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PubMed2005

Convergent Island Statistics: a fast method for determining local alignment score significance.

MOTIVATION: Background distribution statistics for profile-based sequence alignment algorithms cannot be calculated analytically, and hence such algorithms must resort to measuring the significance of an alignment score by assessing its location among a distribution of background alignment scores. The Gumbel parameters that describe this background distribution are usually pre-computed for a limited number of scoring systems, gap schemes, and sequence lengths and compositions. The use of such look-ups is known to introduce errors, which compromise the significance assessment of a remote homology relationship. One solution is to estimate the background distribution for each pair of interest by generating a large number of sequence shuffles and use the distribution of their scores to approximate the parameters of the underlying extreme value distribution. This is computationally very expensive, as a large number of shuffles are needed to precisely estimate the score statistics. RESULTS: Convergent Island Statistics (CIS) is a computationally efficient solution to the problem of calculating the Gumbel distribution parameters for an arbitrary pair of sequences and an arbitrary set of gap and scoring schemes. The basic idea behind our method is to recognize the lack of similarity for any pair of sequences early in the shuffling process and thus save on the search time. The method is particularly useful in the context of profile-profile alignment algorithms where the normalization of alignment scores has traditionally been a challenging task. CONTACT: aleksandar@eidogen.com SUPPLEMENTARY INFORMATION: http://www.eidogen-sertanty.com/Documents/convergent_island_stats_sup.pdf.

Algorithms↗
PubMed1978

Distribution of membrane thickness determined by lineal analysis.

The expected statistical distributions of intercept length are derived in terms of geometrical probability density functions pertaining to plates with known thickness penetrated by lines with random orientation. These expressions provide arithmetic and graphical solutions for obtaining distributions of membrane thickness and reciprocal membrane thickness from empirical distributions of intercept lengths. Furthermore, general relationships between probability density functions of distributions of intercept length and membrane thickness are derived as well as those between their moments. Examples of the application of the method to biological samples are given, and estimated distributions of glomerular basement membrane thickness are compared to those obtained by an independent, direct method. Various sources of bias, which in practice may occur due to departures from the sample model, are discussed and the influence of some of them is estimated. The knowledge of the probability density function of reciprocal intercepts makes it possible to perform a correction of the distribution of measured intercept length, which to some extent eliminates bias.

Animals↗
PubMed2002

A new parametric method based on S-distributions for computing receiver operating characteristic curves for continuous diagnostic tests.

Receiver operating characteristic (ROC) curves provides a method for evaluating the performance of a diagnostic test. These curves represent the true positive ratio, that is, the true positives among those affected by the disease, as a function of the false positive ratio, that is, the false positives among the healthy, corresponding to each possible value of the diagnostic variable. When the diagnostic variable is continuous, the corresponding ROC curve is also continuous. However, estimation of such curve through the analysis of sample data yields a step-line, unless some assumption is made on the underlying distribution of the considered variable. Since the actual distribution of the diagnostic test is seldom known, it is difficult to select an appropriate distribution for practical use. Data transformation may offer a solution but also may introduce a distortion on the evaluation of the diagnostic test. In this paper we show that the distribution family known as the S-distribution can be used to solve this problem. The S-distribution is defined as a differential equation in which the dependent variable is the cumulative. This special form provides a highly flexible family of distributions that can be used as models for unknown distributions. It has been shown that classical statistical distributions can be represented accurately as S-distributions and that they occur in a definite subspace of the parameter space corresponding to the whole S-distribution family. Consequently, many other distributional forms that do not correspond to known distributions are provided by the S-distribution. This property can be used to model observed data for unknown distributions and is very useful in constructing parametric ROC curves in those cases. After fitting an S-distribution to the observed samples of diseased and healthy populations, ROC curve computation is straightforward. A ROC curve can be considered as the solution of a differential equation in which the dependent variable is the ratio of true positives and the independent variable is the ratio of false positives. This equation can be easily obtained from the S-distributions fitted to observed data. Using these results, we can compute pointwise confidence bands for the ROC curve and the corresponding area under the curve. We shall compare this approach with the empirical and the binormal methods for estimating a ROC curve to show that the S-distribution based method is a useful parametric procedure.

