Electromagnetic Radiation Influence on Nonlinear Charge and Energy Transport in Biosystems

The influence of electromagnetic radiation (EMR) on charge and energy transport processes in biological systems is studied in the light of the soliton model. It is shown that in the spectrum of biological effects of EMR there are two frequency resonances corresponding to qualitatively different frequency dependent effects of EMR on solitons. One of them is connected with the quasiresonance dynamic response of solitons to the EMR. At EMR frequencies close to the dynamic resonance frequency the solitons absorb energy from the field and generate intensive vibrational modes in the macromolecule. The second EMR resonance is connected with soliton decay due to the quantum mechanical transition of the system from the bound soliton state into the excited unbound states.     

DNA的振动—内激发—转子模型

本文全面考察了DNA分子链的各种运动自由度,从B型DNA的双螺旋结构出发,建立了DNA的振动动-内激发-转子模型,并由此给出了相应的哈密顿函数、运动方程和孤子解,较为全面地阐明了DNA的动力学特性．     

Nonlinearity,coherence and complexity: Biophysical aspects related to health and disease

Biological organisms are complex open dissipative systems whose dynamical stability is sustained due to the exchange of matter, energy and information. Dynamical stability occurs through a number of mechanisms that sustain efficient adaptive dynamics. Such properties of living matter can be the consequence of a self-consistent state of matter and electromagnetic field (EMF). Based on the soliton model of charge transport in redox processes, we describe a possible mechanism of the origin of endogenous EMF and coherence. Solitons are formed in polypeptides due to electron–lattice interaction. Solitons experience periodical potential barrier, as a result of which their velocity oscillates in time, and, hence, they emit electromagnetic radiation (EMR). Under the effect of such radiation from all other solitons, the synchronization of their dynamics takes place, which significantly increases the intensity of the general EMF. The complex structure of biological molecules, such as helical structure, is not only important for “structure-function” relations, but also the source of the stability of biophysical processes, e.g. effectiveness of energy and charge transport on macroscopic distances. Such a complex structure also provides the framework for the spatiotemporal structure of the endogenous EMF. The highly hierarchical organization of living organisms is a manifestation of their complexity, even at the level of simple unicellular organisms. This complexity increases the dynamical stability of open systems and enhances the possibility of information storage and processing. Our findings provide a qualitative overview of a possible biophysical mechanism that supports health and disease adaptive dynamics.     

Supersonic Vibron Solitons and Their Possible Existence in Polypeptides

Nonlinear interactions of vibrons with lattice solitons due to the soft cubic nonlinearity in a quasi-one-dimensional lattice yield supersonic vibron solitons. Their binding energy is larger than those of the conventional Davydov solitons and vibron solitons, and their propagation velocity is uniquely determined in contrast to the latter two. Examination of parameters in the model Hamiltonian for polypeptides leads to the result that the supersonic vibron solitons obtained here are more likely to be realizable than the Davydov solitons and the conventional vibron solitons in alpha-helical proteins.     

Effect of dust size distribution on ion-acoustic solitons in dusty plasmas with different dust grains

Theoretical studies are carried out for ion acoustic solitons in multicomponent nonuniform plasma considering the dust size distribution. The Korteweg?de Vries equation for ion acoustic solitons is given by using the reductive perturbation technique. Two special dust size distributions are considered. The dependences of the width and amplitude of solitons on dust size parameters are shown. It is found that the properties of a solitary wave depend on the shape of the size distribution function of dust grains.     

Solitons and energy transfer along protein molecules

It is shown that the energy released in the hydrolysis of ATP molecules can be transferred in the form of vibration solitons along α-helical protein molecules. The vibration solitons are collective excitations travelling along a chain of successively arranged peptide groups and corresponding to amide I vibrations. The exceptional stability of solitons in one-dimensional structures can account for the small probability of their energy transforming into that of disordered heat motion.     

Air‐core fiber or photonic‐crystal rod,which is more suitable for energetic femtosecond pulse generation and three‐photon microscopy at the 1700‐nm window?

Energetic femtosecond pulses at the 1700‐nm window are a prerequisite for deep‐tissue three‐photon microscopy (3PM). Soliton self‐frequency shift (SSFS) in photonic‐crystal (PC) rod has been the only technique to generate such pulses suitable for 3PM. Here we demonstrate through SSFS in an air‐core fiber, we can generate most energetic femtosecond soliton pulses at the 1700‐nm window, 5.2 times higher than that from PC rod. However, the air‐core soliton pulse width is 5.9 times longer than that of PC rod soliton. Based on comparative 3PM excited with both air‐core and PC rod solitons, we propose the more suitable source for 3PM. We further elucidate the challenge of generating shorter soliton pulses from air‐core fibers through numerical simulation.     

