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PubMed2025

Multiscale dispersion entropy of resting-state EEG in older adults with Alzheimer's disease, mild cognitive impairment, and remitted major depressive disorder.

BackgroundMultiscale dispersion entropy (MDEnt) is a nonlinear EEG measure that quantifies brain complexity across time scales, reflecting both local and global brain dynamics. Previous research indicates lower complexity at short time scales in Alzheimer's disease (AD) compared to mild cognitive impairment (MCI) and healthy controls (HCs), with MCI also showing lower values than HCs. Major depressive disorder (MDD) has also been preliminarily linked to reduced complexity during acute episodes.ObjectiveTo assess whether MDEnt at short time scales can distinguish AD from MCI and HCs, and to examine complexity differences across additional groups, remitted MDD (rMDD) and rMDD + MCI, while exploring associations with cognitive performance.MethodsThe study included 316 older adults: 44 HCs, 46 with rMDD, 114 with MCI, 71 with rMDD + MCI, and 41 with AD. Resting-state, eyes-closed EEGs were analyzed using MDEnt at 24 ms (short) and 60 ms (long) time scales. Cognitive function was measured with the Montreal Cognitive Assessment and a composite cognitive score.ResultsShort time scale complexity was lowest in AD, followed by MCI, and highest in HCs; rMDD presence had no impact. Only AD showed reduced complexity at long time scales. Complexity at both time scales was significantly correlated with cognitive performance.ConclusionsThis study highlights the value of MDEnt to assess complexity at short time scale and differentiate individuals with AD, MCI, or HCs. Reduced complexity in these individuals may underlie their cognitive impairment. In contrast, our study suggests that any MDD impact on complexity is likely related to active depressive symptoms.

Humans↗

PubMed1999

Maximum entropy methods in electron crystallography.

The maximum entropy (ME) method of solving crystal structures in two or three dimensions from electron diffraction data is described. Applications to organic and inorganic molecules, membrane proteins and surface structures are outlined, and the power of the ME formalism to deal with incomplete and error prone data is demonstrated.

Bacterial Proteins↗

PubMed1999

A minimax entropy registration framework for patient setup verification in radiotherapy.

In external beam radiotherapy (EBRT), patient setup verification over the entire course of fractionated treatment is necessary for accurate delivery of a specified dose to the tumor. We are working on the development of a minimax entropy registration framework for patient setup verification using dual portal images and the treatment planning 3D CT dataset. In this paper, we present an overview of our registration framework, where an iteratively and automatically estimated segmentation of the portal image is utilized to more accurately and robustly register the portal image to the 3D treatment-planning CT data. In addition, we describe initial testing of this approach. We note that, due to low resolution and low contrast of the portal images, this registration presents a difficult problem. We also note that the registration of the images in our proposed method is guided by the bony structure visible in the portal and the 3D CT images. However, since the prostate can move with respect to the pelvic bone, we propose using ultrasound images to quantify this movement.

Algorithms↗

PubMed2003

Entropy and information in flagellar axoneme cybernetics: a radial spokes integrative function.

Radial spokes and the consequences of their relationships with the central apparatus seem to play a very important role in the regulation of axonemal activity. We modeled their behavior and observed that it appears to differ in the cilium and the flagellum with respect to the development of bending as a function of time. Specifically, our calculation raises the question of the real function of the radial spokes in the regulation of the axoneme, because a given curvature of the flagellar axoneme may correspond to two opposite of their tilts. The stable nil/low amplitude shear points that we had characterized along the flagellum allowed us to describe their axoneme as a series of modules [Cibert, 2002: Cell Motil. Cytoskeleton 51:89-111]. We observed that a nil/low shearing point moves along each module during beating when a new bend is created at the base of the flagellum [Cibert, 2001: Cell Motil. Cytoskeleton 49:161-175]. We propose that the structural gradients of isoforms of tubulin could be basic verniers that act as structural references for the axonemal machinery during the beating. This allowed us to interpret the axonemal organization as a segmented structure, that could be analyzed according to the complexion(1) theory and Shannon's information theory, which associate entropy and probability in the creation of information. The important consequence of this interpretation is that regulation of the axonemal machinery appears to be due to the upstream and downstream cross-talk between the axonemal segments that do not involve any dedicated integrative structure but depend on the energy level of the entire length of each module.

Biomechanical Phenomena↗

PubMed2004

Nonclassical splicing mutations in the coding and noncoding regions of the ATM Gene: maximum entropy estimates of splice junction strengths.

