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PubMed2002

Distributional regimes for the number of k-word matches between two random sequences.

When comparing two sequences, a natural approach is to count the number of k-letter words the two sequences have in common. No positional information is used in the count, but it has the virtue that the comparison time is linear with sequence length. For this reason this statistic D(2) and certain transformations of D(2) are used for EST sequence database searches. In this paper we begin the rigorous study of the statistical distribution of D(2). Using an independence model of DNA sequences, we derive limiting distributions by means of the Stein and Chen-Stein methods and identify three asymptotic regimes, including compound Poisson and normal. The compound Poisson distribution arises when the word size k is large and word matches are rare. The normal distribution arises when the word size is small and matches are common. Explicit expressions for what is meant by large and small word sizes are given in the paper. However, when word size is small and the letters are uniformly distributed, the anticipated limiting normal distribution does not always occur. In this situation the uniform distribution provides the exception to other letter distributions. Therefore a naive, one distribution fits all, approach to D(2) statistics could easily create serious errors in estimating significance.

Computer Simulation↗

PubMed2004

[Spatial distribution pattern of Chilo suppressalis analyzed by classical method and geostatistics].

Two original samples of Chilo suppressalis and their grid, random and sequence samples were analyzed by classical method and geostatistics to characterize the spatial distribution pattern of C. suppressalis. The limitations of spatial distribution analysis with classical method, especially influenced by the original position of grid, were summarized rather completely. On the contrary, geostatistics characterized well the spatial distribution pattern, congregation intensity and spatial heterogeneity of C. suppressalis. According to geostatistics, the population was up to Poisson distribution in low density. As for higher density population, its distribution was up to aggregative, and the aggregation intensity and dependence range were 0.1056 and 193 cm, respectively. Spatial heterogeneity was also found in the higher density population. Its spatial correlativity in line direction was more closely than that in row direction, and the dependence ranges in line and row direction were 115 and 264 cm, respectively.

Algorithms↗

PubMed2001

Testing microbiologic response to antiinfective medications with incomplete data.

Clinical trials of antiinfective medications often require estimates of the proportions of patients, n, who are free of disease-causing pathogens at the end of treatment, as well as the proportions of all pathogens that have been eradicated. Each patient is infected with several species of pathogens, but the response to study medication for some of these pathogens may be unknown because some specimens were lost or because the patient received nonstudy medication that was known to be effective against these species. This paper develops a statistical model that estimates pi for each treatment and that accounts for the unknown pathogen responses as well as overdispersion of the remaining responses due to within-patient effects. The data are modeled with the Poisson distribution for the numbers of pathogen species per patient and the beta-binomial model for pathogen eradication. The Poisson and beta-binomial parameters are estimated through maximum likelihood estimation, and the treatment difference in the pi valves and its standard error are estimated by transforming the underlying parameters. Confidence intervals based on these estimates are constructed to test the hypothesis of noninferiority of the test treatment.

Algorithms↗

PubMed1987

Sperm from some infertile men may consist of several populations.

In the hamster ovum penetration (HOP) test, when ova have equal penetrability and sperm have equal penetrating ability, the distribution of zona-free hamster ova classified by number of penetrating human sperm is expected to follow the Poisson distribution (PD). This study reports tests for PD in HOP tests on 9 infertile patients and 11 normal controls. The data, presented in detail, show the expected PD in the control group. In contrast, 3 patients had HOP tests with definite non-PDs, whereas 5 patients have clearcut PDs. The cause of non-PD is unknown, but could result from differences among motile sperm in penetrating ability.

Adult↗

PubMed1967

Fluorescent cell counting as an assay method for respiratory syncytial virus.

The fluorescent cell-counting technique was applied to the enumeration of cell-infecting units of respiratory syncytial (RS) virus in human fetal diploid (HFD) cover-slip cell cultures; it was a sensitive, precise, and rapid assay method. Approximately 2 hr was required for maximal adsorption of RS virus to HFD cell monolayers. However, about 15% of the infectious virus in the inoculum remained unadsorbed; this percentage was not significantly reduced even when the adsorption period was extended to 5 hr. A linear relationship between virus concentration and the number of fluorescent cells existed over a range of 1.2 log(10) units. Variation of the mean of replicate determinations in a single experiment was approximately 7.5%. The distribution of single infected HFD cells on cover-slip cell cultures corresponded with the calculated frequencies of the Poisson distribution. The Chi square test for the extent of fit was calculated for several experiments, and the value of P was never less than 0.5. The addition of immune serum after virus adsorption effectively inhibited the development of detectable levels of viral antigen in secondarily infected cells.

