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 $ 0.67overline M < M_k < 2overline 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 $ 0.67overline M < M_k < 2overline 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.