Molecular dynamics with helical periodic boundary conditions

Helical symmetry is often encountered in nature and thus also in molecular dynamics (MD) simulations. In many cases, an approximation based on infinite helical periodicity can save a significant amount of computer time. However, standard simulations with the usual periodic boundary conditions (PBC) are not easily compatible with it. In the present study, we propose and investigate an algorithm comprising infinitely propagated helicity, which is compatible with commonly used MD software. The helical twist is introduced as a parametric geometry constraint, and the translational PBC are modified to allow for the helical symmetry via a transitional solvent volume. The algorithm including a parallel code was implemented within the Tinker software. The viability of the helical periodic boundary conditions (HPBC) was verified in test simulations including α-helical and polyproline II like peptide structures. For an insulin-based model, the HPBC dynamics made it possible to simulate a fibrillar structure, otherwise not stable within PBC.