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PubMed1991

The effect of linguistic entropy on speech perception in noise in young and elderly listeners.

The rationale for a method to quantify the information content of linguistic stimuli, i.e., the linguistic entropy, is developed. The method is an adapted version of the letter-guessing procedure originally devised by Shannon [Bell Syst. Tech. J. 30, 50-64 (1951)]. It is applied to sentences included in a widely used test to measure speech-reception thresholds and originally selected to be approximately equally redundant. Results of a first experiment reveal that this method enables one to detect subtle differences between sentences and sentence lists with respect to linguistic entropy. Results of a second experiment show that (1) in young listeners and with the sentences employed, manipulating linguistic entropy can result in an effect on SRT of approximately 4 dB in terms of signal-to-noise ratio; (2) the range of this effect is approximately the same in elderly listeners.

Adult↗

PubMed1992

Approximate entropy, a statistic of regularity, applied to fetal heart rate data before and during labor.

OBJECTIVE: To determine whether approximate entropy (ApEn), a new statistic of regularity, when applied to fetal heart rate (FHR) data antepartum or in labor, would offer an advantage over standard statistics of variation in predicting outcome. METHODS: A large data base of antepartum FHR records collected in clinical practice over 10 years was available. Two data sets in labor were stored on disk in small computers interfaced to fetal monitors on-line. Outcomes were assessed using blood gas values on delivery and Apgar scores. RESULTS: Antepartum, when the most favorable form of ApEn was used on 769 good-quality FHR records, the correlation with measurement of short-term variation was high. This was especially true when the fetal pulse interval variation fell below the normal range (less than 6 milliseconds short-term; r = 0.93) and in 20 other records with sinusoidal variation (r = 0.96). Approximate entropy varied with fetal sleep cycles and took longer to calculate than FHR variation. During the last hour of labor, in 319 records, there was no significant correlation between umbilical artery base deficit values on delivery and ApEn measurement. In 871 additional good-quality records of fetuses with normal outcome, the mean (+/- standard error [SE]) ApEn (0.95 +/- 0.005) was significantly greater than in 22 records (0.88 +/- 0.028) from fetuses with abnormal outcome (umbilical artery base deficit more than 12 mmol/L and Apgar score of 3 or less at 1 minute). However, consideration of the frequency distributions of these measurements showed that ApEn did not discriminate between normal and abnormal outcomes. The SD of fetal pulse intervals rose in labor whereas ApEn values fell, confirming that this new statistic of regularity differs from standard statistics of variation. CONCLUSION: Approximate entropy offered no advantage over measurement of short-term FHR variation antepartum, and neither measurement predicted outcome in labor.

Adult↗

PubMed1977

Enthalpy-entropy compensation in dinitrophenyl--anti-dinitrophenyl antibody interaction(s).

The effect of varying the temperature over a wide range (-3 dergees -67 degrees) on the binding of xi-DNP-L-Lysine to bovine colostral anti-DNA IgG1, and also rabbit anti-DNP IgG revealed non-linear van't Hoff plots. The extent of the curvatures were found to be indicative of large positive heat capacity changes; and the thermodynamic parameters, calculated using a non-linear least-squares computer procedure for these anti-DNP antibody preparations, revealed an enthalpy-entropy compensation mechanism for hapten-antibody binding. The enthalpy factor was found to be the primary contributor for the binding process at low temperatures, but at increasing temperatures the entropy factor assumed greater importance. At physiological temperature (37 degrees), the entropy factor was the major contributor to the free energy of reaction for rabbit anti-DNP IgG, while for bovine colostral anti-DNP IgG it was predominant at temperatures higher than 37 degrees.

Animals↗

PubMed2026

Entropy-Driven Electrolyte Design for Lithium Metal Batteries: Achieving Interfacial Stability With Fluorinated Fullerene Nanoparticle Additives.

