Detection of suppressor T lymphocytes and estimation of their frequency in limiting dilution assays by generalized linear regression modeling

The estimate of the frequency of suppressor T lymphocytes in unfractionated cell populations remains challenging, mainly because these regulatory cells do not display specific immunophenotypic markers. In this paper, we describe a novel theoretical approach for quantifying the frequency of suppressor cells. This method is based on limiting dilution data modeling, and allows the simultaneous estimation of the frequencies of both proliferating and suppressor cells. We used previously published biological data, characterizing the inhibiting activity of suppressor T cell clones. Starting from these data, we propose a mathematical model describing the interaction between suppressor and proliferating T cells, and applied to a Poisson process. Limiting dilution data corresponding to this non-single-hit, suppressor two-target Poisson model were artificially generated, then modeled according to a generalized linear regression procedure. Deviation from the single-hit Poisson model was revealed by a statistical slope test, and a stepwise analysis of the regression appeared to be an efficient method that strongly argued in favor of the presence of suppressor cells. By using the frequency of proliferating T cells calculated in the first step of the regression, we demonstrated the possibility to provide a reasonable estimate of the frequency of suppressor T cells. Based on these findings, a practical decision-making procedure is given to perform standard analyses of limiting dilution data.     

Limiting dilution clonal assay of human bone marrow hematopoietic progenitors (granulocytes-macrophages)

We have developed a limiting dilution assay for human bone marrow hematopoietic precursor (granulocytes-macrophages) in microwells. Bone marrow cells were fractionated by discontinuous Percoll gradients and diluted in culture medium containing colony-stimulating factors. They were diluted and cultured in medium containing colony-stimulating factor and 10(-5) M hydrocortisone in microwells over a range of cell densities that allowed calculation of the frequency of growth-inducible precursors. After 10 days, the wells were examined for clonal growth. Clonal proliferation followed the single-hit model of the Poisson distribution. More progenitors were detected in this assay than in simultaneous methylcellulose colony assays or agar cultures. Thymidine suicide experiments led to an increase in the frequency of progenitors detected in this assay, but a decrease in the frequency of methylcellulose colonies. This system may detect additional, less mature progenitors than are detected in semisolid culture systems.     

A Multinomial Model for the Quality Control of Colony Counting Procedures

The so‐called good‐laboratory‐practice (GLP) test provides an experimental design and appropriate statistical analysis for the problem of analyst performance assessment in microbiological laboratories. For a given sample material multiple dilution series are generated yielding colony counts from several dilution levels. Statistical evaluation is based on the assumption of Poisson‐distributed colony forming units. In this paper a new model based on conditional binomial and multinomial distributions is presented and it is shown how it is related to the standard model which assumes Poisson‐distributed colony counts. The effects of common working errors on the statistical evaluation of the GLP‐test are investigated.     

A simplified and rapid limiting dilution assay of T lymphocytes

We report here the development of an alternative limiting dilution assay (LDA) of T lymphocytes (T cells). Blood mononuclear cells were first stimulated for 60 hr with PHA and then cultured in microwells in the presence of recombinant interleukin-2 without feeder cells. After 4 days of culture, wells were scored for proliferation. Clonal expansion of T cells followed the single-hit model of the Poisson distribution. The progenitor frequency (f) in the mononuclear cells and E-rosette-positive cells from normal donors were 0.082 +/- 0.025 (n = 12) and 0.236 +/- 0.029 (n = 5), respectively, but this was markedly decreased in patients who underwent marrow-ablative chemotherapy and autografts with blood hematopoietic stem cells. This LDA system should be of value in routine use for the evaluation of T cell proliferative activities.     

Analysis of multi-type recurrent events in longitudinal studies; application to a skin cancer prevention trial

We consider the statistical modeling and analysis of replicated multi-type point process data with covariates. Such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types. The underlying processes are modeled as nonhomogeneous mixed Poisson processes with random (subject) and fixed (covariate) effects. The method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients. Score tests and likelihood ratio statistics are used for covariate selection. A graphical test of goodness of fit of the selected model is based on generalized residuals. Measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed. An application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer.     

Symbolic modeling of epistasis

The workhorse of modern genetic analysis is the parametric linear model. The advantages of the linear modeling framework are many and include a mathematical understanding of the model fitting process and ease of interpretation. However, an important limitation is that linear models make assumptions about the nature of the data being modeled. This assumption may not be realistic for complex biological systems such as disease susceptibility where nonlinearities in the genotype to phenotype mapping relationship that result from epistasis, plastic reaction norms, locus heterogeneity, and phenocopy, for example, are the norm rather than the exception. We have previously developed a flexible modeling approach called symbolic discriminant analysis (SDA) that makes no assumptions about the patterns in the data. Rather, SDA lets the data dictate the size, shape, and complexity of a symbolic discriminant function that could include any set of mathematical functions from a list of candidates supplied by the user. Here, we outline a new five step process for symbolic model discovery that uses genetic programming (GP) for coarse-grained stochastic searching, experimental design for parameter optimization, graphical modeling for generating expert knowledge, and estimation of distribution algorithms for fine-grained stochastic searching. Finally, we introduce function mapping as a new method for interpreting symbolic discriminant functions. We show that function mapping when combined with measures of interaction information facilitates statistical interpretation by providing a graphical approach to decomposing complex models to highlight synergistic, redundant, and independent effects of polymorphisms and their composite functions. We illustrate this five step SDA modeling process with a real case-control dataset.     

