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 613 records · Page 34Linked to original sources

PubMed2004

Normalized mutual entropy in biology: quantifying division of labor.

Division of labor is one of the primary adaptations of sociality and the focus of much theoretical work on self-organization. This work has been hampered by the lack of a quantitative measure of division of labor that can be applied across systems. We divide Shannon's mutual entropy by marginal entropy to quantify division of labor, rendering it robust over changes in number of individuals or tasks. Reinterpreting individuals and tasks makes this methodology applicable to a wide range of other contexts, such as breeding systems and predator-prey interactions.

Animals↗

PubMed2005

Quantification of synchronization during atrial fibrillation by Shannon entropy: validation in patients and computer model of atrial arrhythmias.

Atrial fibrillation (AF), a cardiac arrhythmia classically described as completely desynchronized, is now known to show a certain amount of synchronized electrical activity. In the present work a new method for quantifying the level of synchronization of the electrical activity recorded in pairs of atrial sites during atrial fibrillation is presented. A synchronization index (Sy) was defined by quantifying the degree of complexity of the distribution of the time delays between sites by Shannon entropy estimation. The capability of Sy to discriminate different AF types in patients was assessed on a database of 60 pairs of endocardial recordings from a multipolar basket catheter. The analysis showed a progressive and significant decrease of Sy with increasing AF complexity classes as defined by Wells (AF type I Sy = 0.73 +/- 0.07, type II Sy = 0.56 +/- 0.07, type III Sy = 0.36 +/- 0.04, p < 0.001). The extension of Sy calculation to the whole right atrium showed the existence of spatial heterogeneities in the synchronization level. Moreover, experiments simulated by a computer model of atrial arrhythmias showed that propagation patterns with different complexity could be the basis of different synchronization levels found in patients. In conclusion the quantification of synchronization by Shannon entropy estimation of time delay dispersion may facilitate the identification of different propagation patterns associated with AF, thus enhancing our understanding of AF mechanisms and helping in its treatment.

Algorithms↗

PubMed2006

Entropy analysis of the EEG background activity in Alzheimer's disease patients.

Alzheimer's disease (AD) is the most common neurodegenerative disorder. Although a definite diagnosis is only possible by necropsy, a differential diagnosis with other types of dementia and with major depression should be attempted. The aim of this study was to analyse the electroencephalogram (EEG) background activity of AD patients to test the hypothesis that the regularity of the AD patients' EEG is higher than that of age-matched controls. We recorded the EEG from 19 scalp electrodes in 11 AD patients and 11 age-matched controls. Two different methods were used to estimate the regularity of the EEG background activity: spectral entropy (SpecEn) and sample entropy (SampEn). We did not find significant differences between AD patients and control subjects' EEGs with SpecEn. On the other hand, AD patients had significantly lower SampEn values than control subjects (p < 0.01) at electrodes P3, P4, O1 and O2. Our results show an increase of EEG regularity in AD patients. These findings suggest that nonlinear analysis of the EEG with SampEn could yield essential information and may contribute to increasing the insight into brain dysfunction in AD in ways which are not possible with more classical and conventional statistical methods.

Aged↗

PubMed1999

Significantly lower entropy estimates for natural DNA sequences.

If DNA were a random string over its alphabet {A, C, G, T}, an optimal code would assign two bits to each nucleotide. DNA may be imagined to be a highly ordered, purposeful molecule, and one might therefore reasonably expect statistical models of its string representation to produce much lower entropy estimates. Surprisingly, this has not been the case for many natural DNA sequences, including portions of the human genome. We introduce a new statistical model (compression algorithm), the strongest reported to date, for naturally occurring DNA sequences. Conventional techniques code a nucleotide using only slightly fewer bits (1.90) than one obtains by relying only on the frequency statistics of individual nucleotides (1.95). Our method in some cases increases this gap by more than fivefold (1.66) and may lead to better performance in microbiological pattern recognition applications. One of our main contributions, and the principle source of these improvements, is the formal inclusion of inexact match information in the model. The existence of matches at various distances forms a panel of experts which are then combined into a single prediction. The structure of this combination is novel and its parameters are learned using Expectation Maximization (EM). Experiments are reported using a wide variety of DNA sequences and compared whenever possible with earlier work. Four reasonable notions for the string distance function used to identify near matches, are implemented and experimentally compared. We also report lower entropy estimates for coding regions extracted from a large collection of nonredundant human genes. The conventional estimate is 1.92 bits. Our model produces only slightly better results (1.91 bits) when considering nucleotides, but achieves 1.84-1.87 bits when the prediction problem is divided into two stages: (i) predict the next amino acid-based on inexact polypeptide matches, and (ii) predict the particular codon. Our results suggest that matches at the amino acid level play some role, but a small one, in determining the statistical structure of nonredundant coding sequences.

