Elastic Membrane Deformations Determine Interaction of Gramicidin a Dimers, Monomers, and Pairs thereby Modulating the Lifetime of the Conducting State

Abstract

Gramicidin A is a 15-mer antimicrobial peptide produced by Bacillus brevis. In a bilayer lipid membrane, two gramicidin A monomers located in opposite monolayers can form an ion channel due to head-to-head transmembrane dimerization. To form a dimer, gramicidin A monomers first have to stand one on top of another, forming axially symmetric structure called the “pair”. We demonstrated that three key gramicidin A structures: monomer, pair, and dimer, cause elastic deformations of the membrane. We calculated the energy of deformations in the framework of a continuum theory of elasticity of liquid crystals adapted to lipid membranes. On the way from isolated monomers to the conducting dimer, the pair corresponds to the top of the energy barrier. Thus, the energy barrier of dimerization is determined by the energies of the pair and two monomers; the energy barrier of dimer dissociation is determined by the energies of the pair and the dimer. We obtained dependences of the membrane elastic energy on the distance between two monomers, two dimers, dimer and pair, dimer and monomer, pair and monomer. Two dimers were shown to strongly attract each other, while the dimer and the pair repel at short distances (< 2 nm) and attract at larger distances (> 2 nm). From the energy profiles it follows that the lifetime of the conducting state should increase about 1000-fold if two dimers are located close to each other, which is the case for the so-called tandem (linked) gramicidin channels. Monomers were shown to be strongly attracted by dimers; highly concentrated monomers, in turn, modulate the energy of the dimer. We predict exponential growth of the conducting state lifetime with monomer concentration, when exceeding a critical one.