Bio-energy in s-Helix Protein Molecules with Three Properties of Soliton-Transported Channels

We study numerically the propagating properties of soliton-transported bio-energy excited in the a-helix protein molecules with three channels in the cases of the short-time and long-time motions and its features of collision at temperature T = 0 and biological temperature T = 300 K by the dynamic equations in the improved Davydov theory and fourth-order Runge-Kutta method, respectively. From these simulation experiments we see that the new solitons in the improved model can move without dispersion at a constant speed retaining its shape and energy in the cases of motion of both short-time or T = 0 and long time or T = 300 K and can go through each other without scattering in their collisions. In these cases its lifetime is, at least, 120 ps at 300 K, in which the soliton can travel over about 700 amino acid residues. This result is consistent with analytic result obtained by quantum perturbed theory in this model. In the meanwhile, the influences of structure disorder of a-helix protein molecules, including the inhomogeneous distribution of amino acids with different masses and fluctuations of spring constant, dipole-dipole interaction, exciton-phonon coupling constant and diagonal disorder, on the solitons are also studied by the fourth-order Runge-Kutta method. The results show that the soliton still is very robust against the structure disorders and thermal perturbation of proteins at biological temperature 300 K. Therefore we can conclude that the new soliton in the a-helix protein molecules with three channels is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

Features of Motion of Soliton Transported Bio-energy in Aperiodic α-Helix Protein Molecules with Three Channels

The structure aperiodicities can influence seriously the features of motion of soliton excited in the α-helix protein molecules with three channels. We study the influence of structure aperiodicities on the features of the soliton in the improved model by numerical simulation and Runge-Kulta method. The results obtained show that the new soliton is very robust against the structure aperiodieities including large disorder in the sequence of mass of the amino acids and fluctuations of spring constant, coupling constant, dipole-dipole interactional constant, ground state energy and chain-chain interaction. However, very strong structure aperiodieities can also destroy the stability of the soliton in the α-helix protein molecules.     

Properties of Soliton-Transported Bio-energy in α-Helix Protein Molecules with Three Channels

We study numerically the propagating properties of soliton-transported bio-energy excited in the α-helix protein molecules with three channels in the cases of the short-time and long-time motions and its features of collision at temperature T = 0 and biological temperature T = 300 K by the dynamic equations in the improved Davydov theory and fourth-order Runge-Kutta method, respectively. From these simulation experiments we see that the new solitons in the improved model can move without dispersion at a constant speed retaining its shape and energy in the cases of motion of both short-time or T = 0 and long time or T = 300 K and can go through each other without scattering in their collisions. In these cases its lifetime is, at least, 120 ps at 300 K, in which the soliton can travel over about 700 amino acid residues. This result is consistent with analytic result obtained by quantum perturbed theory in this model. In the meanwhile, the influences of structure disorder of α-helix protein molecules, including the inhomogeneous distribution of amino acids with different masses and fluctuations of spring constant, dipole-dipole interaction, exciton-phonon coupling constant and diagonal disorder, on the solitons are also studied by the fourth-order Runge-Kutta method. The results show that the soliton still is very robust against the structure disorders and thermal perturbation of proteins at biological temperature 300 K. Therefore we can conclude that the new soliton in the α-helix protein molecules with three channels is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

