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PubMed1999

A multisolution method of phase determination by combined maximization of entropy and likelihood. VI. The use of error-correcting codes as a source of phase permutation and their application to the phase problem in powder, electron and macromolecular crystallography.

The use of error-correcting codes as a source of efficient designs of phase permutation schemes is described. Three codes are used, all taken from the Bricogne BUSTER program [Bricogne (1993). Acta Cryst. D49, 37-60]: the Hamming [7, 4, 3], the Nordström-Robinson (16, 256, 6) and the Golay [24, 12, 8] or its punctured [23, 12, 7] form. These are used in a maximum-entropy-likelihood phasing environment to carry out phase permutation of basis-set reflections instead of the usual quadrant permutation or magic integer approaches. The use of codes in this way inevitably introduces some errors in the phase choices, but for most structures this is not significant especially when the gain in sampling efficiency is considered. For example, the Golay [24, 14, 8] allows the permutation of 24 centric phases in such a way that only 4096 phase sets are produced instead of 2(24) = 16777216, and one of these sets has, at most, only four wrong phases. The method is successfully applied to three powder diffraction data sets of increasing complexity, and with increasing degrees of overlap {Mg(3)BN(3), Sigma-2 ([Si(64)O(128)].4C(10)H(17)N) and the NU-3 zeolite}, a sparse electron diffraction data set for buckminsterfullerene, C(60), and the small protein molecule crambin at 3 Å resolution where 42 reflections are phased with a Uweighted mean phase error of 58.5 degrees.

Journal Article↗

PubMed2004

Importance of chirality and reduced flexibility of protein side chains: a study with square and tetrahedral lattice models.

Side chains of amino acid residues are the determining factor that distinguishes proteins from other unstable chain polymers. In simple models they are often represented implicitly (e.g., by spin states) or simplified as one atom. Here we study side chain effects using two-dimensional square lattice and three-dimensional tetrahedral lattice models, with explicitly constructed side chains formed by two atoms of different chirality and flexibility. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L residues, and their side chains adopt different rotameric states. For short chains, we enumerate exhaustively all possible conformations. For long chains, we sample effectively rare events such as compact conformations and obtain complete pictures of ensemble properties of conformations of these models at all compactness region. This is made possible by using sequential Monte Carlo techniques based on chain growth method. Our results show that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by statistical analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side chain entropy for a given backbone structure. We show that simple rotamer counting underestimates side chain entropy significantly for both extended and near maximally compact conformations. We find that side chain entropy does not always correlate well with main chain packing. With explicit side chains, extended backbones do not have the largest side chain entropy. Among compact backbones with maximum side chain entropy, helical structures emerge as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.

Computer Simulation↗

PubMed2005

Calculation of absolute protein-ligand binding affinity using path and endpoint approaches.

A comparative analysis is provided of rigorous and approximate methods for calculating absolute binding affinities of two protein-ligand complexes: the FKBP protein bound with small molecules 4-hydroxy-2-butanone and FK506. Our rigorous approach is an umbrella sampling technique where a potential of mean force is determined by pulling the ligand out of the protein active site over several simulation windows. The results of this approach agree well with experimentally observed binding affinities. Also assessed is a commonly used approximate endpoint approach, which separately estimates enthalpy, solvation free energy, and entropy. We show that this endpoint approach has numerous variations, all of which are prone to critical shortcomings. For example, conventional harmonic and quasiharmonic entropy estimation procedures produce disparate results for the relatively simple protein-ligand systems studied in this work.

Binding Sites↗

PubMed2000

Identification of ligands for RNA targets via structure-based virtual screening: HIV-1 TAR.

