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At least 217 records · Page 12Linked to original sources

PubMed2005

Minimization of the Renyi entropy production in the space-partitioning process.

The spontaneous division of space in Fleming-Viot processes is studied in terms of non-extensive thermodynamics. We analyze a system of n different types of Brownian particles confined in a box. Particles of different types annihilate each other when they come into close contact. Each process of annihilation is accompanied by a simultaneous nucleation of a particle of the same type, so that the number of particles of each component remains constant. The system eventually reaches a stationary state, in which the available space is divided into n separate subregions, each occupied by particles of one type. Within each subregion, the particle density distribution minimizes the Renyi entropy production. We show that the sum of these entropy productions in the stationary state is also minimized, i.e., the resulting boundaries between different components adopt a configuration which minimizes the total entropy production. The evolution of the system leads to decreasing of the total entropy production monotonically in time, irrespective of the initial conditions. In some circumstances, the stationary state is not unique-the entropy production may have several local minima for different configurations. In the case of a rectangular box, the existence and stability of different stationary states are studied as a function of the aspect ratio of the rectangle.

Journal Article↗

PubMed2005

Generalized entropy arising from a distribution of q indices.

It is by now well known that the Boltzmann-Gibbs (BG) entropy can be usefully generalized using the non-extensive entropies, which have been applied to a wide range of phenomena. However, it seems that even more general entropies could be useful in order to describe other complex physical systems, a task which has already been undertaken in the literature. Following this approach, we introduce here a quite general entropy based on a distribution of q indices thus generalizing S(q). We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the q-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.

Journal Article↗

PubMed2004

Negative entropy of mixing for vanadium-platinum solutions.

The phonon densities of states for pure vanadium and the solid solutions V-6.25% Ni, Pd, Pt were determined from inelastic neutron scattering measurements. The solute atoms caused a large stiffening of the phonons, resulting in large, negative vibrational entropies of mixing. For V-6.25%Pt, the negative vibrational entropy of mixing exceeds the conventional positive chemical entropy of mixing. This negative total entropy of mixing should extend to lower concentrations of Pt, and the effect on the bcc solvus line is discussed. The experimental data were inverted to obtain interatomic force constants by using a Born-von Kármán model with an iterative optimization algorithm. The stiffening of bonds responsible for the decrease of entropy was found to occur mainly in first-nearest-neighbor solute-host bonds, and correlates in part with the solute metallic radius.

Journal Article↗

PubMed2004

Entanglement entropy in a boundary impurity model.

Boundary impurities are known to dramatically alter certain bulk properties of (1+1)-dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling or bosonization scheme. For a Luttinger liquid of length 2L and UV cutoff epsilon, the boundary impurity correction (deltaSimp) to the logarithmic entanglement entropy (Sent proportional, variant lnL/epsilon scales as deltaSimp approximately yrlnL/epsilon, where yr is the renormalized backscattering coupling constant. In this way, the entanglement entropy within a region is related to scattering through the region's boundary. In the repulsive case (g<1), deltaSimp diverges (negatively) suggesting that the entropy vanishes. Our results are consistent with the recent conjecture that entanglement entropy decreases irreversibly along renormalization group flow.

Journal Article↗

PubMed2006

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.

A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We argue that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal agrees perfectly with the entanglement entropy in 2D CFT when applied to AdS(3). We also compare the entropy computed in AdS(5)XS(5) with that of the free N=4 super Yang-Mills theory.

Journal Article↗

PubMed1993

Entropy phase dynamics.

The entropy-dynamics method seeks maxima for the entropy of the electron density for N atoms in a crystal cell, when the Fourier amplitudes are fixed, but their phases are unknown. By analogy with molecular dynamics, the effective potential energy is the negative entropy V = -NS. The kinetic energy is proportional to the squared velocities of the electron densities at grid points in the map. It reduces to a sum of Fourier-mode rotor energies. Each rotor angle experiences a couple equal to the phase gradient of S, and local dynamical equilibrium yields a Boltzmann distribution of S. Discrete phase angles (e.g. signs) are treated as quantized rotor modes. The distributions depend on a popularity function of the entropy histogram. Trial calculations have been made of phase averages and correlations in a centrosymmetric projection of the membrane protein bacteriorhodopsin. The maximum-entropy solution and the correct solution do not always coincide.

Journal Article↗

PubMed2006

A robust method for heart sounds localization using lung sounds entropy.

