Optimal dynamic experiments for bioreactor model discrimination

 This paper describes a general approach fordynamic model discrimination for continuous cultures and presents dynamic models for pure cultures of E. coli and C. utilis obtained using the method. For each pure culture system, four candidate models representing various levels of structure were considered. All models reduce to Monod growth kinetics at steady state. An optimized set of multivariable step inputs in selected manipulative variables was used to discriminate between candidate models. The models that best predicted the dynamic behavior were selected by comparison of model predictions with experimental data. Two discrimination functions were compared in terms of their ability to determine the optimal set of multivariable step inputs to discriminate between candidate models. Results indicate that model discrimination based on maximizing the minimum absolute difference between any two models for a given set of inputs possessed good potential for discrimination between candidate models. Models selected for E. coli andC. utilis from the model discrimination work arepresented and compared with experimental data. Received: 24 May 1994/Received revision: 28 September 1994/Accepted: 5 December 1994     

Robust test method for time-course microarray experiments

Background  

In a time-course microarray experiment, the expression level for each gene is observed across a number of time-points in order to characterize the temporal trajectories of the gene-expression profiles. For many of these experiments, the scientific aim is the identification of genes for which the trajectories depend on an experimental or phenotypic factor. There is an extensive recent body of literature on statistical methodology for addressing this analytical problem. Most of the existing methods are based on estimating the time-course trajectories using parametric or non-parametric mean regression methods. The sensitivity of these regression methods to outliers, an issue that is well documented in the statistical literature, should be of concern when analyzing microarray data.     

A permutation-based multiple testing method for time-course microarray experiments

Background  

Time-course microarray experiments are widely used to study the temporal profiles of gene expression. Storey et al. (2005) developed a method for analyzing time-course microarray studies that can be applied to discovering genes whose expression trajectories change over time within a single biological group, or those that follow different time trajectories among multiple groups. They estimated the expression trajectories of each gene using natural cubic splines under the null (no time-course) and alternative (time-course) hypotheses, and used a goodness of fit test statistic to quantify the discrepancy. The null distribution of the statistic was approximated through a bootstrap method. Gene expression levels in microarray data are often complicatedly correlated. An accurate type I error control adjusting for multiple testing requires the joint null distribution of test statistics for a large number of genes. For this purpose, permutation methods have been widely used because of computational ease and their intuitive interpretation.     

Statistical tests for identifying differentially expressed genes in time-course microarray experiments

MOTIVATION: Microarray technology allows the monitoring of expression levels for thousands of genes simultaneously. In time-course experiments in which gene expression is monitored over time, we are interested in testing gene expression profiles for different experimental groups. However, no sophisticated analytic methods have yet been proposed to handle time-course experiment data. RESULTS: We propose a statistical test procedure based on the ANOVA model to identify genes that have different gene expression profiles among experimental groups in time-course experiments. Especially, we propose a permutation test which does not require the normality assumption. For this test, we use residuals from the ANOVA model only with time-effects. Using this test, we detect genes that have different gene expression profiles among experimental groups. The proposed model is illustrated using cDNA microarrays of 3840 genes obtained in an experiment to search for changes in gene expression profiles during neuronal differentiation of cortical stem cells.     

Cluster-based network model for time-course gene expression data

We propose a model-based approach to unify clustering and network modeling using time-course gene expression data. Specifically, our approach uses a mixture model to cluster genes. Genes within the same cluster share a similar expression profile. The network is built over cluster-specific expression profiles using state-space models. We discuss the application of our model to simulated data as well as to time-course gene expression data arising from animal models on prostate cancer progression. The latter application shows that with a combined statistical/bioinformatics analyses, we are able to extract gene-to-gene relationships supported by the literature as well as new plausible relationships.     

Gene selection and clustering for time-course and dose-response microarray experiments using order-restricted inference

We propose an algorithm for selecting and clustering genes according to their time-course or dose-response profiles using gene expression data. The proposed algorithm is based on the order-restricted inference methodology developed in statistics. We describe the methodology for time-course experiments although it is applicable to any ordered set of treatments. Candidate temporal profiles are defined in terms of inequalities among mean expression levels at the time points. The proposed algorithm selects genes when they meet a bootstrap-based criterion for statistical significance and assigns each selected gene to the best fitting candidate profile. We illustrate the methodology using data from a cDNA microarray experiment in which a breast cancer cell line was stimulated with estrogen for different time intervals. In this example, our method was able to identify several biologically interesting genes that previous analyses failed to reveal.     

Partial mixture model for tight clustering of gene expression time-course

Background  

Tight clustering arose recently from a desire to obtain tighter and potentially more informative clusters in gene expression studies. Scattered genes with relatively loose correlations should be excluded from the clusters. However, in the literature there is little work dedicated to this area of research. On the other hand, there has been extensive use of maximum likelihood techniques for model parameter estimation. By contrast, the minimum distance estimator has been largely ignored.     

Quadratic regression analysis for gene discovery and pattern recognition for non-cyclic short time-course microarray experiments

Background  

Cluster analyses are used to analyze microarray time-course data for gene discovery and pattern recognition. However, in general, these methods do not take advantage of the fact that time is a continuous variable, and existing clustering methods often group biologically unrelated genes together.     

