Vibron-polaron in alpha-helices. I. Single-vibron states

Influence of donor or acceptor presence on excitation states in molecular chains: Nonadiabatic polaron approach

In this paper, we considered a molecular structure that consists of a molecular chain and an additional molecule (donor or acceptor) that can inject (or remove) single excitation (vibron, electron, etc.) onto the molecular chain. We assumed that the excitation forms a self-trapped state due to the interaction with mechanical oscillations of the chain structure elements. We analyzed the energy spectra of the excitation and showed that its state (when it migrates to the molecular chain) has the properties of the nonadiabatic polaron state. The conditions under which the excitation can migrate from one subsystem to another one were considered. It was shown that the presence of a "donor" molecule cannot significantly change the properties of the excitation located on the molecular chain. At the same time, the molecular chain can affect the position of the energy level of the excitation localized on the donor subsystem. Indirectly, this can influence the process of excitation migration from one subsystem to another one. The influence of the basic energy parameters of the system and the environment temperature on this process are discussed. The entire system was assumed to be in thermal equilibrium with the environment.

A review on nonlinear DNA physics

The study and the investigation of structural and dynamical properties of complex systems have attracted considerable interest among scientists in general and physicists and biologists in particular. The present review paper represents a broad overview of the research performed over the nonlinear dynamics of DNA, devoted to some different aspects of DNA physics and including analytical, quantum and computational tools to understand nonlinear DNA physics. We review in detail the semi-discrete approximation within helicoidal Peyrard-Bishop model and show that localized modulated solitary waves, usually called breathers, can emerge and move along the DNA. Since living processes occur at submolecular level, we then discuss a quantum treatment to address the problem of how charge and energy are transported on DNA and how they may play an important role for the functioning of living cells. While this problem has attracted the attention of researchers for a long time, it is still poorly understood how charge and energy transport can occur at distances comparable to the size of macromolecules. Here, we review a theory based on the mechanism of 'self-trapping' of electrons due to their interaction with mechanical (thermal) oscillation of the DNA structure. We also describe recent computational models that have been developed to capture nonlinear mechanics of DNA in vitro and in vivo, possibly under topological constraints. Finally, we provide some conjectures on potential future directions for this field.

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.

Signatures of discrete breathers in coherent state quantum dynamics

In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.

Vibrons in finite size molecular lattices: a route for high-fidelity quantum state transfer at room temperature

A communication protocol is proposed in which vibron-mediated quantum state transfer takes place in a molecular lattice. We consider two distant molecular groups grafted on each side of the lattice. These groups form two quantum computers where vibrational qubits are implemented and received. The lattice defines the communication channel along which a vibron delocalizes and interacts with a phonon bath. Using quasi-degenerate perturbation theory, vibron-phonon entanglement is taken into account through the effective Hamiltonian concept. A vibron is thus dressed by a virtual phonon cloud whereas a phonon is clothed by virtual vibronic transitions. It is shown that three quasi-degenerate dressed states define the relevant paths followed by a vibron to tunnel between the computers. When the coupling between the computers and the lattice is judiciously chosen, constructive interference takes place between these paths. Phonon-induced decoherence is minimized and a high-fidelity quantum state transfer occurs over a broad temperature range.

SOLITONS IN ALPHA-HELIX PROTEINS BY HE'S VARIATIONAL PRINCIPLE

This paper studies the dynamics of solitons due to solitons in α-helix proteins. The analysis is going to be carried out by the aid of He's semi-inverse variational principle. The constraint relation between the soliton parameters will also be determined in order for the soliton to exist.

Nature of the vibron self-trapped states in hydrogen-bonded macromolecular chains

We study the influence of temperature and the values of basic energy parameters on the character of vibron self-trapped states in quasi-one-dimensional hydrogen-bonded molecular chains. Investigations have been carried out within the one-dimensional Holstein molecular crystal model employing the variational extension of the Lang-Firsov unitary transformation. It was found that, in the low-temperature regime, only partially dressed small-polaron states may exist. With the rise of temperature, the system enters the metastability region, where partially dressed (light and mobile) and fully dressed (heavy and practically immobile) small-polaron states may exist simultaneously.

Quantum decoherence in finite size exciton-phonon systems

Based on the operatorial formulation of the perturbation theory, the properties of a confined exciton coupled with phonons in thermal equilibrium is revisited. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. Special attention is thus paid for describing the time evolution of the excitonic coherences at finite temperature. As in an infinite lattice, temperature-enhanced quantum decoherence takes place. However, it is shown that the confinement softens the decoherence. The coherences are very sensitive to the excitonic states so that the closer to the band center the state is located, the slower the coherence decays. In particular, for odd lattice sizes, the coherence between the vacuum state and the one-exciton state exactly located at the band center survives over an extremely long time scale. A superimposition involving the vacuum and this specific one-exciton state behaves as an ideal qubit insensitive to its environment.

