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PubMed2006

Novel statistical-thermodynamic methods to predict protein-ligand binding positions using probability distribution functions.

We present two novel methods to predict native protein-ligand binding positions. Both methods identify the native binding position as the most probable position corresponding to a maximum of a probability distribution function (PDF) of possible binding positions in a protein active site. Possible binding positions are the origins of clusters composed, on the basis of root-mean square deviations (RMSD), from the multiple ligand positions determined by a docking algorithm. The difference between the methods lies in the ways the PDF is derived. To validate the suggested methods, we compare the averaged RMSD of the predicted ligand docked positions relative to the experimentally determined positions for a set of 135 PDB protein-ligand complexes. We demonstrate that the suggested methods improve docking accuracy by as much as 21-24% in comparison with a method that simply identifies the binding position as the energy top-scored ligand position.

Binding Sites↗
PubMed2007

Description of atomic burials in compact globular proteins by Fermi-Dirac probability distributions.

We perform a statistical analysis of atomic distributions as a function of the distance R from the molecular geometrical center in a nonredundant set of compact globular proteins. The number of atoms increases quadratically for small R, indicating a constant average density inside the core, reaches a maximum at a size-dependent distance R(max), and falls rapidly for larger R. The empirical curves turn out to be consistent with the volume increase of spherical concentric solid shells and a Fermi-Dirac distribution in which the distance R plays the role of an effective atomic energy epsilon(R) = R. The effective chemical potential mu governing the distribution increases with the number of residues, reflecting the size of the protein globule, while the temperature parameter beta decreases. Interestingly, betamu is not as strongly dependent on protein size and appears to be tuned to maintain approximately half of the atoms in the high density interior and the other half in the exterior region of rapidly decreasing density. A normalized size-independent distribution was obtained for the atomic probability as a function of the reduced distance, r = R/R(g), where R(g) is the radius of gyration. The global normalized Fermi distribution, F(r), can be reasonably decomposed in Fermi-like subdistributions for different atomic types tau, F(tau)(r), with Sigma(tau)F(tau)(r) = F(r), which depend on two additional parameters mu(tau) and h(tau). The chemical potential mu(tau) affects a scaling prefactor and depends on the overall frequency of the corresponding atomic type, while the maximum position of the subdistribution is determined by h(tau), which appears in a type-dependent atomic effective energy, epsilon(tau)(r) = h(tau)r, and is strongly correlated to available hydrophobicity scales. Better adjustments are obtained when the effective energy is not assumed to be necessarily linear, or epsilon(tau)*(r) = h(tau)*r(alpha,), in which case a correlation with hydrophobicity scales is found for the product alpha(tau)h(tau)*. These results indicate that compact globular proteins are consistent with a thermodynamic system governed by hydrophobic-like energy functions, with reduced distances from the geometrical center, reflecting atomic burials, and provide a conceptual framework for the eventual prediction from sequence of a few parameters from which whole atomic probability distributions and potentials of mean force can be reconstructed.

Amino Acids↗
PubMed1992

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.

Amino Acid Sequence↗
PubMed2003

Estimating the stenosis probabilities in arteriosclerosis obliterans using generalized estimating equations.

For each of 211 arteriosclerosis obliterans patients, the degree of stenosis of arteries at four sites were examined at Hiroshima University Hospital to analyse the relationship between the degree of stenosis and age, sex and site. The generalized estimating equations using a proportional odds model for the stenosis probability with exchangeable correlation was applied to this clustered, ordered polytomous data. Since the correlations between the responses were quite small, we could apply the independence estimating equations. The best mean model selected by Akaike information criterion suggested that age dependency of the stenosis probability was not observed in the central sites but was observed in the peripheral sites, and symmetry of the risk of stenosis was seen in the left and right sites. Details of the analysis will be described.

Adult↗
PubMedDate not supplied

The probability of inevitability: the inherent impossibility of validating criteria for brain death or 'irreversibility' through clinical studies.

