The Davydov/Scott model for energy storage and transport in proteins

Therapeutic processes for eradicating cancerous or benign tumours by laser beams using the excitonic approach of peptide groups

The aim of the present study was to develop a protocol for the treatment of cancerous or benign tumours making use of laser rays, also demonstrating that the destruction process remains exclusively confined in the defective organ. Thermal effects of lasers on biological tissue have been elucidated using vibrational excitations approach of peptide groups (PGs). It was proposed a Hamiltonian which integrate excitations induced by laser pulses and it was shown that the system is governed by a nonlinear equation with strong nonlinearity. It was also exactly described what happens in polypeptide chain once the unwanted organ is irradiated by the Neodymium-doped yttrium aluminium garnet, chosen as incident laser. It was shown that, the advent of incident laser beams contributes to a sudden reinforcement of the vibrational excitations of PGs frequencies and amplitudes. It was also demonstrated that the heating process leads to transverse and longitudinal deformation of the polypeptide chain and these sudden changes lead to the denaturation and subsequently to the destruction of the bulky organ. The drawn curves make it possible to estimate the spatial expansion of the denaturation, in order to effectively control the spread of the heat. Laser irradiation leads to a drastic increase in the vibration amplitudes of the PGs and subsequently results in the destruction of the undesirable tissue. An appropriate choice of the laser can make it possible to circumscribe the destruction only in the defective zone and to protect healthy cells.

Vibrational exciton nanoimaging of phases and domains in porphyrin nanocrystals

Much of the electronic transport, photophysical, or biological functions of molecular materials emerge from intermolecular interactions and associated nanoscale structure and morphology. However, competing phases, defects, and disorder give rise to confinement and many-body localization of the associated wavefunction, disturbing the performance of the material. Here, we employ vibrational excitons as a sensitive local probe of intermolecular coupling in hyperspectral infrared scattering scanning near-field optical microscopy (IR s-SNOM) with complementary small-angle X-ray scattering to map multiscale structure from molecular coupling to long-range order. In the model organic electronic material octaethyl porphyrin ruthenium(II) carbonyl (RuOEP), we observe the evolution of competing ordered and disordered phases, in nucleation, growth, and ripening of porphyrin nanocrystals. From measurement of vibrational exciton delocalization, we identify coexistence of ordered and disordered phases in RuOEP that extend down to the molecular scale. Even when reaching a high degree of macroscopic crystallinity, identify significant local disorder with correlation lengths of only a few nanometers. This minimally invasive approach of vibrational exciton nanospectroscopy and -imaging is generally applicable to provide the molecular-level insight into photoresponse and energy transport in organic photovoltaics, electronics, or proteins.

From Anodic Oxidation of Aliphatic α-Amino Acids to Polypeptides by Quantum Electrochemistry Approach: Beyond Miller-Urey Experiments

For years, polypeptide formation has fascinated the scientific world because its understanding could lead to one of the possible explanations for the origin of life. Anodic oxidation of aliphatic α-amino acids in aqueous electrolytes can result either in their decomposition or in their polymerization into polypeptide. This behavior depends experimentally on both amino acid concentration and pH. The elucidation of the involved mechanisms remains a challenge because of the multitude of products which can be obtained. In this context, the electrochemical behavior of glycine and alanine on a biased platinum surface was examined at the nanoscale by quantum electrochemistry via the effective screening medium method. Several electrochemical systems with different concentrations and pH values have been explored. Simulations of the anodic oxidation of the amino acids have not only confirmed their electropolymerization and decomposition at high and low concentrations, respectively, but also have revealed unsuspected mechanisms at the origin of polypeptide formation. This sheds new light on electrochemistry of α-amino acids, on occurrence of polypeptides, and more generally on organic electrochemistry.

Charge Transfer in Dimer with Dissipation

The study of the charge transfer processes in biomacromolecules such as DNA is essential for the development of nanobioelectronics, design and construction of DNA-based nanowires, memory devices, logical elements, etc. Mathematical and computer modeling of charge transfer in biopolymer chains is an important part of these investigations. Some properties of charge transfer can be demonstrated by modeling of two-site chain. Based on the semi-classical Holstein model we consider a system of two sites and charged particle (electron or hole) in which the oscillations of the first site are not related to the charge motion, and the parameters of the second site correspond to a small-radius polaron. The system steady states depending on the electron energy H at the second site are studied numerically. The dynamics of the charge initially localized at the first site is modeled. Various modes depending on H are demonstrated: charge tunneling, resonant transfer, and lack of transfer.

Exciton dynamics in amide-I [Formula: see text] -helix protein chains with long-range intermolecular interactions

The amide-I [Formula: see text] -helix protein is a long molecular chain made up of regularly spaced peptide groups interacting via C=O bonds. According to the current theory the energy released by hydrolyzed adenosine triphosphate is carried across the protein via vibration modes, caused by C=O bond stretchings which, in the presence of anharmonic molecular vibrations, can promote nonlinear localized excitations called excitons. In this work the effects of long-range interactions between amide-I molecules on the modulational instability of small-amplitude excitons, and on characteristic parameters of soliton wavetrain-type excitons, are investigated with emphasis on long-range interactions saturating at finite intermolecular interaction ranges. It is found that long-range interactions strongly affect the dispersion of vibration modes of the protein chain, causing a narrowing of the modulational-instability regions for small-amplitude excitons. Characteristic parameters of the exciton soliton wavetrain, including its velocity, tail and average width (i.e., the exciton width at half tail), are drastically enhanced with respect to their values when only the short-range interaction is considered. The results suggest a sizable increase of the energy carried by excitons along the protein chain above predictions based on short-range considerations.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.