Phonon anharmonicity-induced decoherence slowing down in exciton-phonon systems

Based on a generalized Fröhlich model, a time-convolutionless master equation is established for studying the dynamics of an exciton coupled with anharmonic phonons. Special attention is paid to describing the influence of the phonon anharmonicity on specific elements of the exciton reduced density matrix. These elements, called coherences, characterize the ability of the exciton to develop quantum states that are superimpositions involving the vacuum and the local one-exciton states. Whether the phonons are harmonic or not, it is shown that dephasing limited-coherent motion takes place. The coherences irreversibly decrease with time, the decay rate being the so-called dephasing rate, so that they experience a localization phenomenon and propagate over a finite length scale. However, it is shown that the phonon anharmonicity softens the influence of the phonon bath and reduces the dephasing rate. A slowdown in the decoherence process appears so that the coherences are able to explore a larger region along the lattice. Moreover, the phonon anharmonicity modifies the way the dephasing rate depends on both the adiabaticity and the temperature. In particular, the dephasing rate increases linearly with the temperature in the weak anharmonicity limit whereas it becomes almost temperature-independent in the strong anharmonicity limit. Note that the present formalism is applied to describe amide-I excitons (vibrons) in a lattice of H-bonded peptide units.

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.

2D-IR experiments and simulations of the coupling between amide-I and ionizable side chains in proteins: application to the Villin headpiece

The carboxylate side chains of Asp and Glu have significant coupling with the amide states of the backbone of the Villin headpiece. In two-dimensional spectroscopy, cross peaks are observed between these side chains and the main amide-I band. To model the absorption of the side chains, the electric field variations of vibrational frequencies of a carboxylic acid group (neutral form, CH(3)-COOH) and a carboxylate group (ionized form, CH(3)-COO(-)) are parametrized by means of density functional theory calculations. Simulations indicate that the side chains significantly couple to only one or two amide-I modes out of all of the amino acid residues which makes them useful as spectroscopic markers, providing information about the local structural behavior of the protein. Both experiment and simulations show that the cross peaks between the carboxylate and the amide-I bands are significantly diminished above the melting temperature.

Periodic sequence distribution of product ion abundances in electron capture dissociation of amphipathic peptides and proteins

The rules for product ion formation in electron capture dissociation (ECD) mass spectrometry of peptides and proteins remain unclear. Random backbone cleavage probability and the nonspecific nature of ECD toward amino acid sequence have been reported, contrary to preferential channels of fragmentation in slow heating-based tandem mass spectrometry. Here we demonstrate that for amphipathic peptides and proteins, modulation of ECD product ion abundance (PIA) along the sequence is pronounced. Moreover, because of the specific primary (and presumably secondary) structure of amphipathic peptides, PIA in ECD demonstrates a clear and reproducible periodic sequence distribution. On the one hand, the period of ECD PIA corresponds to periodic distribution of spatially separated hydrophobic and hydrophilic domains within the peptide primary sequence. On the other hand, the same period correlates with secondary structure units, such as alpha-helical turns, known for solution-phase structure. Based on a number of examples, we formulate a set of characteristic features for ECD of amphipathic peptides and proteins: (1) periodic distribution of PIA is observed and is reproducible in a wide range of ECD parameters and on different experimental platforms; (2) local maxima of PIA are not necessarily located near the charged site; (3) ion activation before ECD not only extends product ion sequence coverage but also preserves ion yield modulation; (4) the most efficient cleavage (e.g. global maximum of ECD PIA distribution) can be remote from the charged site; (5) the number and location of PIA maxima correlate with amino acid hydrophobicity maxima generally to within a single amino acid displacement; and (6) preferential cleavage sites follow a selected hydrogen spine in an alpha-helical peptide segment. Presently proposed novel insights into ECD behavior are important for advancing understanding of the ECD mechanism, particularly the role of peptide sequence on PIA. An improved ECD model could facilitate protein sequencing and improve identification of unknown proteins in proteomics technologies. In structural biology, the periodic/preferential product ion yield in ECD of alpha-helical structures potentially opens the way toward de novo site-specific secondary structure determination of peptides and proteins in the gas phase and its correlation with solution-phase structure.

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.

Amide-I relaxation-induced hydrogen bond distortion: An intermediate in electron capture dissociation mass spectrometry of alpha-helical peptides?

