SEARCH · PubMed Health

Results for “Entropy”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6Linked to original sources

PubMed2006

Evaluating the conformational entropy of macromolecules using an energy decomposition approach.

We have developed a novel method to compute the conformational entropy of any molecular system via conventional simulation techniques. This method only requires that the total energy of the system is available and that the Hamiltonian is separable, with individual energy terms for the various degrees of freedom. Consequently the method, which we call the energy decomposition (Edcp) approach, is general and applicable to any large polymer in implicit solvent. Edcp is applied to estimate the entropy differences due to the peptide and ester groups in polyalanine and polyalanil ester. Ensembles over a wide range of temperatures were generated by replica exchange molecular dynamics, and densities of states were estimated using the weighted histogram analysis method. The results are compared with those obtained via evaluating the P ln P integral or employing the quasiharmonic approximation, other approaches widely employed to evaluate the entropy of molecular systems. Unlike the former method, Edcp can accommodate the correlations present between separate degrees of freedom. In addition, the Edcp model assumes no specific form for the underlying fluctuations present in the system, in contrast to the quasiharmonic approximation. For the molecules studied, the quasiharmonic approximation is observed to produce a good estimate of the vibrational entropy, but not of the conformational entropy. In contrast, our energy decomposition approach generates reasonable estimates for both of these entropy terms. We suggest that this approach embodies a simple yet effective solution to the problem of evaluating the conformational entropy of large macromolecules in implicit solvent.

Chemistry, Physical↗

PubMed2000

Decreased entropy of symbolic heart rate dynamics during daily activity as a predictor of positive head-up tilt test in patients with alleged neurocardiogenic syncope.

Entropy measures of RR interval variability during daily activity over a 24h period were compared in 30 patients with a positive head-up tilt (HUT) test and 30 patients with a negative HUT test who had a history of alleged neurocardiogenic syncope. Two different entropies, approximate entropy (ApEn) and entropy of symbolic dynamics (SymEn), were employed. In patients showing a positive HUT test, the entropies were significantly decreased when compared with the patients with a negative HUT test. In addition, SymEn in the patients with a negative HUT test was significantly lower than in the normal controls. Discriminant analysis using SymEn could correctly identify 89.3% (520/582) of the 1 h RR interval data of the patients with a positive HUT test regardless of the time of day. Baseline entropies of heart rate dynamics during daily activity were found to be significantly lower in patients with alleged neurocardiogenic syncope and a positive HUT test than in those with the same history but with a negative HUT test. The decreased entropy of symbolic heart rate dynamics may be of predictive value of a positive HUT test in patients with alleged neurocardiogenic syncope.

Adult↗

PubMed2006

A comparison of bispectral index and entropy monitoring, in patients undergoing embolization of cerebral artery aneurysms after subarachnoid haemorrhage.

BACKGROUND: Processed EEG monitoring of anaesthetic depth could be useful in patients receiving general anaesthesia following subarachnoid haemorrhage. We conducted an observational study comparing performance characteristics of bispectral index (BIS) and entropy monitoring systems in these patients. METHODS: Thirty-one patients of the World Federation of Neurosurgeons grades 1 and 2, undergoing embolization of cerebral artery aneurysms following acute subarachnoid haemorrhage, were recruited to have both BIS and entropy monitoring during general anaesthesia. BIS and entropy indices were matched to clinical indicators of anaesthetic depth. Anaesthetists were blinded to the anaesthetic depth monitoring indices. Analysis of data from monitoring devices allowed calculation of prediction probability (P(K)) constants, and receiver operating characteristic (ROC) analysis to be performed. RESULTS: BIS and entropy [response entropy (RE), state entropy (SE)] performed well in their ability to show concordance with clinically observed anaesthetic depth. P(K) values were generally high (BIS 0.966-0.784, RE 0.934-0.663, SE 0.857-0.701) for both forms of monitoring. ROC curve analysis shows a high sensitivity and specificity for all monitoring indices when used to detect the presence or absence of eyelash reflex. Area under curve for BIS, RE and SE to detect the absence or presence of eyelash reflex was 0.932, 0.888 and 0.887, respectively. RE provides earlier warning of return of eyelash reflex than BIS. CONCLUSION: BIS and entropy monitoring perform well in patients who receive general anaesthesia after good grade subarachnoid haemorrhage.