Binding of the Tat protein to TAR RNA is necessary for viral replication of HIV-1. We screened the Available Chemicals Directory (ACD) to identify ligands to bind to a TAR RNA structure using a four-step docking procedure: rigid docking first, followed by three steps of flexible docking using a pseudobrownian Monte Carlo minimization in torsion angle space with progressively more detailed conformational sampling on a progressively smaller list of top-ranking compounds. To validate the procedure, we successfully docked ligands for five RNA complexes of known structure. For ranking ligands according to binding avidity, an empirical binding free energy function was developed which accounts, in particular, for solvation, isomerization free energy, and changes in conformational entropy. System-specific parameters for the function were derived on a training set of RNA/ligand complexes with known structure and affinity. To validate the free energy function, we screened the entire ACD for ligands for an RNA aptamer which binds L-arginine tightly. The native ligand ranked 17 out of ca. 153,000 compounds screened, i.e., the procedure is able to filter out >99.98% of the database and still retain the native ligand. Screening of the ACD for TAR ligands yielded a high rank for all known TAR ligands contained in the ACD and suggested several other potential TAR ligands. Eight of the highest ranking compounds not previously known to be ligands were assayed for inhibition of the Tat-TAR interaction, and two exhibited a CD50 of ca. 1 microM.

Arginine↗

PubMed2006

Variational Bayes for continuous hidden Markov models and its application to active learning.

In this paper, we present a varitional Bayes (VB) framework for learning continuous hidden Markov models (CHMMs), and we examine the VB framework within active learning. Unlike a maximum likelihood or maximum a posteriori training procedure, which yield a point estimate of the CHMM parameters, VB-based training yields an estimate of the full posterior of the model parameters. This is particularly important for small training sets since it gives a measure of confidence in the accuracy of the learned model. This is utilized within the context of active learning, for which we acquire labels for those feature vectors for which knowledge of the associated label would be most informative for reducing model-parameter uncertainty. Three active learning algorithms are considered in this paper: 1) query by committee (QBC), with the goal of selecting data for labeling that minimize the classification variance, 2) a maximum expected information gain method that seeks to label data with the goal of reducing the entropy of the model parameters, and 3) an error-reduction-based procedure that attempts to minimize classification error over the test data. The experimental results are presented for synthetic and measured data. We demonstrate that all of these active learning methods can significantly reduce the amount of required labeling, compared to random selection of samples for labeling.

Algorithms↗

PubMed1999

A persistent circhoral ultradian rhythm is identified in human core temperature.

There have been inconclusive reports of intermittent rhythmic fluctuations in human core temperature, with the fluctuations having a period of about an hour. However, there has been no definitive demonstration of the phenomenon. This is likely due to the intermittency and seeming instability of the events. They have been assumed to be secondary rather than autonomous phenomena, putatively arising from the oscillation between rapid eye movement (REM) and non-REM (NREM) sleep. In this study, we report identification of a clear, persistent circhoral ultradian rhythm in core temperature with a period for this study sample of 64 +/- 8 minutes. It appeared simultaneously with an intact circadian core temperature rhythm, persisted despite complex perturbations in core temperature brought about by the sequelae of 40 h of sleep deprivation, and could not be attributed to sleep stage alternation or other endogenous or exogenous factors. Analysis of power spectra using the maximum entropy spectral analysis (MESA) method, which can uncover hidden rhythmicities, demonstrated that the apparent intermittency of the rhythm is due to periodic interference of this rhythm by other rhythmic events. The persistence of this oscillation suggests that, in this system as in the endocrine system, circhoral regulation is an integral component of thermoregulatory control. Identifying the source and functional role of this novel rhythm warrants further work.

Activity Cycles↗

PubMed2002

Entropic recoil separation of long DNA molecules.

A novel technique that can rapidly separate long-strand polymers according to length is presented. The separation mechanism is mediated by a confinement-induced entropic force at the abrupt interface between regions of vastly different configuration entropy. To demonstrate this technique, DNA molecules were partially inserted into a dense array of nanopillars (an entropically unfavorable region) using a pulsed electric field and allowed to relax to their natural state by removal of the field. Molecules of dissimilar lengths (T2 and T7 coliphage DNA) were inserted into this region in such a way that shorter molecules were fully inserted in this region, while longer molecules remained partially across the interface. The longer T2 molecules were observed to recoil entirely out of the pillar array, leaving the shorter T7 molecules inserted, and effecting separation of the two species in a single step. To show how this method can be used for separation of unknown samples, the inserting electric field was pulsed for progressively longer times, allowing passage of progressively longer molecules and producing the equivalent of a conventional electropherogram. The effects limiting resolution in this device are discussed, and the expected separating power of a multistage device is reported. The extracted resolution and running separation time compare favorably with current conventional separation techniques.

Algorithms↗

PubMed1994

Direct observation of the thermal equilibria among lumirhodopsin, metarhodopsin I, and metarhodopsin II in chicken rhodopsin.

Using low-temperature time-resolved spectroscopy, we have directly observed thermal back reaction of metarhodopsin I (meta I) to lumirhodopsin (lumi) and that of metarhodopsin II (meta II) to meta I in chicken rhodopsin to demonstrate the presence of thermal equilibria among lumi, meta I, and meta II. The back reaction from meta I to lumi was observed when the rhodopsin sample irradiated at -35 degrees C was warmed to -20 degrees C, while that from meta II to meta I was observed when the sample irradiated at -10 degrees C was cooled to -20 degrees C. Thermodynamic parameters of lumi, meta I, and meta II were calculated from the equilibrium constants estimated by analyzing the spectra of the equilibrium states at temperatures ranging from -30 to -10 degrees C. The results showed that meta I has an enthalpy and an entropy considerably smaller than those of lumi and meta II, while the difference in thermodynamic parameters between lumi and meta II is not so large. These results suggest that meta I is a crucial stage of conversion of the light energy captured by the chromophore into restricted conformations of the chromophore and/or protein, from which a large conformational change of the protein starts to form meta II.

Animals↗

PubMed2002

Does birth weight predict adult serum cortisol concentrations? Twenty-four-hour profiles in the United kingdom 1920-1930 Hertfordshire Birth Cohort.

Low birth weight and weight in infancy are associated with adult insulin resistance and type 2 diabetes. A proposed mechanism is programming of the hypothalamic-pituitary-adrenal axis by intrauterine undernutrition, leading to persistently elevated cortisol concentrations. We examined 24-h serum cortisol profiles (samples every 20 min) in 83 healthy elderly men and women whose birth weight and infant weight were recorded. Variables derived from these profiles included trough, peak, and area under the curve concentrations; the time of onset, rate of rise, duration, and peak of the early morning cortisol rise; postprandial secretion; and regularity of secretion (approximate entropy). None of these parameters was related to birth weight, weight at 1 yr, or change in weight SD score between birth and 1 yr. Consistent with other studies, 0730-0900 h cortisol concentrations were higher in men and women of lower birth weight, although this was not statistically significant (P = 0.08). Our findings do not support the hypothesis that reduced intrauterine and infant growth are associated with continuously raised cortisol concentrations in old age. Programmed effects on the hypothalamic-pituitary-adrenal axis may influence reactivity rather than resting secretion.

Aged↗

PubMed1993

Optimal sampling interval and edge detection algorithm for measurement of blood vessel diameter on a cineangiogram.

RATIONALE AND OBJECTIVES: The authors studied the effects of image magnification and the type of edge detection filter on the precision of measuring blood vessel diameters on coronary angiograms. METHOD: A blood vessel phantom containing five channels of various diameters filled with contrast medium was filmed. The magnifications examined were x4, x10, and x20, and the edge detection filters used were the first derivative, second derivative, composite, and entropy filters. The regression line y = a+bx was introduced, where x represents the nominal diameter and y the diameter measured by the edge-detection filters. Determination criteria were the offset, slope, and residual variance from the regression equation. RESULTS: The best value among three criteria was obtained with a magnification of x10 or x20. The entropy filter gave the best value of slope and residual variance. The composite filter gave the best value of offset. CONCLUSION: The most precise measurement is obtained when the entropy filter and a magnification of x10 or x20 are applied.

Algorithms↗

PubMed2005

Patterns of spontaneous activity in single rat olfactory receptor neurons are different in normally breathing and tracheotomized animals.