Area Under Curve↗
PubMed2006

Functional MRI of memory in the hippocampus: Laterality indices may be more meaningful if calculated from whole voxel distributions.

Lateralization of memory by functional MRI (fMRI) may be helpful for surgical planning related to the medial temporal lobe (MTL). Most fMRI memory studies have calculated lateralization indices (LI) in the MTL from suprathreshold voxels only, but the selection of threshold remains highly arbitrary. We hypothesized that LIs could be reliably extracted from the distribution of voxels encompassing all positive T statistical values, each weighted by their own statistical significance. We also hypothesized that patient LIs that are two or more standard deviations (SD) away from the control group mean LI may be more clinically relevant than LIs that are not compared to control group. Thirteen healthy subjects had memory fMRI, and five epilepsy patients had both fMRI and the intracarotid amobarbital procedure (IAP). The fMRI task consisted of encoding patterns, scenes, and words. We found that normal subjects' LIs extracted from whole weighted statistical distributions tended to lateralize to the left for words, to the right for patterns, and intermediately for scenes, consistent with previous research. Weighted LIs were less variable than those calculated from suprathreshold voxels only. Using this approach, all patients had fMRI memory lateralizations consistent with IAP results. The weighted LIs provided a more clear-cut distinction of patients from the normal group (in terms of SDs from the group mean) than the suprathreshold voxel count approach. Our results suggest that using weighted distributions can be a useful strategy for assessing memory lateralization by fMRI in the MTL.

Adult↗
PubMed2005

A universally applicable method of operon map prediction on minimally annotated genomes using conserved genomic context.

An important step in understanding the regulation of a prokaryotic genome is the generation of its transcription unit map. The current strongest operon predictor depends on the distributions of intergenic distances (IGD) separating adjacent genes within and between operons. Unfortunately, experimental data on these distance distributions are limited to Escherichia coli and Bacillus subtilis. We suggest a new graph algorithmic approach based on comparative genomics to identify clusters of conserved genes independent of IGD and conservation of gene order. As a consequence, distance distributions of operon pairs for any arbitrary prokaryotic genome can be inferred. For E.coli, the algorithm predicts 854 conserved adjacent pairs with a precision of 85%. The IGD distribution for these pairs is virtually identical to the E.coli operon pair distribution. Statistical analysis of the predicted pair IGD distribution allows estimation of a genome-specific operon IGD cut-off, obviating the requirement for a training set in IGD-based operon prediction. We apply the method to a representative set of eight genomes, and show that these genome-specific IGD distributions differ considerably from each other and from the distribution in E.coli.

Algorithms↗
PubMed1990

Stationarity and normality of distribution of rat cortical brain waves.

Establishing the stationarity and statistical distribution of potentials recorded from the nervous system is crucial for the application of frequency analysis. Both parameters were determined in the electrocorticograms of six adult Wistar rats during wakefulness and desynchronized sleep, during both of which desynchronization prevails. Stationarity of the signals was found to occur during at least 20 s in both states of the wakefulness-sleep cycle. A normal distribution was also found for at least 6.7 s. These findings provide strong support for the use of frequency analysis of brain waves as a reliable method to quantify neural electro-oscillograms.

Animals↗
PubMed1983

Helical sidedness and the distribution of polar residues in trans-membrane helices.

Trans-membrane helices have often been claimed to show "sidedness" in the distribution of polar and hydrophobic residues. However, an analysis of the statistical distribution of polar residues in randomly generated helices shows that the degree of bias commonly observed in real helices is far from statistically significant. It is concluded that "patchy" distributions of residues in such helices should be interpreted with great care.

Bacteriorhodopsins↗
PubMed2001

Quantification and variability analysis of bacterial cross-contamination rates in common food service tasks.

