What is the time scale for α-helix nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ～0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.