Implementation and application of helix-helix distance and crossing angle restraint potentials

Based on the definition of helix-helix distance and crossing angle introduced by Chothia et al. (J Mol Biol 1981, 145, 215), we have developed the restraint potentials by which the distance and crossing angle of two selected helices can be maintained around target values during molecular dynamics simulations. A series of assessments show that calculated restraint forces are numerically accurate. Since the restraint forces are only exerted on atoms which define the helical principal axes, each helix can rotate along its helical axis, depending on the helix-helix intermolecular interactions. Such a restraint potential enables us to characterize the helix-helix interactions at atomic details by sampling their conformational space around specific distance and crossing angle with (restraint) force-dependent fluctuations. Its efficacy is illustrated by calculating the potential of mean force as a function of helix-helix distance between two transmembrane helical peptides in an implicit membrane model.