Adsorption↗

PubMed1977

Avoidance-modified generalised distributions and their application to studies of superparasitism.

Given an underlying distribution for the number of encounters between parasites and a host this may be generalised by the distribution of the number of eggs per encounter. If eggs are already present, a parasite may avoid oviposition at subsequent encounters. A class of avoidance-modified generalised distributions is presented to model such situations. The case of a solitary (single egg-laying) parasite and a Poisson distribution for the number of encounters gives rise to a distribution of particular interest. Various properties of this distribution are derived and alternative estimation procedures investigated. Estimators based on the method of mean and zero frequency are shown to have the dual advantages over other estimators that have been proposed of simplicity of computation and increased efficiency. Over a wide range of parameter values there is virtually no loss of efficiency in comparison with maximum likelihood estimation.

Animals↗

PubMed1995

What determines the size frequency distribution of beta-amyloid (A beta) deposits in Alzheimer's disease patients?

The factors determining the size of individual beta-amyloid (A beta) deposits and their size frequency distribution in tissue from Alzheimer's disease (AD) patients have not been established. In 23/25 cortical tissues from 10 AD patients, the frequency of A beta deposits declined exponentially with increasing size. In a random sample of 400 A beta deposits, 88% were closely associated with one or more neuronal cell bodies. The frequency distribution of A beta deposits which were associated with 0,1,2,...,n neuronal cell bodies deviated significantly from a Poisson distribution, suggesting a degree of clustering of the neuronal cell bodies. In addition, the frequency of A beta deposits declined exponentially as the number of associated neuronal cell bodies increased. A beta deposit area was positively correlated with the frequency of associated neuronal cell bodies, the degree of correlation being greater for pyramidal cells than smaller neurons. These data suggested: (1) the number of closely adjacent neuronal cell bodies which simultaneously secrete A beta was an important factor determining the size of an A beta deposit and (2) the exponential decline in larger A beta deposits reflects the low probability that larger numbers of adjacent neurons will secrete A beta simultaneously to form a deposit.

Aged↗

PubMed2000

Equilibrium distribution of gas molecules adsorbed on an active surface

We evaluate the exact equilibrium distribution of gas molecules adsorbed on an active surface with an infinite number of attachment sites. Our result is a Poisson distribution having mean X=&mgr;PP(s)/P(e), with &mgr; the mean gas density, P(s) the sticking probability, P(e) the evaporation probability in a time interval tau, and P Smoluchowski's exit probability in time interval tau for the surface in question. We then solve for the case of a finite number of attachment sites using the mean field approximation, recovering the Langmuir isotherm in this case.

Journal Article↗

PubMed1975

Non-random distribution of surface immunoglobulins on murine B lymphocytes.

An indirect labeling technique was used to map the surface immunoglobulin (Ig) on murine splenic B lymphocytes by freeze-etching. Cells were labeled first with fluorescein conjugates of monovalent (papain-digested) anti-Ig antibody followed by monovalent anti-fluorescein antibody coupled to ferritin. The technique avoids cross-linking and aggregation of surface Ig. Freeze-etched replicas of cells labeled at 4 degrees C, as well as of cells prefixed with paraformaldehyde showed that surface Ig was distributed in small clusters with interconnecting networks. The observed pattern was analyzed statistically by comparing it with the expected random (Poisson) distribution and shown to be non-random to a high degree of statistical significance. The deviation from randomness could be explained by the presence of clusters and relative excesses of bare membrane. Such an observed distribution of surface Ig suggests that this membrane macromolecule may be organized in a specific manner. The distribution may also play a role in the function of surface Ig as the antigen receptor on B lymphocytes.

Animals↗

PubMed1983

The analysis of rates using Poisson regression models.

