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PubMed1993

Probability model for molecular recognition in biological receptor repertoires: significance to the olfactory system.

A generalized phenomenological model is presented for stereospecific recognition between biological receptors and their ligands. We ask what is the distribution of binding constants psi(K) between an arbitrary ligand and members of a large receptor repertoire, such as immunoglobulins or olfactory receptors. For binding surfaces with B potential subsite and S different types of subsite configurations, the number of successful elementary interactions obeys a binomial distribution. The discrete probability function psi(K) is then derived with assumptions on alpha, the free energy contribution per elementary interaction. The functional form of psi(K) may be universal, although the parameter values could vary for different ligand types. An estimate of the parameter values of psi(K) for iodovanillin, an analog of odorants and immunological haptens, is obtained by equilibrium dialysis experiments with nonimmune antibodies. Based on a simple relationship, predicted by the model, between the size of a receptor repertoire and its average maximal affinity toward an arbitrary ligand, the size of the olfactory receptor repertoire (Nolf) is calculated as 300-1000, in very good agreement with recent molecular biological studies. A very similar estimate, Nolf = 500, is independently derived by relating a theoretical distribution of maxima for psi(K) with published human olfactory threshold variations. The present model also has implications to the question of olfactory coding and to the analysis of specific anosmias, genetic deficits in perceiving particular odorants. More generally, the proposed model provides a better understanding of ligand specificity in biological receptors and could help in understanding their evolution.

Animals↗
PubMed1999

Speed congenics: accelerated genome recovery using genetic markers.

Genetic markers throughout the genome can be used to speed up 'recovery' of the recipient genome in the backcrossing phase of the construction of a congenic strain. The prediction of the genomic proportion during backcrossing depends on the assumptions regarding the distribution of chromosome segments, the population structure, the marker spacing and the selection strategy. In this study simulation was used to investigate the rate of recovery of the recipient genome for a mouse, Drosophila and Arabidopsis genome. It was shown that an incorrect assumption of a binomial distribution of chromosome segments, and failing to take account of a reduction in variance in genomic proportion due to selection, can lead to a downward bias of up to two generations in the estimation of the number of generations required for the formation of a congenic strain.

Animals↗
PubMed2000

Quasi-equilibrium theory for the distribution of rare alleles in a subdivided population: justification and implications.

This paper examines a quasi-equilibrium theory of rare alleles for subdivided populations that follow an island-model version of the Wright-Fisher model of evolution. All mutations are assumed to create new alleles. We present four results: (1) conditions for the theory to apply are formally established using properties of the moments of the binomial distribution; (2) approximations currently in the literature can be replaced with exact results that are in better agreement with our simulations; (3) a modified maximum likelihood estimator of migration rate exhibits the same good performance on island-model data or on data simulated from the multinomial mixed with the Dirichlet distribution, and (4) a connection between the rare-allele method and the Ewens Sampling Formula for the infinite-allele mutation model is made. This introduces a new and simpler proof for the expected number of alleles implied by the Ewens Sampling Formula.

Alleles↗
PubMed2006

Effect of environmental parameters (temperature, pH and a(w)) on the individual cell lag phase and generation time of Listeria monocytogenes.

