Narrow Results

The dynamic behaviors of the new soliton in the improved Davydov model in the protein molecules at biological temperature have been numerically simulated by utilizing the dynamic equations for the bio-energy transport and the Runge–Kutta way. In this simulation the influences of the temperature and structure disorders of the protein molecules on the soliton transporting the bio-energy have been completely considered. We find that the new soliton is quite stable in the cases of motion of a long time of 300 ps and of disorders of the structures of the proteins at biological temperatures of 300 K–320 K. The disorders of the structures contain the disorder of mass sequence of amino acids and the fluctuations of the coupling constant, force constant and dipole- dipole interaction constant and ground state energy of the proteins, designating the features of its structure and interactions between the particles in it. However, the soliton disperses in the cases of higher temperature of 325 K and larger structure disorders. The numerical results show that the new soliton is very robust against the influences of the thermal perturbation and structure disorders at biological temperature 300 K, its lifetime and critical temperature are at least 300 ps at 300 K and 320 K, respectively. These results are also consistent with analytical data.

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.

Combination effects of structure disorder of protein molecules containing the fluctuations of spring constant, dipole-dipole interaction constant and exciton-phonon coupling constant and diagonal disorder, resulting from nonuniform distribution of masses of amino acid residues and impurities, on the soliton transported the bio-energy in the proteins have been numerically simulated by fourth-order Runge–Kutta method in the improved model. The results obtained show that these structure disorders can change the states of solitons but as the solitons are quite robust against these disorder effects, they can only be dispersed or disrupted in the cases of quite large structure disorders. From these results and the properties of molecular structure of biological proteins we can conclude that the new soliton in the improved model is quite stable in normal conditions. Thus the soliton is possibly a carrier of bio-energy transport in the protein molecules.

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 have here an insight into the features of molecular structures of bio-polymers with α-helix structure using infrared spectrum and elucidated theoretically, its relationship with bio-functions. In this case, we analyzed first the features of molecular structure of collagen and collected further the infrared spectrum of absorption of collagen and bovine serum albumin containing α-helix conformation in 400–4000 cm^-1 as well as their changes of strength of infrared absorption with varying temperatures using Fourier Transform–Infrared (FT-IR) spectrometers in the region of 15–95°C. The results show that there is a new band of 1650 cm^-1 close to the amide-I band of 1666 cm^-1 or 1670 cm^-1 in these bio-polymers, its strength decreases exponentially with increasing temperature of the systems, which can be expressed by exp[-(0.437 + 8.987 × 10^-6 T²)], but 1666 cm^-1 band increases linearly with increasing temperature. We calculated the energy spectrum of the protein molecules with α-helix conformation using the Soliton Theory of bio-energy transport, which are basically same with the experimental results measured by us. From these results and soliton theory we can conclude that the nonlinear soliton excitation, corresponding to 1650 cm^-1 band and the exciton excitation, is related to 1666 cm^-1 band, exists in the collagen and bovine serum albumin. In the meanwhile, these results also verified that the soliton theory of bio-energy transport along α-helix bio-polymers is appropriate to the protein molecules with α-helix conformation. Therefore, the studied results are helpful to elucidate the relationship between the molecular structure and bio-function of these bio-polymers.

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.