Heart sounds are the main unavoidable interference in lung sound recording and analysis. Hence, several techniques have been developed to reduce or cancel heart sounds (HS) from lung sound records. The first step in most HS cancellation techniques is to detect the segments including HS. This paper proposes a novel method for HS localization using entropy of the lung sounds. We investigated both Shannon and Renyi entropies and the results of the method using Shannon entropy were superior. Another HS localization method based on multiresolution product of lung sounds wavelet coefficients adopted from was also implemented for comparison. The methods were tested on data from 6 healthy subjects recorded at low (7.5 ml/s/kg) and medium 115 ml/s/kg) flow rates. The error of entropy-based method using Shannon entropy was found to be 0.1 +/- 0.4% and 1.0 +/- 0.7% at low and medium flow rates, respectively, which is significantly lower than that of multiresolution product method and those of other methods reported in previous studies. The proposed method is fully automated and detects HS included segments in a completely unsupervised manner.

Adult↗

PubMed2004

Approximate entropy of respiratory patterns in panic disorder.

OBJECTIVE: Considerable evidence suggests a connection between panic disorder and respiration, but the nature of the respiratory abnormalities in panic disorder remains unclear. The authors investigated the breath-by-breath complexity of respiration dynamics in panic disorder. METHOD: Respiratory physiology was assessed in 40 patients with panic disorder and 31 healthy comparison subjects by using a breath-by-breath stationary system for testing cardiorespiratory function. Irregularity in the breathing pattern was determined by applying the approximate entropy index, which is an indicator of the irregularity and the "disorder" of the measure. RESULTS: The patients with panic disorder showed significantly higher approximate entropy indexes than the healthy subjects for the measured respiratory parameters. Sighs contributed to the irregularity of breathing patterns but did not account for all the differences in approximate entropy between the patients with panic disorder and the comparison subjects. Anxiety state, severity of illness, and somatic and individual variables such as participation in sports and cigarette smoking did not seem to influence the results. CONCLUSIONS: Patients with panic disorder showed greater entropy in baseline respiratory patterns, indicating higher levels of irregularity and complexity in their respiratory function. Greater respiratory entropy could be a factor in vulnerability to panic attacks.

Adult↗

PubMed2006

Kullback relative entropy and characterization of partially polarized optical waves.

Different properties of partially polarized light are discussed using the Kullback relative entropy, which provides a physically meaningful measure of proximity between probability density functions (PDFs). For optical waves with a Gaussian PDF, the standard degree of polarization is a simple function of the Kullback relative entropy between the considered optical light and a totally depolarized light of the same intensity. It is shown that the Kullback relative entropies between different PDFs allow one to define other properties such as a degree of anisotropy and a degree of non-Gaussianity. It is also demonstrated that, in dimension three, the Kullback relative entropy between a partially polarized light and a totally depolarized light can lead to natural definitions of two degrees of polarization needed to characterize the polarization state. These analyses enlighten the physical meaning of partial polarization of light waves in terms of a measure of disorder provided by the Shannon entropy.

Journal Article↗

PubMed1992

Thermodynamic changes in the binding of Ca2+ to a mutant human lysozyme (D86/92). Enthalpy-entropy compensation observed upon Ca2+ binding to proteins.

The thermodynamic change in the binding of Ca2+ to a mutant human lysozyme having an engineered Ca2+ binding site (Kuroki, R., Taniyama, Y., Seko, C., Nakamura, H., Kikuchi, M., and Ikehara, M. (1989) Proc. Natl. Acad. Sci. U. S. A. 86, 6903-6907) was analyzed by calorimetry and interpreted in terms of structural information obtained from x-ray crystallography. It was found that the enthalpic contribution for the Ca2+ binding reaction was small, driven primarily by entropy release (10 kcal/mol). This release of entropy was also observed in some organic chelators. Moreover, through the information of the tertiary structures of the apo- and holomutant lysozyme, it was confirmed that the entropy release (10 kcal/mol) upon the binding of Ca2+ arises primarily from the release of bound water molecules hydrating the free Ca2+. Previous studies of Ca2+ binding to proteins have involved significant changes in protein conformation. They can now be reevaluated to determine the contribution of conformational changes to Ca2+ binding. After removing the thermodynamic contribution of Ca2+ binding itself, it is found that upon the binding of Ca2+ the enthalpy change is negative but is almost compensated by the negative entropy change. The negative change in both enthalpy and entropy is characteristic of values seen in the thermodynamic change upon the folding of proteins.

