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

Hydrophobic interactions between a bilayer and its embedded membrane protei ns couple protein conformational changes to changes in the packing of the s urrounding lipids. The energetic cost of a protein conformational change th erefore includes a contribution from the associated bilayer deformation ene rgy (Delta G(def)(o)), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies ba sed 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 s ingle spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurement s of the spring constant and thereby evaluate quantitatively the Delta G(de f)(o) associated with protein conformational changes. Gramicidin channels c an be used as such reporter proteins because the channels form by the trans membrane assembly of two nonconducting monomers. The monomer<->dimer reacti on thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant descri bing the channel-induced bilayer deformation by examining how Delta G(def)( o) varies as a function of a mismatch between the hydrophobic channel lengt h and the unperturbed bilayer thickness. We show this is possible by analyz ing experimental studies on the relation between bilayer thickness and gram icidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclus ion-induced bilayer deformations using independently measured material cons tants.