Slow dynamics in glass-forming materials

Dynamical properties of glass-formers such as glassy crystals, molecular liquids and model atomic liquids have been investigated in the pico–nanosecond (ps–ns) regime with dl_poly. The change in nature of translation and rotational dynamics are investigated in the supercooled state. Some predictions of the mode-coupling theory and the coupling model are checked. The microscopic origin of the fragility, i.e. the characteristic parameter involved in the liquid–glass transition, is also highlighted: the interaction potential, especially its anharmonicity and capacity for intermolecular coupling, is the key parameter controlling both the long time dynamics in supercooled systems and the short time dynamics in their glassy states.     

Glass Transition and Delocalization in a Binary Hard-Sphere Mixture

Abstract

The glass transition of a disparate-size binary liquid and the delocalization of small particles in a glassy matrix are studied within a mode-coupling theory. The density-relaxation functions together with their long-time limits are investigated by solving space- and time-dependent mode-coupling equations numerically. We focus our attention on the effective-potential fluctuations produced by the glassy matrix, which the small particles will experience when they move through the matrix. It is found that in a strongly localized state the spatial correlations of effective-potential fluctuations are well represented by a Gaussian function. For the small particles with a long localization length, on the other hand, the effective potential is no longer Gaussian, reflecting the structure of the glassy matrix established by the big particles. The time-dependence of the effective potential is also investigated.     

Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm.     

ANCA: Anharmonic Conformational Analysis of Biomolecular Simulations

Anharmonicity in time-dependent conformational fluctuations is noted to be a key feature of functional dynamics of biomolecules. Although anharmonic events are rare, long-timescale (μs–ms and beyond) simulations facilitate probing of such events. We have previously developed quasi-anharmonic analysis to resolve higher-order spatial correlations and characterize anharmonicity in biomolecular simulations. In this article, we have extended this toolbox to resolve higher-order temporal correlations and built a scalable Python package called anharmonic conformational analysis (ANCA). ANCA has modules to: 1) measure anharmonicity in the form of higher-order statistics and its variation as a function of time, 2) output a storyboard representation of the simulations to identify key anharmonic conformational events, and 3) identify putative anharmonic conformational substates and visualization of transitions between these substates.     

Molecular dynamics of ferrocytochrome c: Anharmonicity of atomic displacements

The atomic position distributions obtained from a 32-ps molecular-dynamics simulation of tuna ferrocytochrome c at 297 K are analyzed in terms of their second, third, and fourth moments. Non-Gaussian relations among these moments are found for the majority of atoms in the molecule, indicating anharmonicity in the effective potential functions for the atomic motions. Many atoms exhibit only slightly anharmonic mobility during the 32-ps period, but about half of the atoms exhibit sizeable anharmonicity. For a typical atom, the anharmonic effects are largest for motions in the direction along which the largest displacements occur. Two classes of significantly anharmonic atoms are apparent: those whose effective potentials are distorted toward a square-well shape and those whose effective potentials have secondary minima corresponding to conformational substates.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.     

Modeling hydrogen bonds in three dimensions

The effective potential between two hydrogen bonded atoms is calculated on the basis of the Lippencott-Schroeder bent bond model, taken to be a typical model interaction. We differ from other calculations in that the minimum energy configuration for the proton is treated adiabatically, its position being recomputed at each value of the larger atoms separation. We find the typical hard core to have been a consequence of an artificial restriction of the proton to a fixed angle with the larger atom axis, basically a one-dimensional assumption. Free to move in three dimensions, the proton is squeezed off the axis as the separation narrows, and the hard core feature is gone. Depending on the degree of bond bending, the anharmonicity of the bond may be diminished, eliminated, or even reversed.     

Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.     