Ion-acoustic solitons in dusty plasma

The dynamics of dust ion-acoustic solitons is analyzed in a wide range of dusty plasma parameters. The cases of both a positive dust grain charge arising due to the photoelectric effect caused by intense electromagnetic radiation and a negative grain charge established in the absence of electromagnetic radiation are considered. The ranges of plasma parameters and Mach numbers in which ??conservative?? (nondissipative) solitons can exist are determined. It is shown that, in dusty plasma with negatively charged dust grains, both compression and rarefaction solitons can propagate, whereas in plasma with positively charged dust grains, only compression solitons can exist. The evolution of soliton-like compression and rarefaction perturbations is studied by numerically solving the hydrodynamic equations for ions and dust grains, as well as the equation for dust grain charging. The main dissipation mechanisms, such as grain charging, ion absorption by dust grains, momentum exchange between ions and dust grains, and ion-neutral collisions are taken into account. It is shown that the amplitudes of soliton-like compression and rarefaction perturbations decrease in the course of their evolution and their velocities (the Mach numbers) decrease monotonically in time. At any instant of time, the shape of an evolving soliton-like perturbation coincides with the shape of a conservative soliton corresponding to the current value of the Mach number. It is shown that, after the interaction between any types of soliton-like perturbations, their velocities and shapes are restored (with a certain phase shift) to those of the corresponding perturbations propagating without interaction; i.e., they are in fact weakly dissipative solitons.     

Solitary fast magnetosonic waves propagating obliquely to the magnetic field in cold collisionless plasma

Solutions describing solitary fast magnetosonic (FMS) waves (FMS solitons) in cold magnetized plasma are obtained by numerically solving two-fluid hydrodynamic equations. The parameter domain within which steady-state solitary waves can propagate is determined. It is established that the Mach number for rarefaction FMS solitons is always less than unity. The restriction on the propagation velocity leads to the limitation on the amplitudes of the magnetic field components of rarefaction solitons. It is shown that, as the soliton propagates in plasma, the transverse component of its magnetic field rotates and makes a complete turn around the axis along which the soliton propagates.     

Ion acoustic envelope solitons in explosive ionospheric experiments

The conditions are studied under which stable ion acoustic envelope solitons propagating perpendicular to the magnetic field lines can exist in the ionospheric plasma. The amplitudes, frequencies, and lengths of the waves are determined. The results obtained are compared with the experimental data. It is suggested that such solitons play an important role in both the formation of an ionization front and its motion across the magnetic field and also give rise to a fluctuation precursor in explosive ionospheric experiments.     

Nonlinear mechanism for weak photon emission from biosystems

The nonlinear mechanism for the origin of the weak biophoton emission from biological systems is suggested. The mechanism is based on the properties of solitons that provide energy transfer and charge transport in metabolic processes. Such soliton states are formed in alpha-helical proteins. Account of the electron-phonon interaction in macromolecules results in the self-trapping of electrons in a localized soliton-like state, known as Davydov's solitons. The important role of the helical symmetry of macromolecules is elucidated for the formation, stability and dynamical properties of solitons. It is shown that the soliton with the lowest energy has an inner structure with the many-hump envelope. The total probability of the excitation in the helix is characterized by interspine oscillations with the frequency of oscillations, proportional to the soliton velocity. The radiative life-time of a soliton is calculated and shown to exceed the life-time of an excitation on an isolated peptide group by several orders of magnitude.     

Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg?deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.     

Large-amplitude ion acoustic solitons in a bi-ion plasma

A gas-dynamic model is used to study the conditions for the existence of large-amplitude ion acoustic solitons in a plasma with negative ions. It is shown that the limiting Mach number—the upper boundary of the region of existence of compression solitons—depends nonmonotonically on the temperature of the positive ions. The result is that, for certain fixed densities of the negative ions, there are one or two temperature boundaries between the regions where solitons can and cannot exist. It is found that, for rarefaction solitons, it is fundamentally important to take into account electron inertia and that the Mach number of such solitary waves is restricted not by the complete decompression of electrons within the wave (as thought previously), but by the fact that the electrons at the center of the wave reach the acoustic speed, above which the thermal-pressure-induced action cannot be transferred back to the electron flow and smooth continuous solutions are impossible.     