This study investigated bacterial transfer rates between hands and other common surfaces involved in food preparation in the kitchen. Nalidixic acid-resistant Enterobacter aerogenes B199A was used as a surrogate microorganism to follow the cross-contamination events. Samples from at least 30 different participants were collected to determine the statistical distribution of each cross-contamination rate and to quantify the natural variability associated with that rate. The transfer rates among hands, foods, and kitchen surfaces were highly variable, being as low as 0.0005% and as high as 100%. A normal distribution was used to describe the variability in the logarithm of the transfer rates. The mean +/- SD of the normal distributions were, in log percent transfer rate, chicken to hand (0.94 +/- 0.68), cutting board to lettuce (0.90 +/- 0.59), spigot to hand (0.36 +/- 0.90), hand to lettuce (-0.12 +/- 1.07), prewashed hand to postwashed hand (i.e., hand washing efficiency) (-0.20 +/- 1.42), and hand to spigot (-0.80 +/- 1.09). Quantifying the cross-contamination risk associated with various steps in the food preparation process can provide a scientific basis for risk management efforts in both home and food service kitchens.

Animals↗
PubMed2004

Effects of localization and amplification on intensity distribution of light transmitted through random media.

We numerically study the statistical distribution of intensity of light transmitted through quasi-one-dimensional random media by varying the dimensionless conductance g and the amount of absorption or gain. A markedly non-Rayleigh distribution is found to be well fitted by the analytical formula of Phys. Rev. Lett. 74, 2674 (1995)] with a single parameter g(') . We show that in the passive random system g(') is uniquely related to g , while in amplifying or absorbing random media g(') also depends on the gain or absorption coefficient.

Journal Article↗
PubMed1998

The frequency distribution of the number of ion pairs in irradiated tissue.

The statistical distribution of the number of ion pairs per ionizing event in a small volume simulating a tissue sphere was obtained by applying the Expectation-Maximization (EM) algorithm to experimental spectra measured by exposing a Rossi-type spherical proportional counter to gamma radiation. The normalized experimental spectrum, r(x), which is the distribution of the number of ion pairs per event from both the primary track and the subsequent electron multiplication, can be represented as Sum(n) p(n) x f(n,x), where the f(n,x)'s for n = 1, 2, 3, ..., n are the normalized spectra for exactly 1, 2, 3, ..., n primary ion pairs and are calculated by convoluting the single-electron spectrum. The coefficients pn represent the mixing proportions of the spectra corresponding to 1, 2, 3, ..., n ion pairs in forming the experimental spectrum. The single-electron spectrum used in our calculations is the distribution of the number of ion pairs due to the multiplication process, and it is represented in analytical form by the Gamma distribution f(1,x) = a x x(b) x e(-cx), where x is energy, usually in eV, and a, b and c are constants. The EM algorithm is an iterative procedure for computing the maximum likelihood or maximum a posteriori estimates of the mixing proportions p(n), which we also refer to as the primary distribution of ion pairs in a microscopic spherical tissue-equivalent volume. The experimental and primary spectra are presented for simulated tissue spheres ranging from 0.25 to 8 microm in diameter exposed to 60Co gamma radiation.

Cobalt Radioisotopes↗
PubMed1982

Distribution of aflatoxin in whole peanut kernels, sampling plans for small samples.

It is well known that the distribution of aflatoxin in a lot of whole peanut kernels is extremely heterogeneous. Several different statistical distribution models have been proposed, fitting the experimental data reasonably well as long as the samples are very large, but differing considerably when applied to small samples. Therefore, it is important to know the real distribution between single kernels for the evaluation of the effectiveness of sampling plans for small samples. It is shown by the analysis of 368 samples of 1-10,000 kernels from the same lot of peanuts that the negative binomial distribution represents a good statistical model. The variance can be estimated from the mean concentration of the analysed samples, as confirmed by the comparison of data from several independent investigations. Decisions based on small samples are especially unfavourable to the consumer, as even a lot with a high mean concentration will tend to give negative results. A reasonably small risk of a false decision, both to the consumer and to the producer, can be reached only if very large samples are analysed.

Aflatoxin B1↗
PubMed2003

Digital karyometry in pancreatic adenocarcinoma.

