ENERGETICS OF INCLUSION-INDUCED BILAYER DEFORMATIONS

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning prot eins perturb the structure of the surrounding bilayer. This coupling b etween the protein and the bilayer arises from hydrophobic interaction s between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between th e length of the protein's hydrophobic exterior surface and the average thickness of the bilayer's hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deforma tion is described as the sum of three contributions: compression-expan sion, splay-distortion, and surface tension. When evaluating the inter dependence among the energy components, one modulus renormalizes the o ther: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion en ergy. The surface tension contribution always is negligible in thin so lvent-free bilayers. When evaluating the energy per unit distance (awa y from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion c omponent is more prominent further away from the boundary. Despite thi s complexity, the bilayer deformation energy in many cases can be desc ribed by a linear spring formalism. The results show that, for a prote in embedded in a membrane with an initial hydrophobic mismatch of only 1 Angstrom, an increase in hydrophobic mismatch to 1.3 Angstrom can i ncrease the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.