A great need persists for diagnostic criteria for both brain death in young children and irreversible loss of consciousness at all ages. This article examines the inferences derived from a hypothetical confirmatory study in which all of the N patients who fulfilled the criterion did in fact experience brain death (irreversibility). A Bayesian methodology proves that, for N in the range of a large clinical study, estimations of prior probabilities are, for all practical purposes, irrelevant to the calculation of the posterior probabilities. The risk of a false positive diagnosis for the next patient who meets the criterion is approximately 1/(N + 2). The chance of at least one false positive diagnosis among the next (N + 1) patients who meet the criterion is around 50 per cent. Thus, achievement of the requisite moral certainty of a declaration of death (irreversibility) necessitates an impossibly large N for the study. This does not mean that one cannot diagnose death, but rather that the validity of the diagnostic criteria must be self-evident on a priori grounds, and that confirmatory studies are necessarily either inadequate or superfluous.

Adult↗
PubMed1991

Confidence intervals for post-test probability.

Confidence intervals are a natural way to describe the uncertainty of post-test probability in diagnostic tests. We consider confidence intervals for two different scenarios. At a site, for example, hospital emergency room or student health centre, with measured values of disease prevalence, sensitivity and specificity available, the confidence interval is similar to results in the literature, but at a site where measured values of these indices are unavailable, we develop a method, using the values of disease prevalence, sensitivity and specificity from other sites, to obtain a confidence interval for post-test probability. We use the diagnosis of strep throat to illustrate the results. We also obtain confidence intervals from simulations to compare with the results of both scenarios.

Adult↗
PubMed1993

Use of backcalculation for estimation of the probability of progression from HIV infection to AIDS.

Backcalculation has been used to estimate the rate of past HIV infection and to predict future AIDS incidence. In this study we examine another use: estimating the probability of progression from HIV infection to AIDS as a function of time from infection. Given observed AIDS incidence data, the technique of backcalculation estimates the most likely number of persons infected with HIV in the past. Assumptions about probability of progression from HIV infection to AIDS are necessary. By varying these assumptions and examining the resulting goodness of fit to the AIDS incidence data, we can theoretically estimate parameters of progression. We report on implementation of this method and examine its practical utility in deciding among four competing progression models specified on a priori grounds. The four specific models comprise three Weibull distributions with medians of 8, 10, and 12 years, respectively, and one model that begins as a Weibull with 8 year median but where the hazard is level after 3.5 years. To employ asymptotic maximum likelihood methods, we define a two parameter family of progression models that includes all four a priori models. One parameter sets the scale for an initial Weibull progression (the shape parameter being fixed for all models), and the other specifies a levelling point after which the hazard remains constant. AIDS incidence data from Canada's national surveillance system provided the empiric data for this evaluation. First we corrected these data for reporting delay by Poisson modelling of the delay distribution. We used three parametric families of infection curves: step-function, log-logistic, and logistic. The results support the hypothesis of an early levelling of the hazard function. When we fixed the scale parameter to that of the Weibull curve with 8 year median, the maximum likelihood estimate of the levelling point was 2.7 years, and a clearly superior fit was produced compared to a pure Weibull progression with the same scale parameter (likelihood ratio chi-square of 10.6 on 1 degree of freedom, p = 0.001). The maximum was indistinguishable in fit from the levelling point of 3.5 years hypothesized in advance (chi-square = 0.30, d.f. = 1, p = 0.58). Backcalculation, however, could not determine the Weibull scale parameter itself because the likelihood was quite flat as a function of this parameter. We conclude that one must determine the parameters governing the initial shape of the hazard function from other kinds of data.(ABSTRACT TRUNCATED AT 400 WORDS)

Acquired Immunodeficiency Syndrome↗
PubMed2001

Estimating probability of non-response to treatment using mixture distributions.

Repeat measurements of patient characteristics are often used to assess response to treatment. In this paper we discuss a normal mixture model for the observed change in the characteristic of interest in treated patients. The methods described can be used to estimate the overall proportion of non-response to treatment and also the probability that a patient has not responded to treatment given his or her observed change. The model parameters are estimated using maximum likelihood, and the delta method is used to construct a pointwise confidence band for the conditional probability that a patient is a non-responder to treatment. The work was initially motivated by analysis issues in the Fracture Intervention Trial (FIT), a randomized trial of the osteoporosis drug alendronate, and the method is illustrated with data from that study. We also evaluate key aspects of the estimation procedure with two simulation studies. In the first, the data generation model is the assumed normal mixture model, and in the second, the data are generated according to a shifted and scaled central t-distribution model suggested by the FIT data.