Spontaneous firing of olfactory receptor neurons (ORNs) was recently shown to be required for the survival of ORNs and the maintenance of their appropriate synaptic connections with mitral cells in the olfactory bulb. ORN spontaneous activity has never been described or characterized quantitatively in mammals. To do so we have made extracellular single unit recordings from ORNs of freely breathing (FB) and tracheotomized (TT) rats. We show that the firing behavior of TT neurons was relatively simple: they tended to fire spikes at the same average frequency according to purely random (Poisson) or simple (Gamma or Weibull) statistical laws. A minority of them were bursting with relatively infrequent and short bursts. The activity of FB neurons was less simple: their firing rates were more diverse, some of them showed trends or were driven by breathing. Although more of them were regular, only a minority could be described by simple laws; the majority displayed random bursts with more spikes than the bursts of TT neurons. In both categories bursts and isolated spikes (outside bursts) occurred completely at random. The spontaneous activity of ORNs in rats resembles that of frogs, but is higher, which may be due to a difference in body temperature. These results suggest that, in addition to the intrinsic thermal noise, spontaneous activity is provoked in part by mechanical, thermal, or chemical (odorant molecules) effects of air movements due to respiration, this extrinsic part being naturally larger in FB neurons. It is suggested that spontaneous activity may be modulated by respiration. Because natural sampling of odors is synchronized with breathing, such modulation may prepare and keep olfactory bulb circuits tuned to process odor stimuli.

Action Potentials↗

PubMed2006

Realistic quantitative descriptions of electron transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics.

A general approach to calculate the diabatic surfaces for electron-transfer reactions is presented, based on first-principles molecular dynamics of the active centers and their surrounding medium. The excitation energy corresponding to the transfer of an electron at any given ionic configuration (the Marcus energy gap) is accurately assessed within ground-state density-functional theory via a novel penalty functional for oxidation-reduction reactions that appropriately acts on the electronic degrees of freedom alone. The self-interaction error intrinsic to common exchange-correlation functionals is also corrected by the same penalty functional. The diabatic free-energy surfaces are then constructed from umbrella sampling on large ensembles of configurations. As a paradigmatic case study, the self-exchange reaction between ferrous and ferric ions in water is studied in detail.

Electron Transport↗

PubMed2003

Do growth hormone (GH) serial sampling, insulin-like growth factor-I (IGF-I) or auxological measurements have an advantage over GH stimulation testing in predicting the linear growth response to GH therapy?