Electron capture dissociation (ECD) of peptides and proteins in the gas phase is a powerful tool in tandem mass spectrometry whose current description is not sufficient to explain many experimental observations. Here, we attempt to bridge the current understanding of the vibrational dynamics in alpha-helices with the recent experimental results on ECD of alpha-helical peptides through consideration of amide-I relaxation-induced hydrogen bond distortion. Based on a single spine of H-bonded peptide units, we assume that charge neutralization upon electron capture by a charged alpha-helix excites a nearby amide-I mode, which relaxes over a few picoseconds due to Fermi resonances with intramolecular normal modes. The amide-I population plays the role of an external force, which drives the displacements of each peptide unit. It induces a large immobile contraction of the H bonds surrounding the excited site whose lifetime is about the amide-I lifetime. In addition, it creates two lattice deformations describing H bond stretchings, which propagate from the excited region toward both termini of the alpha-helix, get reflected at the termini and yield H bond contractions which move back to the excited region. Consequently, we show that H bonds experience rather large contractions whose amplitude depends on general features such as the position of the amide-I mode, the peptide length and the H bond force constants. When an H bond contraction is sufficiently large, it may promote a hydrogen atom transfer between two neighboring peptide units leading to the formation of a radical at charge site remote carbonyl carbon which is known to be a precursor to the rupture of the corresponding N[Single Bond]C(alpha) bond. The introduced here way of excitation energy generation and transfer may significantly advance ECD understanding and complement existing ECD mechanisms.

Amide-I lifetime-limited vibrational energy flow in a one-dimensional lattice of hydrogen-bonded peptide units

A time-convolutionless master equation is established for describing the amide-I vibrational energy flow in a lattice of H-bonded peptide units. The dynamics is addressed within the small polaron formalism to account for the strong coupling between the amide-I vibron and the phonons describing the H-bond vibrations. Therefore, special attention is paid to characterize the influence of the amide-I relaxation on the polaron transport properties. This relaxation is modeled by assuming that each amide-I mode interacts with a bath of intramolecular normal modes whose displacements are strongly localized on the C=O groups. It has been shown that the energy relaxation occurs over a very short time scale which prevents any significant delocalization of the polaron. At biological temperature, the polaron explores a finite region around the excited site whose size is about one or two lattice parameters. However, two regimes occur depending on whether the vibron-phonon coupling is weak or strong. For a weak coupling, the energy propagates coherently along the lattice until the polaron disappears. By contrast, for a strong coupling, a diffusive regime occurs so that the polaron explores a finite size region incoherently. In both cases, the finite polaron lifetime favors the localization of the vibron density whose amplitude decreases exponentially.

Two-site realization of the Davydov model in a finite size lattice: a time-convolutionless master equation approach

A two-site realization of the Davydov model is introduced to study the energy flow between two amide-I modes embedded in a finite size lattice of hydrogen-bounded peptide units. The non-Markovian nature of the energy transfer is addressed by using a time convolutionless master equation for the population difference of quanta between the two sites of the dimer. It is shown that both the lattice size and the dimer position discriminate between two dynamical regimes. For specific values of these parameters, the population difference shows damped oscillations. It decreases exponentially and rapidly vanishes, which indicates that the equilibrium corresponds to a uniform energy distribution over the two sites of the dimer. By contrast, for other specific values of the lattice size and dimer position, a slowdown of the decoherence takes place. The population difference does not decay exponentially but evolves by steps during which the damping of the oscillations is very small. In addition, the occurrence of revivals characterizing an amplification of the coherence over a finite time scale is observed. Nevertheless, both the decoherence slowdown and the revivals are limited by pure dephasing so that the population difference finally vanishes, but after a rather large coherent time.

Linking physiological mechanisms of coherent cellular behaviour with more general physical approaches towards the coherence of life

Schrödinger pointed out that one of the most fundamental properties of life is its coherent behaviour. This property has been approached from a physiological point of view by Ling in his 'association-induction hypothesis' and extended by Pollack (gel-sol theory), by Chaplin and by Kaivarainen (detailed studies of cellular water). The question of coherence has also been attacked from general physics in three independent approaches: from non-linear thermodynamics (Fröhlich), from quantum field theory (Del Giudice and his group) and from quantum mechanics (Davydov). In this paper all these approaches are unified. The emerging picture constitutes a new paradigm of life.

Vibron-polaron in α-helices. II. Two-vibron bound states

The two-vibron dynamics associated to amide-I vibrations in a three-dimensional (3D) alpha-helix is described according to a generalized Davydov model. The helix is modeled by three spines of hydrogen-bonded peptide units linked via covalent bonds. It is shown that the two-vibron energy spectrum supports both a two-vibron free states continuum and two kinds of bound states, called two-vibron bound states (TVBS)-I and TVBS-II, connected to the trapping of two vibrons onto the same amide-I mode and onto two nearest-neighbor amide-I modes belonging to the same spine, respectively. At low temperature, nonvanishing interspine hopping constants yield a three-dimensional nature of both TVBS-I and TVBS-II which the wave functions extend over the three spines of the helix. At biological temperature, the pairs are confined in a given spine and exhibit the same features as the bound states described within a one-dimensional model. The interplay between the temperature and the 3D nature of the helix is also responsible for the occurrence of a third bound state called TVBS-III which refers to the trapping of two vibrons onto two different spines. The experimental signature of the existence of bound states is discussed through the simulation of their infrared pump-probe spectroscopic response. Finally, the fundamental question of the breather-like behavior of two-vibron bound states is addressed.