Algorithms↗

PubMed2002

A new distance measure for comparing sequence profiles based on path lengths along an entropy surface.

We describe a new distance measure for comparing DNA sequence profiles. For this measure, columns in a multiple alignment are treated as character frequency vectors (sum of the frequencies equal to one). The distance between two vectors is based on minimum path length along an entropy surface. Path length is estimated using a random graph generated on the entropy surface and Dijkstra's algorithm for all shortest paths to a source. We use the new distance measure to analyze similarities within familes of tandem repeats in the C. elegans genome and show that this new measure gives more accurate refinement of family relationships than a method based on comparing consensus sequences.

Algorithms↗

PubMed2004

Caloric restriction, metabolic rate, and entropy.

Caloric restriction increases life span in many types of animals. This article proposes a mechanism for this effect based on the hypothesis that metabolic stability, the capacity of an organism to maintain steady state values of redox couples, is a prime determinant of longevity. We integrate the stability-longevity hypothesis with a molecular model of metabolic activity (quantum metabolism), and an entropic theory of evolutionary change (directionality theory), to propose a proximate mechanism and an evolutionary rationale for aging. The mechanistic features of the new theory of aging are invoked to predict that caloric restriction extends life span by increasing metabolic stability. The evolutionary model is exploited to predict that the large increases in life span under caloric restriction observed in rats, a species with early sexual maturity, narrow reproductive span and large litter size, and hence low entropy, will not hold for primates. We affirm that in the case of humans, a species with late sexual maturity, broad reproductive span and small litter size, and hence high entropy, the response of life span to caloric restriction will be negligible.

Animals↗

PubMed2003

Cholinergic reversal of isoflurane anesthesia in rats as measured by cross-approximate entropy of the electroencephalogram.

BACKGROUND: Pharmacologic modulation of the state of consciousness is of interest for clinical practice and for a better understanding of anesthetic mechanisms. The cholinergic activating system is an important regulator of the state of consciousness during general anesthesia. Entropy of the electroencephalogram has been proposed as a promising measure of anesthetic depth. The authors have shown that volatile anesthetics decrease cross-approximate entropy (C-ApEn) of the bihemispheric frontal electroencephalogram in rats. The effect of cholinergic agents on C-ApEn has not been examined. Here, the authors test the hypothesis that cholinergic activation reverses the effect of isoflurane anesthesia on C-ApEn. METHODS: An electroencephalogram in the 1- to 100-Hz range was recorded bipolarly, with epidural leads from the frontal cortex of both hemispheres, and used to calculate C-ApEn, which reflects statistical independence of bihemispheric electroencephalographic activity. Cholinesterase inhibitor, neostigmine (25 mug), or the muscarinic agonist oxotremorine (25 mug) were infused intracerebroventricularly while the rats were inhaling 1.0% (0.7 minimum alveolar concentration) isoflurane. In other animals, isoflurane was lowered to 0.4% (0.3 minimum alveolar concentration) to assess the electroencephalogram in a sedated, waking state. RESULTS: At 1.0% isoflurane, C-ApEn decreased by 54% compared with that at 0.4%, but the motor reflex response to tail pinch was still present. Cholinergic agents reversed the electroencephalogram-depressant effect of isoflurane, i.e., C-ApEn rose to the level measured at 0.4% isoflurane. The rise in C-ApEn was paralleled by the appearance of spontaneous limb and orofacial explorative movements, suggesting a return of consciousness. In contrast, cholinergic agents fully blocked the motor reflex to tail pinch. CONCLUSIONS: C-ApEn of the bihemispheric electroencephalogram correlates with the return of spontaneous motor signs but not with the nociceptive reflex. Cerebral cholinergic activation dissociates central and peripheral anesthetic effects. C-ApEn, a novel measure of interhemispheric electroencephalogram independence, is a promising correlate of depth of sedation and state of consciousness.

Algorithms↗

PubMed2005

Multiscale entropy analysis of biological signals.