OBJECTIVE: To compare the relative utility of GH secretion via pharmacological stimulation, overnight serial sampling, IGF-I levels and auxological variables as predictors of change in height standard deviation score (deltaHt SDS) during GH treatment. DESIGN: A multicentre observational study. PATIENTS: Prepubertal children (n = 825) with idiopathic growth failure who were subsequently treated with GH were divided into two groups, based on their maximum GH response to pharmacological stimulation testing: (1) idiopathic GH deficiency (IGHD), defined by a maximum GH response < 10 microg/l (n = 300); and (2) idiopathic short stature (ISS), with a maximum GH response > or = 10 microg/l (n = 525) (GH conversion factor: 3 IU = 1 mg). MEASUREMENTS: Overnight spontaneous GH secretion was measured in all patients. The following characteristics of spontaneous GH secretion were studied: maximum or peak GH, mean peak GH, number of GH peaks, pooled GH, mean GH, and approximate entropy of GH secretion. RESULTS: Although children with IGHD had lower indices of spontaneous GH secretion, there were no differences between IGHD and ISS groups in baseline Ht SDS, growth rate or IGF-I level. The dose and duration of GH therapy were similar. There was no statistically significant difference in the mean (+/- SD) change in Ht SDS (deltaHt SDS) in the two groups (IGHD 1.3 +/- 0.9 and ISS 1.2 +/- 0.8). Measures of spontaneous secretion, such as peak GH, mean of GH peaks, mean area under GH peaks, and mean GH, as well as IGF-I concentrations, were all statistically significantly correlated with deltaHt SDS in IGHD children (P < 0.0001). A significant correlation was also observed for pooled GH (P = 0.002) and approximate entropy (P = 0.01). Children with the most severe ISS (Ht SDS < -3.33) demonstrated a more disorganized pattern of GH secretion compared to children who were not as short (Ht SDS -2.33 to -1.64), as indicated by a higher approximate entropy (0.673 +/- 0.193 vs. 0.607 +/- 0.161, P < 0.004). This increased disorder in GH secretion was accompanied by lower IGF-I levels (104 +/- 99 microg/l vs. 137 +/- 74 microg/l, P < 0.001), even though pooled GH concentrations were indistinguishable between the two groups (2.2 +/- 1.3 microg/l vs. 2.0 +/- 1.0 microg/l). Children with IGHD demonstrated lower approximate entropy than did those with ISS (0.551 +/- 0.235 vs. 0.631 +/- 0.182, P < 0.0001). Duration of GH treatment, height deficit and genetic potential (midparental Ht SDS) were the most important variables influencing deltaHt SDS in children receiving GH therapy. Maximum stimulated GH, IGF-I and indices of spontaneous GH secretion also correlated with deltaHt SDS, but their relative importance varied among diagnostic groups. CONCLUSIONS: Patients with GH deficiency demonstrate a reduced capacity for GH secretion, while those with idiopathic short stature exhibit a more disorderly and less functional secretory pattern. Although effective in predicting a response to GH treatment in patients with severe GH deficiency, overnight serial sampling is less practical than other methods currently available. In addition, serial sampling was less useful as a predictor of growth response to exogenous GH in patients with idiopathic short stature.

Blood Specimen Collection↗

PubMed2005

Influence of smectite hydration and swelling on atrazine sorption behavior.

Smectites, clay minerals commonly found in soils and sediments, vary widely in their ability to adsorb organic chemicals. Recent research has demonstrated the importance of surface charge density and properties of exchangeable cations in controlling the affinity of smectites for organic molecules. In this study, we induced hysteresis in the crystalline swelling of smectites to test the hypothesis that the extent of crystalline swelling (or interlayer hydration status) has a large influence on the ability of smectites to adsorb atrazine from aqueous systems. Air-dried K-saturated Panther Creek (PC) smectite swelled less (d(001) = 1.38 nm) than never-dried K-PC (d(001) = 1.7 nm) when rehydrated in 20 mM KCl. Correspondingly, the air-dried-rehydrated K-PC had an order of magnitude greater affinity for atrazine relative to the never-dried K-PC. Both air-dried-rehydrated and never-dried Ca-PC expanded to approximately 2.0 nm in 10 mM CaCl2 and both samples had similar affinities for atrazine that were slightly lower than that of never-dried K-PC. The importance of interlayer hydration status in controlling sorption affinity was confirmed by molecular modeling, which revealed much greater interaction between interlayer water molecules and atrazine in a three-layer hydrate relative to a one-layer hydrate. The entropy change on moving atrazine from a fully hydrated state in the bulk solution to a partially hydrated state in the smectite interlayers is believed to be a major factor influencing sorption affinity. In an application test, choice of background solution (20 mM KCl versus 10 mM CaCl2) and air-drying treatments significantly affected atrazine sorption affinities for three-smectitic soils; however, the trends were not consistent with those observed for the reference smectite. Further, extending the initial rehydration time from 24 to 240 h (prior to adding atrazine) significantly decreased the soil's sorption affinity for atrazine. We conclude that interlayer hydration status has a large influence on the affinity of smectites for atrazine and that air-drying treatments have the potential to modify the sorption affinity of smectitic soils for organic molecules such as atrazine.

Adsorption↗

PubMed1996

Entropy estimation of symbol sequences.

We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limits for the space and time complexities of the compression algorithms. A scaling law is proposed for extrapolation from finite sample lengths. This is applied to sequences of dynamical systems in non-trivial chaotic regimes, a 1-D cellular automaton, and to written English texts. (c)1996 American Institute of Physics.