Lithium metal batteries are highly attractive for next-generation high-energy-density storage, and ether-based electrolytes such as LiFSI/DME are particularly promising for high-rate operation because of their low viscosity, high ionic conductivity, and favorable compatibility with Li metal. However, current electrolyte optimization strategies still rely mainly on small-molecule additives that regulate bulk solvation or the primary Li+ solvation sheath, whereas entropy-driven modulation of the interfacial solvation environment by large molecular additives remains largely unexplored. Herein, fluorinated fullerene C60F30 (FF) is introduced as a nanoparticle additive to create a dynamically disordered interface that enhances configurational entropy without sacrificing Li+ diffusivity, while accelerating Li+ desolvation and transport. Meanwhile, FF cooperates with FSI--derived species to build a robust fluorine-rich SEI, suppressing dendrite growth and parasitic reactions. As a result, Li||Li symmetric cells cycle stably for 1500 h, while high-loading Li||LiFePO4 cells retain 96.0% capacity after 500 cycles at 2C and 95.9% after 1000 cycles at 10C. Moreover, pouch cells and high-loading Li||NCM811 cells further verify the practical promise of the FF-enabled electrolyte for high-rate, long-cycling LMBs.

Li metal batteries↗

PubMed2026

Quantifying the peripheral surface information entropy from conformational ensembles of globular protein-peptide complexes.

Predicting favorable protein-peptide binding events remains a central challenge in biophysics, with continued uncertainty surrounding how nonlocal effects shape the global energy landscape. Here, we introduce peripheral surface information entropy, SΨ, a quantitative measure of the statistical variability in apolar and charged non-interacting surface (NIS) proportions across conformational ensembles. Within the Gibbs free-energy relation ΔG = ΔH - TΔS, SΨ is proposed as a computationally tractable entropic proxy rather than a direct thermodynamic observable or stand-alone estimator of binding affinity. Using energy-directed molecular docking via HADDOCK3 and explicit-solvent molecular dynamics simulations, it is demonstrated that favorable binding partners exhibit emergent, low-entropy N-states (discrete macrostates in NIS state space) indicative of preferential apolar/charged surface configurations. Across dozens of peptides and multiple receptor systems (WW, PDZ, and MDM2 domains), dominant N-states persisted under varied docking parameters and initial conditions. A meta-ensemble of 657 complexes from 36 experiments over 15 years confirmed the presence of dominant NIS modes independent of in silico methodology, suggesting an evolutionary selection pressure toward specific NIS fingerprints. These findings establish SΨ as a thermoinformatic descriptor that encodes favorable binding constraints into unique statistical signatures of the NIS.

Entropy↗

PubMedDate not supplied

Entropy of the genetic information and evolution.

The entropy of the amino acid sequences coded by DNA is considered as a measure of diversity of variety of proteins, and is taken as a measure of evolution. The DNA or m-RNA sequence is considered as a stationary second-order Markov chain composed of four kinds of bases. Because of the biased nature of the genetic code table, increase of entropy of amino acid sequences is possible with biased nucleotide sequence. Thus the biased DNA base composition and the extreme rarity of the base doublet CpG of higher organisms are explained. It is expected that the amino acid composition was highly biased at the days of the origin of the genetic code table, and the more frequent amino acids have tended to get rarer, and the rarer ones more frequent. This tendency is observed in the evolution of hemoglobin, cytochrome C, fibrinopeptide, immunoglobulin and lysozyme, and protein as a whole.

Amino Acid Sequence↗

PubMed1992

Alcohol interaction with high entropy states of macromolecules: critical temperature hypothesis for anesthesia cutoff.

Nerve excitation generates heat and decreases the entropy (review by Ritchie and Keynes (1985) Q. Rev. Biophys. 18, 451-476). The data suggest the existence of at least two thermodynamically identifiable states: resting and excited, with a thermotropic transition between the two. We envision that nerve excitation is a transition between the two states of the excitation machinery consisting of proteins and lipids, rather than the sodium channel protein alone. Presumably, both proteins and lipids change their conformation at excitation. We proposed (Kaminoh et al. (1991) Ann. N.Y. Acad. Sci. 625, 315-317) that anesthesia occurs when compounds have a higher affinity to the resting state than to the excited state of excitable membranes, and that there is a critical temperature above which the affinity to the excited state becomes greater than to the resting state. When the temperature exceeds this critical level, compounds lose their anesthetic potency. We used thermotropic phase-transition of macromolecules as a model for the excitation process. Anesthetic alcohols decreased the main transition temperature of dipalmitoylphosphatidylcholine (DPPC) membranes and also the temperature of the alpha-helix to beta-sheet transition of poly(L-lysine). The affinity of alcohols to the high- and low-temperature states of the DPPC membranes were separately estimated. The difference in the affinity of n-alcohols to the liquid (high-temperature) and solid (low-temperature) states correlated with their anesthetic potency. It is not the total number of bound anesthetic molecules that determines the anesthesia, rather, the difference in the affinity between the higher and lower entropy states determines the effects. The critical temperatures of the long-chain alcohols were found to be lower than those of the short-chain alcohols. Cutoff occurs when the critical temperature of long-chain alcohols is below the physiological temperature, such that the anesthetic potency is not manifested in the experimental temperature range.

