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PubMed1998

Aging, increasing genomic entropy, and neurodegenerative disease.

The genome, as biologic information, can be conceptualized in terms of entropy. The second law of thermodynamics dictates that entropy must increase over time. Consequently, aging can be viewed as increasing genomic entropy. Genetic instability is the biophysical correlate of increasing genomic entropy. Rates of increasing genomic entropy can be determined from age-specific mortality rate dynamics (e.g., Parkinson's disease and amyotrophic lateral sclerosis). These observations are consistent with a model of neurodegenerative disease as a manifestation of increasing genomic entropy with aging.

Aged↗

PubMedDate not supplied

Differential Shannon entropy analysis identifies molecular property descriptors that predict aqueous solubility of synthetic compounds with high accuracy in binary QSAR calculations.

Prediction of aqueous solubility of organic molecules by binary QSAR was used as a test case for a recently introduced entropy-based descriptor selection method. Property descriptors suitable for solubility predictions were exclusively selected on the basis of Shannon entropy calculations in molecular learning sets, not taking any other information into account. Sets of only five or 10 2D descriptors with largest entropy differences between molecules above or below a defined solubility threshold yielded consistently high prediction accuracy between 80% and 90% in binary QSAR calculations, regardless of the threshold values applied. The top five descriptors with largest differential Shannon entropy (DSE) values achieved an average prediction accuracy of 88%. These findings suggest that differences in entropy and relative information content of descriptors in compared compound data sets correlate with significant differences in physical properties and support the practical relevance of entropy-based descriptor selection routines. The study also demonstrates that binary QSAR methodology can be effectively used to classify small molecules according to aqueous solubility.

Journal Article↗

PubMed2003

Role of entropy in increased rates of intramolecular reactions.

The rates of intramolecular condensation of a series of monoesters of dicarboxylic acids have been shown to be highly dependent on the nature of the intervening groups. To understand the origin of this effect, we estimated DeltaS(NAC,S), the entropy difference between the ensemble of accessible ground state conformers and a single ground state conformer having transition-state-like geometry. DeltaS(NAC,S) differs from the activation entropy for the reaction by DeltaS(TS,NAC), the difference in vibrational entropy between the selected ground state conformer and the transition state. The estimated values of DeltaS(NAC,S) correlate well (R(2) = 0.96 and 0.73 using dielectric constant values of 80 and 1, respectively) with experimentally determined reaction rate constants. Normal-mode analysis performed on minimized ground state conformations of each molecule suggests that the change in vibrational entropy makes only a small contribution to the total activation entropy. These results indicate that the conformational entropy difference between the transition and the ground states contributes significantly to the free energy of activation.

Journal Article↗

PubMed2005

Solvation properties of N-substituted cis and trans amides are not identical: significant enthalpy and entropy changes are revealed by the use of variable temperature 1H NMR in aqueous and chloroform solutions and ab initio calculations.

The cis/trans conformational equilibrium of N-methyl formamide (NMF) and the sterically hindered tert-butylformamide (TBF) was investigated by the use of variable temperature gradient 1H NMR in aqueous solution and in the low dielectric constant and solvation ability solvent CDCl3 and various levels of first principles calculations. The trans isomer of NMF in aqueous solution is enthalpically favored relative to the cis (deltaH(o) = -5.79 +/- 0.18 kJ mol(-1)) with entropy differences at 298 K (298 x deltaS(o) = -0.23 +/- 0.17 kJ mol(-1)) playing a minor role. The experimental value of the enthalpy difference strongly decreases (deltaH(o) = -1.72 +/- 0.06 kJ mol(-1)), and the contribution of entropy at 298 K (298 x deltaS(o) = -1.87 +/- 0.06 kJ mol(-1)) increases in the case of the sterically hindered tert-butylformamide. The trans isomer of NMF in CDCl3 solution is enthalpically favored relative to the cis (deltaH(o) = -3.71 +/- 0.17 kJ mol(-1)) with entropy differences at 298 K (298 x deltaS(o) = 1.02 +/- 0.19 kJ mol(-1)) playing a minor role. In the sterically hindered tert-butylformamide, the trans isomer is enthalpically disfavored (deltaH(o) = 1.60 +/- 0.09 kJ mol(-1)) but is entropically favored (298 x deltaS(o) = 1.71 +/- 0.10 kJ mol(-1)). The results are compared with literature data of model peptides. It is concluded that, in amide bonds at 298 K and in the absence of strongly stabilizing sequence-specific inter-residue interactions involving side chains, the free energy difference of the cis/trans isomers and both the enthalpy and entropy contributions are strongly dependent on the N-alkyl substitution and the solvent. The significant decreasing enthalpic benefit of the trans isomer in CDCl3 compared to that in H2O, in the case of NMF and TBF, is partially offset by an adverse entropy contribution. This is in agreement with the general phenomenon of enthalpy versus entropy compensation. B3LY/6-311++G** and MP2/6-311++G** quantum chemical calculations confirm the stability orders of isomers and the deltaG decrease in going from water to CHCl3 as solvent. However, the absolute calculated values, especially for TBF, deviate significantly from the experimental values. Consideration of the solvent effects via the PCM approach on NMF x H2O and TBF x H2O supermolecules improves the agreement with the experimental results for TBF isomers, but not for NMF.

