“…We focus here on protein-induced lipid bilayer thickness deformations, which have been found [2][3][4][5][6][7][8][9][27][28][29][30] to play central roles in regulation of protein function and bilayer-mediated protein interactions in a wide range of experimental systems [10, 11, 24-28, 31, 38-47, 81-83, 88-97]. Using this mathematical framework we have shown previously that the shape of integral membrane proteins, and resulting structure of lipid bilayer thickness deformations, can play a crucial role in the regulation of protein function by lipid bilayers [47,88], and that bilayer thicknessmediated interactions between integral membrane proteins can be strongly directional and dependent on protein shape [46,47,89,97].…”