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

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 Runge-Kutta 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 < \alpha _k < 2,\Delta W = \pm 8\% \overline W ,\Delta J = \pm 1\% \overline J ,\Delta (\chi _1 + \chi _2 ) = \pm 3\% (\bar \chi _1 + \bar \chi _2 ) $ and $ \Delta L = \pm 1\% \bar L $ and $ \Delta \varepsilon _0 = \varepsilon \left| {\beta _n } \right|,\varepsilon = 0.1 meV,\left| {\beta _n } \right| < 0.5 $ . Therefore, the solitons in the improved model are quite robust against these disorder effects. However, the solitons may be dispersed or disrupted in cases of very large structure disorders. When the influence of temperature on solitons is considered, we find that the new solitons can transport steadily over 333 amino acid residues in the case of motion over a long time period of 120 ps, and can retain their shapes and energies to travel forward along protein molecules after mutual collision of the solitons at the biological temperature of 300 K. Therefore, the soliton is also very robust against thermal perturbation of the α-helix protein molecules at 300 K. However, the soliton disperses in cases of higher temperatures at 325 K and in larger structure disorders. Thus, their critical temperature is about 320 K. When the effects of structure disorder and temperature are considered simultaneously, the soliton has high thermal stability and can transport for a long time along the protein molecular chains while retaining its amplitude, energy and velocity, even though the fluctuations of the structure parameters and temperature of the medium increase continually. However, the soliton disperses in the larger fluctuations of $ 0.67\overline M < M_k < 2\overline M , \Delta (\chi _1 + \chi _2 ) = \pm 2\% (\bar \chi _1 + \bar \chi _2 ), \Delta J = \pm 1.3\% \bar J, \Delta W = \pm 6\% \overline W , \Delta L = \pm 1.5\% \overline L $ and $ \Delta \varepsilon _0 = \varepsilon \left| {\beta _n } \right|, \varepsilon = 0.82 meV, \left| {\beta _n } \right| \leqslant 0.5 $ at T=300 K, and at temperatures higher than 315 K when the fluctuations are $ 0.67\overline M < M_k < 2\overline M , \Delta (\chi _1 + \chi _2 ) = \pm 1\% (\bar \chi _1 + \bar \chi _2 ), \Delta J = \pm 0.7\% \bar J, \Delta W = \pm 7\% \overline W , \Delta L = \pm 0.8\% \overline L $ and $ \Delta \varepsilon _0 = \varepsilon \left| {\beta _n } \right|, \varepsilon = 0.4 meV, \left| {\beta _n } \right| \leqslant 0.5 $ . This means that the critical temperature of the soliton is only 315 K in this condition. In a word, we can conclude from the above investigations that the soliton in the improved model is very robust against the structure disorders and thermal perturbation of proteins at the biological temperature of 300 K in α-helix protein molecules, and is a possible bio-energy transport carrier; the improved model is a possible candidate for the mechanism of this transport.     

Influence of structure disorders and temperaturesof systems on the bio-energy transport in proteinmolecules (Ⅱ)

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 Runge-Kutta 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 and and . Therefore, the solitons in the improved model are quite robust against these disorder effects. However, the solitons may be dispersed or disrupted in cases of very large structure disorders. When the influence of temperature on solitons is considered, we find that the new solitons can transport steadily over 333 amino acid residues in the case of motion over a long time period of 120 ps, and can retain their shapes and energies to travel forward along protein molecules after mutual collision of the solitons at the biological temperature of 300 K. Therefore, the soliton is also very robust against thermal perturbation of the α-helix protein molecules at 300 K. However, the soliton disperses in cases of higher temperatures at 325 K and in larger structure disorders. Thus, their critical temperature is about 320 K. When the effects of structure disorder and temperature are considered simultaneously, the soliton has high thermal stability and can transport for a long time along the protein molecular chains while retaining its amplitude, energy and velocity, even though the fluctuations of the structure parameters and temperature of the medium increase continually. However, the soliton disperses in the larger fluctuations of and at T=300 K, and at temperatures higher than 315 K when the fluctuations are and . This means that the critical temperature of the soliton is only 315 K in this condition. In a word, we can conclude from the above investigations that the soliton in the improved model is very robust against the structure disorders and thermal perturbation of proteins at the biological temperature of 300 K in α-helix protein molecules, and is a possible bio-energy transport carrier; the improved model is a possible candidate for the mechanism of this transport.      

Changes of properties of the soliton with temperature under influences of structure disorder in the α-helix protein molecules with three channels

The changes of property of solitons in α-helix protein molecules with three channels under influences of fluctuations of structure parameters and thermal perturbation of medium are extensively investigated using dynamic equations in the improved theory, numerical simulation and Runge-Kutta method. In this investigation the peculiarities of the solitons are given first in the motions of short-time and long-time and its collision features at T = 0 K and biological temperature T = 300 K. This study shows that the solutions of dynamic equations are solitons, which are very stable at T = 0 and 300 K, although its amplitudes and velocity are somewhat decreased relative to that at T = 0 K, the soliton can transport over 1000 amino acid residues, its lifetime is, at least, 120 ps. Subsequently, studies are made of the changes of properties of the soliton with variations of temperature of the medium and fluctuations of structure parameters including mass sequence of amino acid residues and the coupling constant, force constant, dipole–dipole interaction, chain–chain interaction and ground state energy in the α-helix proteins. The investigations indicate that the soliton has high thermal stability and can transport along the molecular chains retaining amplitude, energy and velocity, although the fluctuations of the structure parameters and temperature of the medium increase continually. However, the solitons disperse in larger fluctuations at T = 300 K and higher temperatures than 315 K. Thus it is determined that the critical temperature of the soliton is 315 K. Finally reasons are given for the generation of high thermal stability of the soliton and the correctness of the improved model is demonstrated. It is concluded that the soliton in the improved model is very robust against structure disorder and thermal perturbation of the α-helix protein molecules at 300 K, and is a possible carrier of bio-energy transport, and the improved model is maybe a candidate for the mechanism of this transport.     