Algorithms↗

PubMed2006

Freezing-in and production of entropy in vitrification.

Following the classical concepts developed by Simon [Z. Anorg. Allg. Chem. 203, 219 (1931)], vitrification in the cooling of glass-forming melts is commonly interpreted as the transformation of a thermodynamically (meta)stable equilibrium system into a frozen-in, thermodynamically nonequilibrium system, the glass. Hereby it is assumed that the transformation takes place at some well-defined sharp temperature, the glass transition temperature Tg. However, a more detailed experimental and theoretical analysis shows that the transition to a glass proceeds in a broader temperature range, where the characteristic times of change of temperature, tauT=-(TT), and relaxation times, tau, of the system to the respective equilibrium states are of similar order of magnitude. In this transition interval, the interplay of relaxation and change of external control parameters determines the value of the structural order parameters. In addition, irreversible processes take place in the transition interval, resulting both in an entropy freezing-in as well as in an irreversible increase of entropy and, as a result, in significant changes of all other thermodynamic parameters of the vitrifying systems. The effect of entropy production on glass transition and on the properties of glasses is analyzed here for the first time. In this analysis, the structural order-parameter concept as developed by de Donder and van Rysselberghe [Thermodynamic Theory of Affinity (Stanford University Press, Stanford, 1936)] and Prigogine and Defay [Chemical Thermodynamics (Longmans, London, 1954)] is employed. In the framework of this approach we obtain general expressions for the thermodynamic properties of vitrifying systems such as heat capacity, enthalpy, entropy, and Gibbs' free energy, and for the entropy production. As one of the general conclusions we show that entropy production has a single maximum upon cooling and two maxima upon heating in the glass transition interval. The theoretical concepts developed allow us to explain in addition to the thermodynamic parameters also specific features of the kinetic parameters of glass-forming melts such as the viscosity. Experimental results are presented which confirm the theoretical conclusions. Further experiments are suggested, allowing one to test several additional predictions of the theory.

Journal Article↗

PubMed1986

Entropy, matter, and cosmology.

The role of irreversible processes corresponding to creation of matter in general relativity is investigated. The use of Landau-Lifshitz pseudotensors together with conformal (Minkowski) coordinates suggests that this creation took place in the early universe at the stage of the variation of the conformal factor. The entropy production in this creation process is calculated. It is shown that these dissipative processes lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Gravitational entropy takes a simple meaning as associated to the entropy that is necessary to produce matter. This leads to an extension of the third law of thermodynamics, as now the zero point of entropy becomes the space-time structure out of which matter is generated. The theory can be put into a convenient form using a supplementary "C" field in Einstein's field equations. The role of the C field is to express the coupling between gravitation and matter leading to irreversible entropy production.

Journal Article↗

PubMed1994

Protein side-chain conformational entropy derived from fusion data--comparison with other empirical scales.

The loss of conformational entropy of protein side-chains is a major effect in the energetics of folding. The simplest approach is to enumerate the number of freely rotatable bonds. Recently, two scales of side-chain conformational entropy have been proposed based on the definition of entropy as the Boltzmann sampling over all accessible states (S = -R sigma p(i)lnp(i), where p(i) is the probability of being in a rotameric state). In one scale, derived only for aliphatic and aromatic side-chains, the values of p(i) were obtained from Monte Carlo simulations. In the other scale, the observed frequencies of different rotameric states in a database of protein crystal structures yielded an estimate for p(i). Here an empirical estimation of the fusion entropy of the side-chains is used to derive a third scale. The fusion entropy is obtained as a sum of empirically derived contributions from component hydrocarbon and functional groups. There is a good agreement between the fusion scale and the other two scales. This suggests that the magnitude of conformational entropy is being correctly established.

