SHAPES AND SHAPE TRANSFORMATIONS OF TWO-COMPONENT MEMBRANES OF COMPLEX TOPOLOGY

The properties of two-component membranes, which form doubly periodic surfaces of complex topology, are studied in the strong-segregation limit. The membrane is described within the framework of curvature elasticity; the two components are distinguished by their spontaneous curvatures in this case. Four different domain morphologies are considered for a square lattice of passages: rings of component a inside the passage and caplets of component a outside the passage, as well as rings and caplets of component b. The dependences of the shape of the membrane and of the shape of the domain boundary are calculated as a function of composition. On the basis of a calculation of the curvature energy we conjecture the existence of doubly periodic, piecewise constant-mean-curvature surfaces. For small and intermediate line tensions, we predict several phase transitions between the investigated morphologies. We also discuss briefly the existence and shapes of vesicles of piecewise constant mean curvature. @S1063-651X~99!02304-1#

[1]  David Andelman,et al.  Equilibrium shape of two-component unilamellar membranes and vesicles , 1992 .

[2]  G. Gompper,et al.  Composition-Driven Shape Transformations of Membranes of Complex Topology , 1998 .

[3]  M. Bloom,et al.  Physical properties of the fluid lipid-bilayer component of cell membranes: a perspective , 1991, Quarterly Reviews of Biophysics.

[4]  F. Bates,et al.  Stability of the perforated layer (PL) phase in diblock copolymer melts , 1997 .

[5]  E. Sackmann,et al.  On Domain Structure and Local Curvature in Lipid Bilayers and Biological Membranes , 1977, Zeitschrift fur Naturforschung. Section C, Biosciences.

[6]  O. G. Mouritsen,et al.  Molecular sorting of lipids by bacteriorhodopsin in dilauroylphosphatidylcholine/distearoylphosphatidylcholine lipid bilayers. , 1997, Biophysical journal.

[7]  Netz,et al.  Inhomogeneous fluid membranes: Segregation, ordering, and effective rigidity. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  P. Kinnunen.  On the principles of functional ordering in biological membranes. , 1991, Chemistry and physics of lipids.

[9]  R. Lipowsky,et al.  Domain-induced budding of vesicles. , 1993, Physical review letters.

[10]  M. Bloom,et al.  Phosphatidylcholine: cholesterol phase diagrams. , 1992, Biophysical journal.

[11]  H. Mcconnell,et al.  Critical mixing in monolayer mixtures of phospholipid and cholesterol , 1987 .

[12]  Jung Y. Huang,et al.  Detection of phase separation in fluid phosphatidylserine/phosphatidylcholine mixtures. , 1994, Biophysical journal.

[13]  R. Lipowsky,et al.  Shape transformations of vesicles with intramembrane domains. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  A. Emons,et al.  Boekbespreking: Molecular biology of the cell, B. Alberts, D. Bray, J. Lewis, M. Raff, K. Robers, D.J. Watson. Garland Publ., New York. 1989. , 1990 .

[15]  E. Pebay-Peyroula,et al.  X-ray structure of bacteriorhodopsin at 2.5 angstroms from microcrystals grown in lipidic cubic phases. , 1997, Science.

[16]  M. Bloom,et al.  Mattress model of lipid-protein interactions in membranes. , 1984, Biophysical journal.

[17]  M. Seul,et al.  Critical mixing in monomolecular films : pressure-composition phase diagram of a two-dimensional binary mixture , 1990 .

[18]  Bensimon,et al.  Fluctuating vesicles of nonspherical topology. , 1994, Physical review letters.

[19]  Samuel A. Safran,et al.  Membrane-induced interactions between inclusions , 1993 .

[20]  M Edidin,et al.  Lipid microdomains in cell surface membranes. , 1997, Current opinion in structural biology.

[21]  H. Lawson,et al.  Complete Minimal Surfaces in S 3 , 1970 .

[22]  R. Lipowsky.  Domain-induced budding of fluid membranes. , 1993, Biophysical journal.

[23]  S. Idziak,et al.  Lamellar Biogels: Fluid-Membrane-Based Hydrogels Containing Polymer Lipids , 1996, Science.

[24]  H. Mcconnell,et al.  Critical shape transitions of monolayer lipid domains. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[25]  F. Bates,et al.  Hexagonal mesophases between lamellae and cylinders in a diblock copolymer melt , 1993 .

[26]  H. Mcconnell,et al.  Phase separations in phospholipid membranes , 1975 .

[27]  James H. Davis,et al.  Phase equilibria of cholesterol/dipalmitoylphosphatidylcholine mixtures: 2H nuclear magnetic resonance and differential scanning calorimetry. , 1990, Biochemistry.

[28]  Fred C. MacKintosh,et al.  Shape Transformations of Domains in Mixed-Fluid Films and Bilayer Membranes , 1994 .

[29]  K. Jørgensen,et al.  Small-scale lipid-membrane structure: simulation versus experiment. , 1997, Current opinion in structural biology.

[30]  S. Leibler,et al.  Ordered and curved meso-structures in membranes and amphiphilic films , 1987 .