Effects of hydrophobic mismatch and spontaneous curvature on ion channel gating with a hinge

We analyze the energetics of an ion-channel gating, focusing on effects of hydrophobic mismatch between the channel protein and the nearby lipid molecules, spontaneous curvature of monolayers, and thickness change of membranes. For the analysis we consider recently proposed open and closed conformations of a potassium channel which has a gating hinge, using the elastic continuum model of membranes. Gating energy, defined as the difference of deformation free energies for open and closed conformations, is quantitatively evaluated for various values of moduli related to the deformation of membranes and spontaneous curvature of monolayer imposing a strong hydrophobic boundary condition. We show that the gating mechanism with a hinge can work successfully even in a continuum model that considers hydrophobic mismatch and spontaneous curvature. When the energy cost for the thickness change of the membrane is neglected, the surface tension is not necessarily strong enough to open the channel. Otherwise, a relatively strong surface tension is required to open the channel.