Models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters. Estimates of the parameters can be obtained by means of iteratively reweighted least squares (IRLS). When the events of interest follow the Poisson distribution, the IRLS algorithm is equivalent to using the method of scoring to obtain maximum likelihood (ML) estimates. The general Poisson regression models include log-linear, quasilinear and intrinsically nonlinear models. The approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model. Standard statistical packages that support IRLS can then be used to obtain ML estimates, their asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. Applications of these methods to epidemiologic follow-up studies with the data organized into a life-table type of format are discussed. The method is illustrated by using a nonlinear model, derived from the multistage theory of carcinogenesis, to analyze lung cancer death rates among British physicians who were regular cigarette smokers.

Models, Theoretical↗

PubMed1977

Three statistical models for estimating length of stay.

The probability density functions implied by three methods of collecting data on the length of stay in an institution are derived. The expected values associated with these density functions are used to calculate unbiased estimates of the expected length of stay. Two of the methods require an assumption about the form of the underlying distribution of length of stay; the third method does not. The three methods are illustrated with hypothetical data exhibiting the Poisson distribution, and the third (distribution-independent) method is used to estimate the length of stay in a skilled nursing facility and in an intermediate care facility for patients enrolled in California's MediCal program.

California↗

PubMed1976

Morphogenesis in Myxococcus xanthus and Myxococcus virescens Myxobacterales.

1. Myxococcus xanthus B and M. virescens V2 were compared with a view to establishing the control of their morphogenetic cycles. Both organisms are typical myxococci and on solid media with low concentrations of nutrient they form fruiting bodies, within which vegetative cells convert to myxospores. Ultrathin sections of vegetative M. virescens resembled those of M. xanthus and contained prominent heavily stained bodies, presumed to be polyphosphate granules. Shadowed preparations showed fimbriae associated with M. xanthus but not with M. virescens. 2. M. xanthus B converted to myxospores in liquid medium in response to certain alcohols. M. virescens V2 produced phase-refractile spheres, which were not viable and had an unusual ultrastructure. 3. The distributions of fruiting bodies on solid media containing 0.02% Casitone were recorded for the two species and were compared with a Poisson distribution. Cells responded to differences in cell density in a manner suggestive of a response to a chemotactic attractant. Cells growing vegetatively and also cells forming fruiting bodies produced 3',5'-cyclic adenosine monophosphate (cAMP) as measured by the incorporation of exogeneous [3H] adenosine into cAMP. 4. The significance of these findings for theories of fruiting body formation are discussed.

Chemotaxis↗

PubMed1991

Evolution of the cytochrome b gene of mammals.

With the polymerase chain reaction (PCR) and versatile primers that amplify the whole cytochrome b gene (approximately 1140 bp), we obtained 17 complete gene sequences representing three orders of hoofed mammals (ungulates) and dolphins (cetaceans). The fossil record of some ungulate lineages allowed estimation of the evolutionary rates for various components of the cytochrome b DNA and amino acid sequences. The relative rates of substitution at first, second, and third positions within codons are in the ratio 10 to 1 to at least 33. For deep divergences (greater than 5 million years) it appears that both replacements and silent transversions in this mitochondrial gene can be used for phylogenetic inference. Phylogenetic findings include the association of (1) cetaceans, artiodactyls, and perissodactyls to the exclusion of elephants and humans, (2) pronghorn and fallow deer to the exclusion of bovids (i.e., cow, sheep, and goat), (3) sheep and goat to the exclusion of other pecorans (i.e., cow, giraffe, deer, and pronghorn), and (4) advanced ruminants to the exclusion of the chevrotain and other artiodactyls. Comparisons of these cytochrome b sequences support current structure-function models for this membrane-spanning protein. That part of the outer surface which includes the Qo redox center is more constrained than the remainder of the molecule, namely, the transmembrane segments and the surface that protrudes into the mitochondrial matrix. Many of the amino acid replacements within the transmembrane segments are exchanges between hydrophobic residues (especially leucine, isoleucine, and valine). Replacement changes at first and second positions of codons approximate a negative binomial distribution, similar to other protein-coding sequences. At four-fold degenerate positions of codons, the nucleotide substitutions approximate a Poisson distribution, implying that the underlying mutational spectrum is random with respect to position.

Amino Acid Sequence↗

PubMed2006

Use of optical density detection times to assess the effect of acetic acid on single-cell kinetics.

