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Quantitative studies on T cell diversity. III. Limiting dilution analysis of precursor cells for T helper cells reactive to xenogeneic erythrocytes.

Splenic T cells exposed to concanavalin A (Con A), and subsequently to factors produced by rat spleen cells in response to Con A (Con A sup), acquire the ability to function as helper T (TH) cells in response to xenogeneic erythrocytes (RBC). Help is measured as the reconstitution of the plaque-forming cell response of a spleen cell population depleted of T cells by treatment with anti-Thy-1 serum and complement. We propose that precursor TH cells differentiate during the in vitro treatment into mature TH cells. As differentiation occurs under limiting dilution conditions, an estimation of the precursor frequency should in principle be possible. However, a single-hit Poisson distribution does not fit our data. Instead, we observe, dependent on the T cell concentration, three separate "peaks" of response. In many experiments, using sheep, horse, and chicken RBC as antigens, we reproducibly find these "peaks" at 40-190, 600-3,000, and 20,000-100,000 T cells, placed into limiting dilution cultures, respectively. By various experiments we can show that the helper activity is not due to passively transferred rat factors, but to the titrated cells themselves. The active cell is a T cell that appears to function in an antigen-specific way and to require direct cell contact to do so. It thus resembles the classical helper T cell. As we find precursor TH cells already at very low concentrations of T cells, we titrated the range between 0 and 100 T cells/well carefully. The bent shape of the titration curves does not always allow a statistically satisfying regression analysis, and we therefore cannot estimate precise precursor frequencies from every experiment. However, a common sense argument can be made that these frequencies must be on the order of 1/10-1/100 T cells. We propose that the limiting dilution curves obtained in this system most likely reflect fundamentally important cellular interactions that regulate immunological effector functions. We favor a concept of independently interacting sets of helper and suppressor T cells of various frequencies, but other models are possible.

Animals↗

A kinetic analysis of calcium-triggered exocytosis.

Although the relationship between exocytosis and calcium is fundamental both to synaptic and nonneuronal secretory function, analysis is problematic because of the temporal and spatial properties of calcium, and the fact that vesicle transport, priming, retrieval, and recycling are coupled. By analyzing the kinetics of sea urchin egg secretory vesicle exocytosis in vitro, the final steps of exocytosis are resolved. These steps are modeled as a three-state system: activated, committed, and fused, where interstate transitions are given by the probabilities that an active fusion complex commits (alpha) and that a committed fusion complex results in fusion, p. The number of committed complexes per vesicle docking site is Poisson distributed with mean n. Experimentally, p and n increase with increasing calcium, whereas alpha and the pn ratio remain constant, reducing the kinetic description to only one calcium-dependent, controlling variable, n. On average, the calcium dependence of the maximum rate (R(max)) and the time to reach R(max) (T(peak)) are described by the calcium dependence of n. Thus, the nonlinear relationship between the free calcium concentration and the rate of exocytosis can be explained solely by the calcium dependence of the distribution of fusion complexes at vesicle docking sites.

Animals↗

Physiological studies during formation and development of rat neuromuscular junctions in tissue culture.

Developing neuromuscular junctions in tissue cultures of rat embryo spinal cord and muscle were studied with intracellular recording. Excitatory junctional potentials (ejps) were found during nerve or spinal cord stimulation, and also arising spontaneously. The time-course of the potentials tended to be shorter in cultures older than 9 days in vitro than in more recently innervated cultures. Evidence of multiple innervation was found in many cells. In order to test the hypothesis that transmitter was released in integral multiples of a quantal amount and according to a Poisson distribution, mean quantum content was calculated from the coefficient of variation of ejp amplitudes, the percentage of zero responses, and the ratio of mean amplitude to mean of the smallest class of amplitudes. The three independent measures were in fair or good mutual agreement, implying that the mechanism of transmitter release in newly developed junctions is the same as in the adult. In newly formed junctions, ejps were subthreshold for action potential generation, but afterwards mean quantum content increased and action potentials were generated by single ejps. In fibers developing both with and without innervation, the entire muscle cell surface was as sensitive to acetylcholine as the adult end plate region. Innervation was related to cross-striation: every cross-striated fiber tested was found to be innervated, and denervation in vitro led to loss of distinct cross-striations.