The effect of the individual environmental factors temperature (2-30 degrees C), pH (4.4-7.4) and a(w) (0.947-0.995) as well as the combinations of these factors on the individual cell lag phase and the generation time of Listeria monocytogenes was investigated. Individual cells were isolated using a serial dilution protocol in microtiter plates, and subsequent growth was investigated by optical density (OD) measurements at 600 nm. About 100 replicates were made for each set of environmental conditions. Part of the data were previously published in Francois et al. (Francois, K., Devlieghere, F., Smet, K., Standaert, A.R., Geeraerd, A.H., Van Impe, J.F., Debevere, J., 2005a. Modelling the individual cell lag phase: effect of temperature and pH on the individual cell lag distribution of Listeria monocytogenes. Int. J. Food Microbiol. 100, 41-53.), but were recalculated here using the calibration curves for transformation of optical density to colony forming units/ml from Francois et al. (Francois, K., Devlieghere, F., Standaert, A.R., Geeraerd, A.H., Cools, I., Van Impe, J.F., Debevere, J., 2005b. Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes. J. Appl. Microbiol. 99, 1503-1515), as this calibration curve appeared to be dependent on the environmental parameters. The previous dataset was also extended with a factor a(w), observed individually and combinations with the above mentioned environmental factors. Individual cell lag phases and subsequent growth rates were calculated assuming an exponential growth model. The results are discussed as mean values to determine the general trends and in addition, histograms are made and statistical distributions are fitted to the different data sets. When stress levels increased, the mean values and the variability observed for the individual cell lag phases increased, resulting in broader histograms and distributions that were shifting to the right. Also the gravity point of the distributions was shifting from a skewed left type to a more symmetrical type. The best description of the data is obtained with an exponential distribution for low stress levels, a gamma distribution for intermediate stress and a Weibull distribution for severe stress levels. When only low stress levels were applied, a significant percentage of the cells showed no lag phase. In those cases, a new approach was used to obtain better fits: cells with a lag phase and those without a lag phase were separated using a binomial distribution while in a second step, a gamma or a Weibull distribution is fitted to the fraction of cells showing a lag phase. A normal distribution is used to describe the variability of the generation times. These distributions can be applied to refine the exposure assessment part of the risk assessment concerning L. monocytogenes by incorporating intercellular variability.

Colony Count, Microbial↗
PubMed1997

Intron distribution in ancient paralogs supports random insertion and not random loss.

The intron positions of ten different protein families were examined to determine (the statistical likelihood of) whether spliceosomal introns are the result of random insertion events into previously intronless genes, on the one hand, or the result of random loss from common ancestral introns, on the other. The number of expected matches for the alternative scenarios was calculated for a binomial distribution by considering currently observed introns relative to all possible locations for insertion or loss. Introns occurring at approximately the same location (hereafter called a "match") were tallied for each of the paired proteins. Matches were identified by their positions in the multiple alignment and were defined as any two introns occurring within a window of 11 possible nucleotide positions, thereby allowing for possible alignment errors and "intron sliding." Matches were tallied from the raw data and compared with the expected number of matches for the two different scenarios. The results suggest that the distribution of introns in genes encoding proteins is due to random insertion and not random loss.

Animals↗
PubMed2003

Longitudinal study on the distribution of proximal sites showing significant bone loss.

BACKGROUND, AIMS: In 1973, a random sample of 574 dentate individuals aged 15, 20, 30, 40, 50, and 60 years in the city of Jönköping, Sweden, were examined clinically and radiographically to assess oral health and overall treatment needs. Periodontal examination included registration of plaque, gingivitis, probing depths at four aspects of each tooth, and interproximal bone height measurements on full-mouth intraoral radiographs. In 1990, 17 years later, the same individuals were invited to participate in a new investigation. Of these, 433 (75%) agreed to participate in the investigation and were re-examined (Hugoson & Laurell 2000). The proximal alveolar bone height at all interproximal sites was measured and expressed as per cent of tooth length. Only teeth that were present in both 1973 and 1990 were included in the assessment of changes in bone score. From the age of 30 years, about 80% of the population had one or more sites with a bone loss of 2-3 mm or more. Seventeen per cent of the individuals had more than six such sites, indicating destructive periodontal disease. Bone loss occurred at sites both with and without previous bone loss. The present study was undertaken to test the hypothesis that sites with a bone loss of 10% or more of the tooth length (2-3 mm) during the 17 years were randomly distributed in the dentition. MATERIAL AND METHODS: Of the 13,197 sites examined in individuals 20-60 years at baseline, 1201 sites (9.0%) in 998 teeth with a bone loss corresponding to 10% or more of the tooth length were found and included in the analysis. A probability test for binomial distribution was used to test the null hypothesis that all teeth had the same risk of losing bone regardless of its position in the dentition. The valid risk for each tooth was 3.571% and the null hypothesis was rejected at the 95% confidence interval. RESULTS: Although all tooth types were affected by tooth loss, some teeth, namely 17, 16, 42, 41, and 31, showed a higher incidence of sites losing bone, whereas 46, 45, 44, and 36 had a lower incidence. Loser sites in smokers appeared more at random. CONCLUSION: Sites that will develop periodontal break-down over time may appear at random, although with higher risk at maxillary molars and lower incisors. For the early detection of destructive periodontitis, periodontal examination that includes all teeth should be made routine in every dental check-up.

