A coarse-grained model for the formation of alpha helix with a noninteger period on simple cubic lattices

Periodicity is an important parameter in the characterization of a helix in proteins. In this work, a coarse-grained model for a homopolypeptide in simple cubic lattices has been extended to build an alpha helix with a noninteger period. The lattice model is based on the bond fluctuation algorithm in which bond lengths and orientations are altered in a quasicontinuous way, and the simulation is performed via dynamic Monte Carlo simulation. Hydrogen bonds are assumed to be formed between a virtual-carbonyl group in a residue and a downstream virtual-imino group in another residue. Consequently, the period of the formed alpha helix is a noninteger. An improved spatial correlation function has been suggested to quantitatively describe the periodicity of the helical conformation, by which helical period and helical persistent length can be calculated by statistics. The resultant periods are very close to 3.6 residues; the persistent length based upon the improved definition can be larger or smaller than the chain length and reflect the inherent regularity of a chain including one or multiple helical blocks. The simulation outputs agree with the calculation of the Zimm-Bragg theory based upon the associated nucleation parameter and propagation parameter as well.