The lifetime of molecular (Davydov) solitons

The lifetime of Davydov solitons in a one-dimensional system is studied theoretically. The process of thermalization and the properties of solitons at finite temperature are investigated and the processes of soliton creation and disintegration are discussed.     

The nature of phonons and solitary waves in alpha-helical proteins.

A parametric study of the Davydov model of energy transduction in alpha-helical proteins is described. Previous investigations have shown that the Davydov model predicts that nonlinear interactions between phonons and amide-I excitations can stabilize the latter and produce a long-lived combined excitation (the so-called Davydov soliton), which propagates along the helix. The dynamics of this solitary wave are approximately those of solitons described using the nonlinear Schr?dinger equation. The present study extends these previous investigations by analyzing the effect of helix length and nonlinear coupling efficiency on the phonon spectrum in short and medium length alpha-helical segments. The phonon energy accompanying amide-I excitation shows periodic variation in time with fluctuations that follow three different time scales. The phonon spectrum is highly dependent upon chain length but a majority of the energy remains localized in normal mode vibrations even in the long chain alpha-helices. Variation of the phonon-exciton coupling coefficient changes the amplitudes but not the frequencies of the phonon spectrum. The computed spectra contain frequencies ranging from 200 GHz to 6 THz, and as the chain length is increased, the long period oscillations increase in amplitude. The most important prediction of this study, however, is that the dynamics predicted by the numerical calculations have more in common with dynamics described by using the Frohlich polaron model than by using the Davydov soliton. Accordingly, the relevance of the Davydov soliton model was applied to energy transduction in alpha-helical proteins is questionable.(ABSTRACT TRUNCATED AT 250 WORDS)     

Tilting after Dutch windmills: probably no long-lived Davydov solitons in proteins

We present a summary of picosecond pump-probe and photon echo experiments in the mid-IR at 6 μm on the protein myoglobin. The intriguing temperature dependence of the amide I band in Mb is rather similar to the temperature dependence of the amide I band of acetanilide, the molecule that launched Al Scott down the road of looking for Davydov solitons in biology. Alas, after much effort, we believe the data show that there is no long-lived Davydov soliton, at least in myoglobin. This work was supported by the Office of Naval Research and the Stichting voor Fundamenteel Onderzoek der Materie (FOM).     

Davydov Soliton Dynamics in Proteins: III. Applications and Calculation of Vibrational Spectra

The mechanism for energy and signal transport in proteins as suggested by Davydov is discussed. The idea is based on a coupling of amide-I oscillators to acoustic phonons in a hydrogen bonded chain. Results as obtained with the usually used ansätze are discussed. The quality of these states for an approximate solution of the time-dependent Schrödinger equation is investigated. It is found that the semiclassical ansatz is a poor approximation, while the more sophisticated |D₁> state seems to represent the exact dynamics quite well. This was shown by extensive calculations, both analytically and numerically in the two preceding papers. Calculations at a temperature of 300K for one chain, as well as for three coupled ones (as they are present in an α-helix) are presented and discussed. From the calculations it is evident, that Davydov solitons are stable for reasonable parameter values at 300K for special initial excitations close to the terminal sites of the chain. Further vibrational spectra are presented and discussed. Our results suggest, that due to their strong dependence on the initial state, the Davydov |D₁> model system might be a (quantum) chaotic one.     

Davydov Soliton Dynamics in Proteins: III. Applications and Calculation of Vibrational Spectra

The mechanism for energy and signal transport in proteins as suggested by Davydov is discussed. The idea is based on a coupling of amide-I oscillators to acoustic phonons in a hydrogen bonded chain. Results as obtained with the usually used ansätze are discussed. The quality of these states for an approximate solution of the time-dependent Schrödinger equation is investigated. It is found that the semiclassical ansatz is a poor approximation, while the more sophisticated |D₁> state seems to represent the exact dynamics quite well. This was shown by extensive calculations, both analytically and numerically in the two preceding papers. Calculations at a temperature of 300K for one chain, as well as for three coupled ones (as they are present in an -helix) are presented and discussed. From the calculations it is evident, that Davydov solitons are stable for reasonable parameter values at 300K for special initial excitations close to the terminal sites of the chain. Further vibrational spectra are presented and discussed. Our results suggest, that due to their strong dependence on the initial state, the Davydov |D₁> model system might be a (quantum) chaotic one.     