1,2-Dipalmitoylphosphatidylcholine↗

PubMed1978

Thermodynamic studies of the interaction of alpha-chymotrypsin with water. II. Statistical analyses of the enthalpy-entropy compensation effect.

Differential enthalpies (deltaH) and entropies (deltaS) of the interaction of water with a high and low temperature conformer of alpha-chymotrypsin were determined previously by multitemperature sorption measurements. The changes in (deltaH) and (deltaS) with water content of the protein were found to show a pronounced compensation pattern. It is known that van 't Hoff data may exhibit enthalpy-entropy compensation, which is entirely due to statistical error propagation. To discriminate between artifactual and significant compensation, the experimental results are analyzed by statistical methods. The results of two different statistical analyses show that a linear, chemically caused compensation effect can be established for the interaction of water with both chymotrypsin conformers. The compensation temperature beta = deltaH/deltaS was found to be 433 +/- 22 K. The compensation effect is detectable only in the water content range above the monolayer volume (upsilonm), computed by the Brunauer, Emmett and Teller equation. This result is discussed in terms of a monolayer hydration mechanism, formulated on the basis of previous thermodynamic results: The interaction of the first water monolayer with the charged and polar surface area of the dry protein, largely stabilizes its tertiary structure. Further water addition then occurs to a practically invariable protein surface. According to this mechanism (which ensures a maximum of conformational stability with a minimum of hydration water), large conformational changes can be expected to occur mainly in the monolayer water content range. This expectation is confirmed by extra-thermodynamic data (infrared and X-ray measurements). The thermodynamic quantities of the sorption process are thus governed by conformational effects below upsilonm. Above the monolayer water content range, however, the water binding process per se strongly predominates. The deltaH/deltaS compensation effect established for this water content range, is thus attributable to phase transitions of water molecules from the gas (or liquid) phase to the protein-bound state (or vice versa). A possible relationship between the linear compensation effect established in this study, and the compensation phenomenon observed in reactions in aqueous solution is discussed.

Calorimetry↗

PubMed1978

Thermodynamic studies of the interaction of alpha-chymotrypsin with water. I. Determination of the isosteric enthalpies and entropies of water binding to the native enzyme.

The enthalpies (deltaH) and entropies (deltaS) of the interaction of water with alpha-chymotrypsin were evaluated from multitemperature sorption isotherms in the temperature range 283--313 K, determined in a fully automatized, computer controlled sorption apparatus. The temperature dependence of deltaH and deltaS shows a marked anomaly in the temperature range 295--298 K. The experimental results are interpreted by a phase transition of the enzyme protein, and by the existence of a low- and high-temperature conformer of alpha-chymotrypsin below and above the transition region. The two conformers differ significantly in their water binding energetics, as proved by two F-tests based on analyses of variance. The deltaH and deltaS versus water content functions of the high and low temperature conformer show markedly different anomalies at and below 70 mol H2O per mol protein. This water content corresponds closely to the monolayer volume vm, (as defined by Brunauer, Emmett and Teller). The protein surface covered by one water-monolayer, agrees well with the polar and charged surface area of chymotrypsin, computed from X-ray data. The experimental results suggest that the interaction of the first water-monolayer with the protein surface induces major conformational changes. The energetic contributions of these structural changes dominate the deltaH and deltaS terms below vm, giving rise to the anomalies observed. Above this water content, their influence is drastically reduced, and the isosteric quantities are predominantly determined by the water binding process per se. This process is possibly related to the pronounced enthalphy-entropy compensation pattern exhibited by the deltaH and deltaS terms. A more detailed analysis and discussion of this compensation effect will be given.

Calorimetry↗

PubMed1992

Quantal analysis using maximum entropy noise deconvolution.

When applying quantal analysis to synaptic transmission it is often unclear how much of the measured postsynaptic signal fluctuation arises from random sampling and noise rather than from the probabilistic transmitter release process. Unconstrained noise deconvolution methods do not overcome this because they tend to overfit the data, often giving a misleading picture of the underlying process. Instead, maximum entropy deconvolution provides a solution which is the smoothest, or most featureless, distribution that is still compatible with the data, taking noise and sample size into account. A simple way of achieving this is described, together with results of Monte Carlo simulations which show that the features present in the maximum entropy solution usually reflect the process underlying the data and not random sampling or noise.

