Membrane deformation and the elastic energy of insertion: Perturbation of membrane elastic constants due to peptide insertion

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Abstract
In peptide insertion, matching of the hydrophobic regions of both peptide and lipid molecules constrains the lipid molecules’ mobility and their ability to adjust position, orientation and conformation. This can be described as an insertion induced modification of membrane elastic constants close to the insertion. The perturbation’s correlation length (λ c ) must be comparable to the length of lipid molecules, ∼1.5 nm . We simulate this effect by introducing a “transition” function with decay length λ c . The deformation profile u(r) and corresponding elasticfree energy E are calculated using Euler-Lagrange equations. The proper choice of boundary conditions is discussed. Perturbation of the membrane’s compressional modulus is shown to have much greater influence than perturbation of the bending modulus. Experiments on gramicidin channels’ lifetime are discussed from this perspective. Possible implications of the nonuniformity of the elastic constants on the membrane-mediated interaction between the insertions is also considered.