TAKENO孤子的量子理论

研究蛋白质分子中能量远距离传输的机理,在Ｔａｋｅｎｏ提出的孤子理论的基础上,进上步考虑了氢键相互作用的非简谐性,并用量子力学对模型进行了处理,在连续近似下,得到的结果表明,能量可以通过以超声速运动的孤子来传输。     

Molecular dynamics study of secondary structure motions in proteins: application to myohemerythrin

The concept of secondary structure motions is examined in a molecular dynamics simulation of the protein myohemerythrin. We extracted from the simulation a corresponding trajectory of helices and demonstrated that the fluctuations of the protein are dominated by a rigid shift of these secondary structure elements. The relative motions of the helices are irregular, with no clear periodicity. They are bounded by approximately 2 A for the center of mass motions and by 20 degrees for the relative orientations. The potential of mean force for the interactions of the helices was calculated, and the correlations between the different extended motions were investigated. It is shown that the one-dimensional mean force potentials are close to quadratic for most of the helices coordinates. The anharmonicity is reflected by changes in the direction of the normal modes as a function of the energy and by the existence of multiple free energy minima for the helices packing. The multiple conformations are associated with a single type of secondary structure coordinate: the angle that describes the relative orientation of the helices in a plane perpendicular to the line connecting their center of mass.     

Quadratic nonlinear optical susceptibility of helical polymers

The quadratic nonlinear optical susceptibility of a solution of helical polymers and of samples with helices oriented parallel to each other is calculated for regions of characteristic vibrations and of their overtones. The important role of electrooptical and of mechanical anharmonicity for exhibition of overtones in nonlinear spectroscopy is shown. The possibility of the appearance of the giant polarizabilities near bound overtone states is analyzed. The overtone spectrum of amide I is modeled numerically. © 1994 John Wiley & Sons, Inc.     

Modeling the dynamics of the solvated SL1 domain of HIV-1 genomic RNA

A mode-coupling solution of the Smoluchowski diffusion equation (MCD theory), designed to describe the dynamics of wobbling macromolecules in water, is applied to a macromolecular bead model including water beads in the nearest layers. The necessary statistical averages are evaluated by time averaging along a molecular dynamics (MD) trajectory where both solute and water are introduced as atomistic models. The cross peaks in (1)H nuclear Overhauser effect spectroscopy (NOESY) NMR spectra that are routinely measured to determine biological structures are here calculated for the mutated 23 nucleotides stem-loop fragment of the SL1 domain in the HIV-1(Lai) genomic RNA. The calculations are in acceptable agreement with experiments without requiring any screening of the hydrodynamic interactions. The screening of hydrodynamics was necessary in previous MCD calculations obtained by using the same full atomistic MD trajectory, but a nonsolvated frictional model.     

Molecular dynamics of solid-state lysozyme as affected by glycerol and water: a neutron scattering study

Glycerol has been shown to lower the heat denaturation temperature (T(m)) of dehydrated lysozyme while elevating the T(m) of hydrated lysozyme (. J. Pharm. Sci. 84:707-712). Here, we report an in situ elastic neutron scattering study of the effect of glycerol and hydration on the internal dynamics of lysozyme powder. Anharmonic motions associated with structural relaxation processes were not detected for dehydrated lysozyme in the temperature range of 40 to 450K. Dehydrated lysozyme was found to have the highest T(m) by. Upon the addition of glycerol or water, anharmonicity was recovered above a dynamic transition temperature (T(d)), which may contribute to the reduction of T(m) values for dehydrated lysozyme in the presence of glycerol. The greatest degree of anharmonicity, as well as the lowest T(d), was observed for lysozyme solvated with water. Hydrated lysozyme was also found to have the lowest T(m) by. In the regime above T(d), larger amounts of glycerol lead to a higher rate of change in anharmonic motions as a function of temperature, rendering the material more heat labile. Below T(d), where harmonic motions dominate, the addition of glycerol resulted in a lower amplitude of motions, correlating with a stabilizing effect of glycerol on the protein.     

