Spring constants for channel-induced lipid bilayer deformations estimates using gramicidin channels

Hydrophobic interactions between a bilayer and its embedded membrane proteins couple protein conformational changes to changes in the packing of the surrounding lipids. The energetic cost of a protein conformational change therefore includes a contribution from the associated bilayer deformation energy (Delta G(def)(o)), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies based on an elastic liquid-crystal model of the bilayer deformation show that Delta G(def)(o) should be quantifiable by a phenomenological linear spring model, in which the bilayer mechanical characteristics are lumped into a single spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurements of the spring constant and thereby evaluate quantitatively the Delta G(def)(o) associated with protein conformational changes. Gramicidin channels can be used as such reporter proteins because the channels form by the transmembrane assembly of two nonconducting monomers. The monomer<->dimer reaction thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant describing the channel-induced bilayer deformation by examining how Delta G(def)(o) varies as a function of a mismatch between the hydrophobic channel length and the unperturbed bilayer thickness. We show this is possible by analyzing experimental studies on the relation between bilayer thickness and gramicidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclusion-induced bilayer deformations using independently measured material constants.