Temperature Dependence of the Distribution of the First Passage Time: Results from Discontinuous Molecular Dynamics Simulations of an All-Atom Model of the Second β-Hairpin Fragment of Protein G

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Abstract
More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Gō-like model of the second β-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature Topt*. The optimal folding temperature Topt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the Topt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than Topt* and start to diverge when the temperature is lower than Topt*. The distribution of FPT is close to a log-normal-like distribution at T* ≥ Topt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

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