OBJECTIVE: To characterize nuclei from pancreatic adenocarcinoma and nonneoplastic pancreatic tissue by digital karyometry, demonstrating specific nuclear signatures for each of them. STUDY DESIGN: Of cells from malignant and nonmalignant pancreatic tissue, 1,300 nuclei were assessed by digital karyometry from paraffin blocks stored at the Pathology Service of Hospital de Clinicas de Porto Alegre. A set of 40 features descriptive of the spatial and statistical distribution of nuclear chromatin was computed for each nucleus. Signatures were created for both types of tissue, and a distance metric from "normal" was defined and calculated for them. RESULTS: There were significant differences in 11 features between the 2 groups, allowing the creation of digital signatures. CONCLUSION: Nuclear chromatin texture signature can offer a specific digital characterization for both pancreatic adenocarcinoma and nonmalignant pancreatic tissue. Several isolated nuclear features serve as markers for the diagnosis of pancreatic adenocarcinoma. The present karyometric study of normal and malignant pancreatic tissue may be of use as a continuing tool to early diagnosis of pancreatic adenocarcinoma as it can be applied to cytologic specimens, also. In the future, studies using this technique should assess the chemopreventive potential of different agents as well as prognosis and treatment options for pancreatic adenocarcinoma.

Adenocarcinoma↗
PubMedDate not supplied

The role of the codon first letter in the relationship between genomic GC content and protein amino acid composition.

Analysis of the statistical distribution of amino acid compositions within 22 protein families shows that a GC bias generally affects proteins with a variety of functions from the extreme thermophile Thermus. This results in evident enrichment in amino acids of the group L, V, A, P, R and G and underrepresentation of amino acids of the group I, M, F, S, T, C and W. The strong amino acid composition biases noted in Thermus proteins are not related to thermoadaptation; they were also found in mesophilic homologues encoded by GC-rich genes. The results of a comparative analysis on large samples of translated sequences from 30 organisms, representing the three major kingdoms of life and including extremophiles, indicate a universal correlation between the usage of particular amino acids and the genomic GC content. It is concluded that the codon first letter plays a dominant role in translating the genomic GC signature into protein amino acid composition and sequences.

Amino Acid Sequence↗
PubMed2004

Two analytical solutions for a model of pulsed arterial spin labeling with randomized blood arrival times.

A fairly general theoretical model for pulsed arterial spin labeling perfusion methods has been available for some time but analytical solutions were derived for only a small number of arterial blood input functions. These mostly assumed a sudden and simultaneous arrival of the tagged blood into the imaged region. More general cases had to be handled numerically. We present analytical solutions for two more realistic arterial input functions. They both allow the arrival times of the molecules of tagged arterial blood to be statistically distributed. We consider cases of (1) a uniform distribution on a finite time interval and (2) a normal distribution characterized by its mean and standard deviation. These models are physiologically meaningful because the statistical nature of the arrival times reflects the distribution of velocities and path lengths that the blood water molecules undertake from the tagging region to the imaged region. The model parameters can be estimated from the measured dependency of the perfusion signal on the tag inversion time.

Algorithms↗
PubMed2005

A distributed parameter model of cerebral blood-tissue exchange with account of capillary transit time distribution.

Quantitative estimates of physiological parameters associated with cerebral blood flow can be derived from the analysis of dynamic contrast-enhanced (DCE) images, using an appropriate model of the underlying tissue impulse residue function. The theoretical formulation of a distributed parameter model of tissue microcirculation, which accounts for the effects of capillary permeability and transit time distribution, is presented here. This model considers a statistical distribution of capillary-tissue units, each described by a distributed parameter model that accounts for convective transport within the capillary and transcapillary axial diffusion. Monte Carlo simulations were performed to study the confidence of the parameter estimates, and the model was used to analyze DCE CT images of patient study cases with metastatic cerebral tumors. The tumors were found to yield significantly higher estimates than normal tissues for the parameters associated with the extravasation of tracer and for the standard deviation of capillary transit times. The proposed model can be used with DCE imaging to study the microcirculatory characteristics of cerebral tumors.

Aged↗
PubMed1986

Comparative sensitivity of survival-adjusted chi-square and normal statistics for the mutagenesis fluctuation assay.

