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PubMed2002

Numerical study of the entropy loss of dimerization and the folding thermodynamics of the GCN4 leucine zipper.

A lattice-based model of a protein and the Monte Carlo simulation method are used to calculate the entropy loss of dimerization of the GCN4 leucine zipper. In the representation used, a protein is a sequence of interaction centers arranged on a cubic lattice, with effective interaction potentials that are both of physical and statistical nature. The Monte Carlo simulation method is then used to sample the partition functions of both the monomer and dimer forms as a function of temperature. A method is described to estimate the entropy loss upon dimerization, a quantity that enters the free energy difference between monomer and dimer, and the corresponding dimerization reaction constant. As expected, but contrary to previous numerical studies, we find that the entropy loss of dimerization is a strong function of energy (or temperature), except in the limit of large energies in which the motion of the two dimer chains becomes largely uncorrelated. At the monomer-dimer transition temperature we find that the entropy loss of dimerization is approximately five times smaller than the value that would result from ideal gas statistics, a result that is qualitatively consistent with a recent experimental determination of the entropy loss of dimerization of a synthetic peptide that also forms a two-stranded alpha-helical coiled coil.

Biophysical Phenomena↗

PubMed2001

NMR relaxation studies of the role of conformational entropy in protein stability and ligand binding.

Recent advances in the measurement and analysis of protein NMR relaxation data have made it possible to characterize the dynamical properties of many backbone and side chain groups. With certain caveats, changes in flexibility that occur upon ligand binding, mutation, or changes in sample conditions can be interpreted in terms of contributions to conformational entropy. Backbone and side chain flexibility can either decrease or increase upon ligand binding. Decreases are often associated with "enthalpy-entropy compensation" and "induced fit" binding, whereas increases in conformational entropy can contribute to stabilization of complexes. In certain cases, conformational entropy appears to play a role in cooperative binding and enzyme catalysis. In addition, variations in conformational entropy and heat capacity may both be important in stabilizing the folded structures of proteins.

Entropy↗

PubMed1998

Enthalpy-entropy compensation for the solubility of drugs in solvent mixtures: paracetamol, acetanilide, and nalidixic acid in dioxane-water.

In earlier work, a nonlinear enthalpy-entropy compensation was observed for the solubility of phenacetin in dioxane-water mixtures. This effect had not been earlier reported for the solubility of drugs in solvent mixtures. To gain insight into the compensation effect, the behavior of the apparent thermodynamic magnitudes for the solubility of paracetamol, acetanilide, and nalidixic acid is studied in this work. The solubility of these drugs was measured at several temperatures in dioxane-water mixtures. DSC analysis was performed on the original powders and on the solid phases after equilibration with the solvent mixture. The thermal properties of the solid phases did not show significant changes. The three drugs display a solubility maximum against the cosolvent ratio. The solubility peaks of acetanilide and nalidixic acid shift to a more polar region at the higher temperatures. Nonlinear van't Hoff plots were observed for nalidixic acid whereas acetanilide and paracetamol show linear behavior at the temperature range studied. The apparent enthalpies of solution are endothermic going through a maximum at 50% dioxane. Two different mechanisms, entropy and enthalpy, are suggested to be the driving forces that increase the solubility of the three drugs. Solubility is entropy controlled at the water-rich region (0-50% dioxane) and enthalpy controlled at the dioxane-rich region (50-100% dioxane). The enthalpy-entropy compensation analysis also suggests that two different mechanisms, dependent on cosolvent ratio, are involved in the solubility enhancement of the three drugs. The plots of deltaH versus deltaG are nonlinear, and the slope changes from positive to negative above 50% dioxane. The compensation effect for the thermodynamic magnitudes of transfer from water to the aqueous mixtures can be described by a common empirical nonlinear relationship, with the exception of paracetamol, which follows a separate linear relationship at dioxane ratios above 50%. The results corroborate earlier findings with phenacetin. The similar pattern shown by the drugs studied suggests that the nonlinear enthalpy-entropy compensation effect may be characteristic of the solubility of semipolar drugs in dioxane-water mixtures.

Acetaminophen↗

PubMed2006

Entropy and enthalpy of polyelectrolyte complexation: Langevin dynamics simulations.