Acetylcholine↗

Receiver operating characteristic analysis. Application to the study of quantum fluctuation effects in optic nerve of Rana pipiens.

Receiver operating characteristic (ROC) analysis of nerve messages is described. The hypothesis that quantum fluctuations provide the only limit to the ability of frog ganglion cells to signal luminance change information is examined using ROC analysis. In the context of ROC analysis, the quantum fluctuation hypothesis predicts (a) the detectability of a luminance change signal should rise proportionally to the size of the change, (b) detectability should decrease as the square root of background, an implication of which is the deVries-Rose law, and (c) ROC curves should exhibit a shape particular to underlying Poisson distributions. Each of these predictions is confirmed for the responses of dimming ganglion cells to brief luminance decrements at scotopic levels, but none could have been tested using classical nerve message analysis procedures.

Animals↗

Geographic prediction of human onset of West Nile virus using dead crow clusters: an evaluation of year 2002 data in New York State.

The risk of becoming a West Nile virus case in New York State, excluding New York City, was evaluated for persons whose town of residence was proximal to spatial clusters of dead American crows (Corvus brachyrhynchos). Weekly clusters were delineated for June-October 2002 by using both the binomial spatial scan statistic and kernel density smoothing. The relative risk of a human case was estimated for different spatial-temporal exposure definitions after adjusting for population density and age distribution using Poisson regression, adjusting for week and geographic region, and conducting Cox proportional hazards modeling, where the week that a human case was identified was treated as the failure time and baseline hazard was stratified by region. The risk of becoming a West Nile virus case was positively associated with living in towns proximal to dead crow clusters. The highest risk was consistently for towns associated with a cluster in the current or prior 1-2 weeks. Weaker, but positive associations were found for towns associated with a cluster in just the 1-2 prior weeks, indicating an ability to predict onset in a timely fashion.

Animals↗

Frailty modelling of testicular cancer incidence using Scandinavian data.

The incidence of testicular cancer is highest among young men, and then decreases sharply with age. This points towards a frailty effect, where some men have a much greater risk of testicular cancer than the majority of the male population. Those with the highest risk get cancer, drain the group of individuals at risk, and leave a healthy male population which has approximately zero risk of testicular cancer. This leads to the observed decrease in incidence. We discuss a frailty model, where the frailty is compound-Poisson-distributed. This allows for a non-susceptible group (of zero frailty). The model is successfully applied to incidence data from the Danish and Norwegian registries. It is indicated that there was a decrease in incidence for males born during World War II in both countries. Bootstrap analysis is used to find the degree of variation in the estimates. In the Armitage-Doll multistage model, the estimated number of transitions needed for a cell to become malignant is close to 3 for non-seminomas and 4 for seminomas in both the Danish and Norwegian data. This paper demonstrates that a model including a frailty effect fits the incidence data well and gives interesting results and interpretations, although this is no proof of the effect's truth.

Adolescent↗

Conditional likelihood score functions for mixed models in linkage analysis.

In this paper, we develop a general strategy for linkage analysis, applicable for arbitrary pedigree structures and genetic models with one major gene, polygenes and shared environmental effects. Extending work of Whittemore (1996), McPeek (1999) and Hossjer (2003d), the efficient score statistic is computed from a conditional likelihood of marker data given phenotypes. The resulting semiparametric linkage analysis is very similar to nonparametric linkage based on affected individuals. The efficient score S depends not only on identical-by-descent sharing and phenotypes, but also on a few parameters chosen by the user. We focus on (1) weak penetrance models, where the major gene has a small effect and (2) rare disease models, where the major gene has a possibly strong effect but the disease causing allele is rare. We illustrate our results for a large class of genetic models with a multivariate Gaussian liability. This class incorporates one major gene, polygenes and shared environmental effects in the liability, and allows e.g. binary, Gaussian, Poisson distributed and life-length phenotypes. A detailed simulation study is conducted for Gaussian phenotypes. The performance of the two optimal score functions S(wpairs) and S(normdom) are investigated. The conclusion is that (i) inclusion of polygenic effects into the score function increases overall performance for a wide range of genetic models and (ii) score functions based on the rare disease assumption are slightly more powerful.

Alleles↗

Functional impact of rate irregularity in patients with heart failure and atrial fibrillation receiving cardiac resynchronization therapy.

