Skip to main content Accessibility help
×
Home

Drag force on a liquid domain moving inside a membrane sheet surrounded by aqueous medium

  • V. Laxminarsimha Rao (a1) and Sovan Lal Das (a1)

Abstract

We compute the drag on a circular and liquid microdomain diffusing in a two-dimensional fluid lipid bilayer membrane surrounded by a fluid above and below. Under the assumptions that the liquids are incompressible and the flow is of low Reynolds number, Stokes’ equations describe the flow in the two-dimensional membrane as well as in the surrounding three-dimensional fluid. The expression for the drag force on the liquid domain involves Fredholm integral equations of the second kind, which we numerically solve using discrete collocation method based on Chebyshev polynomials. We observe that when the domain is more viscous than the surrounding membrane (including the rigid domain case), the drag force is almost independent of the viscosity contrast between the domain and the surrounding membrane, as also observed earlier in experiments by other researchers. The mobility also varies logarithmically with Boussinesq number ${\it\beta}$ for large ${\it\beta}$ . On the other hand, for a less viscous domain the dimensionless drag force reduces with increasing viscosity contrast, and a significant change in the drag force, from that when there is no viscosity contrast or when the domain is rigid, has been observed. Further, the logarithmic behaviour of the mobility no longer holds for less viscous domains. Our method of computing the drag force and diffusion coefficient is valid for arbitrary viscosity contrast between the domain and membrane and any domain size (subject to ${\it\beta}\geqslant 5$ ).

Copyright

Corresponding author

Email address for correspondence: sovandas@iitk.ac.in

References

Hide All
Aliaskarisohi, S., Tierno, P., Dhar, P., Khattari, Z., Blaszczynski, M. & Fischer, T. M. 2010 On the diffusion of circular domains on a spherical vesicle. J. Fluid Mech. 654, 417451.
Atkinson, K. E. 1997 The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press.
Brooks, C. F., Fuller, G. G., Frank, C. W. & Robertson, C. R. 1999 An interfacial stress rheometer to study rheological transitions in monolayers at the air–water interface. Langmuir 15 (7), 24502459.
Brown, D. A. & London, E. 1998 Functions of lipid rafts in biological membranes. Annu. Rev. Cell Dev. Biol. 14 (1), 111136.
Cicuta, P., Keller, S. L. & Veatch, S. L. 2007 Diffusion of liquid domains in lipid bilayer membranes. J. Phys. Chem. B 111 (13), 33283331.
Dietrich, C., Bagatolli, L. A., Volovyk, Z. N., Thompson, N. L., Levi, M., Jacobson, K. & Gratton, E. 2001 Lipid rafts reconstituted in model membranes. Biophys. J. 80 (3), 14171428.
Engelman, D. M. 2005 Membranes are more mosaic than fluid. Nature 438 (7068), 578580.
Evans, E. & Sackmann, E. 1988 Translational and rotational drag coefficients for a disk moving in a liquid membrane associated with a rigid substrate. J. Fluid Mech. 194, 553561.
Fujitani, Y. 2011 Drag coefficient of a liquid domain in a fluid membrane. J. Phys. Soc. Japan 80 (7), 074609.
Fujitani, Y. 2012 Drag coefficient of a liquid domain in a fluid membrane almost as viscous as the domain. J. Phys. Soc. Japan 81 (8), 084601.
Fujitani, Y. 2013 Drag coefficient of a liquid domain in a fluid membrane surrounded by confined three-dimensional fluids. J. Phys. Soc. Japan 82 (8), 084403.
Gambin, Y., Lopez-Esparza, R., Reffay, M., Sierecki, E., Gov, N. S., Genest, M., Hodges, R. S. & Urbach, W. 2006 Lateral mobility of proteins in liquid membranes revisited. Proc. Natl Acad. Sci. USA 103 (7), 20982102.
Guigas, G. & Weiss, M. 2006 Size-dependent diffusion of membrane inclusions. Biophys. J. 91 (7), 23932398.
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, 349372.
Hughes, B. D., Pailthorpe, B. A., White, L. R. & Sawyer, W. H. 1982 Extraction of membrane microviscosity from translational and rotational diffusion coefficients. Biophys. J. 37 (3), 673676.
Ikonen, E. 2001 Roles of lipid rafts in membrane transport. Curr. Opin. Cell Biol. 13 (4), 470477.
Klingler, J. F. & McConnell, H. M. 1993 Brownian motion and fluid mechanics of lipid monolayer domains. J. Phys. Chem. 97 (22), 60966100.
Lee, C. C. & Petersen, N. O. 2003 The lateral diffusion of selectively aggregated peptides in giant unilamellar vesicles. Biophys. J. 84 (3), 17561764.
Mason, J. C. & Handscomb, D. C. 2010 Chebyshev Polynomials. CRC Press.
Naji, A., Levine, A. J. & Pincus, P. A. 2007 Corrections to the Saffman–Delbrück mobility for membrane bound proteins. Biophys. J. 93 (11), L49L51.
Peters, R. & Cherry, R. J. 1982 Lateral and rotational diffusion of bacteriorhodopsin in lipid bilayers: experimental test of the Saffman–Delbrück equations. Proc. Natl Acad. Sci. USA 79 (14), 43174321.
Petrov, E. P. & Schwille, P. 2008 Translational diffusion in lipid membranes beyond the Saffman–Delbrück approximation. Biophys. J. 94 (5), L41L43.
Ramachandran, S., Komura, S., Imai, M. & Seki, K. 2010 Drag coefficient of a liquid domain in a two-dimensional membrane. Eur. Phys. J. E 31 (3), 303310.
Saffman, P. G. 1976 Brownian motion in thin sheets of viscous fluid. J. Fluid Mech. 73 (04), 593602.
Saffman, P. G. & Delbrück, M. 1975 Brownian motion in biological membranes. Proc. Natl Acad. Sci. USA 72 (8), 31113113.
Seki, K., Mogre, S. & Komura, S. 2014 Diffusion coefficients in leaflets of bilayer membranes. Phys. Rev. E 89 (2), 022713.
Seki, K., Ramachandran, S. & Komura, S. 2011 Diffusion coefficient of an inclusion in a liquid membrane supported by a solvent of arbitrary thickness. Phys. Rev. E 84 (2), 021905.
Simons, K. & Ikonen, E. 1997 Functional rafts in cell membranes. Nature 387 (6633), 569572.
Singer, S. J. & Nicolson, G. L. 1972 The fluid mosaic model of the structure of cell membranes. Science 175 (23), 720731.
Stanich, C. A., Honerkamp-Smith, A. R., Putzel, G. G., Warth, C. S., Lamprecht, A. K., Mandal, P., Mann, E., Hua, T.-A. D. & Keller, S. L. 2013 Coarsening dynamics of domains in lipid membranes. Biophys. J. 105 (2), 444454.
Stone, H. A. & Ajdari, A. 1998 Hydrodynamics of particles embedded in a flat surfactant layer overlying a subphase of finite depth. J. Fluid Mech. 369, 151173.
Veatch, S. L. & Keller, S. L. 2005 Seeing spots: complex phase behavior in simple membranes. Biochim. Biophys. Acta 1746 (3), 172185.
Zemyan, S. M. 2012 Singular Integral Equations. Springer.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed