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CRC Press eBooks

The Polymer Conformational Stability and Transitions: A Quantum Decoherence Theory Approach

Aleksandar M. Spasic, Jyh-Ping Hsu

Published Oct 14, 2005• 6 citations
Publisher

Abstract

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.

DOI
10.1201/9781420027662-18

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Abstract ..................................................................................................... 2 1.1 Introduction ...................................................................................... 3 1.2 Valence Bond Theory ....................................................................... 5 1.2.1 Adiabatic Approximation ..................................................... 5 1.2.2 The Virial Theorem on the Molecular Systems .................... 9 1.2.3 The Chemical Bond Through the Valence Bond Method (VBM) ................................................................... 12 1.3 Molecular Orbital Theory of Bonding ........................................... 22 1.4 Sub-Quantum Chemistry: Chemical Bonding Field and Bondons ......................................................................... 34 1.4.1 Introducing Chemical Field ................................................ 35 1.4.2 Predicting the Bondonic’s Existence .................................. 38 1.4.3 Chemical Bonding by Bondons ......................................... 45 1.4.4 Chemical Bonding as a Bosonic Quantum Condensate ..... 55 1.4.4.1 ψ-Theory of Bose-Einstein Condensation ........... 55 1.4.4.2 DFT adapted to Bose-Einstein Condensation ...... 58 1.4.4.3 Local Density Approximation of Bose-Einstein Condensation ................................ 61 1.4.4.4 Heitler-London Bondonic Condensation ............. 64 1.4.4.5 Molecular Orbitals’ Bondonic Condensation ...... 70 1.5 Conclusion ..................................................................................... 82 Keywords ................................................................................................ 84 References ............................................................................................... 85 Author’s Main References ............................................................. 85 Specific References ........................................................................ 85 ABSTRACT The classical quantum methods in characterizing chemical bonding, i.e., the valence orbital theory (of Pauling) and the molecular orbital theory (of Heitler and London) are firstly exposed (and illustrated at least for H2 system) for didactical and benchmarking research purpose on fundamental nature of the chemical bonding. 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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.
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).
Two unresolved issues of the (semi)classically addressed problems in molecular biophysics are unreasonably long time necessary for the change of biopolymer conformations and long-range directedness of selective biomolecular recognition processes - implying their essential quantum origin. In this paper several possible quantum approaches to biomolecular recognition are considered: Theory of Non-Radiative Resonant Structural Transitions, Model of Quantum Decoherence, and Resonant Recognition Model. These approaches might be of fundamental importance in understanding underlying macroscopic quantum-holographic Hopfield-like control mechanisms of morphogenesis, and their backward influence on the expression of genes, with significant potential psychosomatic implications.
Abstract ..................................................................................................... 2 1.1 Introduction ...................................................................................... 3 1.2 Valence Bond Theory ....................................................................... 5 1.2.1 Adiabatic Approximation ..................................................... 5 1.2.2 The Virial Theorem on the Molecular Systems .................... 9 1.2.3 The Chemical Bond Through the Valence Bond Method (VBM) ................................................................... 12 1.3 Molecular Orbital Theory of Bonding ........................................... 22 1.4 Sub-Quantum Chemistry: Chemical Bonding Field and Bondons ......................................................................... 34 1.4.1 Introducing Chemical Field ................................................ 35 1.4.2 Predicting the Bondonic’s Existence .................................. 38 1.4.3 Chemical Bonding by Bondons ......................................... 45 1.4.4 Chemical Bonding as a Bosonic Quantum Condensate ..... 55 1.4.4.1 ψ-Theory of Bose-Einstein Condensation ........... 55 1.4.4.2 DFT adapted to Bose-Einstein Condensation ...... 58 1.4.4.3 Local Density Approximation of Bose-Einstein Condensation ................................ 61 1.4.4.4 Heitler-London Bondonic Condensation ............. 64 1.4.4.5 Molecular Orbitals’ Bondonic Condensation ...... 70 1.5 Conclusion ..................................................................................... 82 Keywords ................................................................................................ 84 References ............................................................................................... 85 Author’s Main References ............................................................. 85 Specific References ........................................................................ 85 ABSTRACT The classical quantum methods in characterizing chemical bonding, i.e., the valence orbital theory (of Pauling) and the molecular orbital theory (of Heitler and London) are firstly exposed (and illustrated at least for H2 system) for didactical and benchmarking research purpose on fundamental nature of the chemical bonding. Then the “missing link” in characterizing chemical bonding field by its associated quantum particle, the bondon B , is revealed by employing the combined Bohmian quantum formalism within the Schrödinger quantum picture of electron motions and characterized by its mass (mB), velocity (vB), charge (eB), and life-time (t B); the mass-velocity-charge-time quaternion properties of bondons’ particles were used in discussing various paradigmatic types of chemical bond towards assessing their covalent, multiple bonding, metallic and ionic features. The bondonic picture was completed by discussing the relativistic charge and life-time (the actual zitterbewegung) problem, i.e., showing that the bondon equals the benchmark electronic charge through moving with almost light velocity. It carries negligible, although non-zero, mass in special bonding conditions and towards observable femtosecond life-time as the bonding length increases in the nanosystems and bonding energy decreases according with the bonding length-energy relationship of Heisenberg type E kcal mol X Abond bond[ / ] [ ]× = 0 182019, providing this way the predictive framework in which the B particle may be observed when either associate Ebond or length Xbond is known. However, being the bondon a boson, as the particle carrying the quantum information of the chemical wave/orbital/ field, further, possibility in assessing the density functional theory (DFT) for of the Kohn-Sham equation within Bose-Einstein condensation (BEC) and of its further reduction to the nonlinear Schrodinger equation under the GrossPitaevsky equation is responded in positive through employing specific DFTBEC exchange functional combined within the Hartree-Fock-Bogoliubov mean-field theory. This non-linear generalization of the Schrödinger equation is then employed in first providing the DFT-BEC connection at the level of the Thomas-Fermi approximation; such connections are further used towards generalizing the classical Heitler-London formalism and bonding-antibonding equations of homopolar chemical bonding with the aid of the mass quantification of the quantum particle of the chemical bonding field – the bondons. Actually, two branches of bosonic-bondonic condensate were identified as physical and chemical bonding BEC, both with bonding and antibonding features. These findings innovatively complete the already “classical” quantum treatment of chemical bonding through the valence orbital theory (dealing with resonances of molecular structures) and then to the orbital molecular theory (providing the hybridization and the bonding/anti-bonding paradox), here also exposed for their main features.
In this paper we describe the biopolymer chain folding problem in the framework of the so-called quantum decoherence theory. As we propose a rather qualitative scenario yet bearing generality, it seems this provides promising basis for the solution-in-principle of the (semi) classically hard kinetic problem of biopolymer chain folding from coiled to native conformation in highly selective ligand proteins/target-receptors biomolecular recognition processes, implying underlying macroscopic quantum nonlocality on the level of biological cell.