AIMS: Atrial fibrillation (AFib) with a rapid ventricular response may adversely impact cardiac performance, especially in patients with heart failure. However, it remains uncertain whether rhythm irregularity per se has unfavourable effects apart from tachycardia, and whether rate regularization alone can improve heart function. METHODS AND RESULTS: Nine subjects with chronic AFib, atrioventricular nodal block, and symptomatic heart failure (ejection fraction 14-30%) were studied using a pressure-volume catheter. Ventricles were biventricularly paced (RV-apex, LV-lateral wall) at 80 or 120 min(-1) mean rate, using regular or irregular, Poisson-distributed stimulation. At 80 min(-1), ventricular function was similar between the two pacing modes. However, at 120 min(-1), irregular pacing impaired systolic (dP/dt(max): -8.2%, P<0.001) and diastolic function (dP/dt(min): +21%, P<0.001, LV end-diastolic pressure: +26%, P=0.007) compared with regular rate pacing. Contractile function during irregular pacing varied with the ratio of preceding/pre-preceding intercycle (RR) interval (dP/dt(max): 80 b.p.m.: r=0.69; 120 b.p.m.: r=0.74), whereas pre-load had little effect on instantaneous contractility. CONCLUSION: In heart failure subjects with AFib, RR-interval irregularity worsens cardiac function at elevated but not at normal range heart rate. Overall rate control is most important in these patients while rate regularization of rapid AFib may impart additional benefits.

Aged↗

Transfer RNA genes are genomic targets for de Novo transposition of the yeast retrotransposon Ty3.

Insertions of the yeast element Ty3 resulting from induced retrotransposition were characterized in order to identify the genomic targets of transposition. The DNA sequences of the junctions between Ty3 and flanking DNA were determined for two insertions of an unmarked element. Each insertion was at position -17 from the 5' end of a tRNA-coding sequence. Ninety-one independent insertions of a marked Ty3 element were studied by Southern blot analysis. Pairs of independent insertions into seven genomic loci accounted for 14 of these insertions. The DNA sequence flanking the insertion site was determined for at least one member of each pair of integrated elements. In each case, insertion was at position -16 or -17 relative to the 5' end of one of seven different tRNA genes. This proportion of genomic loci used twice for Ty3 integration is consistent with that predicted by a Poisson distribution for a number of genomic targets roughly equivalent to the estimated number of yeast tRNA genes. In addition, insertions upstream of the same tRNA gene in one case were at different positions, but in all cases were in the same orientation. Thus, genomic insertions of Ty3 in a particular orientation are apparently specified by the target, while the actual position of the insertion relative to the tRNA-coding sequence can vary slightly.

Base Sequence↗

On the effective size of populations with separate sexes, with particular reference to sex-linked genes.

Inconsistencies between equations for the effective population size of populations with separate sexes obtained by two different approaches are explained. One approach, which is the most common in the literature, is based on the assumption that the sex of the progeny cannot be identified. The second approach incorporates identification of the sexes of both parents and offspring. The approaches lead to identical expressions for effective size under some situations, such as Poisson distributions of offspring numbers. In general, however, the first approach gives incorrect answers, which become particularly severe for sex-linked genes, because then only numbers of daughters of males are relevant. Predictions of the effective size for sex-linked genes are illustrated for different systems of mating.

Animals↗

A formula to predict the transmission frequency of acentric fragments.

A formula, based on the Poisson distribution of radiation-induced chromosomal deletions, was derived to predict the frequency of transmission of acentric fragments between subsequent mitoses. The frequency of deletions observed in the i(th) + 1 division subsequent to fragment distribution at the i(th) division anaphase is independent of the cell death resulting from fragment loss. Further, the transmission frequency of chromosome acentric fragments is mathematically equal to the fragment frequency observed in the i(th) + 1 generation divided by the mean fragment frequency in the i(th) generation. The formula was also extended to chromatid deletions.

Animals↗

Polyallelic mutational equilibria.

