Studying the kinetics of protein folding is the key to understanding the fundamental underlying mechanism. Levinthal (1969) posed the so-called Levinthal paradox 35 years ago. If protein folding proceeds with going through every possible state, then it takes cosmological time to reach the native state. In nature, protein folding finishes in millisecond to second. The recent energy landscape theory of protein folding (Bryngelson and Wolynes, 1989; Bryngelson et al., 1995; Chan and Dill, 1994; Abkevich et al., 1994; Wang et al., 1996) resolves the issue by assuming the underlying energy landscape is funneled toward the native state. Superimposed on that are the bumps and wiggles forming local traps. For folding to complete in biological timescale under physiological temperature (300 K), the slope of the funnel must be steep enough to overcome the local traps. The energy landscape theory is successful in explaining qualitatively and quantitatively many folding experiments (Bryngelson and Wolynes, 1989; Bryngelson et al., 1995; Chan and Dill, 1994; Abkevich et al., 1994; Wang et al., 1996).
Both theoretical and experimental investigations on folding and reaction kinetics show complex kinetics in different ranges of temperature (Bryngelson and Wolynes, 1989; Bryngelson et al., 1995; Chan and Dill, 1994; Abkevich et al., 1994; Wang et al., 1996; Gutin et al., 1996; Cieplak et al., 1999; Seno et al., 1998; Klimov and Thirumalai, 1998; Kaya and Chan, 2000, 2002; Itzhaki et al., 1995; Schuler et al., 2002; Lipman et al., 2003; Sabelko et al., 1999; Nguyen et al., 2003; Frauenfelder et al., 1988, 1991; Yang and Xie, 2002a,b). By varying the temperature, the underlying energy landscape structures can be probed in different levels, from the global to the local detail perspectives (Frauenfelder et al., 1988, 1991). The relationship between dynamics and functions of the biomolecules can be revealed. Although different theoretical approaches explain kinetic behavior within specific temperature ranges, the unified picture of kinetics of the whole temperature range seems still lacking. This is the purpose of the current study. Lately, the diffusive dynamics of folding is shown to have complex kinetics (Nguyen et al., 2003; Lee et al., 2003; Zhou et al., 2003; V. B. P. Leite, J. N. Onuchic, G. Stell, and J. Wang, unpublished results).
In this article, we study the kinetics in the whole temperature range. We show that the Poisson(exponential)-non-Poisson(non-exponential)-Poisson (exponential) kinetics emerge from high to low temperatures. This phenomena seems to be universal not only for protein folding, but might also exist in other biomolecular folding, biomolecular binding and reaction systems, electron transfer, viscous liquid, and glassy materials.
The current results of the study are also relevant to the single molecule studies where the mean of the observables is often unreliable due to the large statistical fluctuations (which are not smeared out by the number of molecules as in the bulk case), and cannot be used to accurately characterize the system. In general, fluctuations of the observables intrinsic for characterizing the system are obtained from the information on moments and distributions (Wang and Wolynes, 1995, 1999; Onuchic et al., 1999; Wang, 2003). The connections of the theory and simulations with the single molecule kinetic experiments can be made through the analysis of the long-time dynamic trajectories or multiple short-time runs where information on the mean, high-order moments and distributions, or histograms of the important observables can be extracted (Lu et al., 1998; Schenter et al., 1999; Moerner, 1996; Zhuang et al., 2000, 2002; Jia et al., 1999).