Requirements for generating sigmoidal time-course aggregation in nucleation-dependent polymerization model

Requirements for generating remarkable sigmoidal time-course of aggregation are found in the nucleation-dependent polymerization model by a numerical calculation method; i.e. there are optimum values of the kinetic constants to afford prominent sigmoidal character by inducing slightly unfavorable nucleation. However, if the nucleus formation is too unfavorable, sigmoidal character is again decreased. This result is in contrast to the generally accepted idea that sigmoid is induced by thermodynamically unfavorable nucleation phase.     

Discrete design of enzyme kinetic experiments

The usefulness of discrete designs in enzyme kinetics as an alternative to continuous designs is discussed in this paper, focusing on designs satisfying the D-optimality criterion. This study has been carried out using a program called DODID, specifically devised for this purpose, which is available by request to the authors. The results presented in this paper show that the relative efficiency of the D-optimal discrete designs with respect to the continuous ones increases rapidly when increasing the number of possible values for the control variables. Relative efficiencies higher than 0.98 are achieved when using 20 possible values for each variable. The power of the tools provided by the computational approach of this work is proved by the analysis made on the robustness of different designs for estimating the kinetic parameters when a wrong assumption on the error structure has been made. The robustness of the designs made assuming medium constant error (error variance proportional to the true response) is thus confirmed. A comparative study of several discriminating designs is also presented. The results obtained show that the designs produced by adding the optimal discrete designs corresponding to both candidate models plus the point where the weighted difference between the predicted values is maximum, is a good choice when designing an experiment for discrimination.     

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

Background  

Time-course microarray experiments produce vector gene expression profiles across a series of time points. Clustering genes based on these profiles is important in discovering functional related and co-regulated genes. Early developed clustering algorithms do not take advantage of the ordering in a time-course study, explicit use of which should allow more sensitive detection of genes that display a consistent pattern over time. Peddada et al. [1] proposed a clustering algorithm that can incorporate the temporal ordering using order-restricted statistical inference. This algorithm is, however, very time-consuming and hence inapplicable to most microarray experiments that contain a large number of genes. Its computational burden also imposes difficulty to assess the clustering reliability, which is a very important measure when clustering noisy microarray data.     

A model for dispersion experiments

Summary A new model is proposed for the dispersion of animals and other organisms and its use is discussed for the analysis of the data from experiments on dispersion. The model is a generalisation of the random walk model, but because of its flexibility it should be much more widely applicable than the random walk model.The new model has been found to fit the results of many dispersion experiments and examples are given of its use with data for millipedes and Drosophila.     

Optimization for two-step biochemical kinetic resolution of enantiomers

A method is presented to optimize the two-step biochemical kinetic resolution of enantiomers. The optimization results were verified experimentally via the enantioselective hydrolysis of ketoprofen methyl ester and the enantioselective esterification of ketoprofen.     

A microcomputer method for designing optimal experiments for estimating enzyme kinetic parameters

A computer program, written in BASIC, for designing optimal experiments with the aim of evaluating estimates of the parameters for any enzyme kinetic model is given. This computer program can be run on any microcomputer with less than 32 Kbytes of random access memory. The program uses the termed D-optimization design criterion, which minimizes the determinant of the variance-covariance matrix. The user only supplies the rate equation, the maximum and minimum concentrations of substrates and inhibitors, the weighting pattern, and the best possible values of the parameters. The computer supplies the optimal substrate and inhibitor concentrations (one for each parameters), for estimating the parameter values, and the determinant of the variance-covariance matrix. Likewise, the microcomputer supplies the eigenvalues and eigenvectors of information and redundancy matrices, the sensitivity and the global redundancy.     

Determination of rate distributions from kinetic experiments.

Rate processes in proteins are often not adequately described by simple exponential kinetics. Instead of modeling the kinetics in the time domain, it can be advantageous to perform a numerical inversion leading to a rate distribution function f(lambda). The features observed in f(lambda) (number, positions, and shapes of peaks) can then be interpreted. We discuss different numerical techniques for obtaining rate distribution functions, with special emphasis on the maximum entropy method. Examples are given for the application of these techniques to flash photolysis data of heme proteins.     

Thermodynamic and kinetic aspects of RNA pulling experiments

Recent single-molecule pulling experiments have shown how it is possible to manipulate RNA molecules using laser tweezers. In this article we investigate a minimal model for the experimental setup which includes an RNA molecule connected to two polymers (handles) and a bead trapped in the optical potential and attached to one of the handles. We start by considering the case of small single-domain RNA molecules, which unfold in a cooperative way. The model qualitatively reproduces the experimental results and allows us to investigate the influence of the bead and handles on the unfolding reaction. A main ingredient of the model is to consider the appropriate statistical ensemble and the corresponding thermodynamic potential describing thermal fluctuations in the system. We then investigate several questions relevant to extract thermodynamic information from experimental data. The kinetics of unfolding is also studied by introducing a dynamical model. Finally, we apply the model to the more general problem of a multidomain RNA molecule with Mg(2+) tertiary contacts that unfolds in a sequential way.     

A model for oscillatory kinetic systems

A kinetic model is proposed for oscillatory kinetic phenomena. The exact analytic solution is exhibited and shown to account for several features exhibited by oscillatory chemical and biological systems.