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PubMed2005

An entropy-based measure of founder informativeness.

Optimizing quantitative trait locus (QTL) mapping experiments requires a generalized measure of marker informativeness because variable information is obtained from different marker systems, marker distribution and pedigree types. Such a measure can be derived from the concept of Shannon entropy, a central concept in information theory. Here we introduce entropy-based founder informativeness (EFI), a new measure of information content generalized across pedigrees, maps, marker systems and mating configurations. We derived equations for inbred- and outbred-derived mapping populations. Mathematical properties of EFI include enhanced sensitivity to mapping population type and extension to any number of founders. To illustrate the use of EFI, we compared experimental designs for QTL mapping for three examples: (i) different marker systems for an F2 pedigree, (ii) different marker densities and sampling sizes for a BC1 pedigree and (iii) a comparison of haplotypic versus zygotic analyses of an outbred pedigree. As an a priori generalized measure of information content, EFI does not require phenotypic data for optimizing experimental designs for QTL mapping.

Alleles↗

PubMed2006

Exploring the relationship between funneled energy landscapes and two-state protein folding.

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.

Diffusion↗

PubMed2002

Atomic displacement parameters for spessartine Mn3Al2Si3O12 and their lattice-dynamical interpretation.

A rigid-ion lattice-dynamical treatment accounts reasonably well for most of the atomic displacement parameters (ADPs) reported in the literature for a synthetic sample of spessartine Mn(3)Al(2)Si(3)O(12); the model accounts less well for the ADPs of the Mn atom. These results are similar to those obtained for the corresponding garnets pyrope Mg(3)Al(2)Si(3)O(12) and almandine Fe(3)Al(2)Si(3)O(12). The results are confirmed by a very good agreement of the lattice-dynamical estimates with the experimental values of the heat capacity that are currently available, as well as those of the Raman and infrared vibrational spectra. The anomalous behaviour of the Mn atom is reflected in the entropy values. As is the case for pyrope and almandine, here the agreement with the experimental results can be markedly improved if the existence of a low-temperature order-disorder transition concerning the Mn atom is considered. The lattice-dynamical estimates for all the atoms presented here do not agree with the corresponding ADPs obtained in a crystal structure refinement of a supposedly 'pure' natural sample from Elba. In turn, these experimental ADPs do not agree with those observed for the synthetic sample, thereby showing a physical difference; such a possibility is in agreement with recent observations by other authors, who found an unexpected fluorine content in several natural specimens of spessartine. Therefore, theoretical estimates of ADPs are reliable enough to point out unexpected situations if disagreement with the observed values occurs.

Journal Article↗

PubMed1999

Disruption of the pulsatile and entropic modes of insulin release during an unvarying glucose stimulus in elderly individuals.

Insulin is secreted in a pulsatile fashion with measurable orderliness (low entropy). Aging is characterized by alterations in pulsatile insulin release in the fasting state. We undertook the current studies to determine whether disruptions in pulsatile insulin release in response to sustained glucose infusion also accompany the age-related changes in carbohydrate metabolism. Healthy young (n = 10; body mass index, 23 +/- 1 kg/m2; age, 23 +/- 1 yr) and old (n = 10; body mass index, 24 +/- 1 kg/m2; age, 80 +/- 2 yr) volunteers underwent a 600-min hyperglycemic glucose clamp. During the entire 600 min, insulin was sampled every 10 min, and insulin release was evaluated by Cluster analysis. From 240-360 min, insulin was sampled every 1 min, and secretory pulse analysis was conducted using a multiparameter deconvolution technique. During the 1-min sampling interval, basal insulin secretion (P < 0.01), insulin production rate (P < 0.01), pulsatile mean and integrated insulin concentration (P < 0.01), insulin secretory burst mass (P < 0.01), and burst amplitude (P < 0.05) were reduced in the elderly. In addition, interpulse interval was increased in the aged (P < 0.05). In the 600-min studies, interpulse interval was greater in the aged (P < 0.01) and burst number (P < 0.01), basal concentration (P < 0.01), and burst increment (P < 0.05) were less. Approximate entropy, a measure of irregularity of insulin release, was increased in the aged, signifying the loss of orderliness of insulin secretion (P < 0.05). We conclude that in response to a sustained (10-h) glucose infusion, normal aging is characterized by a reduction in mass and amplitude of rapid insulin pulses and a decrease in the frequency, amplitude, and regularity of ultradian pulses. Whether these changes in insulin pulsatility contribute directly to the age-related changes in carbohydrate metabolism will require further clinical studies.

