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arXiv:1301.2417

Quantum conformational transition in biological macromolecule

Liaofu Luo

Published Jan 11, 2013• 0 citations

Abstract

The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is proved that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation- transition Hamiltonian the nonradiative matrix element is calculated in two important cases: A, only electrons are fast variables and the electronic state does not change in the transition process; B, fast variables are not limited to electrons but the perturbation approximation can be used. Then, the general formulas for protein folding rate are deduced. The analytical form of the formula is utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation is interpreted. The decoherence time of quantum torsion state is estimated and the quantum coherence degree of torsional angles in the protein folding is studied by using temperature dependence data. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.

DOI: 10.48550/arxiv.1301.2417

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In the context of the macroscopic quantum phenomena of the second kind, we hereby seek for a solution-in-principle of the long standing problem of the polymer folding, which was considered by Levinthal as (semi)classically intractable. To illuminate it, we applied quantum-chemical and quantum decoherence approaches to conformational transitions. Our analyses imply the existence of novel macroscopic quantum biomolecular phenomena, with biomolecular chain folding in an open environment considered as a subtle interplay between energy and conformation eigenstates of this biomolecule, governed by quantum-chemical and quantum decoherence laws. On the other hand, within an open biological cell, a system of all identical (noninteracting and dynamically noncoupled) biomolecular proteins might be considered as corresponding spatial quantum ensemble of these identical biomolecular processors, providing spatially distributed quantum solution to a single corresponding biomolecular chain folding, whose density of conformational states might be represented as Hopfield-like quantum-holographic associative neural network too (providing an equivalent global quantum-informational alternative to standard molecular-biology local biochemical approach in biomolecules and cells and higher hierarchical levels of organism, as well).

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The Levinthal paradox states that it would be impossible for a protein to reach its native conformation in a physically meaningful time by randomly searching over all possible conformations. So far, it has been widely assumed that this random conformational search does not occur in the folding process, for which various putative hypotheses have had to be employed in model studies. Here we show that the quantum approach, describing the folding process as a quantum walk on a definite graph, gives rise to a fast protein-folding time. In terms of the conventional lattice model describing protein conformation, we introduce a procedure to enumerate all possible structures and then determine the definite connection graphs. Evaluating the mean first-passage time, we find it is much shorter than that obtained via random searching, and the magnitude of the quantum approach is reasonably in agreement with the experimental result. Some further discussions of various characteristic average quantities are also made by comparing both cases of quantum walk and classical random walk.