Computer Simulation↗

PubMed2002

Nonextensive entropies derived from form invariance of pseudoadditivity.

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived previously [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. 83, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.

Journal Article↗

PubMed1995

Enthalpy and entropy contributions to the solubility of sulphamethoxypyridazine in solvent mixtures showing two solubility maxima.

The solubility of sulphamethoxypyridazine was measured at several temperatures in mixtures of water:ethanol and ethanol:ethyl acetate. Sulphamethoxypyridazine was chosen as a model drug to compare the solvation effects of proton donor-proton acceptor (water and ethanol) and proton acceptor (ethyl acetate) solvents and mixtures of these solvents because this drug contains functional groups capable of Lewis acid-base interaction. A plot of the mole fraction solubility against the solubility parameter (delta 1 = 30.87 MPa1/2 (20:80 v/v water:ethanol) and another at delta 1 = 20.88 MPa1/2 (30:70 v/v ethanol:ethyl acetate) at all the temperatures under study. The enthalpies and entropies of mixing as well as the enthalpies and entropies of transfer of sulphamethoxypyridazine from ethanol of mixing as well as the enthalpies and entropies of transfer of sulphamethoxypyridazine from ethanol to water:ethanol and ethanol:ethyl acetate mixtures were calculated to compare solvation characteristics of the solvent mixtures toward the drug. As ethanol is added to water, the entropy increases and the structure of the solvent mixture became less ordered, favouring the interaction of the drug with the solvent mixture. On the other hand, in the case of the ethanol:ethyl acetate mixture, solubility is favoured by the more negative enthalpy values. This way, the same result, i.e. a solubility maximum, is obtained by different routes. In the ethanol:water mixtures, the dissolution process if entropy-controlled while enthalpy is the driving force in the case of ethanol:ethyl acetate mixtures. The two solvent systems show enthalpy-entropy compensation. Water deviates from the linear relationship due possibly to its hydrophobic effect.

Acetates↗

PubMed2001

Entropy calculations on a reversibly folding peptide: changes in solute free energy cannot explain folding behavior.

The configurational entropy of a beta-heptapeptide in solution at four different temperatures is calculated. The contributions of the backbone and of the side-chain atoms to the total peptide entropy are analyzed separately and the effective contribution to the entropy arising from correlations between these terms determined. The correlation between the backbone and side-chain atoms amounts to about 17% and is rather insensitive to the temperature. The correlation of motion within the backbone and within side-chains is much larger and decreases with temperature. As the peptide reversibly folds at higher temperatures, its change in entropy and enthalpy upon folding is analyzed. The change in entropy and enthalpy upon folding of the peptide alone cannot account for the observed change in free energy on folding of the peptide in solution. Enthalpic and entropic contributions of the solvent thus also play a key role. Proteins 2001;43:45-56.

Entropy↗

PubMed2004

Entropy considerations in kinetic method experiments.

In extended kinetic method experiments, relative binding enthalpies ('affinities') and relative entropies are obtained based on unimolecular dissociation kinetics. A series of ion-bound dimers A-X-B(i) is formed, in which the sample (A) and structurally similar reference molecules (B(i)) are bridged by a central cation or anion (X). The branching ratios of the A-X-B(i) set to A-X and B(i)-X are determined at different internal energies, usually by subjecting A-X-B(i) to collisionally activated dissociation at various collision energies. The dependence of the natural logarithm of the branching ratios on the corresponding B(i)-X bond enthalpies (X affinities of B(i)) is evaluated as a function of internal energy to thereby deduce the A-X bond enthalpy (X affinity of A) as well as an apparent relative entropy of the competitive dissociation channels, Delta(DeltaS(app)). Experiments with proton- and Na(+)-bound dimers show that this approach can yield accurate binding enthalpies. In contrast, the derived Delta(DeltaS(app)) values do not correlate with the corresponding thermodynamic entropy differences between the channels leading to A-X and B(i)-X, even after scaling. The observed trends are reconciled by the transition state switching model. According to this model, the kinetics of barrierless dissociations, such as those encountered in kinetic method studies, are dominated by a family of tight transition states ('entropy bottlenecks') lying lower in energy than the corresponding dissociation thresholds. In general, the relative energies of these tight transition states approximately match those of the dissociation products, but their relative entropies tend to be much smaller, as observed experimentally.