Aged↗
PubMed2003

Estimating the number of release sites and probability of firing within the nerve terminal by statistical analysis of synaptic charge.

Investigating the function of individual synapses is essential to understanding the mechanisms that influence the efficacy of chemical synaptic transmission. The known simplicity of the synaptic structure at the crayfish neuromuscular junction (NMJ) and its quantal nature of release allows an assessment of discrete synapses within the motor nerve terminals. Our goal in this article is to investigate the effect of the stimulation frequency on the number of active release sites (n) and the probability of release (p) at those active sites. Because methods based on direct counts often provide unstable joint estimates of (n) and (p), we base our analysis on mixture modeling. In particular, the mixture modeling approach is used to estimate (n) and (p) for stimulation frequencies of 1 Hz, 2 Hz, and 3 Hz. Our results indicate that as the stimulation frequency increases, new sites are recruited (thus increasing n) and the probability of release (p) increases.

Action Potentials↗
PubMedDate not supplied

Neuromagnetic evidence for the timing of lexical activation: an MEG component sensitive to phonotactic probability but not to neighborhood density.

Evidence from electrophysiological measures such as ERPs (event-related potentials) and MEG (magnetoencephalography) suggest that the first evoked brain response component sensitive to stimulus properties affecting reaction times in word recognition tasks occurs at 300-400 ms. The present study used the stimulus manipulation of Vitevich and Luce (1999) to investigate whether the M350, an MEG response component peaking at 300-400 ms, reflects lexical or postlexical processing. Stimuli were simultaneously varied in phonotactic probability, which facilitates lexical activation, and in phonological neighborhood density, which inhibits the lexical decision process. The present results indicate that the M350 shows facilitation by phonotactic probability rather than inhibition by neighborhood density. Thus the M350 cannot be a postlexical component.

Adult↗
PubMed1994

A microcomputer program for the design and analysis of phase II cancer clinical trials with two group sequential methods, the sequential probability ratio test, and the triangular test.

We developed an interactive and menu-driven computer program to help investigators design and analyze phase II cancer clinical trials with a group sequential method, namely the sequential probability ratio test or the triangular test. Based on the values selected for the parameters of the trial, the "Design" option allows one to obtain, using simulations, the statistical properties (type I and II error rates and the probability that the test accepts the hypothesis of inefficacy under 21 different assumptions) and the average sample size (under the same assumptions) of the selected test. The "Analysis" option (i) computes, at each analysis, the two statistics V and Z on which the sequential method is based and plots the sample path from the number of successes observed, and (ii), using asymptotic properties, gives the significance level of the test and a point estimate (with its 95% confidence interval) of the parameter of interest at the last analysis.

Algorithms↗
PubMed1995

Bacterial inoculum density and probability of para-nitrophenol biodegradability test response.

This study has been carried out to establish a model linking probability of positive response in para-nitrophenol biodegradability test to controlled variables of the test (suspended solids, SS; total bacteria, AODC; cultivable bacteria, CFU; specific biodegraders, MPN). Series of dilution of 11 raw inocula (6 activated sludges, 5 river waters) were tested. They reveal very dispersed values of biomass measured as SS, AODC, and CFU and quite comparable values of specific biodegraders for each category of inoculum (river or sludge). The proposed model fits well the empirical distribution of the experimental frequency of positive results versus inoculum density for each controlled variable. The constants k of the model, representing the fraction of biodegraders for each inoculum, were tested by the likelihood ratio test and were proven to be different from one another according to the biomass descriptor and the origin of the inoculum. The probabilistic model, in the case of para-nitrophenol biodegradation, indicates that standardized official tests (closed bottle, AFNOR, Sturm, and MITI I) are seldom optimal under those conditions. It allows the determination of which inoculum concentration can lead to a high probability (e.g., 99.9%) of observing paranitrophenol biodegradation by raw inocula.

Bacteria↗
PubMed1994

Environmental tobacco smoke and childhood asthma: comparing exposure metrics using probability plots.

This study demonstrates the use of probability plots for assessing exposure-disease relationships in case-control studies. We reanalyze data from a study of childhood asthma and exposure to environmental tobacco smoke, comparing alternative measures of smoking intensity. Previous analyses showed a higher mean urinary cotinine-to-creatinine ratio (CCR) in cases as compared with controls and a statistically significant odds ratio with exposure defined as 30 ng/mg CCR or higher. Using probability plots, we compare alternative exposure metrics and exposure cutpoints with respect to their ability to detect a statistically significant exposure-disease effect. A strong exposure-disease response is evident, overall, and the results are fairly robust to the choice of exposure cutpoint.

Adolescent↗
PubMed1996

Transcutaneous oxygen (TcPO2) estimates probability of healing in the ischemic extremity.

The severity of arterial ischemia is a major variable affecting healing of extremity wounds. By relating risk of failure to severity of ischemia, the probability of wound healing may be stratified along with assessment of general medical risks. Transcutaneous oxygen tension (TcPO2) arterial segmental pressure (ASP), and arterial segmental indices (ASI) were obtained in 204 ischemic lower extremity sites; 63% of the sites were in patients with diabetes mellitus (DM), 11% in patients with chronic renal failure (CRF), and 37% in patients with neither DM nor CRF (ND). Wounds included 126 amputations and 78 gangrenous ulcerations of the foot or toes. Healing (n = 112) was defined as complete wound closure, without regard to the time required. Failure (n = 92) was defined by the requirement for either arterial reconstruction (n = 45) or proximal amputation (n = 47). Stepwise multiple regression analysis was used to assess the relative contribution of each measurement and to predict the probability of healing; TcP02 was superior to ASP and ASI in all categories. TcP02 was the only test meeting the P < 0.05 entry criteria modeled by the regression. An accuracy of 83% was achieved. However, when each test was evaluated by univariate analysis, ASP and ASI did meet the criteria for the ND group. However, the accuracy was 68 and 72%, respectively. Predictive accuracy of TcP02 was unaffected by DM or CRF. ASP and ASI were satisfactory in the ND group, although of slightly reduced accuracy. ASP and ASI were misleading and inaccurate in DM and CRF. Thus, of the noninvasive tests, TcP02 alone is sufficient for objective risk stratification of arterial ischemia in the lower extremity.

Blood Gas Monitoring, Transcutaneous↗
PubMed2001

Fractal probability measures of learning.

Herein we introduce a technique for determining the fractal dimension of time series obtained from complex systems, in particular brain-wave data in which the fractal dimension is arguably a measure of awareness and learning. The technique is based on determining the probability distribution for the degree of irregularity in random time series and has been shown to be superior in terms of efficiency and reliability to more commonly used methods that rely on the correlation function. We speculate that the scaling behavior of the probability measure is an indicator of an allometric relation between learning and brain-wave activity.

Algorithms↗
PubMed1995

Interpretation of high-pass resolution perimetry with a probability plot.

BACKGROUND: The interpretation of high-pass resolution perimetry (HRP) fields can be difficult. An age-related probability plot was derived from a known data base to determine whether this improved specificity and sensitivity in early glaucoma detection. METHODS: Forty glaucoma patients with minor field loss and 40 normals of equivalent age and sex underwent HRP. All had previous Humphrey field data available for comparison. The detection of previously confirmed field defects by HRP was examined using different parameters. RESULTS: Using the age-corrected 95% confidence levels gave the best results, with sensitivity of 82.5% (33/40) and specificity of 85% (34/40). Using the contour plot yielded lower sensitivity (67.5%), while subjectively "eyeballing" the ring printout gave higher sensitivity (90%), but led to poor specificity (72.5%). CONCLUSION: The use of a probability plot enhances the performance of HRP. A certain proportion of cases may be missed using one criterion alone, but combining the information with other indices can increase the yield.

Adult↗
PubMed1992

Survival probabilities for some multitype branching processes in genetics.

Consider a positively regular, slightly supercritical branching process with K types. An approximation to the probability of survival of a line descended from a single individual of type i has recently been derived by Hoppe. If K is large, however, this approximation may not be easy to compute. A further approximation that is easily computable is given. The result is used to estimate probabilities of survival of an allele A that is originally present in one male or one female in a large, random mating, age-structured population. Both autosomal and sex-linked loci are considered. Another application of the approximation is also discussed.

Alleles↗