Adult↗

PubMed2005

Entropy and GC Content in the beta-esterase gene cluster of the Drosophila melanogaster subgroup.

We perform spectral entropy and GC content analyses in the beta-esterase gene cluster, including the Est-6 gene and the psiEst-6 putative pseudogene, in seven species of the Drosophila melanogaster species subgroup. psiEst-6 combines features of functional and nonfunctional genes. The spectral entropies show distinctly lower structural ordering for psiEst-6 than for Est-6 in all species studied. Our observations agree with previous results for D. melanogaster and provide additional support to our hypothesis that after the duplication event Est-6 retained the esterase-coding function and its role during copulation, while psiEst-6 lost that function but now operates in conjunction with Est-6 as an intergene. Entropy accumulation is not a completely random process for either gene. Structural entropy is nucleotide dependent. The relative normalized deviations for structural entropy are higher for G than for C nucleotides. The entropy values are similar for Est-6 and psiEst-6 in the case of A and T but are lower for Est-6 in the case of G and C. The GC content in synonymous positions is uniformly higher in Est-6 than in psiEst-6, which agrees with the reduced GC content generally observed in pseudogenes and nonfunctional sequences. The observed differences in entropy and GC content reflect an evolutionary shift associated with the process of pseudogenization and subsequent functional divergence of psiEst-6 and Est-6 after the duplication event.

Animals↗

PubMed2004

Spectral entropy and bispectral index as measures of the electroencephalographic effects of sevoflurane.

BACKGROUND: Recently, entropy algorithms have been proposed as electroencephalographic measures of anesthetic drug effects. Datex-Ohmeda (Helsinki, Finland) introduced the Entropy Module, a new electroencephalographic monitor designed for measuring depth of anesthesia. The monitor calculates a state entropy (SE) computed over the frequency range of 0.8-32 Hz and a response entropy (RE) computed over the frequency range of 0.8-47 Hz. The authors investigated the dose-response relation of SE and RE during sevoflurane anesthesia in comparison with the Bispectral Index (BIS). METHODS: Sixteen patients were studied without surgical stimulus. Anesthesia was induced by sevoflurane inhalation with a tight-fitting facemask. Sevoflurane concentrations were increased and subsequently decreased and increased two to four times until the measurement was stopped and patients were intubated for surgery. The performances of SE, RE, and BIS to predict the estimated sevoflurane effect site concentration, obtained by simultaneous pharmacokinetic and pharmacodynamic modeling, were compared by calculating the correlation coefficients and the prediction probability. RESULTS: State entropy, RE, and BIS values decreased continuously over the observed concentration range of sevoflurane. Correlation coefficients were slightly but not significantly better for entropy parameters (0.87 +/- 0.09 and 0.86 +/- 0.10 for SE and RE, respectively) than for BIS (0.85 +/- 0.12). Calculating the prediction probability confirmed these results with a prediction probability of 0.84 +/- 0.05 and 0.82 +/- 0.06 for SE and RE, respectively, and 0.80 +/- 0.06 for BIS. CONCLUSION: State entropy and RE seem to be useful electroencephalographic measures of sevoflurane drug effect.

Adult↗

PubMed2004

Minimum entropy clustering and applications to gene expression analysis.

Clustering is a common methodology for analyzing the gene expression data. In this paper, we present a new clustering algorithm from an information-theoretic point of view. First, we propose the minimum entropy (measured on a posteriori probabilities) criterion, which is the conditional entropy of clusters given the observations. Fano's inequality indicates that it could be a good criterion for clustering. We generalize the criterion by replacing Shannon's entropy with Havrda-Charvat's structural alpha-entropy. Interestingly, the minimum entropy criterion based on structural alpha-entropy is equal to the probability error of the nearest neighbor method when alpha = 2. This is another evidence that the proposed criterion is good for clustering. With a non-parametric approach for estimating a posteriori probabilities, an efficient iterative algorithm is then established to minimize the entropy. The experimental results show that the clustering algorithm performs significantly better than k-means/medians, hierarchical clustering, SOM, and EM in terms of adjusted Rand index. Particularly, our algorithm performs very well even when the correct number of clusters is unknown. In addition, most clustering algorithms produce poor partitions in presence of outliers while our method can correctly reveal the structure of data and effectively identify outliers simultaneously.