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.

Phase space trajectories and Lyapunov exponents in the dynamics of an alpha-helical protein lattice with intra- and inter-spine interactions

The nonlinear dynamics of intra- and inter-spine interaction models of alpha-helical proteins is investigated by proposing a Hamiltonian using the first quantized operators. Hamilton's equations of motion are derived, and the dynamics is studied by constructing the trajectories and phase space plots in both cases. The phase space plots display a chaotic behaviour in the dynamics, which opens questions about the relationship between the chaos and exciton-exciton and exciton-phonon interactions. This is verified by plotting the Lyapunov characteristic exponent curves.

Thermodynamic, kinetic and conformational analysis of proteins diffusion-sorption on a solid surface

In this paper we examine particularly some of the more fundamental properties of protein conformational changes at a solid surface coupled with diffusion from the bulk of an aqueous solution and with the adsorption-desorption processes. We focus our attention on adsorbed protein monolayers upon a solid surface using a thermodynamic and kinetic analytical development. Account is also taken of the effects on the overall rate of the conformational change on a solid surface of deviation from ideality, of protein flexibility, of surface free energy and of interaction with reactive solid sites. Our theory applied to steady states is illustrated by examples such as folding-misfolding-unfolding of RNase and SNase on a solid surface after diffusion and adsorption from an aqueous solution. For this purpose, we put forward the determining steps which shall lead to the steady state. The existence of three situations is highlighted according to the values of the typical constants relevant for the protein considered: reaction rate determining step, diffusion and sorption determining steps, mixed adsorption diffusion and reaction rate. Finally, we have tried to link the developments of our theories to a large literature based on experimental results encountered during proteins diffusion-sorption-reaction processes, fundamental topics that has been since long investigated by Miller's team in MPKG.

Energy transport mechanism in the form of proton soliton in a one-dimensional hydrogen-bonded polypeptide chain

The dynamics of protons in a one-dimensional hydrogen-bonded (HB) polypeptide chain (PC) is investigated theoretically. A new Hamiltonian is formulated with the inclusion of higher-order molecular interactions between peptide groups (PGs). The wave function of the excitation state of a single particle is replaced by a new wave function of a two-quanta quasi-coherent state. The dynamics is governed by a higher-order nonlinear Schrödinger equation and the energy transport is performed by the proton soliton. A nonlinear multiple-scale perturbation analysis has been performed and the evolution of soliton parameters such as velocity and amplitude is explored numerically. The proton soliton is thermally stable and very robust against these perturbations. The energy transport by the proton soliton is more appropriate to understand the mechanism of energy transfer in biological processes such as muscle contraction, DNA replication, and neuro-electric pulse transfer on biomembranes.

Parametric resonance-induced time-convolutionless master equation breakdown in finite size exciton-phonon systems

A detailed analysis is performed to show that the second order time-convolutionless master equation fails to describe the exciton-phonon dynamics in a finite size lattice. To proceed, special attention is paid to characterizing the coherences of the exciton reduced density matrix. These specific elements measure the ability of the exciton to develop superimpositions involving the vacuum and the one-exciton states. It is shown that the coherences behave as wavefunctions whose dynamics is governed by a time-dependent effective Hamiltonian defined in terms of the so-called time-dependent relaxation operator. Due to the confinement, quantum recurrences provide to the relaxation operator an almost periodic nature, so the master equation reduces to a linear system of differential equations with almost periodic coefficients. We show that, in accordance with the Floquet theory, unstable solutions emerge due to parametric resonances involving specific frequencies of the relaxation operator and specific excitonic eigenfrequencies. These resonances give rise to an unphysical exponential growth of the coherences, indicating the breakdown of the second order master equation.

Matter-wave dark solitons: stochastic versus analytical results

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically derived equation for the soliton center based on perturbation theory for dark solitons.

Vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units

An attempt is made to measure the vibron-phonon coupling strength in a finite size lattice of H-bonded peptide units. Within a finite temperature density matrix approach, we compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on the coherence between the ground state and a local one-vibron state. Due to the confinement, it is shown that the vibron-phonon coupling yields a series of dephasing-rephasing mechanisms that prevents the coherence to decay. Similarly, the dipole-dipole interaction gives rise to quantum recurrences for specific revival times. Nevertheless, intense recurrences are rather rare events so that the coherence behaves as a random variable whose most probable value vanishes. By comparing the degree of the coherence for each interaction, a critical coupling chi*(L) is defined to discriminate between the weak and the strong coupling limits. Its size dependence indicates that the smaller the lattice size is, the weaker the vibron-phonon coupling relative to the dipole-dipole interaction is.

Vibron phonon in a lattice of H-bonded peptide units: A criterion to discriminate between the weak and the strong coupling limit

Based on dynamical considerations, a simple and intuitive criterion is established to measure the strength of the vibron-phonon coupling in a lattice of H-bonded peptide units. The main idea is to compare separately the influence of both the vibron-phonon coupling and the dipole-dipole interaction on a specific element of the vibron reduced density matrix. This element, which refers to the coherence between the ground state and a local excited amide-I mode, generalizes the concept of survival amplitude at finite temperature. On the one hand, when the dipole-dipole interaction is neglected, it is shown that dephasing-limited coherent dynamics is induced by the vibron-phonon coupling. On the other hand, when the vibron-phonon coupling is disregarded, decoherence occurs due to dipole-dipole interactions since the local excited state couples with neighboring local excited states. Therefore, our criterion simply states that the strongest interaction is responsible for the fastest decoherence. It yields a critical coupling chi( *) approximately 25 pN at biological temperature.