Ataxia-telangiectasia (A-T) is an autosomal recessive neurological disorder caused by mutations in the ATM gene. Classical splicing mutations (type I) delete entire exons during pre-mRNA splicing. In this report, we describe nine examples of nonclassical splicing mutations in 12 A-T patients and compare cDNA changes to estimates of splice junction strengths based on maximum entropy modeling. These mutations fall into three categories: pseudoexon insertions (type II), single nucleotide changes within the exon (type III), and intronic changes that disrupt the conserved 3' splice sequence and lead to partial exon deletion (type IV). Four patients with a previously reported type II (pseudoexon) mutation all shared a common founder haplotype. Three patients with apparent missense or silent mutations actually had type III aberrant splicing and partial deletion of an exon. Five patients had type IV mutations that could have been misinterpreted as classical splicing mutations. Instead, their mutations disrupt a splice site and use another AG splice site located nearby within the exon; they lead to partial deletions at the beginning of exons. These nonclassical splicing mutations create frameshifts that result in premature termination codons. Without screening cDNA or using accurate models of splice site strength, the consequences of these genomic mutations cannot be reliably predicted. This may lead to further misinterpretation of genotype-phenotype correlations and may subsequently impact upon gene-based therapeutic approaches.

Ataxia Telangiectasia↗

PubMed2001

Allosteric transition and substrate binding are entropy-driven in glucosamine-6-phosphate deaminase from Escherichia coli.

Glucosamine-6P-deaminase (EC 3.5.99.6, formerly glucosamine-6-phosphate isomerase, EC 5.3.1.10) from Escherichia coli is an attractive experimental model for the study of allosteric transitions because it is both kinetically and structurally well-known, and follows rapid equilibrium random kinetics, so that the kinetic K(m) values are true thermodynamic equilibrium constants. The enzyme is a typical allosteric K-system activated by N-acetylglucosamine 6-P and displays an allosteric behavior that can be well described by the Monod-Wyman-Changeux model. This thermodynamic study based on the temperature dependence of allosteric parameters derived from this model shows that substrate binding and allosteric transition are both entropy-driven processes in E. coli GlcN6P deaminase. The analysis of this result in the light of the crystallographic structure of the enzyme implicates the active-site lid as the structural motif that could contribute significantly to this entropic component of the allosteric transition because of the remarkable change in its crystallographic B factors.

Acetylglucosamine↗

PubMed1999

Temperature dependence of intramolecular dynamics of the basic leucine zipper of GCN4: implications for the entropy of association with DNA.

The basic leucine zipper domain of the yeast transcription factor GCN4 consists of a C-terminal leucine zipper and an N-terminal basic DNA-binding region that achieves a stable structure only after association with DNA. Backbone dynamics of a peptide encompassing the basic and leucine zipper bZip domain (residues 226-281) are described using NMR spectroscopy. The 15N longitudinal relaxation rates, 15N transverse relaxation rates, and {1H}-15N nuclear Overhauser effects were measured for the backbone amide nitrogen atoms at 290 K, 300 K, and 310 K. The relaxation data were interpreted using reduced spectral density mapping to determine values of the spectral density function, J(omega), at the frequencies 0, omegaN, and 0.87omegaH to characterize overall and intramolecular motions on picosecond-nanosecond timescales. To account for the temperature dependence of overall rotational diffusion, the J(0) values were normalized using Stoke's Law. At 310 K, the 13Calpha and 13CO chemical shifts in conjunction with the spectral density values indicate that the leucine zipper sequence forms a highly ordered alpha-helix, while the basic region populates an ensemble of highly dynamic transient structures with substantial helical character. The normalized values of J(0) and the values of J(0.87omegaH) for residues in the leucine zipper dimerization domain are independent of temperature. In contrast, residues in the basic region exhibit pronounced increases in the normalized J(0) and decreases in J(0.87omegaH) as temperature is decreased. A strong correlation exists between the temperature dependence of 13CO chemical shifts and of J(0.87omegaH). These results suggest that, for the basic region, lowering the temperature increases the population of transient helical conformations, and concomitantly reduces the amplitude or timescale of conformational fluctuations on picosecond-nanosecond timescales. Changes in the conformational dynamics of the peptide backbone of the basic region that accompany DNA binding contribute to the overall thermodynamics of complex formation. The change in backbone conformational entropy derived from NMR spin-relaxation data agrees well with the result calculated from calorimetric measurements. Restriction of the conformational space accessible to the basic region may significantly reduce the entropic cost associated with formation of the basic region helices consequent to DNA binding.

