Temperature Dependence of Protein Folding Deduced from Quantum Transition

A quantum theory on conformation-electron system is presented. Protein folding is regarded as the quantum transition between torsion states on polypeptide chain, and the folding rate is calculated by nonadiabatic operator method. The theory is used to study the temperature dependences of folding rate of 15 proteins and their non-Arrhenius behavior can all be deduced in a natural way. A general formula on the rate-temperature dependence has been deduced which is in good accordance with experimental data. These temperature dependences are further analyzed in terms of torsion potential parameters. Our results show it is necessary to move outside the realm of classical physics when the temperature dependence of protein folding is studied quantitatively. The non-Arrhenius behavior of protein folding – the nonlinearity of logarithm folding rate on temperature – aroused considerable attention of many investigators. It was conventionally interpreted by the temperature dependence of hydrophobic interaction or by the nonlinear temperature dependence of the configurational diffusion constant on rough energy landscapes [1]. Recent experimental data indicated very different and unusual temperature dependencies of the folding rates existing in the system of 1/ T 6 85 λ − mutants [2,3] and in some de novo designed ultrafast folding protein [4,5]. These unusual Arrhenius plots, as a kind of additional kinetic signatures, provide relatively abundant quantitative data for understanding the mechanism of protein folding [6]. About experimental studies on folding mechanism, apart from the ultrafast folding of small designed proteins, several new experimental techniques for direct observation of ultrafast folding were also proposed [7]. In the meantime, molecular dynamics simulation was commonly used as a theoretical tool for analyzing folding mechanism. However, molecular dynamics simulation is a method based on classical mechanics. When we observe the protein folding at molecular level the application of quantum theory instead of classical mechanics should be more reasonable. Although the classical physics attained part successes in some related studies, detailed observations show that it was mainly used in searching for the energy minimum of folding protein, but the minimum energy seems not sensitive to the method (classical or quantum) by which it is deduced. The widely accepted statistical energy landscape theory on protein folding does not answer whether the folding is classical or quantum [8]. The molecular dynamics simulation was also employed in the solution of Levinthal paradox or the understanding of some folding peculiarity. But here the estimation of folding time is rough and model-dependent or only for small molecules. So, the part success of molecular dynamics simulation only indicates the reasonability of classical approximation in some special cases. The “classical” approach is too limited in the full solution of protein folding problem, especially for the understanding of the fundamental physics underlying