Algorithms↗

PubMed1975

Problems with entropy in biology.

Entropy has been widely referred to as a measure of biological order. The validity of this notion is discussed in conjunction with it's relation to the spontaneous creation of order. Information theory offers a quantitative method for characterization of order, however, it is not fundamentally connected to formalisms of irreversible thermodynamics, and it is severely limited because the meaning and value of the information is neglected. A completely general notation is proposed for including measures of order of a biological system in the entropy balance equation of irreversible thermodynamics. Problems of assigning energetic equivalents to measures of order are indicated, with a final focus on the problem of meaning and value.

Calorimetry↗

PubMed1991

Reconstruction of the antibody affinity distribution from experimental binding data by a minimum cross-entropy procedure.

A new solution is presented for the reconstruction of the distribution of association constants of antigen-antibody binding from a finite number of noisy experimental binding data. This ill-posed problem is solved by utilizing an information-theoretic method based on the principle of minimum cross-entropy (MCE) to select, as the solution, that unique antibody binding distribution which minimizes the cross entropy relative to some prior distribution subject to the constraints imposed by the given measurements. The prior distribution is selected to properly encode all the a priori information on the affinity distribution before the measurement of the experimental binding data. The utility of the method is demonstrated by application to synthetic binding data.

Antibody Affinity↗

PubMed1990

Application of entropy measures derived from the ergodic theory of dynamical systems to rat locomotor behavior.

Measures of complexity derived from ergodic theory of dynamical systems were developed and applied to an exemplary data set describing locomotor movements of rats in a bounded space. A symbolic dynamical system was obtained by partitioning the event space into equally probable partition elements, using a k-dimensional tree. The measures calculated from the symbolic sequences included the topological entropy (ht)--i.e., the rate of increase of all possible sequences with increasing sequence length--and the metric entropy (hm)--i.e., the rate of increase of all likely sequences with increasing sequence length. These measures were used to assess changes in rat locomotor behavior as recorded in the behavioral pattern monitor (BPM) that were induced by amphetamine (0.25, 0.50, 1.0, or 2.0 mg/kg) and 3,4-methylenedioxymethamphetamine (MDMA; 1.25, 2.5, 5.0, or 10.0 mg/kg). Amphetamine increased the mean activity, ht, and hm. MDMA resulted in a monotonic dose-response curve for activity but exhibited a biphasic dose response in ht and hm. In particular, some animals in the higher dose groups showed a ht in the range of the saline controls, whereas other animals exhibited a significantly reduced ht and a greater decrease in hm, suggesting that two different behavioral reactions coexist within the same higher dose range of MDMA. An important implication of our method is that, in applied ergodic measure-theoretic approaches, the partition that determines the elements of the symbolic dynamical system should not be specified a priori on abstract mathematical grounds but should be chosen relative to its significance with respect to the data set in question. Here, the animal constructs its own spatiotemporal partition in behavioral phase space.

3,4-Methylenedioxyamphetamine↗

PubMed1992

On the origin of the enthalpy and entropy convergence temperatures in protein folding.

Temperature dependence of the thermodynamics of folding/unfolding for cytochrome c has been determined as a function of moderate [0-10% (vol/vol)] concentrations of methanol. Heat capacity change (delta Cp) for unfolding decreases with increased concentrations of methanol, consistent with a higher solvent hydrophobicity. For a given transition temperature, this effect results in higher experimental enthalpy (delta H) and entropy (delta S) changes with increased methanol concentrations. When the enthalpy or entropy data sets obtained at different methanol concentrations are plotted as a function of temperature, they are seen to converge and assume common values around 100 degrees C for delta H and 112 degrees C for delta S. These convergence temperatures are similar to those obtained for different proteins in aqueous solution when delta H and delta S are normalized with respect to number of residues. It has been previously hypothesized that these convergence temperatures correspond to the temperatures at which the hydrophobic contributions to delta H and delta S are zero; the results presented here agree with this viewpoint.

Calorimetry, Differential Scanning↗

PubMed1991

A multisolution method of phase determination by combined maximization of entropy and likelihood. V. The use of likelihood as a discriminator of phase sets produced by the SAYTAN program for a small protein.

