Inferring a Transcriptional Regulatory Network from Gene Expression Data Using Nonlinear Manifold Embedding

Transcriptional networks consist of multiple regulatory layers corresponding to the activity of global regulators, specialized repressors and activators of transcription as well as proteins and enzymes shaping the DNA template. Such intrinsic multi-dimensionality makes uncovering connectivity patterns difficult and unreliable and it calls for adoption of methodologies commensurate with the underlying organization of the data source. Here we present a new computational method that predicts interactions between transcription factors and target genes using a compendium of microarray gene expression data and the knowledge of known interactions between genes and transcription factors. The proposed method called Kernel Embedding of REgulatory Networks (KEREN) is based on the concept of gene-regulon association and it captures hidden geometric patterns of the network via manifold embedding. We applied KEREN to reconstruct gene regulatory interactions in the model bacteria E.coli on a genome-wide scale. Our method not only yields accurate prediction of verifiable interactions, which outperforms on certain metrics comparable methodologies, but also demonstrates the utility of a geometric approach to the analysis of high-dimensional biological data. We also describe the general application of kernel embedding techniques to some other function and network discovery algorithms

Inference algorithms for gene networks: a statistical mechanics analysis

The inference of gene regulatory networks from high throughput gene expression data is one of the major challenges in systems biology. This paper aims at analysing and comparing two different algorithmic approaches. The first approach uses pairwise correlations between regulated and regulating genes; the second one uses message-passing techniques for inferring activating and inhibiting regulatory interactions. The performance of these two algorithms can be analysed theoretically on well-defined test sets, using tools from the statistical physics of disordered systems like the replica method. We find that the second algorithm outperforms the first one since it takes into account collective effects of multiple regulators

Distribution of Mutual Information from Complete and Incomplete Data

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sample-to-population inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(1/n^3), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would benefit from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection, is shown to perform significantly better when inductive mutual information is used.Comment: 26 pages, LaTeX, 5 figures, 4 table