Alanine↗

PubMed2004

Relationship between local structural entropy and protein thermostability.

We developed a technique to compute structural entropy directly from protein sequences. We explored the possibility of using structural entropy to identify residues involved in thermal stabilization of various protein families. Examples include methanococcal adenylate kinase, Ribonuclease HI and holocytochrome c(551). Our results show that the positions of the largest structural entropy differences between wild type and mutant usually coincide with the residues relevant to thermostability. We also observed a good linear relationship between the average structural entropy and the melting temperatures for adenylate kinase and its chimeric constructs. To validate this linear relationship, we compiled a large dataset comprised of 1153 sequences and found that most protein families still display similar linear relationships. Our results suggest that the multitude of interactions involved in thermal stabilization may be generalized into the tendency of proteins to maintain local structural conservation. The linear relationship between structural entropy and protein thermostability should be useful in the study of protein thermal stabilization.

Adenylate Kinase↗

PubMed1997

Entropies of redox reactions between proteins and mediators: the temperature dependence of reversible electrode potentials in aqueous buffers.

The temperature dependencies of the reversible electrode potentials for a number of charge transfer reactions of redox mediators were used to evaluate the corresponding charge transfer entropies in Tris-HCl (pH 8) buffer. The redox mediator thermodynamic data, along with reaction enthalpy data for mediator redox protein electron transfer, were used to evaluate the charge transfer entropy for the cytochrome c redox couple [(cytc)ox/(cytc)red] in Tris-HCl (pH 8) buffer and were found to be equal to -16 cal/degrees K mol. Reversible electrode potentials at 298 degrees K for the redox mediator half-reactions were observed to vary from -528 to +657 mV (vs NHE). Charge transfer entropies were observed to depend upon the structure of the redox mediators and to vary from -13.8 to -29.7 cal/degrees K mol for a closely related series of organic dications (viologens) and a value of -43.6 cal/degrees K mol was observed for the [Fe(CN)6]3-/[Fe(CN)6]4- couple under the same conditions. A procedure for determining charge transfer entropies of protein redox couples which cannot be studied by direct electrochemical methods is outlined. The factors contributing to the magnitude of the charge transfer entropies are discussed.

Buffers↗

PubMed2005

Age-associated alteration of sympatho-vagal balance in a female population assessed through the tone-entropy analysis.

Through our recent studies on heart rate variability (Oida et al. J Appl Physiol 82:1794-1801, 1997; J Gerontol 54A:M219-M224, 1999a; Acta Physiol Scand 165:129-134, 1999b; Acta Physiol Scand 165:421-422, 1999c), we discover that autonomic functions could be assessed quantitatively in time domain by the tone-entropy (T-E) methodology, where the tone represents sympatho-vagal balance, and the entropy, autonomic regulatory activity. The purpose of this study was then to elucidate an age-associated alteration of sympatho-vagal balance in a female population through this T-E method. ECG R-R time intervals at rest were acquired on 10 min for 73 female subjects. Ageing influence was examined by comparisons between two groups: middle-aged group (40-50), (51.5 +/- 0.7 year, n = 28) and old-aged (60-70), (69.5 +/- 0.8 year, n = 45)]. Evaluated tone: [-0.058 +/- 0.011 (40-50), and 0.027 +/- 0.003 (60-70) (P < 0.01)], and entropy: [3.46 +/- 0.11 (40-50), and 3.06 +/- 0.08 bit (60-70) (P<0.01)]. The result showed that the tone was high and the entropy was low in the old-aged compared with the middle-aged group. When the result was plotted in two-dimensional T-E space, it revealed a curvi-linear relation between the tone and the entropy, consistent with our previous studies on pharmacological blockades, on heart recovery after dynamic exercise and on a male ageing. In conclusion, the result suggested that the sympatho-vagal balance altered or the vagal predominance was impaired with age significantly in this female population. Interestingly, comparing with corresponding male, the female had better autonomic functions.

Adaptation, Physiological↗

PubMed2005

Information entropy analysis of discrete aiming movements.