We report a systematic study by Langevin dynamics simulation on the energetics of complexation between two oppositely charged polyelectrolytes of same charge density in dilute solutions of a good solvent with counterions and salt ions explicitly included. The enthalpy of polyelectrolyte complexation is quantified by comparisons of the Coulomb energy before and after complexation. The entropy of polyelectrolyte complexation is determined directly from simulations and compared with that from a mean-field lattice model explicitly accounting for counterion adsorption. At weak Coulomb interaction strengths, e.g., in solvents of high dielectric constant or with weakly charged polyelectrolytes, complexation is driven by a negative enthalpy due to electrostatic attraction between two oppositely charged chains, with counterion release entropy playing only a subsidiary role. In the strong interaction regime, complexation is driven by a large counterion release entropy and opposed by a positive enthalpy change. The addition of salt reduces the enthalpy of polyelectrolyte complexation by screening electrostatic interaction at all Coulomb interaction strengths. The counterion release entropy also decreases in the presence of salt, but the reduction only becomes significant at higher Coulomb interaction strengths. More significantly, in the range of Coulomb interaction strengths appropriate for highly charged polymers in aqueous solutions, complexation enthalpy depends weakly on salt concentration and counterion release entropy exhibits a large variation as a function of salt concentration. Our study quantitatively establishes that polyelectrolyte complexation in highly charged Coulomb systems is of entropic origin.

Computer Simulation↗

PubMed2005

A lower level of entropy in circadian rhythm of the sinus R-R intervals suggests a prevalence of the cardiac sympathetic regulation in early physiological pregnancy.

The study estimates the unpredictable disorder (chaos) within the 24 h pattern of sinus R-R intervals (SRRI) in clinically healthy pregnant women (CHPW) and clinically healthy non-pregnant women (CHNPW), in order to evaluate the early gestational changes in neurovegetative cardiac pacing. SRRI were provided by the 24-h Holter ECG of 10 CHPW and 10 CHNPW. SRRI were investigated by descriptive conventional statistics by means of the Time and Frequency Domain Analysis, and subsequently, in their chaotic component by means of entropy analysis. Both the SRRI and entropy were tested via the Cosinor method to better decipher whether or not the periodic disorder in heart rate variability is modified in pregnancy as a result of a gestational tonic resetting of the cardiac sympatho-vagal regulation. Cosinor analysis documented that the circadian rhythm of both the SRRI and entropy were preserved in CHNPW and CHPW. However, the circadian rhythm of SRRI and entropy in CHPW exhibited a significantly decreased 24 h mean. Via the analysis of the rhythmicity of entropy, this study has documented that the chaos in the 24 h pattern of SRRI is less prominent in CHPW than in CHNPW. Such a reduction of level in the deterministic periodic chaos of heart rate variability provides evidence that, in early pregnancy, a tonic elevation of the sympathetic activity regulates cardiac pacing.

Adult↗

PubMed2006

Effect of an intubation dose of rocuronium on Spectral Entropy and Bispectral Index responses to laryngoscopy during propofol anaesthesia.

BACKGROUND: The spectral entropy of the electroencephalogram has been proposed to monitor the depth of anaesthesia. State Entropy (SE) reflects the level of hypnosis. Response Entropy (RE), computed from electroencephalogram and facial muscle activity, reflects the response to nociceptive stimulation. We evaluated the effect of rocuronium on Bispectral Index (BIS) and entropy responses to laryngoscopy. METHODS: A total of 25 patients were anaesthetized with propofol using a target-controlled infusion. At steady state, they randomly received 0.6 mg kg(-1) rocuronium (R) or saline (S). After 3 min, a 20 s laryngoscopy was applied. BIS, RE and SE were recorded continuously and averaged over 1 min during baseline, at steady state, 2 min after R or S administration (R/S+2) and 0, 1, 2 and 3 min after laryngoscopy (L0, L1, L2, L3). RESULTS: At R/S+2, the RE-SE gradient was higher in Group S than in Group R. Laryngoscopy provoked an increase in BIS, RE and SE. Comparing R/S+2 and L0 values in Groups R and S, BIS increased from 43 (6) to 49 (8) and 42 (9) to 51 (15), SE increased from 43 (7) to 50 (8) and 41 (10) to 55 (12), and RE increased from 46 (8) to 54 (9) and 47 (12) to 66 (15), respectively. BIS and SE did not differ between groups. At L0, RE and RE-SE were higher in Group S [66 (15) and 11 (4), respectively] than in Group R [54 (9) and 4 (2), respectively]. CONCLUSIONS: Rocuronium alters the RE-SE gradient and the RE and RE-SE responses to laryngoscopy. Muscle relaxation may confound interpretation of entropy monitoring.

