Fractional protein dynamics seen by nuclear magnetic resonance spectroscopy: Relating molecular dynamics simulation and experiment

We propose a fractional Brownian dynamics model for time correlation functions characterizing the internal dynamics of proteins probed by NMR relaxation spectroscopy. The time correlation functions are represented by a broad distribution of exponential functions which are characterized by two parameters. We show that the model describes well the restricted rotational motion of N-H vectors in the amide groups of lysozyme obtained from molecular dynamics simulation and that reliable predictions of experimental relaxation rates can be obtained on that basis.     

Communication: a minimal model for the diffusion-relaxation backbone dynamics of proteins

We present a model for the local diffusion-relaxation dynamics of the C(α)-atoms in proteins describing both the diffusive short-time dynamics and the asymptotic long-time relaxation of the position autocorrelation functions. The relaxation rate spectra of the latter are represented by shifted gamma distributions, where the standard gamma distribution describes anomalous slow relaxation in macromolecular systems of infinite size and the shift accounts for a smallest local relaxation rate in macromolecules of finite size. The resulting autocorrelation functions are analytic for any time t ≥ 0. Using results from a molecular dynamics simulation of lysozyme, we demonstrate that the model fits the position autocorrelation functions of the C(α)-atoms exceptionally well and reveals moreover a strong correlation between the residue's solvent-accessible surface and the fitted model parameters.     

Evaluation of nonlinear quantum time correlation functions within the centroid dynamics formulation

A method to evaluate nonlinear centroid correlation functions is presented that is amenable to simple numerical computation. It can be implemented with the centroid molecular dynamics method for approximate quantum dynamics with no additional assumptions. Two nonlinear correlation functions are evaluated for a model potential using this scheme and compared with results from exact quantum calculations.     

Centroid molecular dynamics: comparison with exact results for model systems

The relation between the accuracy of centroid molecular dynamics correlation functions, and the geometry of the centroid potential is investigated. It is shown that, depending on the temperature, there exist several regimes, and in each of them certain features of the exact Kubo correlation functions are reproduced. The change of regimes is related to the emergence of barriers in the centroid potential. In order to clarify how the above described picture of regimes is modified in real systems when dissipation is important, a methodology is developed to test the accuracy of centroid correlation functions for the model of a particle coupled to a harmonic heat bath. A modification of the centroid molecular dynamics method to include the influence of the heat bath is introduced. Preliminary results of comparison of centroid molecular dynamics with the numerically exact results of filtered propagator functional method are presented.     

Coarse-graining of protein structures for the normal mode studies

The coarse-grained structural model such as Gaussian network has played a vital role in the normal mode studies for understanding protein dynamics related to biological functions. However, for the large proteins, the Gaussian network model is computationally unfavorable for diagonalization of Hessian (stiffness) matrix for the normal mode studies. In this article, we provide the coarse-graining method, referred to as "dynamic model condensation," which enables the further coarse-graining of protein structures consisting of small number of residues. It is shown that the coarser-grained structures reconstructed by dynamic model condensation exhibit the dynamic characteristics, such as low-frequency normal modes, qualitatively comparable to original structures. This sheds light on that dynamic model condensation and may enable one to study the large protein dynamics for gaining insight into biological functions of proteins.     

RISM study of sulphur dioxide at the liquid-vapour coexistence line

Sulphur dioxide is studied by the reference interaction site model. The site-site potential was modelled by the Lennard-Jones potential functions and direct correlation functions were calculated for thermodynamic points close to the liquid-vapour coexistence line. By means of the correlation functions the pressure and mean potential energy have been calculated. The results were compared with molecular dynamics results and also with experimental data. It turned out that the RISM procedure is competitive with the molecular dynamics method only in a relatively narrow temperature range close to the midpoint between the triple point and the critical point. There the agreement between RISM and molecular dynamics method is quite encouraging and also the experimental values of pressure and mean potential energy and compressibility are satisfactorily reproduced. On either side of this region RISM does not reproduce properly the structure and energetics of the liquid SO₂ system.     

One-dimensional models of polymer dynamics. II. A dashpot-spring model

The assumption of Clark and Zimm that coupled dashpots and springs can be used to model the dynamics of polymer molecules is here applied to a model different from that of Clark and Zimm. The precise differences are given in the preceding paper. The dielectric relaxation spectrum of the model is computed in time and frequency domains. The relaxation spectrum can be fitted reasonably well by the empirical Williams–Watts and Havriliak–Negami functions. The best-fit Williams–Watts and Havriliak–Negami parameters are given as functions of the parameters of the model. The model is compared with several related models found in the literature and possible interpretations are given.     

