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Physica Scripta

Protein folding: the optically induced electronic excitations model

J. Jeknić-Dugić

Published Jul 1, 2009• 2 citations
Publisher

Abstract

The large-molecules conformational transitions problem (the 'protein folding problem') is an open issue of vivid current science research work of fundamental importance for a number of modern science disciplines as well as for nanotechnology. Here, we elaborate the recently proposed quantum-decoherence-based approach to the issue. First, we emphasize a need for detecting the elementary quantum mechanical processes (whose combinations may give a proper description of the realistic experimental situations) and then we design such a model. As distinct from the standard approach that deals with the conformation system, we investigate the optically induced transitions in the molecule electrons system that, in effect, may give rise to a conformation change in the molecule. Our conclusion is that such a model may describe the comparatively slow conformational transitions.

DOI
10.1088/0031-8949/2009/t135/014031

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The large-molecules conformational transitions problem (the 'protein folding problem') is an open issue of vivid current science research work of fundamental importance for a number of modern science disciplines as well as for nanotechnology. Here, we elaborate the recently proposed quantum-decoherence-based approach to the issue. First, we emphasize a need for detecting the elementary quantum mechanical processes (whose combinations may give a proper description of the realistic experimental situations) and then we design such a model. As distinct from the standard approach that deals with the conformation system, we investigate the optically induced transitions in the molecule electrons system that, in effect, may give rise to a conformation change in the molecule. Our conclusion is that such a model may describe the comparatively slow conformational transitions.
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 II. The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 A. The Born-Oppenheimer Adiabatic Approximation . . . . . . . . . . . . . . . . . . . . . 218 B. The Molecules Conformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 C. Levinthal’s Paradox: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 D. Levinthal’s Paradox: Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 III. New Approach: The Clue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 IV. The Fundamentals of the Decoherence Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 A. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 B. Open Quantum Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 C. The Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 D. The Environment-Induced Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 E. The Physical Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 V. New Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A. The Conformation Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 B. Nonstationary State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 C. The Relaxation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 D. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 VI. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 VII. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 In this chapter, we describe the problem of polymer conformational stability and transitions in the framework of the so-called quantum decoherence theory. We propose a rather qualitative scenario yet bearing generality in the context of the quantum decoherence theory, enabling us to reproduce both, existence and stability of the polymers conformations, and the short time scales for the quantum-mechanical processes resulting effectively in the conformational transitions. The proposed model is qualitative yet providing us with the possibility to overcome the main obstacle in resolving the problem of (semi-)classically unreasonably long time necessary for the change of conformation of the polymers in a solution.
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.
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).
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science challenge. We analyze the resource requirements for simulating simplified yet computationally challenging protein folding models on a quantum computer, assessing the feasibility of these existing approaches in the current and near-future technological landscape. We calculate the minimum number of qubits, interactions, and two-qubit gates necessary to build a heuristic quantum algorithm with the specific information of a folding problem. Particularly, we focus on the resources needed to build quantum operations based on the Hamiltonian linked to the protein folding models for a given amino acid count. Such operations are a fundamental component of these quantum algorithms, guiding the evolution of the quantum state for efficient computations. Specifically, we study coarse-grained folding models on the lattice and the fixed backbone side-chain conformation model and assess their compatibility with the constraints of existing quantum hardware given different bit encodings. We conclude that the number of qubits required falls within current technological capabilities. However, the limiting factor is the high number of interactions in the Hamiltonian, resulting in a quantum gate count unavailable today.
Our recently proposed quantum approach to biomolecular recognition processes is hereby additionally supported by biomolecular Resonant Recognition Model and by quantum-chemical theory of biomolecular non-radiative resonant transitions. Previously developed general quantumdecoherence framework for biopolymer conformational changes in very selective ligandproteins/ target-receptors key/lock biomolecular recognition processes (with electron-conformational coupling, giving rise to dynamical modification of many-electron energy-state hypersurface of the cellular quantum-ensemble ligand-proteins/target-receptors biomolecular macroscopic quantum system, with revealed possibility to consider cellular biomolecular recognition as a Hopfield-like quantum-holographic associative neural network) is further extended from nonlocal macroscopicquantum level of biological cell to nonlocal macroscopic-quantum level of biological organism, based on long-range coherent microwave excitations (as supported by macroscopic quantum-like microwave resonance therapy of the acupuncture system) - which might be of fundamental importance in understanding of underlying macroscopic quantum (quantum-holographic Hopfieldlike) control mechanisms of embryogenesis/ontogenesis and morphogenesis, and their backward influence on the expression of genes.