Adult↗

PubMed2001

Solvent entropy-driven searching for protein modeling examined and tested in simplified models.

Solvent entropy is a force to consider in protein folding and protein design but is difficult to model. It is investigated here in the context of the hp model: Two types of residues, hydrophobic and hydrophilic, are modeled on a lattice. Nine chains and two- and three-dimensional simulations are compared. We show that considering solvent entropy alone, efficient folding of lattice chains (identification of the native fold) can be achieved by an entropy-driven simulation on its own. Moreover, in a detailed comparison over a wide range of parameters, entropy-guided searching outperforms an energy-driven search in the model. The combination of energy- and entropy-driven search yields the most efficient searching. It is compared in detail with the above results, indicating also how this solvent shell model may advantageously be implemented in more complex protein modeling simulations.

Computer Simulation↗

PubMed2005

Protein sequence entropy is closely related to packing density and hydrophobicity.

We investigated the correlation between the Shannon information entropy, 'sequence entropy', with respect to the local flexibility of native globular proteins as described by inverse packing density. These are determined at each residue position for a total set of 130 query proteins, where sequence entropies are calculated from each set of aligned residues. For the accompanying aggregate set of 130 alignments, a strong linear correlation is observed between the calculated sequence entropy and the corresponding inverse packing density determined at an associated residue position. This region of linearity spans the range of C(alpha) packing densities from 12 to 25 amino acids within a sphere of 9 angstrom radius. Three different hydrophobicity scales all mimic the behavior of the sequence entropies. This confirms the idea that the ability to accommodate mutations is strongly dependent on the available space and on the propensity for each amino acid type to be buried. Future applications of these types of methods may prove useful in identifying both core and flexible residues within a protein.

Entropy↗

PubMed2006

Comparison of entropy and complexity measures for the assessment of depth of sedation.

Entropy and complexity of the electroencephalogram (EEG) have recently been proposed as measures of depth of anesthesia and sedation. Using surrogate data of predefined spectrum and probability distribution we show that the various algorithms used for the calculation of entropy and complexity actually measure different properties of the signal. The tested methods, Shannon entropy (ShEn), spectral entropy, approximate entropy (ApEn), Lempel-Ziv complexity (LZC), and Higuchi fractal dimension (HFD) are then applied to the EEG signal recorded during sedation in the intensive care unit (ICU). It is shown that the applied measures behave in a different manner when compared to clinical depth of sedation score--the Ramsay score. ShEn tends to increase while the other tested measures decrease with deepening sedation. ApEn, LZC, and HFD are highly sensitive to the presence of high-frequency components in the EEG signal.

Adult↗

PubMed2002

Substrate entropy in enzyme enantioselectivity: an experimental and molecular modeling study of a lipase.

The temperature dependence of the enantioselectivity of Candida antarctica lipase B for 3-hexanol, 2-butanol, 3-methyl-2-butanol, 3,3-dimethyl-2-butanol, and 1-bromo-2-butanol revealed that the differential activation entropy, deltaR-SdeltaS, was as significant as the differential activation enthalpy, DeltaR-SdeltaH, to the enantiomeric ratio, E. 1-Bromo-2-butanol, with isosteric substituents, displayed the largest deltaR-SdeltaS. 3-Hexanol displayed, contrary to other sec-alcohols, a positive deltaR-SdeltaS. In other words, for 3-hexanol the preferred R-enantiomer is not only favored by enthalpy but also by entropy. Molecular dynamics (MD) simulations and systematic search calculations of the substrate accessible volume within the active site revealed that the (R)-3-hexanol transition state (TS) accessed a larger volume within the active site than the (S)-3-hexanol TS. This correlates well with the higher TS entropy of (R)-3-hexanol. In addition, this enantiomer did also yield a higher number of allowed conformations, N, from the systematic search routines, than did the S-enantiomer. The substrate accessible volume was greater for the enantiomer preferred by entropy also for 2-butanol. For 3,3-dimethyl-2-butanol, however, neither MD-simulations nor systematic search calculations yielded substrate accessible volumes that correlate to TS entropy. Ambiguous results were achieved for 3-methyl-2-butanol.

Alcohols↗

PubMed2004

Entropy during propofol hypnosis, including an episode of wakefulness.

