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 order-parameters 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 cross-sectional areas, and 3) between non-transmembrane proteins. 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 are considerably larger than Van der Waals interactions or screened electrostatic interactions and might provide the dominant force inducing aggregation of the membrane proteins.