Activity Cycles↗

PubMed1996

Two mathematically defined expressive language structures in humans and chimpanzees.

Two expressive language structures have been identified mathematically in humans and chimpanzees. The first was found by measuring the waiting times between the invocation of new words or symbols, which consistently yielded individually characteristic rate constants and descending exponential curves that reflect a stochastically lawful Poisson process. The second was discovered by calculating the cumulative informational complexity (entropy) of word usage, which in all cases was a deterministically lawful logarithmic function of the number of words used to a given point in a communicative sequence. Individual and species differences in how this law is obeyed also characterized the sample. The results from the apes resembled those from the works of human poets like Shakespeare. The findings speak for deep, natural, unlearned expressive language structures in apes that are comparable to those seen in humans.

Animals↗

PubMed1987

Maximum entropy and its application to the calculation of drug absorption rates.

A new method is presented for calculating the rate at which a drug enters the bloodstream after dosing, given the concentration of the drug in blood at various times. The method is based on the principle of maximum entropy, which has not been applied previously to pharmacokinetic problems. The resulting input rate functions are smooth and physiologically realistic, free of spurious oscillations yet still showing small-scale structure where there is evidence for it in the data. Blood samples do not need to be taken at equal intervals, and no preliminary smoothing or interpolation of the data is required.

Acetaminophen↗

PubMed2004

Designing generalized statistical ensembles for numerical simulations of biopolymers.

Conformational properties of polymers, such as average dihedral angles or molecular alpha-helicity, display a rather weak dependence on the detailed arrangement of the elementary constituents (atoms). We propose a computer simulation method to explore the polymer phase space using a variant of the standard multicanonical method, in which the density of states associated to suitably chosen configurational variables is considered in place of the standard energy density of states. This configurational density of states is used in the Metropolis acceptance/rejection test when configurations are generated with the help of a hybrid Monte Carlo algorithm. The resulting configurational probability distribution is then modulated by exponential factors derived from the general principle of the maximal constrained entropy by requiring that certain average configurational quantities take preassigned (possibly temperature dependent) values. Thermal averages of other configurational quantities can be computed by using the probability distributions obtained in this way. Moments of the energy distribution require an extra canonical sampling of the system phase space at the desired temperature, in order to locally thermalize the configurational degrees of freedom. As an application of these ideas we present the study of the structural properties of two simple models: a bead-and-spring model of polyethylene with independent hindered torsions and an all-atom model of alanine and glycine oligomers with 12 amino acids in vacuum.

Biopolymers↗

PubMed2000

Repaglinide acutely amplifies pulsatile insulin secretion by augmentation of burst mass with no effect on burst frequency.

OBJECTIVE: Repaglinide is a new oral hypoglycemic agent that acts as a prandial glucose regulator proposed for the treatment of type 2 diabetes by stimulating insulin secretion. The aim of this study was to explore actions of repaglinide on the rapid pulsatile insulin release by high-frequency insulin sampling and analysis of insulin-concentration time series. RESEARCH DESIGN AND METHODS: We examined 8 healthy lean male subjects in a single-dose double-blind placebo-controlled crossover design. After the subjects underwent an overnight fast, blood sampling was initiated and continued every minute for 120 min. After 40 min, a single dose (0.5 mg) of repaglinide or placebo was given. Serum insulin-concentration time series were assessed by deconvolution analyses and the regularity statistic by approximate entropy (ApEn). RESULTS: Average insulin concentration was increased after repaglinide administration (basal vs. stimulated period, P values are placebo vs. repaglinide) (25.1 +/- 3.6 vs. 33.5 +/- 4.1 pmol/l, P < 0.001). Insulin secretory burst mass (15.8 +/- 2.2 vs. 19.6 +/- 2.8 pmol x l(-1) x pulse(-1), P = 0.02) and amplitude (6.1 +/- 0.9 vs. 7.7 +/- 1.2 pmol x l(-1) x min(-1), P = 0.008) were augmented after repaglinide administration. A concomitant trend toward an increase in basal insulin secretion was observed (2.5 +/- 0.3 vs. 3.2 +/- 0.4 pmol x l(-1) x min(-1), p = 0.06), while the interpulse interval was unaltered (6.8 +/- 1.0 vs. 5.4 +/- 0.4 min/pulse, P = 0.38). ApEn increased significantly after repaglinide administration (0.623 +/- 0.045 vs. 0.670 +/- 0.034, P = 0.04), suggesting less orderly oscillatory patterns of insulin release. CONCLUSIONS: In conclusion, a single dose of repaglinide amplifies insulin secretory burst mass (and basal secretion) with no change in burst frequency. The possible importance of these mechanisms in the treatment of type 2 diabetes characterized by disrupted pulsatile insulin secretion remains to be clarified.