Model for dynamics of inhomogeneous and bulk fluids

An accurate model for the density of states (DOS) for strongly inhomogeneous and bulk fluids has been proposed based on gamma distributions. The contribution to the density of states from the collective dynamics is modeled as an incomplete gamma distribution and the high frequency region is obtained from the solution of the memory equation using a sech memory kernel. Using only the frequency moments as input, the model parameters for the collective dynamics are obtained by matching moments of the resulting distribution. The model results in an analytical expression for the self-diffusivity of the fluid. We present results for soft sphere fluids confined in slit-shaped pores as well as bulk soft sphere liquids. Comparisons of the DOS, velocity autocorrelation functions, and memory kernels with molecular dynamics simulations reveal that the model predicts features in the DOS over the entire frequency range and is able to capture changes in the DOS as a function of fluid density and temperature. As a result the predicted VACFs, memory kernels, and self-diffusivities are accurately predicted over a wide range of conditions. Since the frequency moments for bulk liquids can be obtained from pair correlation functions, our method provides a direct route from fluid structure to dynamics. For fluids confined in slit-shaped pores, where the frequency moments are obtained from molecular dynamics simulations, the predicted self-diffusivities capture the resulting oscillations due to variations in the solvation pressure, and in the case of smooth walled pores, the predictions are superior to those obtained using kinetic theory.     

Aging in a Laponite colloidal suspension: a Brownian dynamics simulation study

The authors report Brownian dynamics simulation of the out-of-equilibrium dynamics (aging) in a colloidal suspension composed of rigid charged disks, one possible model for Laponite, a synthetic clay deeply investigated in the last few years by means of various experimental techniques. At variance with previous numerical investigations, mainly focusing on static structure and equilibrium dynamics, the authors explore the out-of-equilibrium aging dynamics. They analyze the wave vector and waiting time dependence of the dynamics, focusing on the single-particle and collective density fluctuations (intermediate scattering functions), the mean-squared displacement, and the rotational dynamics. Their findings confirm the complexity of the out-of-equilibrium dynamical behavior of this class of colloidal suspensions and suggest that an arrested disordered state driven by a repulsive Yukawa potential, i.e., a Wigner glass, can be observed in this model.     

Quantum corrections to classical time-correlation functions: hydrogen bonding and anharmonic floppy modes

Several simple quantum correction factors for classical line shapes, connecting dipole autocorrelation functions to infrared spectra, are compared to exact quantum data in both the frequency and time domain. In addition, the performance of the centroid molecular dynamics approach to line shapes and time-correlation functions is compared to that of these a posteriori correction schemes. The focus is on a tunable model that is able to describe typical hydrogen bonding scenarios covering continuously phenomena from tunneling via low-barrier hydrogen bonds to centered hydrogen bonds with an emphasis on floppy modes and anharmonicities. For these classes of problems, the so-called "harmonic approximation" is found to perform best in most cases, being, however, outperformed by explicit centroid molecular dynamics calculations. In addition, a theoretical analysis of quantum correction factors is carried out within the framework of the fluctuation-dissipation theorem. It can be shown that the harmonic approximation not only restores the detailed balance condition like all other correction factors, but that it is the only one that also satisfies the fluctuation-dissipation theorem. Based on this analysis, it is proposed that quantum corrections of response functions in general should be based on the underlying Kubo-transformed correlation functions.     

Growth dynamics and structural variations of a friable metal deposit during its contact deposition from aqueous solutions

A model is proposed for describing dynamics of contact exchange of metals, which takes into account the side process of hydrogen evolution. The contact exchange dynamics and structural characteristics of the deposit are considered as functions of the concentration of ions that undergo reduction in solution and the cementation EMF. The consideration makes allowance for different densities of microelements and the effect of the solution stirring by hydrogen evolving concurrently.     

The form of an internal reorientational correlation function

A non-Markovian, non-linearly coupled quantum stochastic dynamics model was used to investigate the reorientational correlation function of the internal motion of a methyl group attached to a large molecule. The values for the parameters used were determined by comparing angular momentum correlation functions calculated from the stochastic model to results of a molecular dynamics simulation.The results show that the correlation function has a rapid short time decay due to inertial effects, followed by a slower, exponential tail. Thus if there is significant inertial motion it is necessary to have at least two order parameters as well as two correlation times, one each for the overall and the internal motion, in order to accurately describe the system.The model can also explain data of Lee and McClung that cannot be explained with a Markovian model.     