The growth of Listeria innocua at different acetic acid concentrations (0 to 2,000 ppm) was monitored by optical density measurements in a Bioscreen (Labsystems, Vantaa, Finland). The generated populations came from low inocula that were obtained by serial dilution. A new method to estimate both the growth rate and the lag time of single cells from the detection times (time to reach an optical density of 0.11) was developed. It assumes that the single-cell lag times follow a gamma distribution and takes into account the randomness of the inoculation level. (The initial cell number per well was assumed to follow a Poisson distribution.) In this way, relatively small numbers of replicates are sufficient to obtain a robust estimation of the distribution of single-cell lag times. The results were validated with plate count experiments. It was found that logarithms of both the growth rates and of population lag times increased linearly with the acetic acid concentration. The logarithm of the scale parameter of the gamma distribution of the single-cell lag times also increased linearly with the acetic acid concentration irrespective of the phase of the inoculum.

Acetic Acid↗

PubMed1975

The size and demographic composition of social groups of wild orang-utans.

Mackinnon (1974) observed social sub-groups of wild orang-utans. The groups' distribution of size and age-sex composition can test mathematical models of group formation. As predicted by models published previously, a truncated Poisson distribution describes the group sizes well. The inferred parameters governing group formation conform to a pattern in other primate species. A simple model for the demographic composition of a sub-group assumes that an individual joins a sub-group with a probability independent of his age-sex class and of other members of the sub-group. This model's predictions, which agree poorly with observation, offer a quantitative baseline against which one can infer when a demographic combination occurs with a non-random frequency.

Age Factors↗

PubMed1991

Frequency of trisomy 21 in Germany before and after the Chernobyl accident.

For Berlin (West) the rate of trisomy 21 among newborn and all prenatally diagnosed cases can be almost completely recorded, including the maternal age distribution. During the 9-year-period from 1980 and 1988 the average number of trisomy 21 per month was about 2, following a Poisson distribution. A significant increase (P less than 0.01) was observed in January 1987, exactly 9 months after the Chernobyl accident. In a supraregional study based on greater than 30,000 prenatal diagnoses performed in 1986, no significant effect could be observed. However, the highest rates of trisomy 21 were observed in the more heavily contaminated, southern part of Germany. The majority of these fetuses were conceived during the period of greatest radioactive exposure. The data are discussed with respect to the effect of low-dose radiation around the time of conception on the induction of non-disjunction in man.

Abnormalities, Radiation-Induced↗

PubMed1986

Autoradiographic studies of the synthesis of RNA and protein as a function of cell volume in Streptococcus faecium.

Mid-exponential-phase cultures were either labeled continuously with tritiated leucine and uracil or pulse-labeled with tritiated leucine. The amount of leucine and uracil incorporated into protein or RNA per cell was determined by grain counts of autoradiographs of cells seen in electron micrographs; the volume of each cell was determined by three-dimensional reconstruction. The average number of autoradiographic grains around cells continuously labeled with uracil and leucine increased linearly with cell volume. In contrast, while the average grain count around cells pulse-labeled with leucine increased in a near-linear fashion over most of the volume classes, less than the expected number of grains were seen around cells in large- and small-size classes. The distribution of grains around cells from both the continuously and pulse-labeled populations could be fit at the 5% confidence level with a Poisson distribution modified to take into consideration the volume distribution of each population of cells analyzed. These findings suggested that large changes in the density of RNA and protein do not occur in most cells as they increase in size; however, there may be decreases in the rate of protein synthesis in some large and small cells. The decrease in the rate of protein synthesis appears consistent with the hypothesis that new sites of envelope growth must be introduced into cells that are close to the division event to restore rapid growth.

Autoradiography↗

PubMed1989

A practical method for rescuing desired hybridomas during monoclonal antibody production.

We present a practical method for the rescue of previously stable hybridoma clones which increases the proportion of desired cells in the population before cloning by limiting dilution. When the antibody activity of a culture supernatant was lower than that previously obtained, a precloning distribution at a density of 10 cells per microtiter well greatly improved the chances of obtaining a single active clone by subsequent limiting dilution. The Poisson distribution model was used to evaluate the method. Probabilities calculated clearly demonstrate the advantage of this precloning distribution step when attempting to isolate a hybridoma cell line that is relatively rare in a population.

Animals↗