Traditional approaches to measuring the complexity of biological signals fail to account for the multiple time scales inherent in such time series. These algorithms have yielded contradictory findings when applied to real-world datasets obtained in health and disease states. We describe in detail the basis and implementation of the multiscale entropy (MSE) method. We extend and elaborate previous findings showing its applicability to the fluctuations of the human heartbeat under physiologic and pathologic conditions. The method consistently indicates a loss of complexity with aging, with an erratic cardiac arrhythmia (atrial fibrillation), and with a life-threatening syndrome (congestive heart failure). Further, these different conditions have distinct MSE curve profiles, suggesting diagnostic uses. The results support a general "complexity-loss" theory of aging and disease. We also apply the method to the analysis of coding and noncoding DNA sequences and find that the latter have higher multiscale entropy, consistent with the emerging view that so-called "junk DNA" sequences contain important biological information.

Adult↗

PubMed2006

Protein design based on the relative entropy.

An approach to protein design is proposed based on the relative entropy and a reduced amino acid alphabet. In this approach, the relative entropy is used as a minimization object function. The method has been tested on a real protein's off-lattice model successfully, and the results are similar to those obtained from other design studies. It can be applied as a uniform frame for both folding and inverse folding of protein. An iterative calculation method of the ensemble average of the contact strength is proposed at the same time.

Algorithms↗

PubMed2005

Kolmogorov-Sinai entropy of the dilute wet granular gas.

We present an analytical expression for the Kolmogorov-Sinai entropy of a wet granular gas. The influence of the liquid is modeled by a hysteretic interaction force. For the dilute limit (two-particle collisions only), we find a simple expression accounting for the contribution of both the scattering states and the bound states in arbitrary dimensions. It is shown that the system is significantly more chaotic than a gas of (dry) hard spheres, as reflected by a pronounced increase of the Kolmogorov-Sinai entropy.

Algorithms↗

PubMed2006

Maximum-entropy closures for kinetic theories of neuronal network dynamics.

We analyze (1 + 1)D kinetic equations for neuronal network dynamics, which are derived via an intuitive closure from a Boltzmann-like equation governing the evolution of a one-particle (i.e., one-neuron) probability density function. We demonstrate that this intuitive closure is a generalization of moment closures based on the maximum-entropy principle. By invoking maximum-entropy closures, we show how to systematically extend this kinetic theory to obtain higher-order, kinetic equations and to include coupled networks of both excitatory and inhibitory neurons.

Algorithms↗

PubMed2005

Surface-entropy reduction used in the crystallization of human choline acetyltransferase.

Human choline acetyltransferase (ChAT) synthesizes the neurotransmitter acetylcholine (ACh) from choline and acetyl-CoA. A crystal structure of human ChAT has been a long-standing goal in the neuronal signalling field. Milligram quantities of pure ChAT can be purified [Kim et al. (2005), Protein Expr. Purif. 40, 107-117], but exhaustive crystallization efforts failed to produce any crystals suitable for high-resolution structural studies. To obtain high-quality crystals of human ChAT, a truncation was made in a large poorly conserved loop region and high-entropy side chains were removed from the surface of the protein. The resulting 'entropy-reduced' ChAT (MR = 68.1 kDa) crystallizes readily and reproducibly and the crystals diffract X-rays to approximately 2.2 A. The availability of these crystals will allow us to study the structure of human ChAT on its own as well as in complex with its substrates and inhibitor molecules, leading to a greater understanding of its catalytic mechanism and regulation.

Choline O-Acetyltransferase↗

PubMed1997

Maximum entropy method for magnetoencephalography.

Simulations show that the maximum entropy method is a promising technique for image reconstruction in magnetoencephalography. An algorithm based on the work of Skilling and Bryan [1] and an appropriately modified expression for the "entropy" is shown to provide high-quality reconstructions of both isolated and dense distributions of neural current "dipoles", neglecting return currents. In particular the results are substantially superior to those obtained with the well-known minimum norm procedure.

Artifacts↗

PubMed2005

Monitoring of global cerebral ischemia using wavelet entropy rate of change.