Algorithms↗

PubMed2006

Renyi entropy measures of heart rate Gaussianity.

Sample entropy and approximate entropy are measures that have been successfully utilized to study the deterministic dynamics of heart rate (HR). A complementary stochastic point of view and a heuristic argument using the Central Limit Theorem suggests that the Gaussianity of HR is a complementary measure of the physiological complexity of the underlying signal transduction processes. Renyi entropy (or q-entropy) is a widely used measure of Gaussianity in many applications. Particularly important members of this family are differential (or Shannon) entropy (q = 1) and quadratic entropy (q = 2). We introduce the concepts of differential and conditional Renyi entropy rate and, in conjunction with Burg's theorem, develop a measure of the Gaussianity of a linear random process. Robust algorithms for estimating these quantities are presented along with estimates of their standard errors.

Algorithms↗

PubMed2005

An improved experimental system for determining small folding entropy changes resulting from proline to alanine substitutions.

Changes in protein stability can be achieved by making substitutions that increase or decrease the available conformations of the unfolded protein without altering the conformational freedom of the folded protein. Matthews and coworkers (1987) proposed that proline to alanine (P --> A) substitution would achieve this type of entropic destabilization. By comparing the Ramachandran area associated with alanine and proline residues, Matthews et al. estimated the unfolding entropy change resulting from P --> A substitution to be 4.8 cal mol(-1) K(-1). Although such an entropy difference would produce a substantial free energy change, accurately resolving such free energy changes into entropic and enthalpic components has been difficult. Here, we attempt to quantify the unfolding entropy change produced by P --> A substitution by amplifying the effect through multiple substitutions, and by decreasing the uncertainty in determining the unfolding entropy. Variants of a repeat protein, the Drosophila Notch ankyrin domain, were constructed with a varying number of P --> A substitutions at structurally conserved positions. Unfolding entropy values of the variants were determined from free energy measurements taken over a common temperature range using chemical denaturation. Our findings confirm the prediction that increasing the number of proline residues present in similar local environments increases the unfolding entropy. The average value of this increase in unfolding entropy is 7.7 +/- 4.2 cal mol(-1) K(-1), which is within error of the value estimated by Matthews et al. (1987).

Alanine↗

PubMed1998

Entropy measures of heart rate variation in conscious dogs.

Our goal was to determine the contributions of sympathetic and parasympathetic activity to entropy measures of heart rate variability (HRV). We compared our results with two commonly used methods to analyze HRV: standard deviation (SDNN) and power spectral analysis (HF norm). Beat-by-beat analysis of R-R intervals was performed in conscious dogs. The R-R intervals were analyzed with approximate entropy (ApEn) and entropy of symbolic dynamics (SymDyn) to assess the effects of reducing system complexity. This was achieved by pharmacologically inhibiting sympathetic, parasympathetic, and total autonomic nervous system regulation of heart rate. Three conditions were examined: rest, standing, and systemic hypotension. At rest or standing, sympathetic inhibition (propranolol) had no effect on ApEn or SymDyn, whereas parasympathetic (atropine) and combined (propranolol + atropine) inhibition reduced both entropy measures to near zero. Systemic hypotension reduced both entropy measures in intact dogs. When hypotension was induced after sympathetic inhibition, ApEn was increased compared with hypotension alone, whereas parasympathetic inhibition with hypotension resulted in near-zero ApEn. Changes in the entropy measures of HRV were directionally similar to changes in SDNN and HF norm. These results indicate that the entropy of R-R intervals reflects parasympathetic modulation of heart rate.

Animals↗

PubMed2006

A comparison of state and response entropy versus bispectral index values during the perioperative period.

