Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions

Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed the distribution of GRN structural properties across a large set of distinct prokaryotic organisms and found a set of constrained characteristics such as network density and number of regulators. Our results allowed us to estimate the number of interactions that complete networks would have, a valuable insight that could aid in the daunting task of network curation, prediction, and validation. Using state-of-the-art statistical approaches, we also provided new evidence to settle a previously stated controversy that raised the possibility of complete biological networks being random and therefore attributing the observed scale-free properties to an artifact emerging from the sampling process during network discovery. Furthermore, we identified a set of properties that enabled us to assess the consistency of the connectivity distribution for various GRNs against different alternative statistical distributions. Our results favor the hypothesis that highly connected nodes (hubs) are not a consequence of network incompleteness. Finally, an interaction coverage computed for the GRNs as a proxy for completeness revealed that high-throughput based reconstructions of GRNs could yield biased networks with a low average clustering coefficient, showing that classical targeted discovery of interactions is still needed.Comment: 28 pages, 5 figures, 12 pages supplementary informatio

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Solution Path Clustering with Adaptive Concave Penalty

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of the data shows specific grouping patterns. To address these emerging challenges, we develop a new clustering methodology that introduces the idea of a regularization path into unsupervised learning. A regularization path for a clustering problem is created by varying the degree of sparsity constraint that is imposed on the differences between objects via the minimax concave penalty with adaptive tuning parameters. Instead of providing a single solution represented by a cluster assignment for each object, the method produces a short sequence of solutions that determines not only the cluster assignment but also a corresponding number of clusters for each solution. The optimization of the penalized loss function is carried out through an MM algorithm with block coordinate descent. The advantages of this clustering algorithm compared to other existing methods are as follows: it does not require the input of the number of clusters; it is capable of simultaneously separating irrelevant or noisy observations that show no grouping pattern, which can greatly improve data interpretation; it is a general methodology that can be applied to many clustering problems. We test this method on various simulated datasets and on gene expression data, where it shows better or competitive performance compared against several clustering methods.Comment: 36 page

A model for gene deregulation detection using expression data

In tumoral cells, gene regulation mechanisms are severely altered, and these modifications in the regulations may be characteristic of different subtypes of cancer. However, these alterations do not necessarily induce differential expressions between the subtypes. To answer this question, we propose a statistical methodology to identify the misregulated genes given a reference network and gene expression data. Our model is based on a regulatory process in which all genes are allowed to be deregulated. We derive an EM algorithm where the hidden variables correspond to the status (under/over/normally expressed) of the genes and where the E-step is solved thanks to a message passing algorithm. Our procedure provides posterior probabilities of deregulation in a given sample for each gene. We assess the performance of our method by numerical experiments on simulations and on a bladder cancer data set