Discovering gene regulatory networks of multiple phenotypic groups using dynamic Bayesian networks

Dynamic Bayesian networks (DBNs) can be used for the discovery of gene regulatory networks (GRNs) from time series gene expression data. Here, we suggest a strategy for learning DBNs from gene expression data by employing a Bayesian approach that is scalable to large networks and is targeted at learning models with high predictive accuracy. Our framework can be used to learn DBNs for multiple groups of samples and highlight differences and similarities in their GRNs. We learn these DBN models based on different structural and parametric assumptions and select the optimal model based on the cross-validated predictive accuracy. We show in simulation studies that our approach is better equipped to prevent overfitting than techniques used in previous studies. We applied the proposed DBN-based approach to two time series transcriptomic datasets from the Gene Expression Omnibus database, each comprising data from distinct phenotypic groups of the same tissue type. In the first case, we used DBNs to characterize responders and non-responders to anti-cancer therapy. In the second case, we compared normal to tumor cells of colorectal tissue. The classification accuracy reached by the DBN-based classifier for both datasets was higher than reported previously. For the colorectal cancer dataset, our analysis suggested that GRNs for cancer and normal tissues have a lot of differences, which are most pronounced in the neighborhoods of oncogenes and known cancer tissue markers. The identified differences in gene networks of cancer and normal cells may be used for the discovery of targeted therapies.

Inferring signaling pathways with probabilistic programming

Motivation

Cells regulate themselves via dizzyingly complex biochemical processes called signaling pathways. These are usually depicted as a network, where nodes represent proteins and edges indicate their influence on each other. In order to understand diseases and therapies at the cellular level, it is crucial to have an accurate understanding of the signaling pathways at work. Since signaling pathways can be modified by disease, the ability to infer signaling pathways from condition- or patient-specific data is highly valuable. A variety of techniques exist for inferring signaling pathways. We build on past works that formulate signaling pathway inference as a Dynamic Bayesian Network structure estimation problem on phosphoproteomic time course data. We take a Bayesian approach, using Markov Chain Monte Carlo to estimate a posterior distribution over possible Dynamic Bayesian Network structures. Our primary contributions are (i) a novel proposal distribution that efficiently samples sparse graphs and (ii) the relaxation of common restrictive modeling assumptions.

Results

We implement our method, named Sparse Signaling Pathway Sampling, in Julia using the Gen probabilistic programming language. Probabilistic programming is a powerful methodology for building statistical models. The resulting code is modular, extensible and legible. The Gen language, in particular, allows us to customize our inference procedure for biological graphs and ensure efficient sampling. We evaluate our algorithm on simulated data and the HPN-DREAM pathway reconstruction challenge, comparing our performance against a variety of baseline methods. Our results demonstrate the vast potential for probabilistic programming, and Gen specifically, for biological network inference.

Availability and implementation

Find the full codebase at https://github.com/gitter-lab/ssps.

Supplementary information

Supplementary data are available at Bioinformatics online.

The joint lasso: high-dimensional regression for group structured data

We consider high-dimensional regression over subgroups of observations. Our work is motivated by biomedical problems, where subsets of samples, representing for example disease subtypes, may differ with respect to underlying regression models. In the high-dimensional setting, estimating a different model for each subgroup is challenging due to limited sample sizes. Focusing on the case in which subgroup-specific models may be expected to be similar but not necessarily identical, we treat subgroups as related problem instances and jointly estimate subgroup-specific regression coefficients. This is done in a penalized framework, combining an $\ell_1$ term with an additional term that penalizes differences between subgroup-specific coefficients. This gives solutions that are globally sparse but that allow information-sharing between the subgroups. We present algorithms for estimation and empirical results on simulated data and using Alzheimer's disease, amyotrophic lateral sclerosis, and cancer datasets. These examples demonstrate the gains joint estimation can offer in prediction as well as in providing subgroup-specific sparsity patterns.

Inferring Gene Regulatory Networks from Multiple Datasets

Gaussian process dynamical systems (GPDS) represent Bayesian nonparametric approaches to inference of nonlinear dynamical systems, and provide a principled framework for the learning of biological networks from multiple perturbed time series measurements of gene or protein expression. Such approaches are able to capture the full richness of complex ODE models, and can be scaled for inference in moderately large systems containing hundreds of genes. Related hierarchical approaches allow for inference from multiple datasets in which the underlying generative networks are assumed to have been rewired, either by context-dependent changes in network structure, evolutionary processes, or synthetic manipulation. These approaches can also be used to leverage experimentally determined network structures from one species into another where the network structure is unknown. Collectively, these methods provide a comprehensive and flexible platform for inference from a diverse range of data, with applications in systems and synthetic biology, as well as spatiotemporal modelling of embryo development. In this chapter we provide an overview of GPDS approaches and highlight their applications in the biological sciences, with accompanying tutorials available as a Jupyter notebook from https://github.com/cap76/GPDS .

