Approximate inference of gene regulatory network models from RNA-Seq time series data

Abstract

Background: Inference of gene regulatory network structures from RNA-Seq data is challenging due to the nature of the data, as measurements take the form of counts of reads mapped to a given gene. Here we present a model for RNA-Seq time series data that applies a negative binomial distribution for the observations, and uses sparse regression with a horseshoe prior to learn a dynamic Bayesian network of interactions between genes. We use a variational inference scheme to learn approximate posterior distributions for the model parameters.

Results: The methodology is benchmarked on synthetic data designed to replicate the distribution of real world RNA-Seq data. We compare our method to other sparse regression approaches and find improved performance in learning directed networks. We demonstrate an application of our method to a publicly available human neuronal stem cell differentiation RNA-Seq time series data set to infer the underlying network structure.

Conclusions: Our method is able to improve performance on synthetic data by explicitly modelling the statistical distribution of the data when learning networks from RNA-Seq time series. Applying approximate inference techniques we can learn network structures quickly with only moderate computing resources.

Fig. 1

DBN of five random variables X¹,…,X⁵ over T time steps. Variables are conditionally independent when conditioned on their parent variables (incoming arrows)

Fig. 2

Graphical model representation of our statistical model. Applying variational message passing, the approximating distribution $\widehat{q}$ of a random variable can be updated based on messages passed from connected nodes

Fig. 3

Boxplots of partial AUC-ROC, AUC-PR, and MCC for our method (Nb) and the competing methods benchmarked when learning directed networks of 25 nodes from synthetic data, for 5 subnetworks sampled from the S. cerevisiae gene regulatory network

Fig. 4

Boxplots of partial AUC-ROC, AUC-PR, and MCC for our method (Nb) and the methods benchmarked when learning directed networks of 50 nodes from synthetic data, for 5 subnetworks sampled from the S. cerevisiae gene regulatory network

Fig. 5

DBN inferred from the human neuronal differentiation time series data set. Edges were selected using a posterior probability cut-off of 0.95

Fig. 6

Metrics calculated for networks of 25 nodes separated by individual network structure for the 5 different networks considered. Each bar plot corresponds to 5 simulated data sets from a single network structure

Fig. 7

Metrics calculated for networks of 50 nodes separated by individual network structure for the 5 different networks considered. Each bar plot corresponds to 5 simulated data sets from a single network structure

Fig. 8

Posterior means and standard deviations for the regression coefficients β for a single node when applied to the NPC data considered in “Neural progenitor cell differentiation” section