Nonlinear theory of ion-acoustic waves in an electron-positron-ion plasma

An analytical nonlinear gasdynamic theory of ion-acoustic waves in an e-p-i plasma is developed for the case in which all the plasma components in the wave undergo polytropic compression and rarefaction. An exact solution to the basic equations is found and analyzed by the Bernoulli pseudopotential method. The parameter range in which periodic waves can propagate and the range in which solitary waves (solitons) exist are determined. It is shown that the propagation velocity of a solitary is always higher than the linear ion sound velocity. The profiles of all the physical quantities in both subsonic and supersonic waves are calculated. The results obtained agree well with both the data from other papers and particular limiting cases.     

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.     

The Davydov/Scott Model for Energy Storage and Transport in Proteins

The current status of the Davydov/Scott model for energy transfer in proteins is reviewed. After a brief introduction to the theoretical framework and to the basic results, the problems of finite temperature dynamics and of the full quantum and mixed quantum-classical approximations are described, as well as recent results obtained within each of these approximations. A short survey of experimental evidence in support of the Davydov/Scott model is made and absorption spectra are calculated that show the same temperature dependence as that measured in crystalline acetanilide. Future applications of the Davydov/Scott model to protein folding and function and to misfolding diseases are outlined.     

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.     

The spread of infectious diseases in spatially structured populations: an invasory pair approximation

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.     

Quick sequential procedure for speciation analysis of heavy metals in soils by supersonic extraction

Abstract

In order to improve the extraction efficiency and reduce the operation time, supersonic energy by means of supersonic bath was used to the modified Tessier sequential extraction for speciation analysis of heavy metals in soils. Extractable contents of Cu, Fe, Mn, Ni, Pb and Zn were measured by flame atomic absorption spectroscopy. The merit of the supersonic extraction (SE) applied to the modified Tessier, method is not only that the operation time for the first 4 fractions was reduced from ca 18 h to 8 h, comparing with conventional extraction (CE), but also the extraction efficiency was higher. There were no significant differences between the data obtained by the proposed method using supersonic extraction and the reference values of the standard reference materials of EES-2 and EES-3. The results for both of SE and CE in the soil samples were consistent. The extractable Cu, Ni and Zn in the sample No. 1 were mainly associated with the third fraction (Fe-Mn oxides fraction), and fourth fraction (organic matter fraction) in the sample No. 2. The extractable Fe and Mn were all mainly associated with the third fraction, and Pb the fourth fraction in both of the samples. The effects of varying concentrations of hydroxylamine hydrochloride on the extraction of metals were also studied.     

Core–valence correlation effects on IR calculations: the BF3 and BCl3 cases

We obtain a characterization of quantum shape-phase transitions in the terms of complexity measures in the two-dimensional limit of the vibron model based on the spectrum generating algebra U(3). Complexity measures (in terms of the Rényi entropies) have been calculated for different values of the control parameter for the ground state of this model giving sharp signatures of the quantum shape-phase transition from linear to bent molecules.     

Birds' tails do act like delta wings but delta-wing theory does not always predict the forces they generate

Delta-wing theory, which predicts the aerodynamics of aircraft like the Concorde, is the conventional explanation for the way in which a bird's tail operates in flight. Recently, doubt has been cast on the validity of applying a theory devised for supersonic aircraft to the small tails of slow-flying birds. By testing delta-wing models and birds' tails behind bodies with wings, I empirically show that the tails of birds produce lift in a very similar way to conventional delta-wing models. Both Perspex and birds' tail models produce lift similar to that predicted by delta-wing theory when narrowly spread and at low angles of attack. However, when widely spread and at high angles of attack, both tails and Perspex models produce much less lift than predicted, owing to vortex breakdown after which the assumptions of delta-wing theory are violated. These results indicate that birds' tails can be regarded as delta wings but that the theory predicting the forces produced by delta wings can only be applied within acceptable limits (i.e. tails spread less than 60 degrees and at angles of attack of less than 20 degrees).     