A new deterministic formulation is derived of the equilibrium between mutation and natural selection, which takes into account(a) the possibility of many allelic mutation states, (b) selection coefficients of the order of magnitude of the mutation rate and (c) the possibility of further mutation of already mutant alleles. The frequencies of classes of alleles 0, 1, 2, n mutant steps removed from the type allele are shown to form a Poisson distribution, with a mean and variance of the mutation rate divided by the coefficient of selection against each incremental mutational step.--This formulation is interpreted in terms of the expected frequencies of electromorphs, defined as classes of alleles characterized by common electrophoretic mobilities of their protein products. Electromorph frequencies are predicted to form stable unimodal distributions of relatively few phenotypic classes. Common electromorph frequencies found throughout the ranges of species with large population sizes are interpreted as being a uniquely electrophoretic phenomenon; band patterns on starch and acrylamide gels are phenotypes, not genotypes. It is predicted that individual electromorphs are highly heterogenous with regard to amino acid sequence.

Alleles↗

Demographic factors and cancer mortality. A mathematical model for cancer mortality in Denmark 1943-78.

Deaths from cancer in Denmark from 1943-1978 were extracted from the Danish National Death Register at the Danish Institute for Clinical Epidemiology. This paper illustrates the relationship between demographic factors and mortality from a large group of cancers, which increases progressively from young adult life into old age. One-year age-specific mortality rates between 30 and 79 years of age were computed for 14 different cancer sites among both males and females, in five ten-year birth cohorts and for the capital and provinces. The number of deaths at a particular age were found to follow a Poisson distribution and the mortality rate could be expressed by the function lx = bxk, where lx is the mortality rate at age x, and b and k are parameters to be estimated. With this model a straight line is obtained, when mortality and age are plotted on a double logarithmic scale. The maximum likelihood estimates of b and k were found iteratively for each of the 280 combinations of sex--cancer site--residence--cohort. For fixed sex and cancer site the relationship between age, residence and cohort was examined. It appeared that k was independent of residence. For 10 of the male cancers and 12 of the female cancers, k was found to be independent of cohort and in the last 6 cases k was found to be a linear function of cohort. For 12 out of 14 cancer sites among males the ratio of mortality in the capital to mortality in the provinces was significantly greater than one.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

Modelling of mortality data from a multi-centre study in Japan by means of Poisson regression with error in variables.

BACKGROUND: Death rates of particular categories in epidemiological studies are often based on a small number of occurrences which can be well described by a Poisson distribution. METHOD: We applied this model for the analysis of a multi-centre study in five Japanese counties where the death rates of stomach cancer (ICD-9 code 151) in four age groups are known. In our example some covariates of the cases (e.g. plasma lycopene levels) are unknown values and are estimated from a randomly chosen collective. Therefore these values are subject to a sampling error. The inclusion of errors in variables (e-i-v) into the statistical model can adequately describe such a situation. The model is estimated in a Bayesian framework by means of resampling techniques. RESULTS: Based on the posterior distribution of the parameters the relative risk of stomach cancer is 0.46 (95% confidence interval: 0.23-0.79) comparing the maximum of the population medians of lycopene with the minimum. The estimated overdispersion is close to zero indicating only minor interference with other possible explanatory variables. In addition, we show that inclusion of e-i-v can give more accurate estimates of the parameters even from small sample sizes. CONCLUSIONS: Appropriate statistical methods allow the accurate estimation of relative risks from small sample sizes and from low number of cases. Lycopene plasma levels are good predictors for stomach cancer.

Adult↗

Covariance components models for longitudinal family data.

A longitudinal family study is an epidemiological design that involves repeated measurements over time in a sample that includes families. Such studies, that may also include relative pairs and unrelated individuals, allow closer investigation of not only the factors that cause a disease to arise, but also the genetic and environmental determinants that modulate the subsequent progression of that disease. Knowledge of such determinants may pay high dividends in terms of prognostic assessment and in the development of new treatments that may be tailored to the prognostic profile of individual patients. Unfortunately longitudinal family studies are difficult to analyse. They conflate the complex within-family correlation structure of a cross-sectional family study with the correlation over time that is intrinsic to longitudinal repeated measures. Here we describe an approach to analysis that is relatively straightforward to implement, yet is flexible in its application. It represents a natural extension of a Gibbs-sampling-based approach to the analysis of cross-sectional family studies that we have described previously. The approach can be applied to pedigrees of arbitrary complexity. It is applicable to continuous traits, repeated binary disease states, and repeated counts or rates with a Poisson distribution. It not only supports the analysis of observed determinants, including measured genotypes, but also allows decomposition of the correlation structure, thereby permitting conclusions to be drawn about the effect of unobserved genes and environment on key features of disease progression, and hence to estimate the heritability of these features. We demonstrate the efficacy of our methods using a range of simulated data analyses, and illustrate its practical application to longitudinal blood pressure data measured in families from the Framingham Heart Study.