Evaluating the mean frequency of responding cells in limiting dilution assays

Summary The validity of limiting dilution assays can be compromised or negated by the use of statistical methodology which does not consider all issues surrounding the biological process. This study critically evaluates statistical methods for estimating the mean frequency of responding cells in multiple sample limiting dilution assays. We show that methods that pool limiting dilution assay data, or samples, are unable to estimate the variance appropriately. In addition, we use Monte Carlo simulations to evaluate an unweighted mean of the maximum likelihood estimator, an unweighted mean based on the jackknife estimator, and a log transform of the maximum likelihood estimator. For small culture replicate size, the log transform outperforms both unweighted mean procedures. For moderate culture replicate size, the unweighted mean based on the jackknife produces the most acceptable results. This study also addresses the important issue of experimental design in multiple sample limiting dilution assays. In particular, we demonstrate that optimization of multiple sample limiting dilution assays is achieved by increasing the number of biological samples at the expense of repeat cultures.     

Neutralization of adenoviruses: kinetics, stoichiometry, and mechanisms.

Kinetic curves for neutralization of adenovirus type 2 with anti-hexon serum revealed no lag periods even when the serum was highly diluted or when the temperature was lowered to 4 degrees C, thus indicating a single-hit mechanism. Multiplicity curves determined with anti-hexon serum displayed a linear correlation between the degree of neutralization and dilution of antiserum. Neutralization values experimentally obtained under steady-state conditions fully fitted a single-hit model based on Poisson calculations. Quantitation of the amount of 125I-labeled type-specific anti-hexon antibodies needed for full neutralization of adenovirus showed that 1.4 antibodies were attached per virion under such conditions. Virions already attached to HeLa cells at 4 degrees C were, to a large extent, neutralizable by anti-hexon serum, whereas anti-fiber and anti-penton base antisera were negative. It is suggested that adenovirus may be neutralized by two pathways: aggregation of the virions (extracellular neutralization) as performed by anti-fiber antibodies and blocking of virion entrance from the acidic endosomes into the cytoplasm (intracellular neutralization). The latter effect could be obtained by (i) covering of the penton bases, as performed by anti-penton base antibodies, thereby preventing interaction between the penton bases and the endosomal membrane, which results in trapping of virions within endosomes, and (ii) inhibition of the low-pH-induced conformational change of the viral capsid, which seems to occur in the endosomes and is necessary for proper exposure of the penton bases, as performed by anti-hexon antibodies.     

Inactivation of macromolecules by ionizing radiation. Deterministic single-hit or stochastic multievent process?

A stochastic theory concerning the radiation inactivation of macromolecules such as enzymes or receptors is elaborated. In contrast with the single-hit theory, which assumes a complete inactivation of the target as the result of one hit, the stochastic theory postulates that the degree of inactivation by one hit is a random variable. This distinguishing feature has been considered in order to give a possible interpretation to the observed effect of temperature on the radiation-sensitivity of enzymes. As a consequence of the progressive inactivation during irradiation, the binding affinity of a ligand for the macromolecule is impaired by irradiation. Although this property might discriminate the stochastic theory from the classical single-hit theory on the basis of a statistical analysis of experimentally obtained data, it is shown that the commonly obtained degree of inaccuracy may render the statistical test non-conclusive.     

Test of the validity of the Poisson assumption for analysis of most-probable-number results

A test of the validity of the Poisson assumption for sample replicates in dilution series of finite length is proposed and its properties are examined by using Monte Carlo simulation. The test is based on an examination of the number of intervals between complete sterility and complete infection in a series. The test is applied to a data set of routine influent coliform samples at the Chicago water supply intake. By this test, the data set is rejected as being drawn from a Poisson replication. Tables for direct application to a 3-dilution, 5-tube decimal series are presented, and their application is illustrated.     

Test of the validity of the Poisson assumption for analysis of most-probable-number results.

A test of the validity of the Poisson assumption for sample replicates in dilution series of finite length is proposed and its properties are examined by using Monte Carlo simulation. The test is based on an examination of the number of intervals between complete sterility and complete infection in a series. The test is applied to a data set of routine influent coliform samples at the Chicago water supply intake. By this test, the data set is rejected as being drawn from a Poisson replication. Tables for direct application to a 3-dilution, 5-tube decimal series are presented, and their application is illustrated.     