Cerebral monitoring indices are associated with a large degree of inter-patient variability and electrical signal interference during surgery. We designed this clinical study to test the hypothesis that use of the spectral entropy (Entropy) module is associated with less frequent intraoperative interference with the displayed indices than the bispectral index (BIS) monitor when used during general anesthesia with propofol and desflurane. Thirty consenting patients scheduled for major laparoscopic surgery procedures were enrolled in this prospective study. The elapsed time to obtain a baseline index value was recorded, as well as the simultaneous state entropy (SE), response entropy (RE), and BIS values at specific time intervals during the induction, maintenance, and emergence periods in patients administered a standardized general anesthetic technique. During the maintenance period, the changes in these indices were evaluated after a bolus dose of propofol (20 mg IV) and a 2% increase or decrease in the inspired concentration of desflurane. As expected, the baseline SE values were less than the RE and BIS values (88 +/- 2 versus 96 +/- 3 and 96 +/- 4, respectively). However, the SE and RE values correlated with the BIS value during the induction (r = 0.77 and 0.78, respectively) and emergence (r = 0.86 and 0.91, respectively) periods. The area under the receiver operating characteristic curve for detection of consciousness also indicated a similar performance of the SE (0.93 +/- 0.04) relative to the RE (0.98 +/- 0.04) and BIS (0.97 +/- 0.04). During the maintenance period, the responses to changes in propofol and desflurane concentrations were consistent with all three indices. Finally, the entropy indices were less interfered with by the electrocautery unit during the operation (12% versus 62% for the BIS monitor). Because the average selling prices of the Entropy and BIS disposable electrode strips (14.25 dollars versus 14.95 dollars USD, respectively) are comparable, we conclude that the Entropy module is a cost-equivalent alternative to the BIS monitor.

Adult↗

PubMed2005

Induced fit and the entropy of structural adaptation in the complexation of CAP and lambda-repressor with cognate DNA sequences.

Molecular dynamics (MD) simulations of 5 ns on protein-DNA complexes of catabolite-activator protein (CAP), lambda-repressor, and their corresponding uncomplexed protein and DNA, are reported. These cases represent two extremes of DNA bending, with CAP DNA bent severely and the lambda-operator nearly straight when complexed with protein. The calculations were performed using the AMBER suite of programs and the parm94 force field, validated for these studies by good agreement with experimental nuclear magnetic resonance data on DNA. An explicit computational model of structural adaptation and computation of the quasiharmonic entropy of association were obtained from the MD. The results indicate that, with respect to canonical B-form DNA, the extreme bending of the DNA in the complex with CAP is approximately 60% protein-induced and 40% intrinsic to the sequence-dependent structure of the free oligomer. The DNA in the complex is an energetically strained form, and the MD results are consistent with a conformational-capture mechanism. The calculated quasiharmonic entropy change accounts for the entropy difference between the two cases. The calculated entropy was decomposed into contributions from protein adaptation, DNA adaptation, and protein-DNA structural correlations. The origin of the entropy difference between CAP and lambda-repressor complexation arises more from the additional protein adaptation in the case of lambda, than to DNA bending and entropy contribution from DNA bending. The entropy arising from protein DNA cross-correlations, a contribution not previously discussed, is surprisingly large.

Allosteric Site↗

PubMed2006

Configurational entropy change of netropsin and distamycin upon DNA minor-groove binding.

Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.

Binding Sites↗

PubMed2001

On weighted exponential entropies.

As an alternative to Shannon's classical entropy measure of information, an exponential entropy function was proposed by Pal and Pal in 1989 and 1991. To generalize Pal's entropy further, this author introduced two different families of exponential entropies that are one-parameter generalizations of Pal's entropy. The purpose of the present paper is to define weighted entropies corresponding to those one-parameter generalizations. Some properties and examples of such weighted exponential entropies are discussed.

Entropy↗

PubMed1993

Empirical scale of side-chain conformational entropy in protein folding.

A major effect in the energetics of protein folding is the loss of conformational entropy of the side-chains. The definition of entropy as the Boltzmann sampling over all states (S = -R sigma p(i) ln p(i)) requires evaluation of the probability (p(i)) of the system being in rotameric state i. The principle of this paper is to obtain an estimate of p(i) from the observed distribution of exposed side-chain rotamers in 50 non-homologous protein crystal structures. However because of limited data we show that for all side-chains except Asn, Asp and Glu the side-chain distribution is independent of burial and accordingly all data were pooled in the calculation of p(i). For Asn, Asp and Glu side-chains with relative accessibility > 60% were used. The scale includes effects due to the symmetry of side-chains such as Phe and the free rotation of side-chain amide, carboxyl and hydroxyl groups. An empirical scale for the loss of side-chain conformational entropy during protein folding is thereby obtained. Values of the change in free energy due to entropy (-T delta S) on burying a side-chain range from 0 for Ala, Gly and Pro to +2.1 kcal/mol for Gln (T = 300 K). We explore the consistency of a simple model for protein folding that includes side-chain entropy, main-chain entropy, hydrophobicity and hydrogen bonding. The stability of site-directed mutations is discussed in terms of conformational entropy.

