Alternative formulation of Davydov's theory of energy transport in biomolecular systems

Optimized excitonic transport mediated by local energy defects: Survival of optimization laws in the presence of dephasing

In an extended star with peripheral defects and a core occupied by a trap, it has been shown that exciton-mediated energy transport from the periphery to the core can be optimized [S. Yalouz et al., Phys. Rev. E 106, 064313 (2022)2470-004510.1103/PhysRevE.106.064313]. If the defects are judiciously chosen, then the exciton dynamics is isomorphic to that of an asymmetric chain and a speedup of the excitonic propagation is observed. Here we extend this previous work by considering that the exciton in both an extended star and an asymmetric chain is perturbed by the presence of a dephasing environment. Simulating the dynamics using a Lindblad master equation, two questions are addressed: How does the environment affect the energy transport on these two networks? and Do the two systems still behave equivalently in the presence of dephasing? Our results reveal that the timescale for the exciton dynamics strongly depends on the nature of the network. But quite surprisingly, the two networks behave similarly regarding the survival of their optimization law. In both cases, the energy transport can be improved using the same original optimal tuning of energy defects as long as the dephasing remains weak. However, for moderate or strong dephasing, the optimization law is lost due to quantum Zeno effect.

Energy transfer along Müller cell intermediate filaments isolated from porcine retina: I. Excitons produced by ADH1A dimers upon simultaneous hydrolysis of two ATP molecules

IR exciton propagation was explored in Müller cell (MC) intermediate filaments (IFs) filling a capillary matrix. These IFs have been isolated from porcine retina using different methods, while their properties were almost identical. Therefore, IFs isolated from the whole retinas were used presently. IR excitons were generated by IR radiation at 2 μm wavelength, or by enzymatic ATP hydrolysis, with the energy transferred to IFs. Excitons produced by ATP hydrolysis required simultaneous energy contribution of two ATP molecules, indicating simultaneous hydrolysis of two ATP molecules in the naturally dimeric human alcohol dehydrogenase enzyme (ADH1A). ATP hydrolysis was thus catalyzed by ADH1A…NAD⁺ enzymatic complexes absorbed at the IF extremities protruding out of the capillary matrix. The IR emission spectra of excitons were dependent on the exciton generation method. We believe this resulted from the exciton energy distribution varying in function of the generation method used. The latter seems reasonable, given the very long excited-state lifetimes, implying low nonradiative relaxation rates. The energy liberated by ATP hydrolysis has been measured directly in these experiments, for the first time. The results demonstrate that contrary to the predictions of equilibrium thermodynamics, the liberated energy is independent on the ATP/ADP concentration ratio, indicating that non-equilibrium reactions take place. Time-resolved experiments with excitons produced by pulsed IR radiation evaluated characteristic exciton propagation and emission times. For the first time, biexcitonic processes were observed in biological objects, whereby simultaneous hydrolysis of two ATP molecules bound to the same dimeric ADH1A molecule generated excitons carrying twice the energy liberated by hydrolysis of a single ATP molecule. The results reported indicate that ATP-liberated energy may be transmitted along natural polypeptide nanofibers in vivo, within and between live cells. These ideas could promote new understanding of the biophysics of life.

Influences of Electromagnetic Energy on Bio-Energy Transport through Protein Molecules in Living Systems and Its Experimental Evidence

The influences of electromagnetic fields (EMFs) on bio-energy transport and its mechanism of changes are investigated through analytic and numerical simulation and experimentation. Bio-energy transport along protein molecules is performed by soliton movement caused by the dipole-dipole electric interactions between neighboring amino acid residues. As such, EMFs can affect the structure of protein molecules and change the properties of the bio-energy transported in living systems. This mechanism of biological effect from EMFs involves the amino acid residues in protein molecules. To study and reveal this mechanism, we simulated numerically the features of the movement of solitons along protein molecules with both a single chain and with three channels by using the Runge-Kutta method and Pang's soliton model under the action of EMFs with the strengths of 25,500, 51,000, 76,500, and 102,000 V/m in the single-chain protein, as well as 17,000, 25,500, and 34,000 V/m in the three-chain protein, respectively. Results indicate that electric fields (EFs) depress the binding energy of the soliton, decrease its amplitude, and change its wave form. Also, the soliton disperses at 102,000 V/m in a single-chain protein and at 25,500 and 34,000 V/m in three-chain proteins. These findings signify that the influence of EMFs on the bio-energy transport cannot be neglected; however, these variations depend on both the strength and the direction of the EF in the EMF. This direction influences the biological effects of EMF, which decrease with increases in the angle between the direction of the EF and that of the dipole moment of amino acid residues; however, randomness at the macroscopic level remains. Lastly, we experimentally confirm the existence of a soliton and the validity of our conclusion by using the infrared spectra of absorption of the collagens, which is activated by another type of EF. Thus, we can affirm that both the described mechanism and the corresponding theory are correct and that EMFs or EFs can influence the features of energy transport in living systems and thus have certain biological effects.

