Sulphate ion dynamics in alpha-alums studied by esr at high pressures

The variation of zero-field splitting and linewidth of Cr3+ ion in KCr and KAI alums with hydrostatic pressure and with temperature is investigated. A model for the apparent phase transition is proposed on the basis of the reorientational motion of the SO2�4 groups.

Sulphate ion dynamics in a-alums studied by esr at high pressures

The variation of zero-field splitting and linewidth of Cr3+ ion in KCr and KAI alums with hydrostatic pressure and with temperature is investigated. A model for the apparent phase transition is proposed on the basis of the reorientational motion of the SO2-4 groups.

Rotational cut-off and anharmonicity effects on thermodynamic properties of gases at high temperatures

The exact expressions for the partition function (Q) and the coefficient of specific heat at constant volume (Cv) for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100 to 100,000 K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigid-rotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000 K for O2 and N2. Beyond these temperatures the error in Cv will be significant, because of anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000 K.

Structure, dynamics, and interactions of jacalin. Insights from molecular dynamics simulations examined in conjunction with results of X-ray studies

Molecular dynamics simulations have been carried out on all the jacalin-carbohydrate complexes of known structure, models of unliganded molecules derived from the complexes and also models of relevant complexes where X-ray structures are not available. Results of the simulations and the available crystal structures involving jacalin permit delineation of the relatively rigid and flexible regions of the molecule and the dynamical variability of the hydrogen bonds involved in stabilizing the structure. Local flexibility appears to be related to solvent accessibility. Hydrogen bonds involving side chains and water bridges involving buried water molecules appear to be important in the stabilization of loop structures. The lectin-carbohydrate interactions observed in crystal structures, the average parameters pertaining to them derived from simulations, energetic contribution of the stacking residue estimated from quantum mechanical calculations, and the scatter of the locations of carbohydrate and carbohydrate-binding residues are consistent with the known thermodynamic parameters of jacalin-carbohydrate interactions. The simulations, along with X-ray results, provide a fuller picture of carbohydrate binding by jacalin than provided by crystallographic analysis alone. The simulations confirm that in the unliganded structures water molecules tend to occupy the positions occupied by carbohydrate oxygens in the lectin-carbohydrate complexes. Population distributions in simulations of the free lectin, the ligands, and the complexes indicate a combination of conformational selection and induced fit. Proteins 2009; 77:760-777.

A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of llostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein esponsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

Melting of an Anchored Bilayer: Molecular Dynamics Simulations of the Structural Transition in (CnH2n+1NH3)(2)PbI4 (n=12, 14, 16, 18)

The thermally driven Structural phase transition in the organic-inorganic hybrid perovskite (CnH2n+1NH3)(2)PbI4 has been investigated using molecular dynamics (MD) simulations. This system consists of positively charged alkyl-amine chains anchored to a rigid negatively charged PbI4 sheet with the chains organized as bilayers with a herringbone arrangement. Atomistic simulations were performed using ail isothermal-isobaric ensemble over a wide temperature range from 65 to 665 K for different alkyl chain lengths, n = 12, 14, 16, and 18. The simulations are able to reproduce the essential Features of the experimental observations of this system, including the existence of a transition, the linear variation of the transition temperature with alkyl chain length, and the expansion of the bilayer thickness at the transition. By use of the distance fluctuation Criteria, it is Shown that the transition is associated With a Melting of the alkyl chains of the anchored bilayer. Ail analysis of the conformation of the alkyl chains shows increased disorder in the form of gauche defects above due melting transition. Simulations also show that the melting transition is characterized by the complete disappearance of all-trans alkyl chains in the anchored bilayer, in agreement with experimental observations. A conformationally disordered chain has a larger effective cross-sectional area, and above due transition a uniformly tilted arrangement of the anchored chains call no longer be Sustained. At the melt the angular distribution of the orientation of the chains are 110 longer uniform; the chains are splayed allowing for increased space for individual chains of the anchored bilayer. This is reflected in a sharp rise in the ratio of the mean head-to-head to tail-to-tail distance of the chains of the bilayer at the transition resulting in in expansion of the bilayer thickness. The present MD simulations provide a simple explanation as to how changes in conformation of individual alkyl-chains gives rise to the observed increase in the interlayer lattice spacing of (CnH2n+1NH3)(2)PbI4 at the melting transition.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime.Activation energy is in the order E-a(n-pentane)>E-a(isopentane)>E-a(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen thatD(n pentane)>D(isopentane)>D(neopentane) and E-a(n-pentane)< E-a(isopentane)< E-a(neopentane). Intermediate scattering function for small wavenumbers obtained from MD follows a single exponential decay for neopentane and isopentane. For n-pentane, a single exponential fit provides a poor fit especially at short times. Cage residence time is largest for n-pentane and lowest for neopentane. For neopentane, the width of the self-part of the dynamic structure factor shows a near monotonic decrease with wavenumber. For n-pentane a minimum is seen near k=0.5 A degrees(-1) suggesting a slowing down of motion around the 12-ring window, the bottleneck for diffusion. Finally, the result that the branched isomer has a higher diffusivity as compared with the linear analog is at variation from what is normally seen.

Dynamics of Stick-Slip: Some Universal and Not So Universal Features

Stick-slip is usually observed in driven dissipative threshold systems. In these set of lectures, we discuss, some generic and system specific features of stickslip systems by considering a few examples wherein there has been some progress in understanding the associated dynamics. In most stick slip systems, both at low and high drive rates, the system slides smoothly, but within a window of drive rates, the motion becomes intermittent; the system alternately “sticks” till the stress builds up to a threshold value, and then “slips” when the stress is rapidly released. This intermittent motion can be traced to the existence of an unstable branch separating the two resistive branches in the force-drive-rate relation. While the two resistive branches are experimentally measurable, the unstable branch is usually not measurable and is only inferred.