Adult↗

PubMed2003

Haplotypic analysis of the TNF locus by association efficiency and entropy.

BACKGROUND: To understand the causal basis of TNF associations with disease, it is necessary to understand the haplotypic structure of this locus. We genotyped 12 single-nucleotide polymorphisms (SNPs) distributed over 4.3 kilobases in 296 healthy, unrelated Gambian and Malawian adults. We generated 592 high-quality haplotypes by integrating family- and population-based reconstruction methods. RESULTS: We found 32 different haplotypes, of which 13 were shared between the two populations. Both populations were haplotypically diverse (gene diversity = 0.80, Gambia; 0.85, Malawi) and significantly differentiated (p < 10-5 by exact test). More than a quarter of marker pairs showed evidence of intragenic recombination (29% Gambia; 27% Malawi). We applied two new methods of analyzing haplotypic data: association efficiency analysis (AEA), which describes the ability of each SNP to detect every other SNP in a case-control scenario; and the entropy maximization method (EMM), which selects the subset of SNPs that most effectively dissects the underlying haplotypic structure. AEA revealed that many SNPs in TNF are poor markers of each other. The EMM showed that 8 of 12 SNPs (Gambia) and 7 of 12 SNPs (Malawi) are required to describe 95% of the haplotypic diversity. CONCLUSIONS: The TNF locus in the Gambian and Malawi sample is haplotypically diverse and has a rich history of intragenic recombination. As a consequence, a large proportion of TNF SNPs must be typed to detect a disease-modifying SNP at this locus. The most informative subset of SNPs to genotype differs between the two populations.

Adult↗

PubMed2004

MoDEL: an efficient strategy for ungapped local multiple alignment.

We introduce a method for ungapped local multiple alignment (ULMA) in a given set of amino acid or nucleotide sequences. This method explores two search spaces using a linked optimization strategy. The first search space M consists of all possible words of a given length W, defined on the residue alphabet. An evolutionary algorithm searches this space globally. The second search space P consists of all possible ULMAs in the sequence set, each ULMA being represented by a position vector defining exactly one subsequence of length W per sequence. This search space is sampled with hill-climbing processes. The search of both spaces are coupled by projecting high scoring results from the global evolutionary search of M onto P. The hill-climbing processes then refine the optimization by local search, using the relative entropy between the ULMA and background residue frequencies as an objective function. We demonstrate some advantages of our strategy by analyzing difficult natural amino acid sequences and artificial datasets. A web interface is available at

Algorithms↗

PubMed2005

Rapid NMR data collection.

Rapid data collection is an area of intense research in biomolecular NMR spectroscopy, in particular for high-throughput structure determination in structural genomics. NMR data acquisition and processing protocols for rapidly obtaining high-dimensional spectral information aim at avoiding sampling limited data collection and are reviewed here with emphasis on G-matrix Fourier transform NMR spectroscopy.

Data Collection↗

PubMedDate not supplied

An accelerated procedure for recursive feature ranking on microarray data.

We describe a new wrapper algorithm for fast feature ranking in classification problems. The Entropy-based Recursive Feature Elimination (E-RFE) method eliminates chunks of uninteresting features according to the entropy of the weights distribution of a SVM classifier. With specific regard to DNA microarray datasets, the method is designed to support computationally intensive model selection in classification problems in which the number of features is much larger than the number of samples. We test E-RFE on synthetic and real data sets, comparing it with other SVM-based methods. The speed-up obtained with E-RFE supports predictive modeling on high dimensional microarray data.

Oligonucleotide Array Sequence Analysis↗

PubMed2004

Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy.