Depth of anaesthesia has proved to be a complex process to quantify. Monitors based on bispectral analysis of the electroencephalogram and auditory evoked potential have been available, but only recently has a monitor based on entropy become available. This study determined state entropy and response entropy in nine healthy volunteers during propofol hypnosis with a brief intervening period of wakefulness. Both the calculated entropy indices decreased with increasing levels of sedation (r2 = 0.58 and 0.61, respectively) and they showed a high correlation with each other (r2 = 0.94). However, an overlap was observed in real time indices between different stages of the Observer's Assessment of Alertness/Sedation Scale. Only three of the nine volunteers had explicit memories from the episode of wakefulness. Electroencephalographic entropy monitors seem to have potential for staging clinical hypnotic effects.

Adolescent↗

PubMed2002

Sample entropy analysis of neonatal heart rate variability.

Abnormal heart rate characteristics of reduced variability and transient decelerations are present early in the course of neonatal sepsis. To investigate the dynamics, we calculated sample entropy, a similar but less biased measure than the popular approximate entropy. Both calculate the probability that epochs of window length m that are similar within a tolerance r remain similar at the next point. We studied 89 consecutive admissions to a tertiary care neonatal intensive care unit, among whom there were 21 episodes of sepsis, and we performed numerical simulations. We addressed the fundamental issues of optimal selection of m and r and the impact of missing data. The major findings are that entropy falls before clinical signs of neonatal sepsis and that missing points are well tolerated. The major mechanism, surprisingly, is unrelated to the regularity of the data: entropy estimates inevitably fall in any record with spikes. We propose more informed selection of parameters and reexamination of studies where approximate entropy was interpreted solely as a regularity measure.

Entropy↗

PubMed2006

Error entropy in classification problems: a univariate data analysis.

Entropy-based cost functions are enjoying a growing attractiveness in unsupervised and supervised classification tasks. Better performances in terms both of error rate and speed of convergence have been reported. In this letter, we study the principle of error entropy minimization (EEM) from a theoretical point of view. We use Shannon's entropy and study univariate data splitting in two-class problems. In this setting, the error variable is a discrete random variable, leading to a not too complicated mathematical analysis of the error entropy. We start by showing that for uniformly distributed data, there is equivalence between the EEM split and the optimal classifier. In a more general setting, we prove the necessary conditions for this equivalence and show the existence of class configurations where the optimal classifier corresponds to maximum error entropy. The presented theoretical results provide practical guidelines that are illustrated with a set of experiments with both real and simulated data sets, where the effectiveness of EEM is compared with the usual mean square error minimization.

Classification↗

PubMed2006

Electroencephalogram--entropy and acupuncture.

Computer-based measuring of the level of sedation and hypnosis is difficult and has proven to be challenging. The electroencephalogram (EEG) has been proposed as a potential method. Response entropy (RE) and state entropy (SE) are multifactor, dimensionless parameters of a new technology of EEG monitoring, and we investigated them for the first time in acupuncture research within this study. Both parameters have been alleged to reflect changes in the clinical state of sedation. Two different acupuncture schemes were tested in a randomized crossover trial with nine healthy volunteers (mean age +/- sd, 28.8 +/- 3.6 yr; 25-36 yr). Applying and stimulating acupuncture needles or performing laserneedle acupuncture at special sedation points decreased RE and SE significantly (P < or = 0.01; paired t-test) compared with the reference interval before acupuncture. In contrast, acupuncture of points for increasing "Qi-energy" did not decrease parameters of entropy. Specific acupuncture schemes produce specific, reproducible, and quantifiable effects on entropy parameters in the EEG. Therefore, entropy measurements during acupuncture seem to be worthy of further evaluation with a larger series of subjects.

Acupuncture Points↗

PubMed2004

Calculation of cyclodextrin binding affinities: energy, entropy, and implications for drug design.

The second generation Mining Minima method yields binding affinities accurate to within 0.8 kcal/mol for the associations of alpha-, beta-, and gamma-cyclodextrin with benzene, resorcinol, flurbiprofen, naproxen, and nabumetone. These calculations require hours to a day on a commodity computer. The calculations also indicate that the changes in configurational entropy upon binding oppose association by as much as 24 kcal/mol and result primarily from a narrowing of energy wells in the bound versus the free state, rather than from a drop in the number of distinct low-energy conformations on binding. Also, the configurational entropy is found to vary substantially among the bound conformations of a given cyclodextrin-guest complex. This result suggests that the configurational entropy must be accounted for to reliably rank docked conformations in both host-guest and ligand-protein complexes. In close analogy with the common experimental observation of entropy-enthalpy compensation, the computed entropy changes show a near-linear relationship with the changes in mean potential plus solvation energy.

