Statistical Mechanical Representation Research Articles

A Two-State Model Describes the Temperature-Dependent Conformational Equilibrium in the Alanine-Rich Domains in Elastin.

Elastin is the insoluble elastomeric protein that provides extensibility and resilience to vertebrate tissues. Limited high-resolution structural data for elastin are notably complex. To access this information, this protein is considered in the simplified context of its two general domain types, that is, hydrophobic (HP) and crosslinking (CL). The question of elastin's structure-function has directed the focus of nearly all previous studies in the literature to the unique repeating sequences characteristic of this protein, found primarily in the HP domains. The CL domains were assumed to play a very limited role in biological elasticity due in part to the significant α-helical character that was (incorrectly) predicted for these regions. In this study, the conformational heterogeneity of alanines in native elastin's CL domains is examined in the context of helix-coil transition theory (HCTT) using solid-state nuclear magnetic resonance (SSNMR) spectroscopy in tandem with strategic isotopic labeling. Helix and coil populations are observed at all temperatures, but the former increases significantly at lower temperatures. Below the glass transition temperature (Tg), two major populations of alanines in the CL regions are resolved by two-dimensional SSNMR; one-dimensional methods are used for characterization in nativelike conditions. The spectra of 13CO-Ala in the CL regions are simulated using an HCTT-based statistical mechanical representation. Below Tg, longer segments with significant helical probabilities are consistent with the experimental data. At higher temperatures, the SSNMR lineshapes are best fit with a distribution of shorter (Ala)n segments, most in random coil. These results are used to refine a structure-function model for elastin in the context of HCTT, redirecting attention to the CL domains and their role in elasticity.

Mapping the Conformational Mobility of Multidomain Proteins

Mapping the Conformational Mobility of Multidomain Proteins

Excluded volume effect on entropy and clustering behaviors in supercooled liquids and glasses

We study the significant entropy changes in supercooling and glass transition by developing a two (H and L) state cluster model, where the H-state represents the clusters with the coordination number z being larger than the reference size z R and the L-state those with z < z R , respectively. We exploit the excluded volume effect on the clustering behaviors of various glass-formers and the temperature dependence (at fixed pressure of 1 atmosphere) of the entropy difference Δ s o between the two cluster states on the basis of z R = 1 + z R o [ exp ( − Δ s o / k B ) − 1 ] , where z R o = 1.8 as taken universally for all the glass-formers investigated. The temperature dependence of the average size 〈 z c ∗ 〉 of clusters with z ≥ z R is then determined for some representative glass-formers, such as GeO 2, 1-propanol, glycerol, propylene carbonate, o-terphenyl, and so forth, covering the entire fragility spectrum studied experimentally. As a result, the temperature dependence of 〈 z c ∗ 〉 is found to highly depend on the fragility index ϑ associated with the temperature dependence of the excluded volume B ∗ ( ϕ , T ) of which statistical mechanical representation is given by the generic van der Waals equation of state. With decreasing T toward the glass transition temperature T g , 〈 z c ∗ 〉 increases to attain universally about 13 at T g regardless of the fragility and molecular details of the glass-formers. We specifically analyze in depth the theoretical predictions for the cluster sizes and the experimental estimations for the length scales associated with temporary clusters of slow segments in supercooled glycerol as about 1.4±0.5 nm for glycerol at 10 K above T g . Given the large uncertainties associated with the experiment, the present theory appears to be in good agreement with the experiment.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.

Survey of exact results in low density Coulomb systems

Exact results on correlations and screening of low density classical and quantum Coulomb systems are reviewed in the frame work of the functional integral representation of statistical mechanics.

Statistical mechanics on axially symmetric space-times with the Killing horizon and entropy of rotating black holes in induced gravity

We develop a method for computing the free-energy of a canonical ensemble of quantum fields near the horizon of a rotating black hole. We show that the density of energy levels of a quantum field on a stationary background can be related to the density of levels of the same field on a fiducial static space-time. The effect of the rotation appears in the additional interaction of the "static" field with a fiducial abelian gauge-potential. The fiducial static space-time and the gauge potential are universal, i.e., they are determined by the geometry of the given physical space-time and do not depend on the spin of the field. The reduction of the stationary axially symmetric problem to the static one leads to a considerable simplification in the study of statistical mechanics and we use it to draw a number of conclusions. First, we prove that divergences of the entropy of scalar and spinor fields at the horizon in the presence of rotation have the same form as in the static case and can be removed by renormalization of the bare black hole entropy. Second, we demonstrate that statistical-mechanical representation of the Bekenstein-Hawking entropy of a black hole in induced gravity is universal and does not depend on the rotation.

Preculiarities in the Crystallization of Iron Containing up to 2.0 wt% of Carbon

In order to determine the peculiarities of iron-carbon alloys crystallization, the magnetic susceptibility was measured in a wide temperature range during heating and subsequent cooling. It was found that if the carbon content is 0.5 + 1.0 wt.% then the metastable δ-phase appears while cooling. On the other hand, the behaviour of other alloys can be described by the equilibrium diagram. The assumption of δ ←→ γ phase transition in the Fe-C melt was made on the basis of the obtained results. In the framework of local state representation of statistical mechanics of classical systems, proposed by A. Patashinski and M. Chertkov, all necessary calculations were made and the probable position of the new line in the phase diagram was indicated.

