Quantum mechanical justification for induced fit model conformational changes in allosteric enzymes based on the quantum perturbation theory and Davydov's soliton theory.

In the 1970-s Davydov proposed a soli ton mechanism of energy transport in biological macromolecules1. At present the concept of the “Davydov soliton” has been used in many studies. In particular, the Davydov soliton has been put into operation as a mechanism useful in the description of a variety of biological phenomena2, 3. Numerical studies by Scott and co-workers2−4 supported the appearance of Davydov solitons in Alpha-helix protein molecules. Therefore an experimental detection of solitons appear to be natural.

The frequency-dependent, resonance-type biological effects of electromagnetic radiation on a-helical protein macromolecules were treated in terms of Davydov soliton (DS) theory. We studied DS over the temperature range from 0 to 350 K. An important characteristic of the autolocalized state is the bond energy, which defines the soliton stability. As the DSs are stable, only a small probability exists of their energy dissipation into heat providing for the high efficiency of energy and charge transduction in bio-systems. However, under the influence of electromagnetic radiation (EMR), the DS decay (photodissociation) probability increases. This approach allows for the qualitative explanation of the resonant effects of low-intensity microwaves on living organisms found in a number of experiments. The dependence of resonance frequency on temperature was obtained this way. The direct charge transfer along the protein molecule may result from the capture of an extra electron by the moving acoustic soliton (electrosoliton). Decay of the electrosoliton under the influence of EMR (photodisintegration) is also examined.

Davydov's soliton theory is formulated for finite temperatures by generalizing the simple product trial function. An estimate of soliton temperature stability is presented.

The Thermodynamic Properties of the Solitons Excited in the Protein Molecules

We simulate numerically the dynamic properties of new soliton with quasi-coherent two quanta in the improved model by fourth-order Runge–Kutta way. We observed that the window of formation of new soliton is shifted toward smaller values of coupling constants when compared with the Davydov's soliton with one quantum and Förner's soliton with two quantum model. The new soliton formation starts at (χ1+χ2)=20 PN , and pinning starts from (χ1+χ2)=86 PN . The pinned solitons are also observed if both quanta are on the same end of the chain in the initial state. The behaviors of new soliton are varied under influences for variations of characteristic parameters arising from the structure nonuniformity of protein molecules. Although the new soliton is also sensitive to the dipole-dipole interaction and diagonal disorder, the sensitivity to the impurity is weaker than that of the Davydov's and Förner's solitons. Therefore, the new soliton is robust against the fluctuations of coupled constant, dipole-dipole interaction and diagonal disorder arising from the impurity or structure nonuniformity, when compared with that of the Davydov's and Förner's solitons.

Multi-hump bright solitons in a Schrödinger–mKdV system

Based on Emin's idea of deformation potential in deformable continuum, a bipolaron Hamiltonian is generalized to two-dimensional deformable electron–phonon system with the assumption of localized deformation potential of function. The dynamic properties of bipolaron are studied in the framework of Davydov's soliton theory, and a nonlinear Schrödinger equation is derived using the principle of least action. By function-series method, an exact two-dimensional (2D) soliton solution is obtained. We find that the center-of-mass motion of bipolaron is shown in a solitary wave form, and its relative motion is a harmonic one.

Apparent co-operativity for highly concentrated Michaelian and allosteric enzymes

The Davydov's soliton propagation in the linear polymer chain is analyzed numerically by solving the discrete equations of motion for exciton and phonon amplitudes. The main difference with respect to the results of continual approximation is that two exciton–phonon coupling constants influence separately the soliton behavior. Their influence is studied both in the ideal chain and the chain with single impurity.

Analytic Studies on the Helmholtz Spatial Solitons in Power-Law Optical Materials

For pt.IV see ibid. vol.5, p.3883 (1993). For the two approximations commonly used in the Davydov soliton theory (called |D1> and |D2> ansatz), expressions for states which give the deviation of the approximation from the Schrodinger equation, i.e. [ih(cross)(partial/partial t)-H(hat)] |D1> = J|delta>, can be derived. The author presents numerically calculated expectation values of various operators formed with the deviation states and compare them with the corresponding expectation values formed with H(hat)|D1>. Together with the fact that the basis space of the |D1> state is sufficient to reproduce the exactly solvable small-polaron limit, the author concludes from his results that the |D1> model should be an at least qualitatively correct approximation.

Dynamical self-trapping of waves or particles, originally put forward by Landau long time ago, by their nonlinear self-interactions in classical and quantum systems has received much attention in recent years. The principal reason for the upsurge of the renewed interest is due to: (i) The development of the soliton theory in mathematical physics. (ii) Ever-lasting interest in Davydov solitons and their possible implication to biological energy transfer.1 (iii) Generalization of the concept of Davydov solitons in various directions,2 in which vibron solitons are one of such examples.3 (iv) Several experiments which can be accounted for by the concept of the dynamical self-trapping, such as the shift of the infrared absorption spectra of molecular crystals acetanilide,4 local modes in benzene,5 the anomalous temperature dependence of the Raman spectra in ℓ-alanine,6 and so on. (v) Numerical experiments which show the existence of dynamical self-trapped states under certain conditions in various model dynamical nonlinear systems.7–9 (vi) Elucidation of the existence of intrinsic an-harmonic localized or resonant modes in lattice dynamics of pure crystal lattices.10,11 KeywordsCoherent StateLocalize ModeAcoustic PhononNonlinear Eigenvalue ProblemEnvelope SolitonThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

There are two effects which tend to delocalize the Davydov soliton. First, quantum fluctuations which can also be seen as a zero point motion of the soliton position. Second, thermal fluctuations produced by the interaction with the surrounding solvent. This solvent, which we now call heatbath, wants to force the system into thermal equilibrium. We discuss under what circumstances a soliton in the Alpha-helix can be seen as a thermodynamic equilibrium state. We show how the principle of a minimal free energy, formulated in a variational principle of thermodynamics, can be used to optimize a given ansatz for the density operator. Thermal soliton theories of Davydov and Krumhansl are discussed within this theory. Both, in principle, use the same ansatz with no freedom to adjust for maximum entropy. In using a more realistic ansatz, we always get the result that the soliton is delocalized. Finally, we discuss how the strength of interaction, together with the internal structure of the heatbath, determines the thermal lifetime of the soliton.

The exact Schroedinger equation involving a modified Froehlich Hamiltonian used in Davydov soliton theory is formulated in terms of unitary time displacement and phonon coordinate displacement operators. Use is made of the sparse nature of the resulting matrix operators to develop an algorithm for vector processing on the Cyber 205 supercomputer. All numerical calculations lead us to conclude that the Schroedinger equation does not support the existence of the Davydov soliton as a persistent localized entity.

We present a unified theory of polaron and soliton dynamics by combining time-dependent variational methods recently applied to the theory of Davydov solitons with partial-dressing methods well known from polaron theory. We focus on the simplest partial-dressing assumption, applying a common dressing fraction to all phonon modes. Our fundamental result is a system of nonlinear evolution equations in which the tendency of a system to form Davydov solitons is balanced against its tendency to form small polarons. We subsequently apply time-independent variational methods to determine the optimal dressing fraction in a mean-field manner. The characterization of the partially dressed soliton states that results is complete with respect to the system parameter space. Consistent with prior works from polaron theory, we find a self-trapping transition that is only weakly modified by our inclusion of nonlinearities, and we reinterpret this transition in terms of our newly obtained soliton states. Applying our results to a central problem in bioenergetics, we obtain results markedly different from well-known results of Davydov's theory.