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

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 self-trapping 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/τ₀ ≥ 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.     

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

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 case, bio-energy is carried and transported by the new soliton along protein molecular chains. The soliton is formed through the self-trapping 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 life-time 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.      

The lifetime of the soliton in the improved Davydov model at the biological temperature 300 K for protein molecules

We study the effects of quantum fluctuations and thermal perturbations on the lifetime of the soliton in the improved Davydov model proposed by us with two-quanta and with an added interaction. By using quantum perturbation theory, we compute the soliton lifetime for a wide ranges of parameter values relevant for protein molecules. The lifetime of the new soliton at the biological temperature 300 K is of the order of 10^-10 second or τ/τ≥ 500 for parameters appropriate to α-helical protein molecules. This shows clearly that the new soliton in the improved model is a viable mechanism for the bio-energy transport in the α-helix region of proteins. Received 7 January 1999 and Received in final form 16 August 2000     

Stabilization of the Soliton Transported Bio-energy in Protein Molecules in the Improved Model

We study the stabilization of the soliton transported bio-energy by the dynamic equations in the improved Davydov theory from four aspects containing the feature of free motion and states of the soliton at the long-time motion and at biological temperature 300 K and behaviors of collision of the solitons by Runge-Kutta method and physical parameter values appropriate to the $\alpha$-helix protein molecules. We prove that the new solitons can move without dispersion at a constant speed retaining its shape and energy in free and long-time motions and can go through each other without scattering. If considering further influence of the temperature effect of heat bath on the soliton, it is still thermally stable at biological temperature 300 K and in a time as long as 300 ps and amino acid spacings as large as 400, which shows that the lifetime of the new soliton is at least 300 ps, which is consistent with analytic result obtained by quantum perturbation theory. These results exhibit that the new soliton is a possible carrier of bio-energy transport and the improved model is possibly a candidate for the mechanism of this transport.     

The theory of bio-energy transport in the protein molecules and its properties

The bio-energy transport is a basic problem in life science and related to many biological processes. Therefore to establish the mechanism of bio-energy transport and its theory have an important significance. Based on different properties of structure of α-helical protein molecules some theories of bio-energy transport along the molecular chains have been proposed and established, where the energy is released by hydrolysis of adenosine triphosphate (ATP). A brief survey of past researches on different models and theories of bio-energy, including Davydov's, Takeno's, Yomosa's, Brown et al.'s, Schweitzer's, Cruzeiro-Hansson's, Forner's and Pang's models were first stated in this paper. Subsequently we studied and reviewed mainly and systematically the properties, thermal stability and lifetimes of the carriers (solitons) transporting the bio-energy at physiological temperature 300 K in Pang's and Davydov's theories. From these investigations we know that the carrier (soliton) of bio-energy transport in the α-helical protein molecules in Pang's model has a higher binding energy, higher thermal stability and larger lifetime at 300 K relative to those of Davydov's model, in which the lifetime of the new soliton at 300 K is enough large and belongs to the order of 10(-10) s or τ/τ(0)≥700. Thus we can conclude that the soliton in Pang's model is exactly the carrier of the bio-energy transport, Pang's theory is appropriate to α-helical protein molecules.     

Improved Five-Parameter Exponential-Type Potential Energy Model for Diatomic Molecules

The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-parameter exponential-type potential is identical to the Tietz potential for diatomic molecules. It is observed that the improved five-parameter exponential-type potential can well model the internuclear interaction potential energy curve for the ground electronic state of the carbon monoxide molecule by the utilization of the experimental values of three molecular constants.     

自旋-轨道耦合对磁性绝缘体磁光Kerr效应的影响

采用单原子能级跃迁模型,导出在同时考虑自旋交换劈裂和自旋轨道耦合时磁光Kerr旋转的微观表达式,并就四能级跃迁情况,研究了磁光效应随原子基态及激发态能级自旋轨道耦合常数的变化规律.结果表明:磁光Kerr旋转角与自旋轨道耦合劈裂能量不成正比;单原子能级自旋轨道耦合常数为正或中间激发态自旋轨道耦合常数为负时,有利于提高磁光Kerr旋转. 关键词： 磁光Kerr效应 自旋轨道耦合 线性响应核 劈裂     

Magnetic vortices in small ferromagnetic particles with the strong dipolar interaction

The ground state of cylindrical magnetic samples of different sizes at nonzero applied magnetic field is studied theoretically taking into account the exchange and dipole-dipole interactions at an arbitrary ratio of coupling constants. In addition to the weakly inhomogeneous and standard vortex states well known for the case of the weak dipole-dipole interaction, the vortex states with the complicated structure of the vortex core have been found. The state diagram for these particles has been constructed and analyzed in terms of scaling consideration.     

