Special Issue "Configurational Entropy"
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A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (30 April 2010)
Special Issue Editor
Guest Editor
Dr. Vladimir Hnizdo
National Institute for Occupational Safety and Health, Morgantown, West Virginia 26505, USA
E-Mail: vbh5@cdc.gov
Special Issue Information
Dear Colleagues,
Changes in the configurational part of entropy contribute significantly to the free energy of conformational change and binding in biomolecular systems. In particular, the change in configurational entropy is an important determinant of the energetics of the binding affinity in receptor-ligand systems. However, calculating the configurational entropy of complex non-harmonic systems is a highly challenging problem in need of innovative approaches to a practicable solution. Recently, information-theoretic methods and nonparametric statistical methods have been brought to bear on the problem of estimating configurational entropy from molecular simulations. This special issue of Entropy will provide a forum for contributions on both theoretical and computational aspects of the entropic characteristics of complex systems.
Vladimir Hnizdo, Ph. D.
Guest Editor
Related Special Issues in other Journals
Gibbs Paradox and Its Resolutions in Entropy
Submission
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Keywords
- configurational entropy or configuration entropy
- configurational free energy
- entropy of mixing
- entropy
- thermodynamics
- statistical mechanics
- information theory
- mutual information
- nearest neighbor
- complex systems
- dimension reduction
- many-body correlations
- non-Gaussian correlations
- molecular simulations
- receptor-ligand binding
Published Papers (11 papers)
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Received: 28 July 2008; in revised form: 19 August 2008 / Accepted: 19 August 2008 / Published: 23 August 2008
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Abstract: The Maier-Saupe model for binary mixtures of uniaxial discotic nematogens, formulated in a previous study [1], is used to compute and characterize orientational entropy [2] and orientational specific heat. These thermodynamic quantities are used to determine mixture type (ideal or non-ideal) which arise due to their different intrinsic properties, determined by the molecular weight asymmetry ΔMw and the molecular interaction parameter β. These molecular properties are also used to characterize the critical concentration where the mixture behaves like a single component system and exhibits the minimum nematic to isotropic (NI) transition temperature (pseudo-pure mixture). A transition within the nematic phase takes place at this specific concentration. According to the Maier-Saupe model, in a single mesogen, entropy at NI transition is a universal value; in this work we quantify the mixing effect on this universal property. The results and analysis provide a new tool to characterize molecular interaction and molecular weight differences in mesogenic mixtures using standard calorimetric measurements.
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Received: 24 June 2008; in revised form: 20 August 2008 / Accepted: 20 August 2008 / Published: 26 August 2008
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Abstract: Different equations have been proposed for estimating the glass transition temperature of amorphous mixtures. All such expressions lack a term to account for the effect of the entropy of mixing on the glass transition. An entropy based analysis for the glass transition of amorphous mixtures is presented. The treatment yields an explicit mixing term in the expression for the glass transition temperature of a mixture. The obtained expression reduces to the Couchman-Karasz equation in the limiting case where the contribution of the entropy of mixing approaches zero. Equivalent expressions are obtained for the glass transition temperature of a mixture of two glass formers as for the effect of a plasticizing liquid diluent on the glass transition temperature of an amorphous material.
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Received: 24 July 2008; in revised form: 10 September 2008 / Accepted: 15 September 2008 / Published: 20 September 2008
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Abstract: A novel thermodynamic treatment of residual entropy in crystals, involving the configurational partition function, is suggested, which is consistent with both classical and statistical thermodynamics. It relates residual entropy to the inherent latent heat which would be released upon cooling if the reversible path were available. The nature of this heat is that if the crystal possessing residual entropy freezes above its Boltzmann’s characteristic temperature of molecular alignment, the difference in energy between different molecular arrangements is overcome by the kT heat bath to form a nearly-ideal solution. However, upon cooling below this characteristic temperature, they would separate with a concomitant release of the corresponding energy, provided the reversible path were available.
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Received: 31 July 2008; in revised form: 9 September 2008 / Accepted: 22 September 2008 / Published: 24 September 2008
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Abstract: Thermodynamic parameters of configurons – elementary excitations resulting from broken bonds in amorphous materials – are found from viscosity-temperature relationships. Glass-liquid transition phenomena and most popular models are described along with the configuron model of glass transition. The symmetry breaking, which occurs as a change of Hausdorff dimension of bonds, is examined at glass-liquid transition. Thermal history effects in the glass-liquid transition are interpreted in terms of configuron relaxation.
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Received: 15 August 2008; in revised form: 24 September 2008 / Accepted: 24 September 2008 / Published: 6 October 2008
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Abstract: Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime
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Received: 2 September 2009 / Accepted: 26 October 2009 / Published: 29 October 2009
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Abstract: A homogeneous solution of a chiral substance is acquired with an overall asymmetry which is expressed by a specific rotation of a linearly polarized light. Such a solution, despite being at a complete equilibrium, stores configurational entropy in a form of negative entropy which can be nullified by mixing with a solution of the opposite enantiomer. This abundant, yet quite a specific case of inherent negative entropy, resides predominantly in the chiral configuration of the solvent envelopes surrounding the chiral centers. Heat release, amounting to several cal/mol, associated with the annulment of negative entropy in aqueous solutions of D- and L-amino acids, was recently documented by Shinitzky et al. [1]. This heat corresponds almost exclusively to TΔS stored in the solvent envelope upon adoption of a chiral configuration. Simple fundamental expressions which combine configurational entropy and information capacity in chiral solutions have been developed and were found to comply well with the observed heat release upon intermolecular racemization.