Quantitating effector and regulatory T lymphocytes in immune responses by limiting dilution analysis modeling

Although there is currently no doubt that regulatory lymphocytes represent a master player in the immune system, a major unresolved problem is the accurate quantitation of these cells among unfractionated cell populations. This difficulty mainly arises because there are no specific immunophenotypic markers that can reliably discriminate between effector and regulatory lymphocytes. To face this problem, we have developed computational models of limiting dilution analyses addressing the question of the accurate estimation of the frequencies of effector and regulatory cells functionally engaged in an immune response. A set of generic equations were provided to form a framework for modeling limiting dilution data, enabling discrimination between qualitatively different models of suppression. These models include either one or two subpopulations of regulatory cells, featured by either low or potent regulatory activity. The potential of this modeling approach was illustrated by the accurate determination of the frequencies of effector and regulatory T lymphocytes in one real limiting dilution experiment of CD4+ CD25+ T lymphocytes performed in the context of an allogeneic response in the human system. The crucial advantage of the limiting dilution method over the "static, phenotype-based" method is the dynamic evaluation of effector and regulatory T cell biology through their actual functional activity.     

Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls

We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.     

A procedure for the statistical evaluation of Ames Salmonella assay results. Comparison of results among 4 laboratories

Ames Salmonella test data collected in our laboratory and 3 National Cancer Institute contract laboratories were analyzed to study the distribution of experimental errors associated with the test. It is shown that the Poisson distribution is not appropriate, and that the power transformation model Y = (revertants/plate)lambda, with lambda = 0.2 as estimated by the methods of Box and Cox, produced a measurement scale on which the experimental errors could be adequately described by a normal (Gaussian) distribution with a constant variance. The modeling procedure enables one to properly use analysis of variance, regression analysis, and Student's t test to analyze Ames Salmonella test results, and well-known statistical quality control procedures to monitor laboratory performance. The method detects weak mutagenic activity and measures the amount and uncertainty of the increase in revertants/plate. The development of the power transformation model is discussed and examples of its use in the interpretation of Ames Salmonella assay results are included.     

A practical method for rescuing desired hybridomas during monoclonal antibody production

Summary We present a practical method for the rescue of previosly 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 hydridoma cell line that is relatively rare in a population. This work was supported in part by grants EY 06225 and EY 06226 from the National Eye Institute of the National Institutes of Health, Bethesda, MD and by an unrestricted departmental award from Research to Prevent Blindness, Inc.     

A statistical model for testing the pleiotropic control of phenotypic plasticity for a count trait

The differences of a phenotypic trait produced by a genotype in response to changes in the environment are referred to as phenotypic plasticity. Despite its importance in the maintenance of genetic diversity via genotype-by-environment interactions, little is known about the detailed genetic architecture of this phenomenon, thus limiting our ability to predict the pattern and process of microevolutionary responses to changing environments. In this article, we develop a statistical model for mapping quantitative trait loci (QTL) that control the phenotypic plasticity of a complex trait through differentiated expressions of pleiotropic QTL in different environments. In particular, our model focuses on count traits that represent an important aspect of biological systems, controlled by a network of multiple genes and environmental factors. The model was derived within a multivariate mixture model framework in which QTL genotype-specific mixture components are modeled by a multivariate Poisson distribution for a count trait expressed in multiple clonal replicates. A two-stage hierarchic EM algorithm is implemented to obtain the maximum-likelihood estimates of the Poisson parameters that specify environment-specific genetic effects of a QTL and residual errors. By approximating the number of sylleptic branches on the main stems of poplar hybrids by a Poisson distribution, the new model was applied to map QTL that contribute to the phenotypic plasticity of a count trait. The statistical behavior of the model and its utilization were investigated through simulation studies that mimic the poplar example used. This model will provide insights into how genomes and environments interact to determine the phenotypes of complex count traits.     

Visinets: A Web-Based Pathway Modeling and Dynamic Visualization Tool

In this report we describe a novel graphically oriented method for pathway modeling and a software package that allows for both modeling and visualization of biological networks in a user-friendly format. The Visinets mathematical approach is based on causal mapping (CMAP) that has been fully integrated with graphical interface. Such integration allows for fully graphical and interactive process of modeling, from building the network to simulation of the finished model. To test the performance of Visinets software we have applied it to: a) create executable EGFR-MAPK pathway model using an intuitive graphical way of modeling based on biological data, and b) translate existing ordinary differential equation (ODE) based insulin signaling model into CMAP formalism and compare the results. Our testing fully confirmed the potential of the CMAP method for broad application for pathway modeling and visualization and, additionally, showed significant advantage in computational efficiency. Furthermore, we showed that Visinets web-based graphical platform, along with standardized method of pathway analysis, may offer a novel and attractive alternative for dynamic simulation in real time for broader use in biomedical research. Since Visinets uses graphical elements with mathematical formulas hidden from the users, we believe that this tool may be particularly suited for those who are new to pathway modeling and without the in-depth modeling skills often required when using other software packages.