共心双环外势中两分量偶极玻色-爱因斯坦凝聚体的基态结构研究

利用虚时演化方法研究了共心双环外势中具有偶极-偶极相互作用的两分量玻色-爱因斯坦凝聚体的基态结构, 探索了接触相互作用和长程各向异性的偶极-偶极相互作用对系统基态的影响. 研究发现, 偶极-偶极相互作用作为系统的又一调控参数, 可用于得到系统的不同的基态相, 并用于控制不同基态相间的转化.     

Exciton eigenstates and biexciton interaction energies in a spherical core/shell semiconductor hetero-nano structure

The exciton eigenstates and biexciton interaction energies in a spherical core–shell hetero-nano structure in the type II and the quasi-type II carrier localization regimes have been analyzed. For the analysis, we have evaluated the electron–hole overlap integral, the binding energy of exciton ground state, and the interaction energy of bi-exciton ground state in the structure. In the evaluation, the first order perturbation approach has been employed, where the direct Coulomb interaction energy, the surface polarization energy and the dielectric solvation energy are included. Our results show that the exciton eigenenergies and exciton–exciton interaction energy strongly depend on the choice of materials on which both the dielectric constants and the electron and hole effective masses rely.     

Thermodynamic calculations of linear chain molecules using a SAFT model

The recently proposed model of statistical associated-fluid theory (SAFT) by Tang, Y. and Lu, B. C.-Y. (2000, Fluid Phase Equilibria, 171, 27) is applied to phase diagram calculations of non-associating and associating linear chain molecules in which n-alkanes and n-alkenes (representing the non-associating type) and water, 1-alkanols, acids and amines (representing the associating type) are investigated. For polar molecules, the dipole-dipole interaction is taken into consideration. Overall, the proposed model yields similar accuracy to the original SAFT model, It is found that the volume and energy parameters of non-associating chain segments in the same family follow certain linear relations with the carbon number. Remarkably, these linear relations are found to hold equally well in associating chain molecules. These observations suggest that SAFT may be implemented in a more predictive manner. Furthermore, the inclusion of the contribution from dipole-dipole interaction improves the calculated values for strong polar molecules like water.     

Spiral spin state in high-temperature copper-oxide superconductors: evidence from neutron scattering measurements

An effective spiral spin phase ground state provides a new paradigm for the high-temperature superconducting cuprates. It accounts for the recent neutron scattering observations of spin excitations regarding both the energy dispersion and the intensities, including the "universal" rotation by 45 degrees around the resonance energy . The intensity has a 2D character even in a single twin crystal. The value of is related to the nesting properties of the Fermi surface. The excitations above are shown to be due to in-plane spin fluctuations, a testable difference from the stripe model. The form of the exchange interaction function reveals the effects of the Fermi surface, and the unique shape predicts large quantum spin fluctuations in the ground state.     

Spin-charge density waves in the Hubbard model

The ground state of the Hubbard model in a square lattice is examined in the Hartree-Fock mean field approximation at zero temperature. At small finite hole doping, the system has periodically distributed soliton like structures whose modulations are incommensurate. In a self-consistent way, the Fermi energy can always be located in a gap. The incommensurate states have lower energies than the commensurate antiferromagnetic states calculated at the same filling. These soliton structures persist even when a sizeable nearest neighbor repulsive interaction is included.     

Determination of the calcium ground state scattering length by photoassociation spectroscopy at large detunings

Photoassociation spectroscopy was used to determine the s-wave scattering length of ⁴⁰Ca atoms in their electronic ground state. Vibrational levels were observed in an extended range of up to 182 GHz below the dissociation limit 4s^{2 1}S₀–4s4p ¹P₁. Thus, the frequency interval was nearly tripled, in which photoassociation was observed compared to previous measurements. The spectra were analyzed by means of quantum mechanical simulations. With the new data it was possible to resolve the discrepancy concerning the ground state scattering length presented in earlier publications [Phys. Rev. A 67, 043408 (2003); Eur. Phys. J. D 26, 155 (2003)]. An improved dipole-dipole coupling constant C₃ ^Σ = 0.52306(20) ×10³ cm^-1 nm³ is obtained.