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The changes of property of solitons in alpha-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 alpha-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 alpha-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.

The dynamic features of soliton transporting the bio-energy in the α-helix protein molecules with three channels under influences of temperature of systems and chain–chain interaction among these channels have been numerically studied by using the dynamic equations in a new model and the fourth-order Runge–Kutta method. This result obtained shows that the chain–chain interaction depresses the stability of the soliton due to the dispersed effect, but the stability of the soliton in the case of simultaneous motivation of three channels by an initial conditions is better than that in another initial condition. We also find from this investigation that the new soliton can transport steadily over 1000 amino acid residues in the cases of motion of long time of 120 ps, and retain their shapes and energies to travel towards the protein molecules after mutual collision of the solitons at the biological temperatures of 300 K. Therefore the soliton is very robust against the thermal perturbation of the α-helix protein molecules at 300 K. From the investigation of changes of features of the soliton with increasing temperature, we find that the amplitudes and velocities of the solitons decrease with increasing temperature of proteins, but the soliton disperses in the cases of higher temperature of 325 K and larger structure disorders. Thus we find that the critical temperature of the soliton occurring in the α-helix protein molecules is about 320 K. Therefore we can conclude that the soliton in the new model can play an important role in the bio-energy transport in the α-helix protein molecules with three channels at biological temperature, and the new model is possibly a candidate for the mechanism of this transport.

We studied numerically the influences of damping and temperature of medium on the properties of the soliton transported bio-energy in the α-helix protein molecules with three channels by using the dynamic equations in the improved Davydov theory and fourth-order Runge–Kutta method. From the simulation experiments, we see that the new solitons can move along the molecular chains without dispersion at a constant speed, in which the shape and energy of the soliton can remain in the cases of motion, whether short-time at T=0 or long time at T=300 K. In these motions, the soliton can travel over about 700 amino acid residues, thus its lifetime is, at least, 120 ps at 300 K. When the two solitons undergo a collision, they can also retain themselves forms to transport towards. These results are consistent with the analytic result obtained by quantum perturbed theory in this model. However, the amplitudes of the solitons depress along with increase of temperature of the medium, and it begins to disperse at 320 K. In the meanwhile, the damping of the medium can influence the states and properties of the soliton excited in α-helix protein molecules. The investigation indicates that the amplitude and propagated velocity of the soliton decrease, when the damping of medium increases. The soliton is dispersed at the large damping coefficient Γ=4 Γ0 at 300 K. The results show that the soliton excited in the α-helix protein molecules with three channels is very robust against the damping and thermal perturbation of medium at biological temperature of 300 K. Thus we can conclude that the soliton can play important part in the bio-energy transport and the improved model is possibly a candidate for the mechanism of the energy transport in the α-helix proteins.

We study numerically the propagating properties of soliton-transported bio-energy excited in the alpha-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.