Inference of genetic regulatory networks with regulatory hubs using vector autoregressions and automatic relevance determination with model selections

The inference of genetic regulatory networks (GRNs) reveals how genes interact with each other. A few genes can regulate many genes as targets to control cell functions. We present new methods based on the order-1 vector autoregression (VAR1) for inferring GRNs from gene expression time series. The methods use the automatic relevance determination (ARD) to incorporate the regulatory hub structure into the estimation of VAR1 in a Bayesian framework. Several sparse approximation schemes are applied to the estimated regression weights or VAR1 model to generate the sparse weighted adjacency matrices representing the inferred GRNs. We apply the proposed and several widespread reference methods to infer GRNs with up to 100 genes using simulated, DREAM4 in silico and experimental E. coli gene expression time series. We show that the proposed methods are efficient on simulated hub GRNs and scale-free GRNs using short time series simulated by VAR1s and outperform reference methods on small-scale DREAM4 in silico GRNs and E. coli GRNs. They can utilize the known major regulatory hubs to improve the performance on larger DREAM4 in silico GRNs and E. coli GRNs. The impact of nonlinear time series data on the performance of proposed methods is discussed.

RVAgene: Generative modeling of gene expression time series data

Methods to model dynamic changes in gene expression at a genome-wide level are not currently sufficient for large (temporally rich or single-cell) datasets. Variational autoencoders offer means to characterize large datasets and have been used effectively to characterize features of single-cell datasets. Here we extend these methods for use with gene expression time series data. We present RVAgene: a recurrent variational autoencoder to model gene expression dynamics. RVAgene learns to accurately and efficiently reconstruct temporal gene profiles. It also learns a low dimensional representation of the data via a recurrent encoder network that can be used for biological feature discovery, and can generate new gene expression data by sampling from the latent space. We test RVAgene on simulated and real biological datasets, including embryonic stem cell differentiation and kidney injury response dynamics. In all cases, RVAgene accurately reconstructed complex gene expression temporal profiles. Via cross validation, we show that a low-error latent space representation can be learnt using only a fraction of the data. Through clustering and gene ontology term enrichment analysis on the latent space, we demonstrate the potential of RVAgene for unsupervised discovery. In particular, RVAgene identifies new programs of shared gene regulation of Lox family genes in response to kidney injury.

Inference of gene networks from gene expression time series using recurrent neural networks and sparse MAP estimation

Background: The inference of genetic regulatory networks (GRNs) provides insight into the cellular responses to signals. A class of recurrent neural networks (RNNs) capturing the dynamics of GRN has been used as a basis for inferring small-scale GRNs from gene expression time series. The Bayesian framework facilitates incorporating the hypothesis of GRN into the model estimation to improve the accuracy of GRN inference. Results: We present new methods for inferring small-scale GRNs based on RNNs. The weights of wires of RNN represent the strengths of gene-to-gene regulatory interactions. We use a class of automatic relevance determination (ARD) priors to enforce the sparsity in the maximum a posteriori (MAP) estimates of wire weights of RNN. A particle swarm optimization (PSO) is integrated as an optimization engine into the MAP estimation process. Likely networks of genes generated based on estimated wire weights are combined using the majority rule to determine a final estimated GRN. As an alternative, a class of [Formula: see text]-norm ([Formula: see text]) priors is used for attaining the sparse MAP estimates of wire weights of RNN. We also infer the GRN using the maximum likelihood (ML) estimates of wire weights of RNN. The RNN-based GRN inference algorithms, ARD-RNN, [Formula: see text]-RNN, and ML-RNN are tested on simulated and experimental E. coli and yeast time series containing 6–11 genes and 7–19 data points. Published GRN inference algorithms based on regressions and mutual information networks are performed on the benchmark datasets to compare performances. Conclusion: ARD and [Formula: see text]-norm priors are used for the estimation of wire weights of RNN. Results of GRN inference experiments show that ARD-RNN, [Formula: see text]-RNN have similar best accuracies on the simulated time series. The ARD-RNN is more accurate than [Formula: see text]-RNN, ML-RNN, and mostly more accurate than the reference algorithms on the experimental time series. The effectiveness of ARD-RNN for inferring small-scale GRNs using gene expression time series of limited length is empirically verified.

Increasing Power by Sharing Information from Genetic Background and Treatment in Clustering of Gene Expression Time Series

Clustering of gene expression time series gives insight into which genes may be co-regulated, allowing us to discern the activity of pathways in a given microarray experiment. Of particular interest is how a given group of genes varies with different conditions or genetic background. This paper develops a new clustering method that allows each cluster to be parameterised according to whether the behaviour of the genes across conditions is correlated or anti-correlated. By specifying correlation between such genes,more information is gain within the cluster about how the genes interrelate. Amyotrophic lateral sclerosis (ALS) is an irreversible neurodegenerative disorder that kills the motor neurons and results in death within 2 to 3 years from the symptom onset. Speed of progression for different patients are heterogeneous with significant variability. The SOD1G93A transgenic mice from different backgrounds (129Sv and C57) showed consistent phenotypic differences for disease progression. A hierarchy of Gaussian isused processes to model condition-specific and gene-specific temporal co-variances. This study demonstrated about finding some significant gene expression profiles and clusters of associated or co-regulated gene expressions together from four groups of data (SOD1G93A and Ntg from 129Sv and C57 backgrounds). Our study shows the effectiveness of sharing information between replicates and different model conditions when modelling gene expression time series. Further gene enrichment score analysis and ontology pathway analysis of some specified clusters for a particular group may lead toward identifying features underlying the differential speed of disease progression.