Interactions between Membrane Inclusions on Fluctuating Membranes

Abstract

We model membrane proteins as anisotropic objects characterized by symmetric-traceless tensors and determine the coupling between these order-parameters and membrane curvature. We consider the interactions between transmembrane proteins that respect up-down (reflection) symmetry of bilayer membranes and that have circular or non-circular cross-sectional areas in the tangent-plane of membranes. Using a field theoretic approach, we find non-entropic $1/R^4$ interactions between reflection-symmetry-breaking transmembrane proteins with circular cross-sectional area and entropic $1/R^4$ interactions between transmembrane proteins with circular cross-section that do not break up-down symmetry in agreement with previous calculations. We also find anisotropic $1/R^4$ interactions between reflection-symmetry-conserving transmembrane proteins with non-circular cross-section, anisotropic $1/R^2$ interactions between reflection-symmetry-breaking transmembrane proteins with non-circular cross-section, and non-entropic $1/R^4$ many-particle interactions among non-transmembrane proteins. For large $R$, these interactions might provide the dominant force inducing aggregation of the membrane proteins.

REVTEX, 29 pages with 4 postscript figures compressed using uufiles. Introduction and Discussion sections revised. To appear in J. Phys. France I (September)

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