Amino Acid Sequence↗

PubMed2002

Evidence for an internal entropy contribution to phosphoryl transfer: a study of domain closure, backbone flexibility, and the catalytic cycle of cAMP-dependent protein kinase.

While there is no question that ligands can induce large-scale domain movements that narrow (close) the active-site cleft of the catalytic (C) subunit of cAMP-dependent protein kinase (cAPK), the results from small-angle X-ray scattering, protein footprinting, and thermostability studies are inconsistent with regard to which ligands induce these movements. This inconsistency suggests a greater complexity of cAPK conformational dynamics than is generally recognized. As an initial step to study this issue in relation to the catalysis, a new method to measure cAPK domain closure was developed, and the state of domain closure and the local segmental flexibility at major steps of the cAPK catalytic cycle were examined with site-directed labeling and fluorescence spectroscopy. To achieve this, a C subunit mutant (F239C/C199A) was engineered that allowed for fluorescein 5-maleimide (donor) conjugation of F239C in the large lobe and tetramethylrhodamine (acceptor) conjugation of C343 in the small lobe. Domain closure was assessed as an increase in the efficiency of energy transfer between donor and acceptor. The anisotropy decay of fluoroscein 5-maleimide, conjugated to a site of cysteine substitution (K81C) in the small lobe of the C subunit was used to assess the local backbone flexibility around the B helix. The effects of substrate/pseudosubstrate (ATP and PKI(5-24)), a fragment of protein kinase inhibitor) and products (ADP and phosphorylated PKS) on domain closure and B helix flexibility were measured. The results show that domain closure is not tightly coupled to the flexibility around K81C. Moreover, although substrates/pseudosubstrate and products independently close the active-site cleft, only the substrates substantially decreased the backbone flexibility around the B helix. Because this order-to-disorder transition coincides with the phosphoryl transfer transition, the results suggest the existence of an internal entropy contribution to catalysis.

Amino Acid Substitution↗

PubMed1998

Distributed parallel processing for multidimensional maximum entropy reconstruction.

We have developed a two-dimensional maximum entropy spectrum reconstruction program designed to run in parallel on workstation clusters. Test reconstructions of planes extracted from a three-dimensional NMR data set indicate that the parallel speedup is nearly equal to the number of processors provided that the individual processors have comparable performance and that there are at least as many planes as processors. The program also works well in a typical laboratory setting consisting of heterogeneous workstations.

Algorithms↗

PubMedDate not supplied

Maximum-entropy three-dimensional reconstruction with deconvolution of the contrast transfer function: a test application with adenovirus.

We have developed an objective, quantitative, and general algorithm to improve the fidelity of three-dimensional reconstructions made from electron micrographs while at the same time filtering much of the noise present in the recorded data. The new technique is called constrained maximum entropy tomography (COMET). The essence of the method is that it will produce the most featureless reconstruction that fits the projection data within their observational accuracy. In particular, the COMET procedure will minimise the detrimental effects of errors in the measured data and deconvolute the effects of the contrast transfer function. An objective test has been performed using COMET on a conventional image reconstruction obtained from cryo-electron micrographs of adenovirus. The density for hexon, the major coat protein of the virus, which is known to high resolution from X-ray crystallography, provided a known high-resolution control. The COMET reconstruction is in considerably better agreement with the crystallographic electron density than the original reconstruction, throughout the entire resolution range.

Adenoviridae↗

PubMed1997

Entropy and charge in molecular evolution--the case of phosphate.

Biopoesis, the creation of life, implies molecular evolution from simple components, randomly distributed and in a dilute state, to form highly organized, concentrated systems capable of metabolism, replication and mutation. This chain of events must involve environmental processes that can locally lower entropy in several steps; by specific selection from an indiscriminate mixture, by concentration from dilute solution, and in the case of the mineral-induced processes, by particular effectiveness in ordering and selective reaction, directed toward formation of functional biomolecules. Numerous circumstances provide support for the notion that negatively charged molecules were functionally required and geochemically available for biopoesis. Sulfite ion may have been important in bisulfite complex formation with simple aldehydes, facilitating the initial concentration by sorption of aldehydes in positively charged surface active minerals. Borate ion may have played a similar, albeit less investigated role in forming charged sugar complexes. Among anionic species, oligophosphate ions and charged phosphate esters are likely to have been of even more wide ranging importance, reflected in the continued need for phosphate in a proposed RNA world, and extending its central role to evolved biochemistry. Phosphorylation is shown to result in selective concentration by surface sorption of compounds, otherwise too dilute to support condensation reactions. It provides protection against rapid hydrolysis of sugars and, by selective concentration, induces the oligomerization of aldehydes. As a manifestation of life arisen, phosphate already appears in an organic context in the oldest preserved sedimentary record.