Adolescent↗
PubMed1997

Square sampling. An easy method of estimating numerical densities of cells or particles within a tissue.

OBJECTIVE: A new parametric method is presented, called "square sampling," which speeds up the estimate of the number of cells or particles that are randomly distributed within a tissue. STUDY DESIGN: The principle of square sampling is subdivision of a biopsy into at least 100 squares of the same size using a measuring ocular or computer-based morphometric system and estimating the cell number by counting "positive" squares, squares with at least one cell of interest, assuming a binomial distribution of positive squares, depending on numerical density. RESULTS: The derived estimate yielded almost identical results when compared with the exact count of pseudo-Gaucher cells within bone marrow biopsies from untreated patients with chronic myeloid leukemia (r = .97, examined area = 94 x 2 mm2, with 400 squares/2 mm2), but (1) the total time of investigation could be halved by square sampling (25.1 versus 55.3 hours, P < .00005), and (2) the estimated number of cells did not very more widely around the mean exact count than the cell numbers exactly counted (P > .05). CONCLUSION: Square sampling is an easy, fast and effective alternative to nonparametric approaches in order to quantify the numerical density of cells randomly distributed within a tissue. The method can also be applied to test hypotheses of random distribution as well as to quantify a clustering of cells in cases of nonrandom cell distribution.

Bone Marrow↗
PubMed1993

Bimodality in age of onset of psoriasis, in both patients and their relatives.

The ages at onset of 245 female and 211 male psoriasis (Ps) patients were recorded. The distribution of age of onset in both sexes is bimodal, with separation at the age of 40 years into an early-onset group and a late-onset group. These distributions were normal (Gaussian) with equal variances. These data are compatible with the hypothesis that there are two genotypes for Ps. Further evidence for this hypothesis is provided by the relationship between age of onset and number of affected relatives. The latter, corrected for age at time of study, demonstrates a mixture of two negative binomial distributions, also with likely separation at the age of 40 years. The age distribution of Ps patients reflects the bimodality of age of onset, but with larger means and variances.

Adolescent↗
PubMed1992

Multivariate methods for clustered binary data with multiple subclasses, with application to binary longitudinal data.

Clustered binary data occur frequently in biostatistical work. Several approaches have been proposed for the analysis of clustered binary data. In Rosner (1984, Biometrics 40, 1025-1035), a polychotomous logistic regression model was proposed that is a generalization of the beta-binomial distribution and allows for unit- and subunit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of subunits within a cluster are equally correlated. This is appropriate for ophthalmologic work where clusters are generally of size 2, but may be inappropriate for larger cluster sizes. A beta-binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of unit-, class-, and subunit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, Massachusetts, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.

Adolescent↗
PubMed1996

Sampling distributions of p(pos) and p(neg).

In the absence of a gold standard, assessment of clinimetric properties of dichotomous variables should include reporting of the proportions of positive agreement (ppos) and negative agreement (pneg). For example, for a patient considering whether or not to undergo elective surgery, ppos represents the probability that a second physician would concur with a recommendation to undergo surgery and pneg represents the probability that a second physician would concur with a recommendation not to undergo surgery. This article uses a conditional binomial distribution to derive the sampling distributions of ppos and pneg. The sampling distribution can be used as a basis for confidence intervals and hypothesis tests.

Confidence Intervals↗
PubMedDate not supplied

Problems of Salmonella sampling.

