Bayesian hierarchical modeling for signaling pathway inference from single cell interventional data

Recent technological advances have made it possible to simultaneously measure multiple protein activities at the single cell level. With such data collected under different stimulatory or inhibitory conditions, it is possible to infer the causal relationships among proteins from single cell interventional data. In this article we propose a Bayesian hierarchical modeling framework to infer the signaling pathway based on the posterior distributions of parameters in the model. Under this framework, we consider network sparsity and model the existence of an association between two proteins both at the overall level across all experiments and at each individual experimental level. This allows us to infer the pairs of proteins that are associated with each other and their causal relationships. We also explicitly consider both intrinsic noise and measurement error. Markov chain Monte Carlo is implemented for statistical inference. We demonstrate that this hierarchical modeling can effectively pool information from different interventional experiments through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS425 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Corrected score methods for estimating Bayesian networks with error-prone nodes

Motivated by inferring cellular signaling networks using noisy flow cytometry data, we develop procedures to draw inference for Bayesian networks based on error-prone data. Two methods for inferring causal relationships between nodes in a network are proposed based on penalized estimation methods that account for measurement error and encourage sparsity. We discuss consistency of the proposed network estimators and develop an approach for selecting the tuning parameter in the penalized estimation methods. Empirical studies are carried out to compare the proposed methods and a naive method that ignores measurement error with applications to synthetic data and to single cell flow cytometry data

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.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Structure Learning in Nested Effects Models

Nested Effects Models (NEMs) are a class of graphical models introduced to analyze the results of gene perturbation screens. NEMs explore noisy subset relations between the high-dimensional outputs of phenotyping studies, e.g. the effects showing in gene expression profiles or as morphological features of the perturbed cell. In this paper we expand the statistical basis of NEMs in four directions: First, we derive a new formula for the likelihood function of a NEM, which generalizes previous results for binary data. Second, we prove model identifiability under mild assumptions. Third, we show that the new formulation of the likelihood allows to efficiently traverse model space. Fourth, we incorporate prior knowledge and an automated variable selection criterion to decrease the influence of noise in the data

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.This work was supported by the National Institutes of Health National Cancer Institute (grant U54 CA112970 to J.W.G., G.B.M., S.M., and P.T.S.). S.M.H. and S.M. were supported by the UK Medical Research Council (unit program numbers MC_UP_1302/1 and MC_UP_1302/3). S.M. was a recipient of a Royal Society Wolfson Research Merit Award. The MD Anderson Cancer Center RPPA Core Facility is funded by the National Institutes of Health National Cancer Institute (Cancer Center Core Grant CA16672)

Inferring causal molecular networks: empirical assessment through a community-based effort.

It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense

Inferring causal molecular networks: empirical assessment through a community-based effort

It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense

Inferring causal molecular networks: empirical assessment through a community-based effort

Inferring molecular networks is a central challenge in computational biology. However, it has remained unclear whether causal, rather than merely correlational, relationships can be effectively inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge that focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results constitute the most comprehensive assessment of causal network inference in a mammalian setting carried out to date and suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess the causal validity of inferred molecular networks

Inferring causal molecular networks: empirical assessment through a community-based effort

It remains unclear whether causal, rather than merely correlational, relationships in molecular networks can be inferred in complex biological settings. Here we describe the HPN-DREAM network inference challenge, which focused on learning causal influences in signaling networks. We used phosphoprotein data from cancer cell lines as well as in silico data from a nonlinear dynamical model. Using the phosphoprotein data, we scored more than 2,000 networks submitted by challenge participants. The networks spanned 32 biological contexts and were scored in terms of causal validity with respect to unseen interventional data. A number of approaches were effective, and incorporating known biology was generally advantageous. Additional sub-challenges considered time-course prediction and visualization. Our results suggest that learning causal relationships may be feasible in complex settings such as disease states. Furthermore, our scoring approach provides a practical way to empirically assess inferred molecular networks in a causal sense

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 nonlinear 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. © The Author 2014. Published by Oxford University Press