Structural inference using nonlinear dynamics

Network inference methods are widely used to study regulatory interplay in biological systems. Such methods are usually based on simple, often linear, approximations to underlying dynamics. We present a network inference methodology that is rooted in nonlinear biochemical kinetics. This is done by considering a dynamical system that depends on a reaction graph, summarizing all biochemical reactions and associated parameters. We assume that neither graph nor parameters are known; inference regarding the graph is carried out within a Bayesian framework, using an efficient Monte Carlo approach to integrate out parameters. In this way, we take account of model complexity as well as fit-to-data. Focusing on protein signaling networks, we show results on data simulated from a recent dynamical model of MAPK signaling. We find that the method is able to effectively recover regulatory relationships. Furthermore, the approach facilitates modeling of interventional data, since it respects the roles of individual variables. Statistical network inference techniques are widely used in the analysis of multivariate biochemical data [5, 11, 21, 24, 31, 36]. The objective is to make inferences regarding a network N whose vertices are identified with biomolecular components (e.g. genes or proteins) and edges with regulatory interplay between those components. Network edges often have the causal interpretation that intervention on the parent influences the child. Network inference methods are typically rooted in simple descriptions of biological dynamics, usually linear or discrete [4, 5, 11, 25, 31, 36, 39]. The statistical and computational tractability of such formulations facilitates inference over large spaces of networks. However, biochemical networks are structural summaries of dynamical systems that are generally nonlinear. There is a extensive literature on relevant chemical kinetics [3]; in the absence of structural uncertainty, nonlinear ordinary differential equations (ODEs) are widely used to model dynamics [3, 7, 18, 19, 32]. However, the case where structure is unknown or uncertain has received less attention and to date nonlinear dynamical models have not been integrated into network inference over large model spaces. ∗University of Warwick, Coventry, United Kingdom †Netherlands Cancer Institute, Amsterdam, The Netherlands