Blood Pressure↗

Functional diversity of natural IgM.

This paper proposes a method for the quantitative characterization of repertoire diversity of an unknown mixture of antibodies on the basis of its reactivity profile in the quantitative immunoblot (QIB). The QIB is calibrated by measuring the reactivity profiles of supernatants of known 'diversity' (i.e. known numbers of B cell clones). We define a quantitative 'index of variability' (IV) which decreases regularly as the diversity increases and the profiles tend towards a common 'convergence profile'. The calibration procedure is consolidated by a mathematical model based on the Poisson distribution; this theoretical model accounts correctly for the observed convergence behavior. On the basis of this calibration curve, it is possible to estimate the diversity of an unknown antibody mixture from a measure of its IV. We conclude that the functional diversity of natural serum IgM in mice can be estimated at approximately 16,000 clones.

Animals↗

A quantitative model for neutrophil response and delayed-type hypersensitivity reaction in rats orally inoculated with various doses of Salmonella Enteritidis.

Our aim was to investigate the quantitative relationship between inoculation doses and physiological responses to infection by Salmonella enterica serovar Enteritidis. Rats were orally inoculated with 10-10(9) c.f.u. of S. Enteritidis and monitored for 6 days. Neutrophil and delayed-type hypersensitivity (DTH) responses were assessed, and the spleens were analyzed for the pathogen. The experimental data were analyzed by a mathematical model for the host response to salmonella infection, which is based on the assumptions that: (i) the number of pathogens in the inoculum is Poisson distributed, (ii) any cell that is inoculated can multiply and form a clone to infect the animal, (iii) the probability of infection by any cell of the pathogen is independent of the number of cells ingested, and (iv) the magnitude of the immune response increases with dose, but eventually saturates to a maximum level. The probability of infection assessed by the DTH response is 7.5 x 10(-3)/c.f.u. of the inoculum (confidence interval 5.1 x 10(-5), 1.2 x 10(-2)). When five S. Enteritidis independently initiated the infection, the DTH response to the resulting clones of the salmonellae saturated to the maximum level. The probability of infection assessed by the neutrophil response is 3.4 x 10(-4)/c.f.u. (1.0 x 10(-4), 6.8 x 10(-4)). The response saturated when six S. Enteritidis independently initiated the infection. The probability of infection assessed by the analysis of spleens is 1.2 x 10(-3)/c.f.u. (4.1 x 10(-4), 2.6 x 10(-3)). We conclude that at low inocula, infections are initiated by very small numbers of bacteria. The magnitude of the immune responses is similar whether only a few or a larger number of bacteria initiated the infection.

Animals↗

Trends in reported incidence of primary malignant brain tumors in children in the United States.

BACKGROUND: The reported incidence of primary malignant brain tumors among children in the United States increased by 35% during the period from 1973 through 1994. The purpose of our study was twofold: 1) to determine whether the reported incidence rates for this period are better represented by a linear increase over the entire period ("linear model") or, alternatively, by a step function, with a lower rate in the years preceding 1984-1985 and a constant higher rate afterward ("jump model"); and 2) to identify the specific brain regions and histologic subtypes that have increased in incidence. METHODS: Incidence data from the Surveillance, Epidemiology, and End Results Program of the National Cancer Institute for the period from 1973 through 1994 for primary malignant brain tumors in children were used to model the number of cases in a year as a random variable from a Poisson distribution by use of either a linear model or a jump model. RESULTS/CONCLUSIONS: The increase in reported incidence of childhood primary malignant brain tumors is best explained by the jump model, with a step increase in incidence occurring in the mid-1980s. The brain stem and the cerebrum are the primary sites for which an increase in tumor incidence has been reported. The increase in reported incidence of low-grade gliomas in the cerebrum and the brain stem (unaccompanied by an increase in mortality for these sites) supports the substantial contribution of low-grade gliomas to the overall increase in reported incidence for childhood brain tumors. IMPLICATIONS: The significantly better fit of the data to a jump model supports the hypothesis that the observed increase in incidence somehow resulted from changes in detection and/or reporting of childhood primary malignant brain tumors during the mid-1980s.

Adolescent↗