Bright and peaklike pulse solitary waves and analogy with modulational instability in an extended nonlinear Schrödinger equation

The modulational instability (MI) phenomenon in the nonlinear Schrödinger equation (NLSE) extended by two different nonlinear dispersion terms and the gradient term is investigated. We find that the possibility of instability of plane waves depends on the sign of the nonlinear dispersion parameters with regard to the linear dispersion coefficient. In contrast to the basic NLSE, the system may exhibit instability in the defocusing media for amplitude exceeding a critical value depending on the magnitude of the nonlinear dispersion. An additional feature, namely the higher order or the infinite gain band, absent in the NLSE case, may appear and in which MI induces the birth of the nonlinear localized wave (NLW) of different carrier wave numbers. The result of the qualitative investigations of the system's dynamics indicates the existence of the NLW, such as peak, bright, dark, and compact dark solitary waves which can be well predicted by the MI criteria. In addition the nonlinear dispersion induces the existence of a pair of bright-dark solitary waves which is usually exhibited by the coupled NLSEs only, and the pairs of peak-dark and compact dark-bright solitary waves.

Properties of the moving Holstein large polaron in one-dimensional molecular crystals

The features of the moving large polaron are investigated within Holstein's molecular crystal model. The necessity to account for the phonon dispersion is emphasized and its impact on polaron properties is examined in detail. It was found that the large polaron dynamics is described by the nonlocal nonlinear Schrödinger equation. The character of its solutions is determined by the degree of nonlocality, which is specified by the polaron velocity and group velocity of the lattice modes. An analytic solution for the polaron wavefunction is obtained in the weakly nonlocal limit. It was found that the polaron velocity and phonon dispersion have a significant impact on the parameters and dynamics of large polarons. The polaron amplitude and effective mass increase while its spatial extent decreases with a rise in the degree of nonlocality. The criterion for the stability of large polaron is formulated in terms of the values of the degree of nonlocality, the magnitude of the basic energy parameters of the system and the polaron velocity. It turns out that the large polaron velocity cannot exceed a relatively small limiting value. A similar limitation on large polaron velocity has not been found in previous studies. The consequences of these results on polaron dynamics in realistic conditions are discussed.

Generic features of modulational instability in nonlocal Kerr media

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general response function. Several generic properties are proven mathematically, with emphasis on how new gain bands are formed through a bifurcation process when the degree of nonlocality, sigma, passes certain bifurcation values and how the bandwidth and maximum of each individual gain band depends on sigma. The generic properties of the MI gain spectrum, including the bifurcation phenomena, are then demonstrated for the exponential and rectangular response functions. For a focusing nonlinearity the nonlocality tends to suppress MI, but can never remove it completely, irrespectively of the shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. For response functions with a positive-definite spectrum, such as Gaussians and exponentials, plane waves are always stable, whereas response functions with spectra that are not positive definite (such as the rectangular) will lead to MI if sigma exceeds a certain threshold. For the square response function, in both the focusing and defocusing case, we show analytically and numerically how new gain bands that form at higher wave numbers when sigma increases will eventually dominate the existing gain bands at lower wave numbers and abruptly change the length scale of the periodic pattern that may be observed in experiments.

Collapse arrest and soliton stabilization in nonlocal nonlinear media

We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrödinger type equation. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.

Modulational instability in nonlocal nonlinear Kerr media

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose-Einstein condensates.