Protein Folding as a Quantum Transition Between Conformational States: Basic Formulas and Applications

TL;DR

This paper reviews and extends a quantum transition model for protein folding, providing formulas and applications that explain folding rates, temperature effects, denaturant influence, and ultrafast folding limits, supported by experimental data.

Contribution

It introduces a generalized quantum transition rate formula for protein folding, unifies two-state and multi-state theories, and explores folding dynamics through quantum principles and statistical energy landscapes.

Findings

Folding rates depend on frequency variation and inertial moments.

The quantum model explains non-Arrhenius temperature dependence.

A new quantum speed limit for ultrafast folding is proposed.

Abstract

The protein folding is regarded as a quantum transition between torsion states on polypeptide chain. The deduction of the folding rate formula in our previous studies is reviewed. The rate formula is generalized to the case of frequency variation in folding. Then the following problems about the application of the rate theory are discussed: 1) The unified theory on the two-state and multi-state protein folding is given based on the concept of quantum transition. 2) The relationship of folding and unfolding rates vs denaturant concentration is studied. 3) The temperature dependence of folding rate is deduced and the non-Arrhenius behaviors of temperature dependence are interpreted in a natural way. 4) The inertial moment dependence of folding rate is calculated based on the model of dynamical contact order and consistent results are obtained by comparison with one-hundred-protein experimental dataset. 5) The exergonic and endergonic foldings are distinguished through the comparison between theoretical and experimental rates for each protein. The ultrafast folding problem is viewed from the point of quantum folding theory and a new folding speed limit is deduced from quantum uncertainty relation. And finally, 6) since only the torsion-accessible states are manageable in the present formulation of quantum transition how the set of torsion-accessible states can be expanded by using statistical energy landscape approach is discussed. All above discussions support the view that the protein folding is essentially a quantum transition between conformational states.