Interactions between Membrane Inclusions on Fluctuating Membranes

We model membrane proteins as anisotropic objects characterized by symmetric-traceless tensors and determine the coupling between these orderparameters and membrane curvature. We consider the interactions 1) 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, 2) between transmembrane proteins that break reflection symmetry and have circular or non-circular crosssectional areas, and 3) between non-transmembrane proteins. Using a field theoretic approach, we find non-entropic 1/R4 interactions between reflection-symmetry-breaking transmembrane proteins with circular crosssectional area and entropic 1/R4 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/R4 interactions between reflection-symmetry-conserving transmembrane proteins with non-circular cross-section, anisotropic 1/R2 interactions between reflectionsymmetry-breaking transmembrane proteins with non-circular cross-section, and non-entropic 1/R4 many-particle interactions among non-transmembrane proteins. For large R, these interactions are considerably larger than Van der Waals interactions or screened electrostatic interactions and might provide 1 the dominant force inducing aggregation of the membrane proteins. PACS numbers: 87.20, 82.65D, 34.20 Typeset using REVTEX 2