Amino Acid Sequence↗

PubMed1986

Effects of trifluoperazine on calcium binding by calmodulin. Heat capacity and entropy changes.

The possible structural changes of the calmodulin-trifluoperazine (TFP) complex caused by Ca2+ binding have been analyzed by microcalorimetric titrations. Titrations of calmodulin with Ca2+ in the presence of 8-fold molar excess TFP have been made both in the absence and presence of Mg2+, at pH 7.0, and at 5, 15, and 25 degrees C. At high concentrations of TFP calmodulin forms a complex with TFP even in the absence of Ca2+. The reaction of the calmodulin-TFP complex with Ca2+ is exothermic, both in the presence and absence of Mg2+. In the presence of Mg2+ the reaction is driven almost entirely by a favorable enthalpy change. The magnitudes of the hydrophobic and internal vibrational contributions to the heat capacity and entropy changes of this complex on Ca2+ binding have been estimated by the empirical method of Sturtevant (Sturtevant, J. M. (1977) Proc. Natl. Acad. Sci. U. S. A. 74, 2236-2240). In the presence of Mg2+, the vibrational as well as hydrophobic entropy is slightly increased in a parallel manner by Ca2+ binding to each of the binding sites. In contrast, when Mg2+ is absent, the hydrophobic entropy gradually increases on Ca2+ binding, but the vibrational entropy decreases. These changes of entropy indicate the assembling of non-polar groups on the surface of the complex and suggest that the overall structure is loosened in the presence of Mg2+, but tightened in the absence of Mg2+.

Calcium↗

PubMed2005

Direct estimation of entropy loss due to reduced translational and rotational motions upon molecular binding.

The entropic cost due to the loss of translational and rotational (T-R) degree of freedom upon binding has been well recognized for several decades. Tightly bound ligands have higher entropic costs than loosely bound ligands. Quantifying the ligand's residual T-R motions after binding, however, is not an easy task. We describe an approach that uses a reduced Hessian matrix to estimate the contributions due to translational and rotational degrees of freedom to entropy change upon molecular binding. The calculations use a harmonic model for the bound state but only include the T-R degrees of freedom. This approximation significantly speeds up entropy calculations because only 6 x 6 matrices need to be treated, which makes it easier to be used in computer-aided drug design for studying many ligands. The methodological connection with other methods is discussed as well. We tested this approximation by applying it to study the binding of ATP, peptide inhibitor (PKI), and several bound water molecules to protein kinase A (PKA). These ligands span a wide range in size. The model gave reasonable estimates of the residual T-R entropy of bound ligands or water molecules. The residual T-R entropy demonstrated a wide range of values, e.g., 4 to 16 cal/K.mol for the bound water molecules of PKA.

Adenosine Triphosphate↗

PubMed2005

New and fast statistical-thermodynamic method for computation of protein-ligand binding entropy substantially improves docking accuracy.

We present a novel method to estimate the contributions of translational and rotational entropy to protein-ligand binding affinity. The method is based on estimates of the configurational integral through the sizes of clusters obtained from multiple docking positions. Cluster sizes are defined as the intervals of variation of center of ligand mass and Euler angles in the cluster. Then we suggest a method to consider the entropy of torsional motions. We validate the suggested methods on a set of 135 PDB protein-ligand complexes by comparing the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock docking program, thus reducing the percent of incorrectly docked ligands by 1.4-fold to four-fold, so that in some cases the percent of ligands correctly docked to within an RMSD of 2 A is above 90%. We show that the suggested method to account for entropy of relative motions is identical to the method based on the Monte Carlo integration over intervals of variation of center of ligand mass and Euler angles in the cluster.

Algorithms↗

PubMed2007

Nearest-neighbor nonparametric method for estimating the configurational entropy of complex molecules.

