Diffusion-controlled kinetics of the helix–coil transition with square barrier hydrogen bonds

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Abstract
The coil α-helix (and reverse) transition in peptides is modeled as a sequential diffusive kinetic process in which the fundamental event is the diffusion back and forth over a square barrier to propagate or dissolve a single hydrogen bond. The model is solved exactly numerically in one-dimension (the reaction coordinate), for helix and coil probabilities as a function of (1) time, (2) the number of hydrogen bonds, and (3) temperature. In addition, a modified first-passage time is calculated as the time scale of the coil to helix transition. The results of the diffusion model calculations are compared with recent experiments and we show how the model may give insight into protein folding kinetics. The mechanistic diffusion model complements the Master equation model applied previously to the coil–helix folding problem and provides insight into the choice of a useful reaction coordinate for the process.