The arrival of very high field magnets and cryogenic circuitries, and the development of relaxation-optimized pulse sequences have added powerful tools for increasing sensitivity and resolution in NMR studies of biomacromolecules. The potential of these advances is not fully realized in practice, however, since current experimental protocols do not permit sufficient data sampling for optimal resolution in the indirect dimensions. Here we analyze quantitatively how increasing resolution in indirect dimensions affects the S/N ratio and compare this with currently used sampling routines. Optimal resolution would require sampling up to approximately 3 R (2)(-1), and the S/N reaches a maximum at approximately 1.2 R (2)(-1). Currently used data acquisition protocols rarely sample beyond 0.4 R (2)(-1), and extending evolution times would result in prohibitively long experiments. We show that a general solution to this problem is to use non-uniform sampling, where only a small subset of data points in the indirect sampling space are measured, and possibly different numbers of transients are collected for different evolution times. Coupled with modern methods of spectrum analysis, this strategy delivers substantially improved resolution and/or reduced measuring times compared to uniform sampling, without compromising sensitivity. Higher resolution in the indirect dimensions will facilitate the use of automated assignment programs.

Entropy↗

PubMed1991

An evaluation of new processing protocols for in vivo NMR spectroscopy.

In vivo NMR spectroscopy is often complicated with problems of low signal-to-noise, poor resolution, undefined peak shapes, and nonlinear baselines despite the efforts of investigators to optimize their experiments. Several data processing options are available to spectroscopists to enhance resolution and signal-to-noise and/or to flatten baselines. There is some question about how these processing protocols affect quantitative information. This paper evaluates five different processing protocols for their ability to extract quantitative information from a set of nonideal spectra. Three of the protocols involve recently developed statistical signal processing methods, maximum entropy Fourier spectral deconvolution, linear prediction singular value decomposition, and baseline deconvolution. These protocols are compared with the conventional processing methods of convolution difference and zeroing initial data points of the FID. The methods are evaluated by use of a quantitative 31P model sample and also are demonstrated on surface coil 31P data.

2,3-Diphosphoglycerate↗

PubMed2004

Mesoscopic analysis of conformational and entropic contributions to nonspecific adsorption of HP copolymer chains using dynamic Monte Carlo simulations.

Dynamic Monte Carlo simulations of short linear HP-type copolymers exhibiting proteinlike characteristics are used to investigate both chain dynamics and changes in chain conformational entropy and their contributions to the energetics of adsorption onto a solid-liquid interface. The dMC results show that the conformations and energies of adsorbed chains are highly degenerate. The ensemble-averaged energy of the adsorbed state is dependent on temperature, chain sequence, native-state stability, and sorbent surface geometry and hydrophobicity. Mesoscopic thermodynamic analyses reveal that, although increased chain conformational entropy contributes to the driving force for adsorption in certain cases, many conditions exist where the change in conformational entropy is either negligible or unfavorable due to constraints imposed by the need to form a large and specific number of favorable intra- and intermolecular contacts and by the impenetrable nature of the sorbent surface. Step-number-averaged energy trajectories, based on sampling of a large number of energy trajectories and thus conformational states at each step number, suggest that the search for a global energy minimum is gradual, so that adsorption is first reversible but becomes apparently irreversible with longer exposure to the sorbent. These results appear to be connected to the conformational adaptability of the chain both on the surface and in solution, and an adsorption model taking chain conformational dynamics into account is proposed.

Journal Article↗

PubMedDate not supplied

Bayesian model based clustering analysis: application to a molecular dynamics trajectory of the HIV-1 integrase catalytic core.

This work describes the application of a Bayesian method for clustering protein conformations sampled during a molecular dynamics simulation of the HIV-1 integrase catalytic core. A clustering analysis is carried out under the assumption of normal distribution without fixing the number of clusters in advance. Some performance measures, such as posterior probability and class cross entropy, are used to determine the most probable set of clusters. The Bayesian clustering method results in meaningful groups identifying transitions between conformational ensembles. The dihedral angles involved in such transitions are also examined in detail. The conformations in high dimensional space are projected into 3D space employing a multidimensional scaling technique to provide a visual inspection.

Algorithms↗

PubMed2004

Short-term aromatase-enzyme blockade unmasks impaired feedback adaptations in luteinizing hormone and testosterone secretion in older men.

