Temperature effects on the Davydov soliton

2008

Front. Phys. China

The influence of molecular structure disorders and physiological temperature on the states and properties of solitons as transporters of bio-energy are numerically studied through the fourth-order RungeKutta method and a new theory based on my paper [Front. Phys. China, 2007, 2(4): 469]. The structure disorders include fluctuations in the characteristic parameters of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the chain-chain interaction coefficient among the three channels and ground state energy resulting from the disorder distributions of masses of amino acid residues and impurities. In this paper, we investigate the behaviors and states of solitons in a single protein molecular chain, and in α-Helix protein molecules with three channels. In the former we prove first that the new solitons can move without dispersion, retaining its shape, velocity and energy in a uniform and periodic protein molecule. In this case of structure disorder, the fluctuations of the spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant, as well as the ground state energy and the disorder distributions of masses of amino acid residues of the proteins influence the states and properties of motion of solitons. However, they are still quite stable and are very robust against these structure disorders, even in the presence of larger disorders in the sequence of masses, spring constants and coupling constants. Still, the solitons may disperse or be destroyed when the disorder distribution of the masses and fluctuations of structure parameters are quite great. If the effect of thermal perturbation of the environment on the soliton in nonuniform proteins is considered again, it is still thermally stable at the biological temperature of 300 K, and at the longer time period of 300 ps and larger spacing of 400 amino acids. The new soliton is also thermally stable in the case of motion over a long time period of 300 ps in the region of 300− 320 K under the influence of the above structure disorders. However, the soliton disperses in the case of a higher temperature of 325 K and in larger structure disorders. Thus, we determine that the soliton's lifetime and critical temperature are 300 ps and 300−320 K, respectively. These results are also consistent with analytical data obtained via quantum perturbed theory. In α-helix protein molecules with three channels, results obtained show that these structure disorders and quantum fluctuations can change the states and features of solitons, decrease their amplitudes, energies and velocities, but they still cannot destroy the solitons, which can still transport steadily along the molecular chains while retaining energy and momentum when the quantum fluctuations are small, such as in structure disorders and quantum fluctuations of 0.67 < α k < 2, ΔW = ±8%W , ΔJ = ±1%J, Δ(χ 1 + χ 2 ) = ±3%(χ 1 + χ 2 ) and ΔL = ±1%L and Δε 0 = ε|β n |, ε=0.1 meV, |β n | < 0.5. Therefore, the solitons in the improved model are qui...

Section: Fig 16mentioning

confidence: 77%

Influence of structure disorders and temperatures of systems on the bio-energy transport in protein molecules (II)

2008

Front. Phys. China

“…Some numerical simulations indicated that the Davydov soliton is not stable at the biological temperature of 300 K [62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80]. Other simulations indicated that the Davydov soliton was stable at 300 K [30][31][32][33][34][35][36][37][38][39], but they were based on the classical equations of motion which were likely to yield unreliable estimates of the stability of the soliton [13][14][15][16][17][18]. The simulations based on the 2 | D 〉 state in Eq.…”

Section: Review Articlementioning

confidence: 99%

“…Since the dynamical equations used in the simulations are not equivalent to the dinger o Schr equation, the stability of the soliton obtained by these numerical simulations is unavailable or unreliable. The simulation [34] based on the 1 | D 〉 state in Eq. (3) with the thermal treatment of Davydov [31][32][33], where the equations of motion are derived from a thermally averaged Hamiltonian, yields the confusing result that the stability of the soliton is enhanced with the increase in temperature, predicting that the 1 | D 〉 -type soliton is stable in the region of biological temperature.…”

Section: Review Articlementioning

confidence: 99%

Theory of bio-energy transport in protein molecules and its experimental evidences as well as applications (I)