Theory of lattice Boltzmann simulations of glacier flow

AbstractA lattice Boltzmann technique for modeling Navier–Stokes fluid flow is extended to allow steady-state simulations of glaciers and other slow-flowing solids. The technique is based on a statistical mechanical representation of flowing ice as a set of particles (populations) which translate and collide on a face-centered cubic lattice. The average trajectories of the populations give the velocities of the ice at any point in the glacier. The method has considerable advantages over other techniques, including its ability to handle complex realistic geometries without additional complications to the code Examples are presented for two-dimensional simulations.

Theory of lattice Boltzmann simulations of glacier flow

AbstractA lattice Boltzmann technique for modeling Navier–Stokes fluid flow is extended to allow steady-state simulations of glaciers and other slow-flowing solids. The technique is based on a statistical mechanical representation of flowing ice as a set of particles (populations) which translate and collide on a face-centered cubic lattice. The average trajectories of the populations give the velocities of the ice at any point in the glacier. The method has considerable advantages over other techniques, including its ability to handle complex realistic geometries without additional complications to the code Examples are presented for two-dimensional simulations.

Influence of Fluctuations on DNA Curvature: A Comparison of Flexible and Static Wedge Models of Intrinsically Bent DNA

Matrix-generator and Monte Carlo methods have been employed to study the influence of thermal fluctuations on the overall sizes and shapes of curved pieces of DNA. The DNA model involves the independent angular parameters relating successive base-pair steps: the sequence-dependent equilibrium values and fluctuations of the twist, tilt, and roll angles. The curved sequence under study is the (A 5X 5) n repeating polymer, the AA and XX steps having different equilibrium roll and twist values. Both planar circles and superhelices are analysed. Detailed comparison is made between the rigorous statistical mechanical representation of the DNA and simplified static models currently used in the literature. That is, a more realistic "flexible wedge" model is contrasted with the existing "static wedge" model of DNA curvature, which is demonstrated to be inadequate. The size of the coils is described by the unperturbed root-mean-square end-to-end distance and the shape by a ratio of the principal moments of the radius of gyration. The moment ratios indicate that when DNA is relatively short (e.g. its length is shorter than half a turn of the static superhelix), the flexible chains are more "short and thick" than the static structure. The end-to-end distances, however, are practically the same in the two models. For longer DNA fragments, the flexible chain is more extended in terms of the end-to-end distance and more globular in terms of the moment ratio. Thus, fluctuations "blur" the curvature of longer DNA fragments compared with static models. Furthermore, the overall average shape of slightly curved DNA subject to natural bending and twisting fluctuations is essentially indistinguishable from that of the corresponding "straight" DNA. Such configurational similarities are apparently responsible for the relative insensitivity of the polyacrylamide gel matrix to small degrees of DNA curvature. These findings raise serious questions regarding the quantitative estimation of wedge angles in DNA from electrophoretic experiments, based on static models. Comparison between planar circles and superhelices shows that when fluctuations are considered, the flexible circles are more spherical than the superhelices. The results imply that when DNA bending is exactly "in phase" with the helical repeat (i.e. when the DNA loop is exactly planar at 0 K), the DNA coil is packed more tightly than when bending and twisting are "out of phase" (and a superhelix is formed at 0 K). This finding is consistent with polyacrylamide gel electrophoresis data testifying to an increase in DNA retardation when twisting is more precisely "tuned". Finally, it is found that asymmetry of bending in the roll co-ordinate can produce significant macroscopic curvature of DNA. "Skewed" bending of AA steps in the A 5X 5 polymer is indistinguishable from symmetric bending with the same mean value and fluctuation of roll. Asymmetric rolling in the AA dimer thus can introduce substantial curvature in DNAs containing A n · T n blocks, even if the lowest energy stacked arrangement of AA base-pair steps is nearly flat, thereby resolving apparent contradictions between the crystallographic and solution structures of chains containing A n · T n tracts.

A stochastic master equation representation of statistical mechanics

A functional master equation for a probability density of the velocity distribution function is presented. This constitutes a representation of statistical mechanics which is equivalent to the BBGKY hierarchy but makes alternative approximation schemes available.

Secular Behavior and Friedman's Multiple-Time-Scale Theory of Irreversible Processes

The functional integral representation of statistical mechanics is used to derive the multiple-time-scale theory of irreversible processes. It is shown that the functional integral representation inherently removes secular behavior in the description of the irreversible process. This observation is related to the nature of the auxiliary conditions introduced by Frieman and to the properties of perturbation expansions in general.

Re-examination of Homogeneous Nucleation Theory: Statistical Thermodynamics Aspects

An analysis of the equilibrium concentration of critical clusters in a supersaturated vapor is developed from the grand canonical ensemble representation of statistical mechanics, Callen's axiomatic formulation of thermodynamics and the standard capillarity approximation of nucleation theory. It is concluded that: (1) There is a small correction to the Kelvin equation for the equilibrium of a small droplet with the vapor; (2) The conclusion of Frenkel and Lothe and Pound in regard to the equilibrium concentration of critical nuclei is essentially correct for the case of no orientational degeneracy in the rigid-body rotation of a cluster; (3) For an orientationally degenerate cluster, the Lothe-Pound 1017 factor of correction to classical nucleation theory is no longer valid, but is replaced by a 108 correction factor; (4) The revision of nucleation theory proposed by Reiss and Katz is erroneous.