Algorithms↗

PubMed2003

Entropy evaluation using the kinetic method: is it feasible?

The kinetic method is one of the most widely used experimental techniques for the measurement of thermochemical parameters by mass spectrometry. Recently it has been realized that it can also be used to determine reaction entropies, but the validity of this approach has not been established. This Perspective evaluates kinetic method plots in cases where there is a significant entropy difference between the competing fragmentation channels (i.e. between sample and reference compounds in the dissociating cluster ion). The concept underlying this study is to calculate mass spectra theoretically, based on known thermochemical parameters and as a function of experimental conditions. This can be done accurately using the RRKM-based MassKinetics software. The resulting mass spectra are then interpreted by the kinetic method, yielding DeltaH and DeltaS values. These values are, in turn, compared with the true values used to generate the calculated mass spectra. The results show that the reaction entropy difference between sample and reference has a very large influence on kinetic method plots. This should always be considered when studying energy-dependent mass spectra (using metastable ions or low- or high-energy collision-induced dissociation (CID)), even if only DeltaH is to be determined. Kinetic method plots are not strictly linear and this becomes a serious issue in the case of small molecules showing a large entropy effect. In such cases, results obtained at a low degree of excitation are more accurate. Energy and entropy effects can be evaluated in a relatively straightforward manner: first, the apparent Gibbs energy (DeltaG(app)) and effective temperature (T(eff)) are determined from kinetic method plots (intercept and slope, respectively), obtained from experiments using various degrees of excitation. Second, the resulting DeltaG(app) is plotted against T(eff), the slope yielding DeltaS while the intercept (extrapolation to zero temperature) yields DeltaH. This data evaluation yields more accurate results than alternative methods used in the literature. The resulting DeltaH values are fairly accurate, with errors, in most cases, <4 kJ mol(-1). On the other hand, DeltaS is systematically underestimated by 20-40%. Empirically scaling DeltaS values determined by the kinetic method by 1.35 results in a DeltaS value within 20% (or 10 J mol(-1) K(-1)) of the theoretical value.

Journal Article↗

PubMed2004

Systematic and random errors in ion affinities and activation entropies from the extended kinetic method.

An evaluation of the extended kinetic method with full entropy analysis was conducted using RRKM theory to simulate data for collision-induced dissociation under single-collision conditions. A rigorous method for analyzing kinetic method data, orthogonal distance regression, is introduced and compared with previous methods in the literature. The results demonstrate that the use of the extended kinetic method is definitely superior to the standard kinetic method, but final ion affinities and activation entropies differ intrinsically from the correct values. Considering the effects of both systematic and random error in Monte Carlo simulations of the full entropy analysis, error distributions of +/-4 to +/-12 kJ mol(-1) for ion affinities and of +/-9 to +/-30 J mol(-1) K(-1) for activation entropy differences are found (+/-2 standard deviations of the sample populations). The systematic errors in ion affinities are larger for systems with large activation entropy differences. These uncertainties do not include any error in the absolute calibration of the reference ion affinity scale. We argue that application of an empirical correction factor is inadvisable.

Journal Article↗

PubMed1993

Aging and mortality: manifestations of increasing informational entropy of the genome?

Information theory has provided insight to the means by which organisms maintain life against the inevitable influence of the second law of thermodynamics. The low entropy content of genetic information is used to harness the energy that an organism in an open system must utilize to maintain its low entropy and life. Redundancy lowers informational entropy, enhances meaning and promotes complexity. The genome is characterized by large quantities of 'redundant' DNA. Longitudinal Gompertzian analysis has shown that 'the rate of loss of vitality' (from the Strehler-Mildvan modification of the Gompertz model of aging and mortality) has remained constant for general and disease-specific mortality. Applying the concepts of information theory to aging and mortality suggests that 'the rate of loss of vitality' may be synonymous with the rate of degradation of redundant genetic information (or alternatively, the rate of increase in informational entropy of the genome). This interpretation is consistent with the hypothesis that genetic instability of repeated DNA sequences may be fundamentally related to the process of aging. Consequently, there may be no specific aging or 'death' genes per se, but rather aging and mortality are the inevitable natural consequence of increasing informational entropy (decreasing redundancy) contained within the genome.

Adolescent↗