Time-dependent electron localization functions for coupled nuclear-electronic motion

We study the quantum dynamics in a model system consisting of two electrons and a nucleus which move between two fixed ions in one dimension. The numerically determined wave functions allow for the calculation of time-dependent electron localization functions in the case of parallel spin and of the time-dependent antiparallel spin electron localization functions for antiparallel spin. With the help of these functions, it becomes possible to illustrate how electronic localization is modified through the vibrational wave-packet motion of the nucleus.     

Directionally negative friction: a method for enhanced sampling of rare event kinetics

A method exploiting the properties of an artificial (nonphysical) Langevin dynamics with a negative frictional coefficient along a suitable manifold and positive friction in the perpendicular directions is presented for the enhanced calculation of time-correlation functions for rare event problems. Exact time-correlation functions that describe the kinetics of the transitions for the all-positive, physical system can be calculated by reweighting the generated trajectories according to stochastic path integral treatment involving a functional weight based on an Onsager-Machlup action functional. The method is tested on a prototypical multidimensional model system featuring the main elements of conformational space characteristic of complex condensed matter systems. Using the present method, accurate estimates of rate constants require at least three order of magnitudes fewer trajectories than regular Langevin dynamics. The method is particularly useful in calculating kinetic properties in the context of multidimensional energy landscapes that are characteristic of complex systems such as proteins and nucleic acids.     

Ambiguities in the interpretation of time-resolved fluorescence anisotropy measurements on lipid vesicle systems

Analysis of time-resolved fluorescence anisotropy measurements on DPH and TMA-DPH in POPC vesicles with and without cholesterol in terms of the rotational diffusion model shows two distinct χ_r² minima which are statistically equivalent. This is explained by the fact that the anisotropy decay function is given by a sum of three correlation functions which cannot be uniquely separated into individual contributions. The two solutions yield contradictory results for the effect of cholesterol on the probe dynamics. It is shown that the Maier-Saupe potential and the “wobble-in-cone” model do not give an adequate picture of the orientational order and the reorientational dynamics.     

On the calculation of single-particle time correlation functions from Bose-Einstein centroid dynamics

The calculation of single-particle time correlation functions using the Bose-Einstein centroid dynamics formalism is discussed. A new definition of the quasidensity operator is used to calculate the centroid force on a given particle for an anharmonic system. The force includes correlation effects due to quantum statistics and is used for the calculation of the classical-like dynamics of phase-space centroid variables within the centroid molecular dynamics approximation. Time correlation functions are then obtained for single-particle quantities. These correspond to the double-Kubo transform of exact quantum-mechanical correlation functions. The centroid dynamics results are compared to those of exact basis-set calculations and a good agreement is found. The level of accuracy is in fact the same as what was observed earlier for the calculation of center-of-mass correlation functions for Fermi-Dirac and Bose-Einstein statistics, and for any correlation function for Boltzmann statistics. These results show that it is now possible to use Bose-Einstein centroid molecular dynamics to calculate single-particle correlation functions for systems where quantum exchange effects are present.     

The structure of molten AgCl, AgI and their eutectic mixture as studied by molecular dynamics simulations of polarizable ion model potentials

The structure of molten AgCl, AgI, and their eutectic mixture Ag(Cl(0.43)I(0.57)) is studied by means of molecular dynamics simulations of polarizable ion model potentials. The corresponding static coherent structure factors reproduce quite well the available neutron scattering data. The qualitative behavior of the simulated partial structure factors and radial distribution functions for molten AgCl and AgI is that predicted by the reverse Monte Carlo modeling of the experimental data. The AgI results are also in qualitative agreement with those calculated from ab initio molecular dynamics.     

Evaluation of quantum correlation functions from classical data: Anharmonic models

The previously introduced method of evaluating quantum mechanical time correlation functions using as input only classical simulation data is generalized and applied to two anharmonic model systems, as a further test. The quantum correction approach utilizes the relation between a general quantum correlation function and its classical analog. For the tested models, we obtain numerical results of nonlinear correlation functions with comparable accuracy to that of the centroid molecular dynamics method, although the present method is much simpler to implement and not limited to real valued quantum correlation functions.     

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.