2007

Front. Phys. China

A new theory of bio-energy transport along protein molecules, where energy is released by the hydrolysis of adenosine triphosphate (ATP), has recently been proposed for some physical and biological reasons. In this theory, Davydov's Hamiltonian and wave function of the systems are simultaneously improved and extended. A new interaction has been added into the original Hamiltonian. The original wave function of the excitation state of single particles has been replaced by a new wave function of the two-quanta quasi-coherent state. In such a case, bio-energy is carried and transported by the new soliton along protein molecular chains. The soliton is formed through the selftrapping of two excitons interacting with amino acid residues. The exciton is generated by the vibration of amide-I (C=O stretching) arising from the energy of the hydrolysis of ATP. The properties of the soliton are extensively studied by analytical methods and its lifetime for a wide range of parameter values relevant to protein molecules is calculated using the nonlinear quantum perturbation theory. The lifetime of the new soliton at the biological temperature of 300 K is large enough and belongs to the order of 10 −10 s or τ/τ 0 ≥ 700. The different properties of the new soliton are further studied. The results show that the new soliton in the new model is a better carrier of bio-energy transport and it can play an important role in biological processes. This model is a candidate of the bio-energy transport mechanism in protein molecules. sis, amide, exciton, life time, amino acid, quasi-coherent state, binding energy PACS numbers 87.15.He, 31.50.+w, 36.20.-r p S v E J J Jr

“…Subsequently, Cruzeiro et al 105 used also the thermodynamic average Hamiltonian H T = ν ρ νν H νν mentioned above, but H νν = D 1 |(H ex + H int + H ph )|D 1 . From again i ∂ϕn ∂t = ∂HT ∂ϕ * n and i ∂βn,q ∂t = ∂HT ∂β * n,q they obtained the dynamic equations of ϕ n and β n,q , respectively, where β * n,q + β −q,n = − ν|U + n (a + q + a −q )U n |ν , which are all nonlinear Schrödinger equations.…”

Section: Investigations On Thermal Stability Of the Davydov Solitons mentioning

confidence: 99%

“…This is due to the fact that previous analytical and numerical studies [12][13][14][15][16][17][18][19][20][21][22][23][84][85][86][87][88][89][90][91]104,105 have not adequately addressed the effects of thermal phonons, which may act to disperse exciton energy. Thus they finished a numerical calculation, in which they indicated that the excitations are strongly dispersed at physiological temperature.…”

Section: Investigations On Thermal Stability Of the Davydov Solitons mentioning

confidence: 99%

The Checkout and Verification of Theory of Bio-Energy Transport in the Protein Molecules

2014

Biophys. Rev. Lett.

The phosphorylation and de-phosphorylation reactions in the cell, through which the bio-energy is released from ATP hydrolysis in biological systems, are described in this paper. Firstly, the bio-energy is accepted by the vibrational amides in protein molecules in virtue of resonant mechanism of frequency or energy, and can transport along the protein molecules in soliton, which is formed by self-trapping of vibrational quantum (or exciton), by means of dipole-dipole interaction among the neighboring peptide groups (or amino acids). Theory and properties of bio-energy transport were proposed and described by many researchers. We here reviewed mainly the theories and features of Davydov's and Pang's models. However these theoretical models including Davydov's and Pang's model were all established based on a periodic and uniform proteins, which are different from practically biological proteins molecules. Therefore, it is necessary to inspect and verify the validity of the theory of bio-energy transport in real biological protein molecules. These problems were extensively studied by a lot of researchers using different methods in past thirty years, a considerable number of research results were obtained. I review here the situation and progresses of study on this problem, in which we reviewed the correctness of the theory of bio-energy transport including Davydov's and Pang's model and its investigated progresses under influences of structural nonuniformity and disorder, side groups and imported impurities of protein chains as well as the thermal perturbation and damping of medium arising from the biological temperature of the systems. The structural non-uniformity arises from the disorder distribution of sequence of masses of amino acid residues, side groups and imported impurities, which results in the changes and fluctuations of the spring constant, dipole-dipole interaction, exciton-phonon coupling constant, diagonal disorder or ground state energy and chainchain interaction of the molecular channels in the dynamic equations in different models. The influences of structural non-uniformity, side groups and imported impurities as well as the thermal perturbation and damping of medium on the bio-energy transport in the proteins with single chain and three chains were studied by different numerical simulation techniques and methods including the average Hamiltonian way of thermal 1 Biophys. Rev. Lett. 2014.09:1-79. Downloaded from www.worldscientific.com by KING MONGKUT'S UNIVERSITY OF TECHNOLOGY THONBURI on 10/14/14. For personal use only. 2 X.-F. Pangperturbation, fourth-order Runge-Kutta method, Monte Carlo method, quantum perturbed way and thermodynamic and statistical method, and so on. In this review, the numerical simulation results of bio-energy transport in uniform protein molecules, the influence of structural non-uniformity on the bio-energy transport, the effects of system temperature on the bio-energy transport and the simultaneous effects of structural nonuniformity, damping and thermal perturbation o...