Two-Phase Thermodynamic Model for Efficient and Accurate Absolute Entropy of Water from Molecular Dynamics Simulations

Presented here is the two-phase thermodynamic (2PT) model for the calculation of energy and entropy of molecular fluids from the trajectory of molecular dynamics (MD) simulations. In this method, the density of state (DoS) functions (including the normal modes of translation, rotation, and intramolecular vibration motions) are determined from the Fourier transform of the corresponding velocity autocorrelation functions. A fluidicity parameter (f), extracted from the thermodynamic state of the system derived from the same MD, is used to partition the translation and rotation modes into a diffusive, gas-like component (with 3Nf degrees of freedom) and a nondiffusive, solid-like component. The thermodynamic properties, including the absolute value of entropy, are then obtained by applying quantum statistics to the solid component and applying hard sphere/rigid rotor thermodynamics to the gas component. The 2PT method produces exact thermodynamic properties of the system in two limiting states: the nondiffusive solid state (where the fluidicity is zero) and the ideal gas state (where the fluidicity becomes unity). We examine the 2PT entropy for various water models (F3C, SPC, SPC/E, TIP3P, and TIP4P-Ew) at ambient conditions and find good agreement with literature results obtained based on other simulation techniques. We also validate the entropy of water in the liquid and vapor phases along the vapor-liquid equilibrium curve from the triple point to the critical point. We show that this method produces converged liquid phase entropy in tens of picoseconds, making it an efficient means for extracting thermodynamic properties from MD simulations.

Effect of coordinated ions on structure and flexibility of parallel G-quadruplexes: A molecular dynamics study

ingle tract guanine residues can associate to form stable parallel quadruplex structures in the presence of certain cations. Nanosecond scale molecular dynamics simulations have been performed on fully solvated fibre model of parallel d(G(7)) quadruplex structures with Na+ or K+ ions coordinated in the cavity formed by the O6 atoms of the guanine bases. The AMBER 4.1 force field and Particle Mesh Ewald technique for electrostatic interactions have been used in all simulations. There quadruplex structures are stable during the simulation, with the middle four base tetrads showing root mean square deviation values between 0.5 to 0.8 Angstrom from the initial structure as well the high resolution crystal structure. Even in the absence of any coordinated ion in the initial structure, the G-quadruplex structure remains intact throughout the simulation. During the 1.1 ns MD simulation, one Nai counter ion from the solvent as well as several water molecules enter the central cavity to occupy the empty coordination sites within the parallel quadruplex and help stabilize the structure. Hydrogen bonding pattern depends on the nature of the coordinated ion, with the G-tetrad undergoing local structural variation to accommodate cations of different sizes. in the absence of any coordinated ion. due to strong mutual repulsion, O6 atoms within G-tetrad are forced farther apart from each other, which leads to a considerably different hydrogen bonding scheme within the G-tetrads and very favourable interaction energy between the guanine bases constituting a G-tetrad. However, a coordinated ion between G-tetrads provides extra stacking energy for the G-tetrads and makes the quadruplex structure more rigid. Na+ ions, within the quadruplex cavity, are more mobile than coordinated K+ ions. A number of hydrogen bonded water molecules are observed within the grooves of all quadruplex structures.

Polarization relaxation, dielectric dispersion, and solvation dynamics in dense dipolar liquid

A unified treatment of polarization relaxation, dielectric dispersion and solvation dynamics in a dense, dipolar liquid is presented. It is shown that the information of solvent polarization relaxation that is obtained by macroscopic dielectric dispersion experiments is not sufficient to understand dynamics of solvation of a newly created ion or dipole. In solvation, a significant contribution comes from intermediate wave vector processes which depend critically on the short range (nearest‐neighbor) spatial and orientational order that are present in a dense, dipolar liquid. An analytic expression is obtained for the time dependent solvation energy that depends, in addition to the translational and rotational diffusion coefficients of the liquid, on the ratio of solute–solvent molecular sizes and on the microscopic structure of the polar liquid. Mean spherical approximation (MSA) theory is used to obtain numerical results for polarization relaxation, for wave vector and frequency dependent dielectric function and for time dependent solvation energy. We find that in the absence of translational contribution, the solvation of an ion is, in general, nonexponential. In this case, the short time decay is dominated by the longitudinal relaxation time but the long time decay is dominated by much slower large wave vector processes involving nearest‐neighbor molecules. The presence of a significant translational contribution drastically alters the decay behavior. Now, the long‐time behavior is given by the longitudinal relaxation time constant and the short time dynamics is controlled by the large wave vector processes. Thus, although the continuum model itself is conceptually wrong, a continuum model like result is recovered in the presence of a sizeable translational contribution. The continuum model result is also recovered in the limit of large solute to solvent size ratio. In the opposite limit of small solute size, the decay is markedly nonexponential (if the translational contribution is not very large) and a complete breakdown of the continuum model takes place. The significance of these results is discussed.

Phase space methods and the Hamilton-Jacobi form of dynamics

A general analysis of the Hamilton-Jacobi form of dynamics motivated by phase space methods and classical transformation theory is presented. The connection between constants of motion, symmetries, and the Hamilton-Jacobi equation is described.

The nature of dislocation motion in quasicrystals

Calculations in a hydrodynamic model of quasicrystal dynamics show that dislocation motion in these systems is impeded by a drag far greater than that in crystals.