Statistical Network Inference for Time-Varying Molecular Data with Dynamic Bayesian Networks

In this chapter, we review the problem of network inference from time-course data, focusing on a class of graphical models known as dynamic Bayesian networks (DBNs). We discuss the relationship of DBNs to models based on ordinary differential equations, and consider extensions to nonlinear time dynamics. We provide an introduction to time-varying DBN models, which allow for changes to the network structure and parameters over time. We also discuss causal perspectives on network inference, including issues around model semantics that can arise due to missing variables. We present a case study of applying time-varying DBNs to gene expression measurements over the life cycle of Drosophila melanogaster. We finish with a discussion of future perspectives, including possible applications of time-varying network inference to single-cell gene expression data.

Bayesian Graphical Regression

We consider the problem of modeling conditional independence structures in heterogeneous data in the presence of additional subject-level covariates - termed Graphical Regression. We propose a novel specification of a conditional (in)dependence function of covariates - which allows the structure of a directed graph to vary flexibly with the covariates; imposes sparsity in both edge and covariate selection; produces both subject-specific and predictive graphs; and is computationally tractable. We provide theoretical justifications of our modeling endeavor, in terms of graphical model selection consistency. We demonstrate the performance of our method through rigorous simulation studies. We illustrate our approach in a cancer genomics-based precision medicine paradigm, where-in we explore gene regulatory networks in multiple myeloma taking prognostic clinical factors into account to obtain both population-level and subject-level gene regulatory networks.

Context Specificity in Causal Signaling Networks Revealed by Phosphoprotein Profiling

Signaling networks downstream of receptor tyrosine kinases are among the most extensively studied biological networks, but new approaches are needed to elucidate causal relationships between network components and understand how such relationships are influenced by biological context and disease. Here, we investigate the context specificity of signaling networks within a causal conceptual framework using reverse-phase protein array time-course assays and network analysis approaches. We focus on a well-defined set of signaling proteins profiled under inhibition with five kinase inhibitors in 32 contexts: four breast cancer cell lines (MCF7, UACC812, BT20, and BT549) under eight stimulus conditions. The data, spanning multiple pathways and comprising ∼70,000 phosphoprotein and ∼260,000 protein measurements, provide a wealth of testable, context-specific hypotheses, several of which we experimentally validate. Furthermore, the data provide a unique resource for computational methods development, permitting empirical assessment of causal network learning in a complex, mammalian setting.

Time-course assays of signaling proteins in cancer cell lines under kinase inhibition

Causal conceptual framework for network analysis

Data shed light on causal protein networks that are specific to biological context

Resource for signaling biology and for benchmarking computational methods

Inferring orthologous gene regulatory networks using interspecies data fusion

Motivation: The ability to jointly learn gene regulatory networks (GRNs) in, or leverage GRNs between related species would allow the vast amount of legacy data obtained in model organisms to inform the GRNs of more complex, or economically or medically relevant counterparts. Examples include transferring information from Arabidopsis thaliana into related crop species for food security purposes, or from mice into humans for medical applications. Here we develop two related Bayesian approaches to network inference that allow GRNs to be jointly inferred in, or leveraged between, several related species: in one framework, network information is directly propagated between species; in the second hierarchical approach, network information is propagated via an unobserved ‘hypernetwork’. In both frameworks, information about network similarity is captured via graph kernels, with the networks additionally informed by species-specific time series gene expression data, when available, using Gaussian processes to model the dynamics of gene expression.

Results: Results on in silico benchmarks demonstrate that joint inference, and leveraging of known networks between species, offers better accuracy than standalone inference. The direct propagation of network information via the non-hierarchical framework is more appropriate when there are relatively few species, while the hierarchical approach is better suited when there are many species. Both methods are robust to small amounts of mislabelling of orthologues. Finally, the use of Saccharomyces cerevisiae data and networks to inform inference of networks in the budding yeast Schizosaccharomyces pombe predicts a novel role in cell cycle regulation for Gas1 (SPAC19B12.02c), a 1,3-beta-glucanosyltransferase.

Availability and implementation: MATLAB code is available from http://go.warwick.ac.uk/systemsbiology/software/.

Contact:d.l.wild@warwick.ac.uk

Supplementary information:Supplementary data are available at Bioinformatics online.

Quantifying the multi-scale performance of network inference algorithms

Graphical models are widely used to study complex multivariate biological systems. Network inference algorithms aim to reverse-engineer such models from noisy experimental data. It is common to assess such algorithms using techniques from classifier analysis. These metrics, based on ability to correctly infer individual edges, possess a number of appealing features including invariance to rank-preserving transformation. However, regulation in biological systems occurs on multiple scales and existing metrics do not take into account the correctness of higher-order network structure. In this paper novel performance scores are presented that share the appealing properties of existing scores, whilst capturing ability to uncover regulation on multiple scales. Theoretical results confirm that performance of a network inference algorithm depends crucially on the scale at which inferences are to be made; in particular strong local performance does not guarantee accurate reconstruction of higher-order topology. Applying these scores to a large corpus of data from the DREAM5 challenge, we undertake a data-driven assessment of estimator performance. We find that the "wisdom of crowds" network, that demonstrated superior local performance in the DREAM5 challenge, is also among the best performing methodologies for inference of regulation on multiple length scales.