Pathogen invasion and host extinction in lattice structured populations

We examined the propagation of an infectious disease and the eventual extinction of the host population in a lattice-structured population. Both the host colonization and pathogen transmission processes are assumed to be restricted to act between the nearest neighbor sites. The model is analyzed by an improved version of pair approximation (IPA). Pair approximation is a technique to trace the dynamics of the number of nearest neighbor pairs having particular states, and IPA takes account of the clustering property of lattice models more precisely. The results are checked by computer simulations. The analysis shows: (i) in a one-dimensional lattice population, a pathogen cannot invade a host population no matter how large is the transmission rate; (ii) in a two-dimensional lattice population, pathogens will drive the host to extinction if the transmission rate is larger than a threshold. These results indicate that spatially structured population models may give qualitatively different results from conventional population models, such as Lotka-Volterra ones, without spatial structure.     

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.     

VenusA206 Dimers Behave Coherently at Room Temperature

Fluorescent proteins (FPs) have revolutionized cell biology by allowing genetic tagging of specific proteins inside living cells. In conjunction with Förster’s resonance energy transfer (FRET) measurements, FP-tagged proteins can be used to study protein-protein interactions and estimate distances between tagged proteins. FRET is mediated by weak Coulombic dipole-dipole coupling of donor and acceptor fluorophores that behave independently, with energy hopping discretely and incoherently between fluorophores. Stronger dipole-dipole coupling can mediate excitonic coupling in which excitation energy is distributed near instantaneously between coherently interacting excited states that behave as a single quantum entity. The interpretation of FP energy transfer measurements to estimate separation often assumes that donors and acceptors are very weakly coupled and therefore use a FRET mechanism. This assumption is considered reasonable as close fluorophore proximity, typically associated with strong excitonic coupling, is limited by the FP β-barrel structure. Furthermore, physiological temperatures promote rapid vibrational dephasing associated with a rapid decoherence of fluorophore-excited states. Recently, FP dephasing times that are 50 times slower than traditional organic fluorophores have been measured, raising the possibility that evolution has shaped FPs to allow stronger than expected coupling under physiological conditions. In this study, we test if excitonic coupling between FPs is possible at physiological temperatures. FRET and excitonic coupling can be distinguished by monitoring spectral changes associated with fluorophore dimerization. The weak coupling mediating FRET should not cause a change in fluorophore absorption, whereas strong excitonic coupling causes Davydov splitting. Circular dichroism spectroscopy revealed Davydov splitting when the yellow FP Venus_A206 dimerizes, and a novel approach combining photon antibunching and fluorescence correlation spectroscopy was used to confirm that the two fluorophores in a Venus_A206 homodimer behave as a single-photon emitter. We conclude that excitonic coupling between Venus_A206 fluorophores is possible at physiological temperatures.     

Bisoliton mechanism of electron transport in biological systems

A nonlinear mechanism describing the transport of paired electrons in protein molecules is suggested. It is shown that electron-phonon interaction leads to the pairing of two electrons with local chain deformation in a state called a bisoliton. The parameters of the bisoliton and the stability conditions with respect to its decay into two-soliton state are estimated.I dedicate this paper to the memory of my teacher Professor A.S. Davydov, who attracted me to nonlinear science and was my colleague.     

Fröhlich's condensation in a biological membrane viewed as a Davydov soliton

A model Hamiltonian is postulated for a biological membrane involving phospholipid tails and heads accounting for the presence of dielectrically-active material. It is subsequently demonstrated that under specific conditions, Bose condensation of dipolar oscillations of the head groups may take place in support of Fröhlich's earlier conjecture. A new effect is found here that this condensation phenomenon can be interpreted as the emergence of a Davydov soliton in the momentum space for dipole oscillations.     

Developmental Teaching and Learning Activity

In presenting this material, I shall rely on the works of a large group of psychologists under the leadership of D. B. El'konin and V. V. Davydov. These works led to the formulation of certain theoretical concepts of learning activity—of its content as a special form of the personality's learning activeness, of its structure, and of the laws and conditions under which it is produced in the teaching process.