The use of a likelihood criterion associated with maximum-entropy (ME) extrapolation for selecting phase sets as part of a new multisolution phasing strategy, already applied to solving small crystal structures from single-crystal data [Gilmore, Bricogne & Bannister (1990). Acta Cryst. A46, 297-308] and X-ray powder diffraction data [Gilmore, Henderson & Bricogne (1991). Acta Cryst. A47, 830-841], has been tested on the small protein avian pancreatic polypeptide (APP) with 301 non-H atoms in the asymmetric unit in space group C2. A collection of 50 phase sets for APP were provided by Woolfson & Yao. They had been generated from random starting phases by the SAYTAN procedure [Woolfson & Yao (1990). Acta Cryst. A46, 409-413] using data to a resolution of 0.98 A. Six of these had an unweighted mean absolute phase error, mean value of magnitude of delta phi, of less than 50 degrees, the remainder having phase errors of 60 degrees or more. However, none of the conventional figures of merit were able to identify these preferred sets. Each phase set was subjected to our standard procedure of entropy maximization and of evaluation of the log-likelihood gain resulting from the associated ME extrapolation. With only a small subset of data (to 2 A resolution), the likelihood criterion identified unambiguously the phase sets with mean value of magnitude of delta phi less than 50 degrees. In contrast, conventional figures of merit showed no such ability.(ABSTRACT TRUNCATED AT 250 WORDS)

Pancreatic Polypeptide↗

PubMed1976

Mechanoelectrical transduction in hyaluronic acid salt solution is an entropy-driven process.

An electrical potential develops between the ends of a column of hyaluronic salt solution displaced from a resting position by gentle pressure. A previous study demonstrated that such displacement changes the optical rotary dispersion properties of the salt, either increasing the rotation in the direction already shown by the salt before displacement or changing and increasing the rotation in the opposite direction, depending on the direction of the displacement. The present investigation demonstrates that the loss of bound water component across a membrane separating the solution and water is corelated with the extent of the column displacement. In addition, a return of the column to the position before displacement is correlated with a return of the water component across the membrane-but not at the same rate as the exodus. The data seem consistent with the hypothesis that the hyaluronic acid salt, when strained, adopts a less entropic configuration, releasing bound water and thus increasing the entropy of water component. This change in the distribution of entropy is reversible; i.e., Eddington's "time's arrow" is reversible with respect to the water component of the solution.

Female↗

PubMed1975

Phosphorylation of solubilized sarcoplasmic reticulum by orthophosphate and its thermodynamic characteristics. The dominant role of entropy in the phosphorylation.

A large fraction of the Ca-2plus- and Mg-2plus-dependent ATPase (EC 3.6.1.3) in sarcoplasmic reticulum membranes solubilized with Triton X-100 was phosphorylated with Pi. The phosphorylation required Mg-2plus but was strongly inhibited by low concentrations of Ca-2plus. A Ca-2plus ion concentration of 30 muM caused half-maximum inhibition in the presence of 50 mM MgCl2. The phosphorylated enzyme showed a rapid turnover and was in dynamic equilibrium with Pi in the medium. At equilibrium the amount of the phosphorylated enzyme increased markedly with increased in the reaction temperature. The apparent standard free energy change, the apparent standard enthalpy change, and the apparent standard entropy change in the formation of the phosphorylated enzyme from the enzyme-phosphate complex in the presence of excess Mg-2plus at 37 degrees and pH 7.0 were, respectively, 0.35 Cal per mol, 15.9 Cal per mol, and 50.2 e.u. per mol. The susceptibility of the acid-denatured phosphorylated enzyme to hydroxylamine showed that the phosphorylated enzyme is of an acyl phosphate type. The present results are consistent with the probability that the phosphorylation results from reversal of late steps in the Ca-2plus transport process. The results clearly show that the phosphorylated enzyme is stabilized by a great increase in entropy upon its formation from the enzyme-phosphate complex.

Adenosine Triphosphatases↗

PubMedDate not supplied

[Radiation entropy and its role in the process of photosynthesis].

The paper deals with the following problems: 1) radiation entropy and the value of maximum performance coefficient of photosynthesizing systems eta m; 2) problem of physical meaning of eta m and on its association with real processes in photosynthesis. It has been shown that for calculating entropy of nonequilibrium radiation its origin should be known and that the value eta m does not practically limit the processes which proceed in photosynthesis.

Mathematics↗