Modern husbandry practices, regional concentration of the industry, high stocking densities, uniform age-distribution of birds and continuous feeding promote the spread of poultry diseases. Moreover, the immature state of the intestinal microflora or disturbance of the developing flora by antibiotics increases susceptibility of chicks to salmonellas. If an estimate of the number of salmonella-positive birds in a flock is needed, then the required number of samples can be assessed by using the binomial distribution function. Whenever a qualitative result is sufficient, the samples can be pooled or the flock litter can be sampled using an 'overshoe method', which is a novel, low-cost and rapid technique. An optimal pooling factor can be assessed at low prevalence levels (less than 10%). Serological methods will only detect the presence of antibodies to invasive strains of Salmonella. The sampling interval depends on the strategy of the Salmonella Control Programme. Breeder flocks should be sampled more frequently than meat flocks and laying flocks. The new salmonella standard, ISO 6579-1990, is applicable in the poultry industry. When bacterial numbers are likely to be low, or the organisms in a stressed condition, a pre-enrichment step should be included. In the case of faecal samples, however, pre-enrichment should be omitted. A whole carcass rinsing and massaging method is preferred for the examination of finished carcasses.

Animal Husbandry↗
PubMed2002

Sensitivity of two-stage sampling to detect sheep biting lice (Bovicola ovis) in infested flocks.

The sampling distribution of Bovicola ovis (Schrank) on sheep was examined in two flocks, one with a light and one with a heavy infestation of lice. The derived distributions were used to calculate the sensitivity of detecting lice on individual sheep and in flocks by fleece parting regimes that varied in number of parts per animal and number of sheep per flock, different scenarios of flock sizes, proportion infested and louse density were examined. Lice were aggregated among fleece partings in the heavily infested flock and described by a negative binomial distribution with k values between 0.3 and 1.92. The distribution was indistinguishable from Poisson in the lightly infested flock. The assumed distribution had little effect on sensitivity, except when only one fleece part per animal was examined. On individual sheep where louse density was 0.5 per 10 cm part or greater, there were only marginal gains from inspecting more than 10 parts per animal. Increasing the number of sheep inspected always increased sensitivity more than increasing number of parts per sheep by an equivalent amount. This advantage was greatest in situations where a low proportion of sheep in the flock were infested with a high density of lice, and less where a low proportion of sheep were infested with a low density of lice, or a high proportion of sheep were infested with a high density of lice.

Animals↗
PubMed1979

Dual action of ouabain on transmitter release at neuromuscular junctions of the frog.

Ouabain increased both spontaneous and evoked transmitter release in Mg++-treated frog neuromuscular junctions. This action developed as a two-step process which affected both miniature end-plate potential (m.e.p.p.) frequency and the binomial distribution of e.p.p.s. During the first part of its action, which lasts for approximately 60 min, ouabain (10(-5) M) increased the m.e.p.p. frequency following a saturable process. The increase in m.e.p.p. frequency was blocked by tetrodotoxin (15 nM). The quantal parameters of release, m and n, showed a significant increase but the parameter p was unaffected. Since the same changes in the binomial parameters were observed in Mg++-treated junctions exposed to low [Na+]0 in the absence of ouabain, it can be concluded that Na+ concentration played an important role in the increase of transmitter release. After 60 min in ouabain (10(-5) M) m.e.p.p. frequency increased by an exponential process. The binomial parameters of transmitter release, m and p, increased while n remained unchanged. This action was not influenced by TTX pretreatment nor was it reproduced by decreasing [Na+]0. The mechanism responsible for this action seems to be the Ca++- releasing effect of ouabain from the cytoplasmic sequestering sites.

Action Potentials↗
PubMed1976

Random distribution of centromere regions at mitosis in cultured cells of Muntiacus muntjak.

The manner in which centromere regions of mitotic chromosomes are distributed with respect to the age of their DNA was studied. Cells of the Indian deer Muntiacus muntjak, were grown in the presence of bromodeoxyuridine (BrdU) for two generations and stained with the fluorescent dye Hoechst 33258. Chromatids containing "granddaughter DNA" appear dim when compared with those containing "grandparental DNA". The frequencies of the various anaphase patterns of bright and dim centromere regions were binomially distributed, indicating random distribution of chromatids with respect to the age of their DNA templates.

Animals↗
PubMed1990

Maximum likelihood estimation of the parameters of the prior distributions of three variables that strongly influence reproductive performance in cows.