Animals↗

PubMed2005

Cross entropy: a new solver for Markov random field modeling and applications to medical image segmentation.

This paper introduces a novel solver, namely cross entropy (CE), into the MRF theory for medical image segmentation. The solver, which is based on the theory of rare event simulation, is general and stochastic. Unlike some popular optimization methods such as belief propagation and graph cuts, CE makes no assumption on the form of objective functions and thus can be applied to any type of MRF models. Furthermore, it achieves higher performance of finding more global optima because of its stochastic property. In addition, it is more efficient than other stochastic methods like simulated annealing. We tested the new solver in 4 series of segmentation experiments on synthetic and clinical, vascular and cerebral images. The experiments show that CE can give more accurate segmentation results.

Algorithms↗

PubMed2005

MRI tissue classification with neighborhood statistics: a nonparametric, entropy-minimizing approach.

We introduce a novel approach for magnetic resonance image (MRI) brain tissue classification by learning image neighborhood statistics from noisy input data using nonparametric density estimation. The method models images as random fields and relies on minimizing an entropy-based metric defined on high dimensional probability density functions. Combined with an atlas-based initialization, it is completely automatic. Experiments on real and simulated data demonstrate the advantages of the method in comparison to other approaches.

Algorithms↗

PubMed2002

Approximate entropy: a regularity statistic for assessment of intracranial pressure.

INTRODUCTION: Waveform analysis of ICP and mABP provideqs important information about cerebrovascular reactivity and intracranial compliance. Traditionally spectral analysis and correlation statistics have been used despite certain limitations. Approximate entropy (ApEn) is an established measure of system regularity; which can change with pathology. This study defines a novel method for application of ApEn to the ICP/mABP waveform, and reports changing ApEn with pathophysiology in the rodent brain. METHODS: Nine Sprague-Dawley rats were anesthetized for mABP, and ICP recording. Rats were exposed to 15 minutes hypotension (45-50 mmHg), followed by resuscitation, equilibration and infusion of a 500 ul subdural hematoma. Raw data, ApEn(RAW), and wave-period, ApEn(PERIOD), were assessed for stochastic fluctuations using ApEn (m = 2, r = 0.2 SD). Results were compared with the established parameters: standard deviation, harmonic transfer function, Pressure Reactivity Index and Correlation Coefficient. RESULTS: At baseline, ApEn(ABP-PERIOD) and ApEn(ICP-PERIOD) were 1.464 +/- 0.003, and 0.690 +/- 0.020 respectively, suggesting that random heart rate fluctuations are damped during transfer to the ICP waveform. ApEn(ICP-PERIOD) consistently rose during hypotension (ICP 7 +/- 2: ApEn(ICP-PERIOD) 1.086 +/- 0.074, p < 0.05) and after SDH infusion (ICP 35 +/- 12: ApEn(ICP-PERIOD) 1.24 +/- 0.03, p < 0.01). These values were closer to mABP and suggest enhanced transfer of random fluctuations. Significant changes in ApEn were seen in the absence of significant changes in other parameters. CONCLUSIONS: This study defines a system for analyzing the transfer of random fluctuations in mABP waveform to the ICP waveform. ApEn appears to be responsive to changes in intracranial compliance and/or cerebrovascular resistance, therefore more formal studies of the sensitivity and specificity of this novel measure are warranted. These initial findings suggest that ApEn may be a useful adjunct measure of the ICP waveform.

Animals↗

PubMed1997

New technique for time series analysis combining the maximum entropy method and non-linear least squares method: its value in heart rate variability analysis.