In this paper, the subband wavelet entropy (SWE) and its time difference are proposed as two quantitative measures for analyzing and segmenting the electroencephalographic (EEG) signals. SWE for EEG subbands, namely Delta, Theta, Alpha, Beta, and Gamma, is calculated and segmented using wavelet analysis. In addition, a time difference entropy measure was calculated because it does not require a baseline and equals to zero in all clinical bands as the initial condition. Visual and quantitative results were obtained from 11 rodents that were subjected to 3, 5, and 7 min of global ischemic brain injury by asphyxic cardiac arrest. We found that the time difference of SWE is capable of amplifying the variations between clinical bands during the various stages of the recovery process and may serve as a novel analytical approach to grade and classify brain rhythms during global ischemic brain injury and recovery.

Algorithms↗

PubMed2004

Learning mixture models with the regularized latent maximum entropy principle.

This paper presents a new approach to estimating mixture models based on a recent inference principle we have proposed: the latent maximum entropy principle (LME). LME is different from Jaynes' maximum entropy principle, standard maximum likelihood, and maximum aposteriori probability estimation. We demonstrate the LME principle by deriving new algorithms for mixture model estimation, and show how robust new variants of the expectation maximization (EM) algorithm can be developed. We show that a regularized version of LME (RLME), is effective at estimating mixture models. It generally yields better results than plain LME, which in turn is often better than maximum likelihood and maximum a posterior estimation, particularly when inferring latent variable models from small amounts of data.

Algorithms↗

PubMed2002

Side-chain conformational entropy at protein-protein interfaces.

Protein-protein interactions are the key to many biological processes. How proteins selectively and correctly associate with their required protein partner(s) is still unclear. Previous studies of this "protein-docking problem" have found that shape complementarity is a major determinant of interaction, but the detailed balance of energy contributions to association remains unclear. This study estimates side-chain conformational entropy (per unit solvent accessible area) for various protein surface regions, using a self-consistent mean field calculation of rotamer probabilities. Interfacial surface regions were less flexible than the rest of the protein surface for calculations with monomers extracted from homodimer datasets in 21 of 25 cases, and in 8 of 9 for the large protomer from heterodimer datasets. In surface patch analysis, based on side-chain conformational entropy, 68% of true interfaces were ranked top for the homodimer set and 66% for the large protomer/heterodimer set. The results indicate that addition of a side-chain entropic term could significantly improve empirical calculations of protein-protein association.

Binding Sites↗

PubMed2003

The effect of the polyproline II (PPII) conformation on the denatured state entropy.

Polyproline II (PPII) is reported to be a dominant conformation in the unfolded state of peptides, even when no prolines are present in the sequence. Here we use isothermal titration calorimetry (ITC) to investigate the PPII bias in the unfolded state by studying the binding of the SH3 domain of SEM-5 to variants of its putative PPII peptide ligand, Sos. The experimental system is unique in that it provides direct access to the conformational entropy change of the substituted amino acids. Results indicate that the denatured ensemble can be characterized by at least two thermodynamically distinct states, the PPII conformation and an unfolded state conforming to the previously held idea of the denatured state as a random collection of conformations determined largely by hard-sphere collision. The probability of the PPII conformation in the denatured states for Ala and Gly were found to be significant, approximately 30% and approximately 10%, respectively, resulting in a dramatic reduction in the conformational entropy of folding.

Alanine↗

PubMed2001

Rational design of enantioselective enzymes requires considerations of entropy.

Entropy was shown to play an equally important role as enthalpy for how enantioselectivity changes when redesigning an enzyme. By studying the temperature dependence of the enantiomeric ratio E of an enantioselective enzyme, its differential activation enthalpy (Delta(R-S)DeltaH(++)) and entropy (Delta(R-S)DeltaS(++)) components can be determined. This was done for the resolution of 3-methyl-2-butanol catalyzed by Candida antarctica lipase B and five variants with one or two point mutations. Delta(R-S)DeltaS(++) was in all cases equally significant as Delta(R-S)DeltaH(++) to E. One variant, T103G, displayed an increase in E, the others a decrease. The altered enantioselectivities of the variants were all related to simultaneous changes in Delta(R-S)DeltaH(++) and Delta(R-S)DeltaS(++). Although the changes in Delta(R-S)DeltaH(++) and Delta(R-S)DeltaS(++) were of a compensatory nature the compensation was not perfect, thereby allowing modifications of E. Both the W104H and the T103G variants displayed larger Delta(R-S)DeltaH(++) than wild type but exhibited a decrease or increase, respectively, in E due to their different relative increase in Delta(R-S)DeltaS(++).

Candida↗