Influence of hydration on the dynamics of lysozyme

Quasielastic neutron and light-scattering techniques along with molecular dynamics simulations were employed to study the influence of hydration on the internal dynamics of lysozyme. We identified three major relaxation processes that contribute to the observed dynamics in the picosecond to nanosecond time range: 1), fluctuations of methyl groups; 2), fast picosecond relaxation; and 3), a slow relaxation process. A low-temperature onset of anharmonicity at T approximately 100 K is ascribed to methyl-group dynamics that is not sensitive to hydration level. The increase of hydration level seems to first increase the fast relaxation process and then activate the slow relaxation process at h approximately 0.2. The quasielastic scattering intensity associated with the slow process increases sharply with an increase of hydration to above h approximately 0.2. Activation of the slow process is responsible for the dynamical transition at T approximately 200 K. The dependence of the slow process on hydration correlates with the hydration dependence of the enzymatic activity of lysozyme, whereas the dependence of the fast process seems to correlate with the hydration dependence of hydrogen exchange of lysozyme.     

"Fluctuograms" reveal the intermittent intra-protein communication in subtilisin Carlsberg and correlate mechanical coupling with co-evolution

The mechanism of intra-protein communication and allosteric coupling is key to understanding the structure-property relationship of protein function. For subtilisin Carlsberg, the Ca2+-binding loop is distal to substrate-binding and active sites, yet the serine protease function depends on Ca2+ binding. The atomic molecular dynamics (MD) simulations of apo and Ca2+-bound subtilisin show similar structures and there is no direct evidence that subtilisin has alternative conformations. To model the intra-protein communication due to Ca2+ binding, we transform the sequential segments of an atomic MD trajectory into separate elastic network models to represent anharmonicity and nonlinearity effectively as the temporal and spatial variation of the mechanical coupling network. In analogy to the spectrogram of sound waves, this transformation is termed the "fluctuogram" of protein dynamics. We illustrate that the Ca2+-bound and apo states of subtilisin have different fluctuograms and that intra-protein communication proceeds intermittently both in space and in time. We found that residues with large mechanical coupling variation due to Ca2+ binding correlate with the reported mutation sites selected by directed evolution for improving the stability of subtilisin and its activity in a non-aqueous environment. Furthermore, we utilize the fluctuograms calculated from MD to capture the highly correlated residues in a multiple sequence alignment. We show that in addition to the magnitude, the variance of coupling strength is also an indicative property for the sequence correlation observed in a statistical coupling analysis. The results of this work illustrate that the mechanical coupling networks calculated from atomic details can be used to correlate with functionally important mutation sites and co-evolution.     

Solitons in DNA

DNA is modeled as a homogeneous, cylindrical rod with nonlinear elasticity using the Ostrovskii-Sutin equation (OSE) with periodic boundary conditions. This equation predicts that longitudinal sound waves will be concentrated into packets called solitons. From a study of the damped OSE, we conclude that decay time is almost independent of the solitonic character of the solution. For the damped, driven OSE, on the other hand, we find that spectral features (such as absorption line widths and fine structure) are strongly influenced by the presence of anharmonicity. This effect is enhanced as the length of the DNA is increased.     

Deuterium isotope effects on <Superscript>15</Superscript>N backbone chemical shifts in proteins

Quantum mechanical calculations are presented that predict that one-bond deuterium isotope effects on the ¹⁵N chemical shift of backbone amides of proteins, ¹Δ¹⁵N(D), are sensitive to backbone conformation and hydrogen bonding. A quantitative empirical model for ¹Δ¹⁵N(D) including the backbone dihedral angles, Φ and Ψ, and the hydrogen bonding geometry is presented for glycine and amino acid residues with aliphatic side chains. The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N–H bond length. Another contributing factor is the effect of increased anharmonicity of the N–H stretching vibrational state upon hydrogen bonding, which results in an altered N–H/N–D equilibrium bond length ratio. The N–H stretching anharmonicity contribution falls off with the cosine of the N–H···O bond angle. For residues with uncharged side chains a very good prediction of isotope effects can be made. Thus, for proteins with known secondary structures, ¹Δ¹⁵N(D) can provide insights into hydrogen bonding geometries. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.