Chris J. Oates

Network Inference and Biological Dynamics.

Network inference approaches are now widely used in biological applications to probe regulatory relationships between molecular components such as genes or proteins. Many methods have been proposed for this setting, but the connections and differences between their statistical formulations have received less attention. In this paper, we show how a broad class of statistical network inference methods, including a number of existing approaches, can be described in terms of variable selection for the linear model. This reveals some subtle but important differences between the methods, including the treatment of time intervals in discretely observed data. In developing a general formulation, we also explore the relationship between single-cell stochastic dynamics and network inference on averages over cells. This clarifies the link between biochemical networks as they operate at the cellular level and network inference as carried out on data that are averages over populations of cells. We present empirical results, comparing thirty-two network inference methods that are instances of the general formulation we describe, using two published dynamical models. Our investigation sheds light on the applicability and limitations of network inference and provides guidance for practitioners and suggestions for experimental design.

Causal network inference using biochemical kinetics

Motivation: Networks are widely used as structural summaries of biochemical systems. Statistical estimation of networks is usually based on linear or discrete models. However, the dynamics of biochemical systems are generally non-linear, suggesting that suitable non-linear formulations may offer gains with respect to causal network inference and aid in associated prediction problems. Results: We present a general framework for network inference and dynamical prediction using time course data that is rooted in non-linear biochemical kinetics. This is achieved by considering a dynamical system based on a chemical reaction graph with associated kinetic parameters. Both the graph and kinetic parameters are treated as unknown; inference is carried out within a Bayesian framework. This allows prediction of dynamical behavior even when the underlying reaction graph itself is unknown or uncertain. Results, based on (i) data simulated from a mechanistic model of mitogen-activated protein kinase signaling and (ii) phosphoproteomic data from cancer cell lines, demonstrate that non-linear formulations can yield gains in causal network inference and permit dynamical prediction and uncertainty quantification in the challenging setting where the reaction graph is unknown. Availability and implementation: MATLAB R2014a software is available to download from warwick.ac.uk/chrisoates. Contact: c.oates@warwick.ac.uk or sach@mrc-bsu.cam.ac.uk Supplementary information: Supplementary data are available at Bioinformatics online.

The Controlled Thermodynamic Integral for Bayesian Model Evidence Evaluation

ABSTRACT Approximation of the model evidence is well known to be challenging. One promising approach is based on thermodynamic integration, but a key concern is that the thermodynamic integral can suffer from high variability in many applications. This article considers the reduction of variance that can be achieved by exploiting control variates in this setting. Our methodology applies whenever the gradient of both the log-likelihood and the log-prior with respect to the parameters can be efficiently evaluated. Results obtained on regression models and popular benchmark datasets demonstrate a significant and sometimes dramatic reduction in estimator variance and provide insight into the wider applicability of control variates to evidence estimation. Supplementary materials for this article are available online.

RNA editing generates cellular subsets with diverse sequence within populations

RNA editing is a mutational mechanism that specifically alters the nucleotide content in transcribed RNA. However, editing rates vary widely, and could result from equivalent editing amongst individual cells, or represent an average of variable editing within a population. Here we present a hierarchical Bayesian model that quantifies the variance of editing rates at specific sites using RNA-seq data from both single cells, and a cognate bulk sample to distinguish between these two possibilities. The model predicts high variance for specific edited sites in murine macrophages and dendritic cells, findings that we validated experimentally by using targeted amplification of specific editable transcripts from single cells. The model also predicts changes in variance in editing rates for specific sites in dendritic cells during the course of LPS stimulation. Our data demonstrate substantial variance in editing signatures amongst single cells, supporting the notion that RNA editing generates diversity within cellular populations.

Joint estimation of multiple related biological networks

Graphical models are widely used to make inferences concerning interplay in multivariate systems. In many applications, data are collected from multiple related but nonidentical units whose underlying networks may differ but are likely to share features. Here we present a hierarchical Bayesian formulation for joint estimation of multiple networks in this nonidentically distributed setting. The approach is general: given a suitable class of graphical models, it uses an exchangeability assumption on networks to provide a corresponding joint formulation. Motivated by emerging experimental designs in molecular biology, we focus on time-course data with interventions, using dynamic Bayesian networks as the graphical models. We introduce a computationally efficient, deterministic algorithm for exact joint inference in this setting. We provide an upper bound on the gains that joint estimation offers relative to separate estimation for each network and empirical results that support and extend the theory, including an extensive simulation study and an application to proteomic data from human cancer cell lines. Finally, we describe approximations that are still more computationally efficient than the exact algorithm and that also demonstrate good empirical performance.

Exact estimation of multiple directed acyclic graphs

This paper considers structure learning for multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs. Unlike previous work, we do not require that the vertices in each DAG share a common ordering. Furthermore, we allow for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.

Decoupling of the PI3K pathway via mutation necessitates combinatorial treatment in HER2+ breast cancer

We report here on experimental and theoretical efforts to determine how best to combine drugs that inhibit HER2 and AKT in HER2+ breast cancers. We accomplished this by measuring cellular and molecular responses to lapatinib and the AKT inhibitors (AKTi) GSK690693 and GSK2141795 in a panel of 22 HER2+ breast cancer cell lines carrying wild type or mutant PIK3CA. We observed that combinations of lapatinib plus AKTi were synergistic in HER2+/PIK3CAmut cell lines but not in HER2+/PIK3CAwt cell lines. We measured changes in phospho-protein levels in 15 cell lines after treatment with lapatinib, AKTi or lapatinib + AKTi to shed light on the underlying signaling dynamics. This revealed that p-S6RP levels were less well attenuated by lapatinib in HER2+/PIK3CAmut cells compared to HER2+/PIK3CAwt cells and that lapatinib + AKTi reduced p-S6RP levels to those achieved in HER2+/PIK3CAwt cells with lapatinib alone. We also found that that compensatory up-regulation of p-HER3 and p-HER2 is blunted in PIK3CAmut cells following lapatinib + AKTi treatment. Responses of HER2+ SKBR3 cells transfected with lentiviruses carrying control or PIK3CAmut sequences were similar to those observed in HER2+/PIK3CAmut cell lines but not in HER2+/PIK3CAwt cell lines. We used a nonlinear ordinary differential equation model to support the idea that PIK3CA mutations act as downstream activators of AKT that blunt lapatinib inhibition of downstream AKT signaling and that the effects of PIK3CA mutations can be countered by combining lapatinib with an AKTi. This combination does not confer substantial benefit beyond lapatinib in HER2+/PIK3CAwt cells.

A stochastic model dissects cell states in biological transition processes.

Many biological processes, including differentiation, reprogramming, and disease transformations, involve transitions of cells through distinct states. Direct, unbiased investigation of cell states and their transitions is challenging due to several factors, including limitations of single-cell assays. Here we present a stochastic model of cellular transitions that allows underlying single-cell information, including cell-state-specific parameters and rates governing transitions between states, to be estimated from genome-wide, population-averaged time-course data. The key novelty of our approach lies in specifying latent stochastic models at the single-cell level, and then aggregating these models to give a likelihood that links parameters at the single-cell level to observables at the population level. We apply our approach in the context of reprogramming to pluripotency. This yields new insights, including profiles of two intermediate cell states, that are supported by independent single-cell studies. Our model provides a general conceptual framework for the study of cell transitions, including epigenetic transformations.

Investigation of the widely applicable Bayesian information criterion

The widely applicable Bayesian information criterion (WBIC) is a simple and fast approximation to the model evidence that has received little practical consideration. WBIC uses the fact that the log evidence can be written as an expectation, with respect to a powered posterior proportional to the likelihood raised to a power