of a viscous fluid and a few applications from it). Abh. Theoret. Phys. 1, 23–42.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. Sail Acad. Sci. USA 79, 4317–4321.Google Scholar
Pink, D. A., Laidlaw, D. J. & Chilsholm, D. M. 1986 Protein lateral movement in lipid bilayers: Monte Carlo simulation studies of its dependence upon attractive protein—protein interactions Biochim. Biophys. Acta 863, 9–17.Google Scholar
Russel, W. B. & Gast, A. P. 1986 Nonequilibrium statistical mechanics of concentrated colloidal dispersions: hard spheres in weak flows. J. Chem. Phys. 84, 1815–1826.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. & Delbritck, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72, 3111–3113.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
Schtjlz, G. E. & Schirmer, R. H. 1979 Principles of Protein Structure. Springer.
Vaz, W. L. C., Goodsaid-zalduondo, F. & Jacobson, K. 1984 Lateral diffusion of lipids and proteins in bilayer membranes. FEBS Lett. 174, 199–207.Google Scholar