Three statistics for analysis of microtitre plate mutagenesis fluctuation tests were studied by simulation, and in enzyme-activated assays of dimethylnitrosamine and diethylnitramine. A survival-adjusted chi 2 statistic ('Gsq') was compared with Katz's normally distributed statistic ('Phi'), and with the survival-independent statistic ('Zsq') of Gilbert. When toxicity was either very low or high, the Phi statistic either could not be evaluated over the whole range of possible background mutant frequencies, or sometimes it indicated unusually high levels of statistical significance, even when the other tests were negative. The survival-adjusted Gsq closely followed the Zsq statistic throughout the experimentally useful range of toxicities and mutant background values, with some improvement in sensitivity. Within the range 80 +/- 10% survival approximately, Katz's statistic 'Phi' was the most sensitive. The choice of statistical test could affect the estimate of the minimal effective mutagenic concentration by a factor of 10-100. For screening unknowns, both types of test (Phi and Gsq (or Zsq] may help in detecting suspect pro-mutagens and in designing a confirmatory assay. Bacterial population statistics are needed to assess the value of statistically positive results.

Cell Survival↗
PubMed2004

The difficult interpretation of transcriptome data: the case of the GATC regulatory network.

Genomic analyses on part of Escherichia coli's chromosome had suggested the existence of a GATC regulated network. This has recently been confirmed through a transcriptome analysis. Two hypotheses about the molecular control mechanism have been proposed-(i) the GATC network regulation is caused by the presence of GATC clusters within the coding sequences; the regulation is the direct consequence of the clusters' hemi-methylation and therefore their elevated melting temperature, (ii) the regulation is caused by the presence of GATCs in the non-coding 500 bp upstream regions of the affected genes; it is the consequence of an interaction with a regulatory protein like Fnr or CAP. An analysis of the transcriptome data has not allowed us to decide between the two hypotheses. We have therefore taken a classic genomic approach, analyzing the statistical distribution of GATC along the chromosome, using a realistic model of the chromosome as theoretical reference. We observe no particular distribution of GATC in the non-coding upstream regions; however, we confirm the presence of GATC clusters within the genes. In order to verify that the particular distribution observed in E. coli is not a statistical artefact, but has a physiological role, we have carried out the same analysis on Salmonella, making the hypothesis that the genes containing a GATC clusters should be largely the same in the two bacteria. This has been indeed observed, showing that the genes containing a GATC cluster are part of a regulation network. The present is a case study, which demonstrates that the analysis of transcriptome data does not always permit to identify the primary cause of a phenomenon observed; on the other hand, a classic genomic approach linked with a comparative study of related genomes may allow this identification.

Computational Biology↗
PubMedDate not supplied

Fine structure analysis of temporal patterns in the light response of cells in the lateral geniculate nucleus of cat.

This study focuses on the analysis of temporal patterns in the spike train of cells in the lateral geniculate nucleus (LGN) of cat. Two-hundred eighty-three units have been recorded extracellularly in anesthetized animals during visual stimulation with flashing spot stimuli of different size. We used a novel method of temporally local computed interval distributions (intervalogram; Funke & Wörgötter, 1995) to visualize the statistical distribution of interspike intervals during different phases of the visual response. Multimodal interval distributions were observed mainly in X- and Y-ON cells, reflecting the tendency of these cells to fire with preferred intervals during the sustained light response. The shortest preferred interval is called the fundamental interval and the longer ones (higher-order intervals) are, in general, multiples thereof. During increasing surround inhibition a redistribution of the intervals towards the higher orders was observed. We regarded the different in the interval distributions as different components of possible temporal spike sequences and performed a pattern search up to the level of five subsequent intervals. While it is obvious, that the dominant peak is most strongly represented in any interval sequence, we also show that a significant overrepresentation of short sequences of similar intervals exists. The repetition rate is rather small (4-5 intervals) and, therefore, no long-lasting oscillatory pattern was observed in the autocorrelograms. Power spectral analysis of the peristimulus-time histograms, however, revealed that the sequential firing pattern is strongly stimulus locked at least for the majority of sweeps in the records. The mean firing rate of an LGN cell decreases with increasing stimulus size as well as with decreasing contrast. Therefore, the mean rate cannot be used to distinguish between these situations. While in the whole network this tradeoff can be resolved by the combined activity of multiple cells, our findings additionally suggest that contrast and size can be distinguished already at the single-cell level using different temporal patterns.

Animals↗