Compressive and rarefactive DIA solitons beyond the KdV limit

The modified Gardner equation (MGE), showing the existence of compressive and rarefactive dust-ion-acoustic (DIA) solitons in a nonplanar dusty plasma (containing inertial ions, Boltzmann electrons, and negatively charged stationary dust) beyond the KdV Korteweg-de Vries (KdV) limit, is derived and numerically solved. The basic features of the compressive and rarefactive cylindrical and spherical DIA solitons, which are found to exist beyond the KdV limit, i.e., exist for μ ∼ 2/3 (where μ = Z _n n _d0/n _i0, z _d is the number of electrons residing onto the dust grain surface, n _d0(n _i0) is the dust (ion) number density at equilibrium, and μ ∼ 2/3 means that μ is not equal to 2/3, but it is around 2/3) are identified. These solitons (which can be referred to as DIA Gardner solitons (DIA-GSs)) are completely different from the KdV solitons because μ = 2/3 corresponds to the vanishing of the nonlinear coefficient of the KdV equation, and μ ∼ 2/3 corresponds to extremely large amplitude KdV solitons for which the validity of the reductive perturbation method breaks down. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.     

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.     

Heavy Ion-Acoustic Solitary Waves and Double Layers in a Multi-Ion Plasma

The formation and propagation of small-amplitude heavy-ion-acoustic (HIA) solitary waves and double layers in an unmagnetized collisionless multicomponent plasma system consisting of superthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions are theoretically investigated. The reductive perturbation technique is employed to derive the modified Korteweg–de Vries (mKdV) and standard Gardner (SG) equations. The solitary wave (SW) solution of mKdV and SG equations, as well as double layers (DLs) solution of SG equation, is studied for analysis of higher order nonlinearity. It is found that the plasma system under consideration supports positive and negative potential Gardner solitons, but only positive potential mKdV solitons. In addition, it is shown that, the basic properties of HIA mKdV and Gardner solitons and DLs (viz. polarity, amplitude, width, and phase speed) are incomparably influenced by the adiabaticity effect of heavy ions and the superthermality effect of electrons. The relevance of the present findings to the system of space plasmas, as well as to the system of researchers interest, is specified.     

Ion-acoustic supersolitons in plasma

A new class of solitary waves??supernonlinear solitons (supersolitons)??the phase trajectories of which envelop one or several inner separatrices on the wave phase portrait has been revealed. It is shown that supersolitons of the ion-acoustic type can exist in an unmagnetized plasma that contains no less than four kinds of charged particles. The conditions for the existence of supersolitons are specified. The profile of the electrostatic potential in an ion-acoustic supersoliton is determined. It is shown that a supersoliton can be easily recognized experimentally among conventional solitons by using a differentiating circuit in the measuring channel.     

Slow electromagnetic solitons in electron-ion plasmas

A set of nonlinear differential equations that describe moving relativistic solitons is investigated analytically and solved numerically. The influence of the ion motion on the soliton structure is investigated. It is demonstrated that, depending on the propagation velocity, relativistic solitary waves can occur in the form of bright solitons, dark solitons, or collisionless electromagnetic shock waves. In the limit of a low propagation velocity, a dark soliton can trap the ions and accelerate them. In the case of a bright soliton, the effects of ion dynamics limit the soliton amplitude. The constraint on the maximum amplitude is related to either the breaking of ion motion or the intersection of electron trajectories. The soliton breaking provides a new mechanism for ion and electron acceleration in the interaction of high-intensity laser pulses with plasmas.     

Soliton behaviour in a bistable reaction diffusion model

We analyze a generic reaction-diffusion model that contains the important features of Turing systems and that has been extensively used in the past to model biological interesting patterns. This model presents various fixed points. Analysis of this model has been made in the past only in the case when there is only a single fixed point, and a phase diagram of all the possible instabilities shows that there is a place where a Turing-Hopf bifurcation occurs producing oscillating Turing patterns. In here we focus on the interesting situation of having several fixed points, particularly when one unstable point is in between two equally stable points. We show that the solutions of this bistable system are traveling front waves, or solitons. The predictions and results are tested by performing extensive numerical calculations in one and two dimensions. The dynamics of these solitons is governed by a well defined spatial scale, and collisions and interactions between solitons depend on this scale. In certain regions of parameter space the wave fronts can be stationary, forming a pattern resembling spatial chaos. The patterns in two dimensions are particularly interesting because they can present a coherent dynamics with pseudo spiral rotations that simulate the myocardial beat quite closely. We show that our simple model can produce complicated spatial patterns with many different properties, and could be used in applications in many different fields.