The mechanisms subserving hypoandrogenemia and relative hypogonadotropism in older men are not known. The present study tests the clinical hypothesis that aging impairs hypothalamopituitary adaptations to feedback withdrawal induced by antagonism of estrogen biosynthesis. To this end, we appraised gonadal axis responses to estrogen depletion induced by anastrozole (a potent and selective aromatase inhibitor) in nine older and 11 young men vs. placebo in 17 other older and eight young men. The study design comprised a prospectively randomized, double-blind, parallel-cohort intervention. To monitor LH release, blood was sampled every 10 min for 24 h; LH concentrations were assayed by two-site monoclonal immunoradiometric assay; pulsatile LH release quantitated by a model-free discrete peak-detection technique (Cluster); feedback-dependent orderliness of LH secretion via the approximate entropy statistic; and 24-h rhythmicity of LH concentrations by cosine analysis. At baseline, older men had comparable estradiol and testosterone but lower LH concentrations than young controls. Exposure to anastrozole reduced (24-h pooled) serum estradiol concentrations by 50% (P < 0.001) and elevated mean LH concentrations by 2.1-fold (P < 0.001) in both the young and older cohorts. However, older men failed to achieve young adult augmentation of the following: 1) total testosterone concentrations (P < 0.01) or molar testosterone to SHBG ratios (P < 0.01); 2) incremental LH pulse amplitude (P < 0.001) and LH peak area (P < 0.01); 3) mean LH pulse frequency (P = 0.0044); and 4) quantifiable irregularity (approximate entropy) of LH release patterns (P < 0.001). FSH concentrations became comparable in the two age cohorts. In summary, administration of a potent and selective aromatase antagonist reduces estradiol and elevates mean LH concentrations equivalently in young and older men. The low estrogen-feedback state in elderly men unmasks diminished incremental LH pulse amplitude and area; absence of further acceleration of LH pulse frequency; impaired regulation of the orderliness of LH release; and reduced testosterone to SHBG ratios. Thus, aging alters expected hypothalamopituitary-gonadal adaptations to short-term partial estrogen depletion in healthy men.

Adaptation, Physiological↗

PubMed1998

Glucagon-like peptide 1 increases mass but not frequency or orderliness of pulsatile insulin secretion.

Glucagon-like peptide 1 (GLP-1) is a peptide hormone that is released from the gut after luminal stimulation. The hormone is a potent insulin secretagogue and is a potential novel pharmaceutical adjuvant in the treatment of NIDDM. Insulin is secreted as a series of punctuated secretory bursts superimposed on a basal insulin release. Recently, the contribution of these secretory bursts to overall insulin secretion has been evaluated, and studies using catheterization across the pancreas in a canine model and studies using deconvolution in humans have revealed that the majority of insulin is released during these secretory bursts. Moreover, the main regulation of insulin secretion is through perturbation of mass and frequency of these secretory bursts. The mode of delivery of insulin into the circulation seems important for insulin action, and it is therefore important to know the impact of a potential therapeutic insulin secretagogue on the mode of insulin secretion. To assess the effects of GLP-1 on the mass, frequency, amplitude, and overall contribution of pulsatile insulin secretion, we used a recently validated deconvolution model to examine these variables before and during infusion of GLP-1 in eight healthy men (age 28 +/- 2 years; BMI 24 +/- 2 kg/m2). At a constant glucose infusion (2.5 mg x kg-1 x min-1), near-steady state was reached at 75 min, and sampling was performed every minute at t = 75-115 and 145-185 min. At t = 115 min, an infusion of saline or GLP-1 (50 pmol x kg-1 x min-1) was given. The regularity of insulin secretion was measured by approximate entropy, a recently developed mathematical statistic, applied herein to assess the regularity in a hormone concentration time series. After GLP-1 infusion, there was an abrupt increase in the peripheral concentrations of serum C-peptide (696 +/- 65 vs. 1,538 +/- 165 pmol/l) and insulin (49 +/- 8 vs. 138 +/- 21 pmol/l) concentrations. This increase was mainly due to an increase in the pulsatile component of insulin secretion that was achieved by a fourfold increase in secretory burst mass (28.2 +/- 4.4 vs. 100.1 +/- 15.8 pmol x l-1 x pulse-1; P < 0.001), and amplitude (12.7 +/- 2.2 vs. 4.3 +/- 7.7 pmol x l-1 x min-1; P < 0.002), whereas the secretory burst frequency was not affected by GLP-1 (11.5 +/- 0.7 vs. 12.6 +/- 0.6 pulses/h; P = 0.4). As a consequence, the detected contribution of pulsatile to overall insulin secretion was increased from 56 +/- 4 to 77 +/- 4% (P < 0.005). The orderliness of the insulin release process was not deteriorated by short-term GLP-1 infusion as assessed by approximate entropy (1.19 +/- 0.04 vs. 1.18 +/- 0.04; P = 0.7).

Adult↗