Penalized likelihood for sparse contingency tables with an application to full-length cDNA libraries.

BACKGROUND: The joint analysis of several categorical variables is a common task in many areas of biology, and is becoming central to systems biology investigations whose goal is to identify potentially complex interaction among variables belonging to a network. Interactions of arbitrary complexity are traditionally modeled in statistics by log-linear models. It is challenging to extend these to the high dimensional and potentially sparse data arising in computational biology. An important example, which provides the motivation for this article, is the analysis of so-called full-length cDNA libraries of alternatively spliced genes, where we investigate relationships among the presence of various exons in transcript species. RESULTS: We develop methods to perform model selection and parameter estimation in log-linear models for the analysis of sparse contingency tables, to study the interaction of two or more factors. Maximum Likelihood estimation of log-linear model coefficients might not be appropriate because of the presence of zeros in the table's cells, and new methods are required. We propose a computationally efficient l1-penalization approach extending the Lasso algorithm to this context, and compare it to other procedures in a simulation study. We then illustrate these algorithms on contingency tables arising from full-length cDNA libraries. CONCLUSION: We propose regularization methods that can be used successfully to detect complex interaction patterns among categorical variables in a broad range of biological problems involving categorical variables.

Multivariate analysis and visualization of splicing correlations in single-gene transcriptomes.

BACKGROUND: RNA metabolism, through 'combinatorial splicing', can generate enormous structural diversity in the proteome. Alternative domains may interact, however, with unpredictable phenotypic consequences, necessitating integrated RNA-level regulation of molecular composition. Splicing correlations within transcripts of single genes provide valuable clues to functional relationships among molecular domains as well as genomic targets for higher-order splicing regulation. RESULTS: We present tools to visualize complex splicing patterns in full-length cDNA libraries. Developmental changes in pair-wise correlations are presented vectorially in 'clock plots' and linkage grids. Higher-order correlations are assessed statistically through Monte Carlo analysis of a log-linear model with an empirical-Bayes estimate of the true probabilities of observed and unobserved splice forms. Log-linear coefficients are visualized in a 'spliceprint,' a signature of splice correlations in the transcriptome. We present two novel metrics: the linkage change index, which measures the directional change in pair-wise correlation with tissue differentiation, and the accuracy index, a very simple goodness-of-fit metric that is more sensitive than the integrated squared error when applied to sparsely populated tables, and unlike chi-square, does not diverge at low variance. Considerable attention is given to sparse contingency tables, which are inherent to single-gene libraries. CONCLUSION: Patterns of splicing correlations are revealed, which span a broad range of interaction order and change in development. The methods have a broad scope of applicability, beyond the single gene--including, for example, multiple gene interactions in the complete transcriptome.

Profiling the array of Ca(v)3.1 variants from the human T-type calcium channel gene CACNA1G: alternative structures, developmental expression, and biophysical variations.

We describe the regulated transcriptome of CACNA1G, a human gene for T-type Ca(v)3.1 calcium channels that is subject to extensive alternative RNA splicing. Fifteen sites of transcript variation include 2 alternative 5'-UTR promoter sites, 2 alternative 3'-UTR polyadenylation sites, and 11 sites of alternative splicing within the open reading frame. A survey of 1580 fetal and adult human brain full-length complementary DNAs reveals a family of 30 distinct transcripts, including multiple functional forms that vary in expression with development. Statistical analyses of fetal and adult transcript populations reveal patterns of linkages among intramolecular splice site configurations that change dramatically with development. A shift from nearly independent, biased splicing in fetal transcripts to strongly concerted splicing in adult transcripts suggests progressive activation of multiple "programs" of splicing regulation that reorganize molecular structures in differentiating cells. Patch-clamp studies of nine selected variants help relate splicing regulation to permutations of the gating parameters most likely to modify T-channel physiology in expressing neurons. Gating behavior reflects combinatorial interactions between variable domains so that molecular phenotype depends on ensembles of coselected domains, consistent with the observed emergence of concerted splicing during development. We conclude that the structural gene and networks of splicing regulatory factors define an integrated system for the phenotypic variation of Ca(v)3.1 biophysics during nervous system development.

The effect of higher order RNA processes on changing patterns of protein domain selection: a developmentally regulated transcriptome of type 1 inositol 1,4,5-trisphosphate receptors.

The domain structure of proteins synthesized from a single gene can be remodeled during tissue development by activities at the RNA level of gene expression. The impact of higher order RNA processing on changing patterns of protein domain selection may be explored by systematically profiling single-gene transcriptomes. itpr1 is one of three mammalian genes encoding receptors for the second messenger inositol 1,4,5-trisphosphate (InsP3). Some phenotypic variations of InsP3 receptors have been attributed to hetero-oligomers of subunit isoforms from itpr1, itpr2, and itpr3. However, itpr1 itself is subject to alternative RNA splicing, with 7 sites of transcript variation, 6 within the ORF. We have identified 17 itpr1 subunit species expressed in mammalian brain in ensembles that change with tissue differentiation. Statistical analyses of populations comprising >1,300 full-length clones suggest that subunit variation arises from a variably biased stochastic splicing mechanism. Surprisingly, the protein domains of this highly allosteric receptor appear to be assembled in a partially randomized way, yielding stochastic arrays of subunit species that form tetrameric complexes in single cells. Nevertheless, functional expression studies of selected subunits confirm that splicing regulation is connected to phenotypic variation. The potential for itpr1 subunits to form hetero-tetramers in single cells suggests the expression of a developmentally regulated continuum of molecular forms that could display diverse properties, including incremental sensitivities to agonist activation and varying patterns of Ca2+ mobilization. These studies illuminate the extent to which itpr1 molecular phenotype is induced by higher order RNA processing.