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

Bayesian causal inference of cell signal transduction from proteomics experiments

Cell signal transduction describes how a cell senses and processes signals from the environment using networks of interacting proteins. In computational systems biology, investigators apply machine learning methods for causal inference to develop causal Bayesian network models of signal transduction from experimental data. Directed edges in the network represent causal regulatory relationships, and the model can be used to predict the effects of interventions to signal transduction. Causal inference approaches applied to proteomics experiments use statistical associations between observed signaling protein concentrations to infer a causal Bayesian network model, but there is no experimental and analysis framework for applying these methods to this experimental context. The goal of this dissertation is to provide a Bayesian experimental design and modeling framework for causal inference of signal transduction. We evaluate how different high-throughput experimental settings affect the performance of algorithms that detect conditional dependence relationships between proteins. We present a Bayesian active learning approach for designing intervention experiments that reveal the direction of causal influence between proteins. Finally, we present a Bayesian model for inferring the parameters of the conditional probability density functions in a causal Bayesian network. The parameters are directly interpretable as a function of the rate constants in the biochemical reactions between interacting proteins. The work pays special attention to analysis of single-cell snapshot data such as mass cytometry, where each cell is a multivariate cell-level replicate of signal transduction at a single time point. We also address the role of large-scale bulk experiments such as mass-spectrometry-based proteomics, and small-scale time-course experiments in causal inference

Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community

Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Modeling dependent gene expression

In this paper we propose a Bayesian approach for inference about dependence of high throughput gene expression. Our goals are to use prior knowledge about pathways to anchor inference about dependence among genes; to account for this dependence while making inferences about differences in mean expression across phenotypes; and to explore differences in the dependence itself across phenotypes. Useful features of the proposed approach are a model-based parsimonious representation of expression as an ordinal outcome, a novel and flexible representation of prior information on the nature of dependencies, and the use of a coherent probability model over both the structure and strength of the dependencies of interest. We evaluate our approach through simulations and in the analysis of data on expression of genes in the Complement and Coagulation Cascade pathway in ovarian cancer.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS525 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org