Journal Article↗

PubMed2001

Thermodynamic and structural aspects of the potential energy surface of simulated water.

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition is a topic of considerable interest. The potential energy surface of model liquids has been increasingly studied, since it provides a connection between the configurational component of the partition function on the one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent interbasin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model have been studied in great detail in recent years. We locate the minima sampled by the liquid by "quenches" from equilibrium configurations generated via molecular dynamics simulations, and then calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling.

Journal Article↗

PubMed1994

Genetic differences between blood- and brain-derived viral sequences from human immunodeficiency virus type 1-infected patients: evidence of conserved elements in the V3 region of the envelope protein of brain-derived sequences.

Human immunodeficiency virus type 1 (HIV-1) sequences were generated from blood and from brain tissue obtained by stereotactic biopsy from six patients undergoing a diagnostic neurosurgical procedure. Proviral DNA was directly amplified by nested PCR, and 8 to 36 clones from each sample were sequenced. Phylogenetic analysis of intrapatient envelope V3-V5 region HIV-1 DNA sequence sets revealed that brain viral sequences were clustered relative to the blood viral sequences, suggestive of tissue-specific compartmentalization of the virus in four of the six cases. In the other two cases, the blood and brain virus sequences were intermingled in the phylogenetic analyses, suggesting trafficking of virus between the two tissues. Slide-based PCR-driven in situ hybridization of two of the patients' brain biopsy samples confirmed our interpretation of the intrapatient phylogenetic analyses. Interpatient V3 region brain-derived sequence distances were significantly less than blood-derived sequence distances. Relative to the tip of the loop, the set of brain-derived viral sequences had a tendency towards negative or neutral charge compared with the set of blood-derived viral sequences. Entropy calculations were used as a measure of the variability at each position in alignments of blood and brain viral sequences. A relatively conserved set of positions were found, with a significantly lower entropy in the brain-than in the blood-derived viral sequences. These sites constitute a brain "signature pattern," or a noncontiguous set of amino acids in the V3 region conserved in viral sequences derived from brain tissue. This brain-derived signature pattern was also well preserved among isolates previously characterized in vitro as macrophage tropic. Macrophage-monocyte tropism may be the biological constraint that results in the conservation of the viral brain signature pattern.

Acquired Immunodeficiency Syndrome↗

PubMed1999

Joint basal and pulsatile hypersecretory mechanisms drive the monotropic follicle-stimulating hormone (FSH) elevation in healthy older men: concurrent preservation of the orderliness of the FSH release process: a general clinical research center study.

To appraise the neuroendocrine mechanisms that underlie a selective (monotropic) elevation of serum FSH concentrations in healthy older men, we sampled blood in 11 young (ages 21-34) and 8 older men (ages 62-72) men every 2.5 min overnight. Serum FSH concentrations were quantitated in an automated, high-sensitivity, chemiluminescence-based assay. Rates of basal and pulsatile FSH secretion were estimated by deconvolution analysis, and the orderliness of the FSH release process via quantitated the approximate entropy statistic. Statistical analysis revealed that healthy older men manifest dual neuroendocrine hypersecretory mechanisims; specifically, a 2-fold increase in the basal (nonpulsatile) FSH secretion rate, and a concurrent 50% amplification of FSH secretory burst mass (and amplitude). The regularity or orderliness of ad seriatim FSH release is preserved in older individuals. We postulate that higher basal FSH secretion in older men is a consequence of reduced testosterone negative feedback, whereas amplified FSH secretory burst mass reflects net enhanced stimulation of gonadotrope cells by endogenous FSH secretagogues (e.g. GnRH and/or activin). The foregoing specific mechanisms driving heightened FSH secretion in older men contrast with the lower-amplitude pulsatility and more disorderly patterns of LH release in the same individuals. Thus, the present data illuminate an age-dependent disparity in the disruption of FSH neuroregulation in the aging male.

Adult↗