Protein folding as a quantum transition between conformational states

Abstract

Assuming that the main variables in the life processes at the molecular level are the conformation of biological macromolecules and their frontier electrons a formalism of quantum theory on conformation-electron system is proposed. Based on the quantum theory of conformation-electron system, the protein folding is regarded as a quantum transition between torsion states on polypeptide chain, and the folding rate is calculated by nonadiabatic operator method. The rate calculation is generalized to the case of frequency variation in folding. An analytical form of protein folding rate formula is obtained, which can be served as a useful tool for further studying protein folding. The application of the rate theory to explain the protein folding experiments is briefly summarized. It includes the inertial moment dependence of folding rate, the unified description of two-state and multistate protein folding, the relationship of folding and unfolding rates versus denaturant concentration, the distinction between exergonic and endergonic foldings, the ultrafast and the downhill folding viewed from quantum folding theory, and, finally, the temperature dependence of folding rate and the interpretation of its non-Arrhenius behaviors. All these studies support the view that the protein folding is essentially a quantum transition between conformational states.

The dynamical contact order: Protein folding rate parameters based on quantum conformational transitions

“…Following the work of Kamagata et al [24] and from our own statistical analyses, we propose that multi-state protein folding can be described as a joint process of several quantum transitions that occur at different degrees of freedom of the torsion angle. The proposal is supported by its consistency with quantum transition theory [21]. The folding rate of a multi-state protein can be expressed by the formula for two-state folding with an additional factor e −τ that indicates the time delay while in the intermediate state.…”

“…We assumed that multi-state protein folding can be represented as the joining of several quantum transitions and that each quantum transition occurs at independent degrees of freedom for the torsion angles. Thus, the total collapse process can be approximately described as a non-radiative transition of many degrees of freedom [21]. The transition rate of multi-state protein can then be defined as…”

“…Apart from limitations due to computational capability currently available, molecular dynamics simulations are based on classical mechanics while protein folding is mainly a quantum mechanical process of conformational change between different torsion states of the polypeptide chain. Luo [18][19][20][21] was one of the first to study protein folding problem from the point of quantum transition theory and to calculate the protein folding rate based on quantum conformational dynamics. Luo's results explain why the time scale of the fundamental folding event is generally in the order of milliseconds to microseconds and show that the folding rate can be represented by several physical parameters related to the dynamics of the polypeptide chain.…”

“…Luo's results explain why the time scale of the fundamental folding event is generally in the order of milliseconds to microseconds and show that the folding rate can be represented by several physical parameters related to the dynamics of the polypeptide chain. The relationships between the folding rate and chain length, moment of inertia, energy gap and temperature have been deduced [18,20,21]. Based on Luo's theory we now propose a new contact order, the dynamical contact order (DCO), and use it to kinetically study protein folding rates.…”

Statistical analyses of protein folding rates from the view of quantum transition

“…Compared with other dynamic variables, such as mobile electrons, chemical bonds and stretching-bending vibrations, also called fast variables, molecular torsion has the lowest energy and can be viewed as the slow variable of the macromolecular system. Assuming that "the slow variables slave the fast ones" and using the nonadiabaticity operator method, a formula for protein folding rate in analytical form was deduced in previous results [36,39], as…”