A method for estimating the configurational (i.e., non-kinetic) part of the entropy of internal motion in complex molecules is introduced that does not assume any particular parametric form for the underlying probability density function. It is based on the nearest-neighbor (NN) distances of the points of a sample of internal molecular coordinates obtained by a computer simulation of a given molecule. As the method does not make any assumptions about the underlying potential energy function, it accounts fully for any anharmonicity of internal molecular motion. It provides an asymptotically unbiased and consistent estimate of the configurational part of the entropy of the internal degrees of freedom of the molecule. The NN method is illustrated by estimating the configurational entropy of internal rotation of capsaicin and two stereoisomers of tartaric acid, and by providing a much closer upper bound on the configurational entropy of internal rotation of a pentapeptide molecule than that obtained by the standard quasi-harmonic method. As a measure of dependence between any two internal molecular coordinates, a general coefficient of association based on the information-theoretic quantity of mutual information is proposed. Using NN estimates of this measure, statistical clustering procedures can be employed to group the coordinates into clusters of manageable dimensions and characterized by minimal dependence between coordinates belonging to different clusters.

Computer Simulation↗

PubMed2004

Statistical sequence analyses of G-protein-coupled receptors: structural and functional characteristics viewed with periodicities of entropy, hydrophobicity, and volume.

G-protein-coupled receptors (GPCRs) play a crucial role in signal transduction and receive a wide variety of ligands. GPCRs are a major target in drug design, as nearly 50% of all contemporary medicines act on GPCRs. GPCRs are membrane proteins possessing a common structural feature, seven transmembrane helices. In order to design an effective drug to act on a GPCR, knowledge of the three-dimensional (3D) structure of the target GPCR is indispensable. However, as GPCRs are membrane bound, their 3D structures are difficult to obtain. Thus we conducted statistical sequence analyses to find information about 3D structure and ligand binding using the receptors' primary sequences. We present statistical sequence analyses of 270 human GPCRs with regard to entropy (Shannon entropy in sequence alignment), hydrophobicity and volume, which are associated with the alpha-helical periodicity of the accessibility to the surrounding lipid. We found periodicity such that the phase changes once in the middle of each transmembrane region, both in the entropy plot and in the hydrophobicity plot. The phase shift in the entropy plot reflects the variety of ligands and the generality of the mechanism of signal transduction. The two periodic regions in the hydrophobicity plot indicate the regions facing the hydrophobic lipid chain and the polar phospholipid headgroup. We also found a simple periodicity in the plot of volume deviation, which suggests conservation of the stable structural packing among the transmembrane helices.

Entropy↗

PubMed2006

Entropy capacity determines protein folding.

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.

Amino Acids↗

PubMed2006

Alpha-helix stabilization by alanine relative to glycine: roles of polar and apolar solvent exposures and of backbone entropy.

The energetics of alpha-helix formation are fairly well understood and the helix content of a given amino acid sequence can be calculated with reasonable accuracy from helix-coil transition theories that assign to the different residues specific effects on helix stability. In internal helical positions, alanine is regarded as the most stabilizing residue, whereas glycine, after proline, is the more destabilizing. The difference in stabilization afforded by alanine and glycine has been explained by invoking various physical reasons, including the hydrophobic effect and the entropy of folding. Herein, the contribution of these two effects and that of hydrophilic area burial is evaluated by analyzing Ala and Gly mutants implemented in three helices of apoflavodoxin. These data, combined with available data for similar mutations in other proteins (22 Ala/Gly mutations in alpha-helices have been considered), allow estimation of the difference in backbone entropy between alanine and glycine and evaluation of its contribution and that of apolar and polar area burial to the helical stabilization typically associated to Gly-->Ala substitutions. Alanine consistently stabilizes the helical conformation relative to glycine because it buries more apolar area upon folding and because its backbone entropy is lower. However, the relative contribution of polar area burial (which is shown to be destabilizing) and of backbone entropy critically depends on the approximation used to model the structure of the denatured state. In this respect, the excised-peptide model of the unfolded state, proposed by Creamer and coworkers (1995), predicts a major contribution of polar area burial, which is in good agreement with recent quantitations of the relative enthalpic contribution of Ala and Gly residues to alpha-helix formation.

Alanine↗

PubMed1997

The entropy cost of protein association.

The temperature induced unfolding/dissociation of the dimeric subtilisin inhibitor from Streptomyces and its mutant D83C having an S-S crosslink between the subunits has been studied calorimetrically. Comparison of the entropies measured at different concentrations of dimer showed that the entropy cost of crosslinking is small. Its value at the standard concentration of 1 M is of the order of -(5+/-4) cal/K.mol, i.e. it is more than one order of magnitude smaller than the values of translational entropies calculated on the base of statistical thermodynamics, using in particular the Sackur-Tetrode equation, and is close to the cratic entropy value suggested by classical mixing theory.

Bacterial Proteins↗