Information entropy and mutual information were investigated in discrete movement aiming tasks over a wide range of spatial (20-160 mm) and temporal (250-1250 ms) constraints. Information entropy was calculated using two distinct analyses: (1) with no assumption on the nature of the data distribution; and (2) assuming the data have a normal distribution. The two analyses showed different results in the estimate of entropy that also changed as a function of task goals, indicating that the movement trajectory data were not from a normal distribution. It was also found that the information entropy of the discrete aiming movements was lower than the task defined indices of difficulty (ID) that were selected for the congruence with Fitts' law. Mutual information between time points of the trajectory was strongly influenced by the average movement velocity and the acceleration/deceleration segments of the movement. The entropy analysis revealed structure to the variability of the movement trajectory and outcome that has been masked by the traditional distributional analyses of discrete aiming movements.

Adult↗

PubMed2005

Photosynthesis and negative entropy production.

The widely held view that the maximum efficiency of a photosynthetic pigment system is given by the Carnot cycle expression (1-T/Tr) for energy transfer from a hot bath (radiation at temperature Tr) to a cold bath (pigment system at temperature T) is critically examined and demonstrated to be inaccurate when the entropy changes associated with the microscopic process of photon absorption and photochemistry at the level of single photosystems are considered. This is because entropy losses due to excited state generation and relaxation are extremely small (DeltaS << T/Tr) and are essentially associated with the absorption-fluorescence Stokes shift. Total entropy changes associated with primary photochemistry for single photosystems are shown to depend critically on the thermodynamic efficiency of the process. This principle is applied to the case of primary photochemistry of the isolated core of higher plant photosystem I and photosystem II, which are demonstrated to have maximal thermodynamic efficiencies of xi > 0.98 and xi > 0.92 respectively, and which, in principle, function with negative entropy production. It is demonstrated that for the case of xi > (1-T/Tr) entropy production is always negative and only becomes positive when xi < (1-T/Tr).

Energy Transfer↗

PubMed2004

Comparative estimation of vibrational entropy changes in proteins through normal modes analysis.

We compare the vibrational entropy changes of proteins calculated using a full and a number of approximate normal modes analysis methods. The vibrational entropy differences for three conformational changes and three protein binding interactions were computed. In general, the approximate methods yield good estimates of the vibrational entropy change in a fraction of the time required by full normal modes analysis. The absolute entropies are either overestimated or greatly underestimated, but the difference is sufficiently accurate for some methods. This indicates that some of the approximate methods can give reasonable estimates of the associated vibrational entropy changes, making them suitable for inclusion in free energy calculations.

Animals↗

PubMed2000

A maximum entropy analysis of protein orientations using fluorescence polarization data from multiple probes.

Techniques have recently become available to label protein subunits with fluorescent probes at predetermined orientation relative to the protein coordinates. The known local orientation enables quantitative interpretation of fluorescence polarization experiments in terms of orientation and motions of the protein within a larger macromolecular assembly. Combining data obtained from probes placed at several distinct orientations relative to the protein structure reveals functionally relevant information about the axial and azimuthal orientation of the labeled protein segment relative to its surroundings. Here we present an analytical method to determine the protein orientational distribution from such data. The method produces the broadest distribution compatible with the data by maximizing its informational entropy. The key advantages of this approach are that no a priori assumptions are required about the shape of the distribution and that a unique, exact fit to the data is obtained. The relative orientations of the probes used for the experiments have great influence on information content of the maximum entropy distribution. Therefore, the choice of probe orientations is crucial. In particular, the probes must access independent aspects of the protein orientation, and two-fold rotational symmetries must be avoided. For a set of probes, a "figure of merit" is proposed, based on the independence among the probe orientations. With simulated fluorescence polarization data, we tested the capacity of maximum entropy analysis to recover specific protein orientational distributions and found that it is capable of recovering orientational distributions with one and two peaks. The similarity between the maximum entropy distribution and the test distribution improves gradually as the number of independent probe orientations increases. As a practical example, ME distributions were determined with experimental data from muscle fibers labeled with bifunctional rhodamine at known orientations with respect to the myosin regulatory light chain (RLC). These distributions show a complex relationship between the axial orientation of the RLC relative to the fiber axis and the azimuthal orientation of the RLC about its own axis. Maximum entropy analysis reveals limitations in available experimental data and supports the design of further probe angles to resolve details of the orientational distribution.

Biophysical Phenomena↗