A new technique for time series analysis, which is a combination of the maximum entropy method (MEM) for spectral analysis and the non-linear least squares method (LSM) for fitting analysis, is described. In this technique, the MEM power spectral density (MEMPSD) is calculated using a very large lag that could diminish the lag dependence of dominant periods estimated by the MEM analysis. The validity of this large lag is confirmed by the LSM, given that the ten dominant MEM periods are known quantities. To validate the MEM plus LSM technique, it is compared with autoregressive (AR) modelling, by analysing heart rate variability under pharmacological interventions (phenylephrine and trinitroglycerine), using 16 young males. The results indicate that the MEMPSD, when compared with the ARPSD, has numerous periods that could reproduce the original time series much more accurately, as revealed by the LSM analysis. However, both the low- and high-frequency powers with MEMPSD and ARPSDs shift in the expected directions in accordance with the pharmacological effects on the cardiovascular system. The implications of these results are discussed from the theoretical and practical standpoints of the MEM plus LSM technique, compared with AR modelling.

Adolescent↗

PubMedDate not supplied

Approximate entropy and point correlation dimension of heart rate variability in healthy subjects.

The contribution of nonlinear dynamics to heart rate variability in healthy humans was examined using surrogate data analysis. Several measures of heart rate variability were used and compared. Heart rates were recorded for three hours and original data sets of 8192 R-R intervals created. For each original data set (n = 34), three surrogate data sets were made by shuffling the order of the R-R intervals while retaining their linear correlations. The difference in heart rate variability between the original and surrogate data sets reflects the amount of nonlinear structure in the original data set. Heart rate variability was analyzed by two different nonlinear methods, point correlation dimension and approximate entropy. Nonlinearity, though under 10 percent, could be detected with both types of heart rate variability measures. More importantly, not only were the correlations between these measures and the standard deviation of the R-R intervals weak, the correlation among the nonlinear measures themselves was also weak (generally less than 0.6). This suggests that in addition to standard linear measures of heart rate variability, the use of multiple nonlinear measures of heart rate variability might be useful in monitoring heart rate dynamics.

Adult↗

PubMed1999

Conditional entropy approach for the evaluation of the coupling strength.

A method that enables measurement of the degree of coupling between two signals is presented. The method is based on the definition of an uncoupling function calculating, by means of entropy rates, the minimum amount of independent information (i.e. the information carried by one signal which cannot be derived from the other). An estimator of the uncoupling function able to deal with short segments of data (a few hundred samples) is proposed, thus enabling the method to be used for usual experimental recordings. A synchronisation index is derived from the estimate of the uncoupling function by means of a minimisation procedure. It quantifies the maximum amount of information exchanged between the two signals. Simulations in which non-linear coordination schemes are produced and changes in the coupling strength are artificially induced are used to check the ability of the proposed index to measure the degree of synchronisation between signals. The synchronisation analysis is utilised to measure the coupling strength between the beat-to-beat variability of the sympathetic discharge and ventilation in decerebrate artificially ventilated cats and the degree of synchronisation between the beat-to-beat variability of the heart period and ventricular repolarisation interval in normal subjects and myocardial infarction patients. The sympathetic discharge and ventilation are strongly coupled and the coupling strength is not affected by manoeuvres capable of increasing or depressing sympathetic activity. The synchronisation is lost after spinalisation. The synchronisation analysis confirms that the heart period and ventricular repolarisation interval are well coordinated. In normal subjects, the synchronisation index is not modified by experimental conditions inducing changes in the sympathovagal balance. On the contrary, it strongly decreases after myocardial infarction, thus detecting and measuring the uncoupling between the heart period and ventricular repolarisation interval.

Animals↗

PubMed2003

Entropy-based SNP selection for genetic association studies.

Because of their abundance, density, and ease of practical use, single-nucleotide polymorphisms (SNPs) have become the major source of information for association gene mapping in humans. Sensible strategies for selecting practically useful SNPs are therefore required. Among the factors influencing the mapping utility of a given set of SNPs are (1). their individual diversity, (2). their haplotype structure in the population of interest, and (3). their physical distribution. We propose a strategy integrating these aspects into a single mapping utility measure, which is based upon Shannon entropy, and which maximizes the amount of information extracted from a genomic region under a Malecot model of linkage disequilibrium (LD) decay. The same utility measure has also been used to define a criterion guiding SNP discovery and rational decision-making about the continuation or termination of a mapping study. The proposed strategy performs consistently well in a data set comprising 549 German control individuals, genotyped for 136 SNPs from four genomic regions of different LD structure. Adoption of the method in practice is estimated to save up to 30% of genotyping load when compared with equidistant SNP localization or pair-wise LD minimization alone.

DNA↗