How to cluster gene expression dynamics in response to environmental signals

Organisms usually cope with change in the environment by altering the dynamic trajectory of gene expression to adjust the complement of active proteins. The identification of particular sets of genes whose expression is adaptive in response to environmental changes helps to understand the mechanistic base of gene-environment interactions essential for organismic development. We describe a computational framework for clustering the dynamics of gene expression in distinct environments through Gaussian mixture fitting to the expression data measured at a set of discrete time points. We outline a number of quantitative testable hypotheses about the patterns of dynamic gene expression in changing environments and gene-environment interactions causing developmental differentiation. The future directions of gene clustering in terms of incorporations of the latest biological discoveries and statistical innovations are discussed. We provide a set of computational tools that are applicable to modeling and analysis of dynamic gene expression data measured in multiple environments.     

Estimating mutual information using B-spline functions – an improved similarity measure for analysing gene expression data

Background

The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. In the context of the clustering of genes with similar patterns of expression it has been suggested as a general quantity of similarity to extend commonly used linear measures. Since mutual information is defined in terms of discrete variables, its application to continuous data requires the use of binning procedures, which can lead to significant numerical errors for datasets of small or moderate size.

Results

In this work, we propose a method for the numerical estimation of mutual information from continuous data. We investigate the characteristic properties arising from the application of our algorithm and show that our approach outperforms commonly used algorithms: The significance, as a measure of the power of distinction from random correlation, is significantly increased. This concept is subsequently illustrated on two large-scale gene expression datasets and the results are compared to those obtained using other similarity measures.A C++ source code of our algorithm is available for non-commercial use from kloska@scienion.de upon request.

Conclusion

The utilisation of mutual information as similarity measure enables the detection of non-linear correlations in gene expression datasets. Frequently applied linear correlation measures, which are often used on an ad-hoc basis without further justification, are thereby extended.

     

Continuous representations of time-series gene expression data.

We present algorithms for time-series gene expression analysis that permit the principled estimation of unobserved time points, clustering, and dataset alignment. Each expression profile is modeled as a cubic spline (piecewise polynomial) that is estimated from the observed data and every time point influences the overall smooth expression curve. We constrain the spline coefficients of genes in the same class to have similar expression patterns, while also allowing for gene specific parameters. We show that unobserved time points can be reconstructed using our method with 10-15% less error when compared to previous best methods. Our clustering algorithm operates directly on the continuous representations of gene expression profiles, and we demonstrate that this is particularly effective when applied to nonuniformly sampled data. Our continuous alignment algorithm also avoids difficulties encountered by discrete approaches. In particular, our method allows for control of the number of degrees of freedom of the warp through the specification of parameterized functions, which helps to avoid overfitting. We demonstrate that our algorithm produces stable low-error alignments on real expression data and further show a specific application to yeast knock-out data that produces biologically meaningful results.     

A data-driven clustering method for time course gene expression data

Gene expression over time is, biologically, a continuous process and can thus be represented by a continuous function, i.e. a curve. Individual genes often share similar expression patterns (functional forms). However, the shape of each function, the number of such functions, and the genes that share similar functional forms are typically unknown. Here we introduce an approach that allows direct discovery of related patterns of gene expression and their underlying functions (curves) from data without a priori specification of either cluster number or functional form. Smoothing spline clustering (SSC) models natural properties of gene expression over time, taking into account natural differences in gene expression within a cluster of similarly expressed genes, the effects of experimental measurement error, and missing data. Furthermore, SSC provides a visual summary of each cluster's gene expression function and goodness-of-fit by way of a 'mean curve' construct and its associated confidence bands. We apply this method to gene expression data over the life-cycle of Drosophila melanogaster and Caenorhabditis elegans to discover 17 and 16 unique patterns of gene expression in each species, respectively. New and previously described expression patterns in both species are discovered, the majority of which are biologically meaningful and exhibit statistically significant gene function enrichment. Software and source code implementing the algorithm, SSClust, is freely available (http://genemerge.bioteam.net/SSClust.html).     

ESPD: a pattern detection model underlying gene expression profiles

MOTIVATION: DNA arrays permit rapid, large-scale screening for patterns of gene expression and simultaneously yield the expression levels of thousands of genes for samples. The number of samples is usually limited, and such datasets are very sparse in high-dimensional gene space. Furthermore, most of the genes collected may not necessarily be of interest and uncertainty about which genes are relevant makes it difficult to construct an informative gene space. Unsupervised empirical sample pattern discovery and informative genes identification of such sparse high-dimensional datasets present interesting but challenging problems. RESULTS: A new model called empirical sample pattern detection (ESPD) is proposed to delineate pattern quality with informative genes. By integrating statistical metrics, data mining and machine learning techniques, this model dynamically measures and manipulates the relationship between samples and genes while conducting an iterative detection of informative space and the empirical pattern. The performance of the proposed method with various array datasets is illustrated.