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Received: 17 December 2009; in revised form: 27 February 2010 / Accepted: 2 March 2010 / Published: 16 March 2010
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Abstract: The differential Shannon entropy of information theory can change under a change of variables (coordinates), but the thermodynamic entropy of a physical system must be invariant under such a change. This difference is puzzling, because the Shannon and Gibbs entropies have the same functional form. We show that a canonical change of variables can, indeed, alter the spatial component of the thermodynamic entropy just as it alters the differential Shannon entropy. However, there is also a momentum part of the entropy, which turns out to undergo an equal and opposite change when the coordinates are transformed, so that the total thermodynamic entropy remains invariant. We furthermore show how one may correctly write the change in total entropy for an isothermal physical process in any set of spatial coordinates.
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Received: 2 March 2010; in revised form: 10 April 2010 / Accepted: 17 April 2010 / Published: 23 April 2010
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Abstract: In order to clarify the adsorption behavior of cationic surfactants on the air/aqueous electrolyte solution surface, we derived the theoretical equation for the surface tension. The equation includes the electrical work required for charging the air/water surface and the work attributable to the configurational entropy in the adsorbed film. By fitting the equation to the experimental data, we determined the binding constant between adsorbed surfactant ion and counterion, and found that the bromide ions, rather than the chloride ions, are preferentially adsorbed by the air/water surface. Furthermore, it was suggested that the contribution of configurational entropy to the surface tension is predominant in the presence of electrolytes because of the increase in the surface density of surfactant molecules associated with decreasing the repulsive interaction between their hydrophilic groups.
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Received: 26 February 2010 / Accepted: 29 April 2010 / Published: 6 May 2010
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Abstract: In molecular sciences, the estimation of entropies of molecules is important for the understanding of many chemical and biological processes. Motivated by these applications, we consider the problem of estimating the entropies of circular random vectors and introduce non-parametric estimators based on circular distances between n sample points and their k th nearest neighbors (NN), where k (≤ n – 1) is a fixed positive integer. The proposed NN estimators are based on two different circular distances, and are proven to be asymptotically unbiased and consistent. The performance of one of the circular-distance estimators is investigated and compared with that of the already established Euclidean-distance NN estimator using Monte Carlo samples from an analytic distribution of six circular variables of an exactly known entropy and a large sample of seven internal-rotation angles in the molecule of tartaric acid, obtained by a realistic molecular-dynamics simulation.
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Received: 10 March 2010; in revised form: 18 May 2010 / Accepted: 19 May 2010 / Published: 25 May 2010
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Abstract: Small clusters violate the Gibbs phase rule by exhibiting two or more phases in thermodynamic equilibrium over bands of temperature and pressure. The reason is the small number of particles comprising each system. We review recent results concerning the size ranges for which this behavior is observable. The principal characteristic determining the coexistence range is the transitions entropy change. We review how this happens, using simulations of 13-atom Lennard-Jones and metal clusters to compare dielectric clusters with the more complex clusters of metal atoms. The dominating difference between the narrower coexistence bands of dielectrics and the wider bands of metal clusters is the much higher configurational entropy of the liquid metal clusters.
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Received: 12 June 2010; in revised form: 2 August 2010 / Accepted: 17 August 2010 / Published: 25 August 2010
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Abstract: A mobile loop changes its conformation from “open” (free enzyme) to “closed” upon ligand binding. The difference in the Helmholtz free energy, ΔFloop between these states sheds light on the mechanism of binding. With our “hypothetical scanning molecular dynamics” (HSMD-TI) method ΔFloop = Ffree − Fbound where Ffree and Fbound are calculated from two MD samples of the free and bound loop states; the contribution of water is obtained by a thermodynamic integration (TI) procedure. In previous work the free and bound loop structures were both attached to the same “template” which was “cut” from the crystal structure of the free protein. Our results for loop 287−290 of AcetylCholineEsterase agree with the experiment, ΔFloop~ −4 kcal/mol if the density of the TIP3P water molecules capping the loop is close to that of bulk water, i.e., Nwater = 140 − 180 waters in a sphere of a 18 Å radius. Here we calculate ΔFloop for the more realistic case, where two templates are “cut” from the crystal structures, 2dfp.pdb (bound) and 2ace.pdb (free), where Nwater = 40 − 160; this requires adding a computationally more demanding (second) TI procedure. While the results for Nwater ≤ 140 are computationally sound, ΔFloop is always positive (18 ± 2 kcal/mol for Nwater = 140). These (disagreeing) results are attributed to the large average B-factor, 41.6 of 2dfp (23.4 Å2 for 2ace). While this conformational uncertainty is an inherent difficulty, the (unstable) results for Nwater = 160 suggest that it might be alleviated by applying different (initial) structural optimizations to each template.
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Last update: 12 January 2011