Models, Chemical↗

PubMed1993

Entropy and convergence in dynamics and demography.

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.

Demography↗

PubMed1993

Configurational entropy is the driving force of ethanol action on membrane architecture.

A colligative thermodynamic framework is developed to describe the action of ethanol on membranes. The partitioning of ethanol into a membrane structure imparts a randomness, configurational entropy, that stabilizes that structure from an energetic standpoint. When partitioning between membrane structures differs, the equilibrium between them is altered to favor the structure with the largest partition coefficient for ethanol. The action of ethanol and temperature originate in entropy and are equated through entropy. Membrane equilibria that are predicted to be most sensitive to the action of ethanol (where dilute concentrations of ethanol cause a perturbation equal to a large change in temperature) are those that exhibit a small thermal entropy change and a large difference in solute partitioning between membrane structures. Our model predicts that ethanol does not act on a single membrane structure, but on both structures in an equilibrium. The thermodynamic framework is applied to the action of ethanol on cooperative equilibria in a dipalmitoyl lecithin model membrane. Ethanol-induced perturbations are monitored by electron paramagnetic resonance (EPR) using the spin label, Tempo. The equilibrium between the gel and ripple-structures (L beta'-->P beta', pretransition) exhibits a small change in thermal entropy and, as predicted, is more sensitive to the action of ethanol than the equilibrium between the ripple and fluid bilayer-structures (P beta'-->L alpha, main transition) which exhibits a large thermal entropy change. The framework suggests that ethanol acts through entropy, as does temperature, thereby upsetting the natural thermal balance that maintains membrane architecture.

Chemical Phenomena↗

PubMed2003

A measure of conformational entropy change during thermal protein unfolding using neutron spectroscopy.

Thermal unfolding of proteins at high temperatures is caused by a strong increase of the entropy change which lowers Gibbs free energy change of the unfolding transition (DeltaG(unf) = DeltaH - TDeltaS). The main contributions to entropy are the conformational entropy of the polypeptide chain itself and ordering of water molecules around hydrophobic side chains of the protein. To elucidate the role of conformational entropy upon thermal unfolding in more detail, conformational dynamics in the time regime of picoseconds was investigated with neutron spectroscopy. Confined internal structural fluctuations were analyzed for alpha-amylase in the folded and the unfolded state as a function of temperature. A strong difference in structural fluctuations between the folded and the unfolded state was observed at 30 degrees C, which increased even more with rising temperatures. A simple analytical model was used to quantify the differences of the conformational space explored by the observed protein dynamics for the folded and unfolded state. Conformational entropy changes, calculated on the basis of the applied model, show a significant increase upon heating. In contrast to indirect estimates, which proposed a temperature independent conformational entropy change, the measurements presented here, demonstrated that the conformational entropy change increases with rising temperature and therefore contributes to thermal unfolding.

Bacillus↗

PubMed2005

Exact solutions for the entropy production rate of several irreversible processes.

We investigate thermal conduction described by Newton's law of cooling and by Fourier's transport equation and chemical reactions based on mass action kinetics where we detail a simple example of a reaction mechanism with one intermediate. In these cases we derive exact expressions for the entropy production rate and its differential. We show that at a stationary state the entropy production rate is an extremum if and only if the stationary state is a state of thermodynamic equilibrium. These results are exact and independent of any expansions of the entropy production rate. In the case of thermal conduction we compare our exact approach with the conventional approach based on the expansion of the entropy production rate near equilibrium. If we expand the entropy production rate in a series and keep terms up to the third order in the deviation variables and then differentiate, we find out that the entropy production rate is not an extremum at a nonequilibrium steady state. If there is a strict proportionality between fluxes and forces, then the entropy production rate is an extremum at the stationary state even if the stationary state is far away from equilibrium.

Journal Article↗