Ovulation detection rate, pregnancy rate, and embryo loss rate greatly affect the reproductive performance of cows. A previous model described the separate effects of these variables on the resulting calving patterns and assumed that the variables have the same value for all cows belonging to the same herd. This is not a realistic biological assumption, so the beta distribution is used to introduce "between-cow" variation in the three variables. Two approaches are used to find maximum likelihood estimates of the parameters of these prior beta distributions. The first considers sequences of ovulations, artificial inseminations, and pregnancies, separately. For both ovulation detection rate and pregnancy rate this approach considers the number of "successes" of each event for a particular cow (e.g., in the case of an ovulation, a success is a detection), and conditions on the total number of occurrences of that event in the cow, so that beta-binomial distributions are considered. However, for embryo loss rate the number of pregnancies required until a particular cow calves is considered, so that a beta-geometric distribution results. If the cow is removed before she calves, a censored sequence will result. The second approach considers the sequences of ovulations, artificial inseminations, pregnancies, and embryo losses, together, which will stop only when the cow calves. Otherwise, if she is removed before that time, a censored sequence will result. In this case, a joint distribution, with three independent prior beta distributions, is considered. The results of the analysis of data from 22 herds are discussed.

Animals↗
PubMed2002

Mortalities induced by the copepod Sinergasilus polycolpus in farmed silver and bighead carp in a reservoir.

The frequency distributions of the parasitic copepod Sinergasilus polycolpus were examined in silver carp Hypophthalmichthys molitrix and bighead carp Aristichthys nobilis during a disease outbreak of the 2 species of fish in a reservoir in China. The mean abundance of the copepod was positively related with host length and age, and the overdispersion of the copepod in both silver and bighead carp was fitted well with negative binomial distribution. Although parasite-induced host mortality was observed, a peaked age-parasite abundance curve was not detected in the present parasite-host system. It is also proposed that this peaked age-abundance curve is unlikely to be observed in its natural host populations.

Age Factors↗
PubMed1991

Distribution and sampling of Aedes taeniorhynchus (Diptera: Culicidae) eggs in a Florida mangrove forest.

The distribution of Aedes taeniorhynchus (Wiedemann) eggs in a Florida mangrove basin forest was quantified and used to design a sampling plan. Eggs were found in detritus-rich soil with the highest densities in a band at elevations 0.1-0.2 m above the water line. Dispersion indices (k and Taylor's b) indicated that the eggs were aggregated; 14 of 16 populations tested fit the negative binomial distribution. A fixed-size sampling plan using systematic sampling was designed from these data.

Aedes↗
PubMed2006

Use of the pupal survey technique for measuring Aedes aegypti (Diptera: Culicidae) productivity in Puerto Rico.

The hypothesis tested was that most pupae of Aedes aegypti are produced in a few types of containers so that vector control efforts could concentrate on eliminating the most productive ones and thus prevent dengue outbreaks. Pupal surveys were conducted twice in 2004 in an urban area in southern Puerto Rico. A total 35,030 immature mosquitoes (III and IV instars, pupae) was counted in 1,367 containers found with water in 624 premises during the first survey. Only pupae were counted in the second survey in 829 premises, 257 of which had containers with water, and 124 contained Ae. aegypti pupae (15%, 22% in the first survey). We found fewer (583) containers with water than in the first survey, but 202 had pupae (35%; 18.5% in first survey). Containers yielded 3,189 Ae. aegypti pupae, which was slightly fewer than those found in the first survey (3,388 pupae). The hypothesis was supported by the data, showing that 7 of 18 types of containers contained 80% of all female pupae. The most productive containers generally were also common. We used several criteria (i.e., container use, two-step cluster analysis based on environmental variables of containers and premises) to classify the containers and premises and to evaluate pupal distribution at various spatial scales (container, premise, and residences versus public areas). Most pupae were in 4 of 10 types of container usage categories. The cluster technique showed that most pupae were in unattended, rain-filled containers in the yards, particularly in receptacles in the shade of trees that received rainfall through foliage and had lower water temperatures. Pupal counts were adjusted to a negative binomial distribution, confirming their highly aggregated dispersal pattern. Cluster analysis showed that 61.3% of female pupae were in 40 (6.4%) of 624 premises that had in common their larger yards, number of trees, and container water volume. Using number of Ae. aegypti larvae, Breteau Index, or the presence of immature forms as indicators of pupal productivity is not as efficient in identifying the most productive types of containers as direct pupal counts.

Aedes↗