Abstract

BackgroundReverse engineering cellular networks is currently one of the most challenging problems in systems biology. Dynamic Bayesian networks (DBNs) seem to be particularly suitable for inferring relationships between cellular variables from the analysis of time series measurements of mRNA or protein concentrations. As evaluating inference results on a real dataset is controversial, the use of simulated data has been proposed. However, DBN approaches that use continuous variables, thus avoiding the information loss associated with discretization, have not yet been extensively assessed, and most of the proposed approaches have dealt with linear Gaussian models.ResultsWe propose a generalization of dynamic Gaussian networks to accommodate nonlinear dependencies between variables. As a benchmark dataset to test the new approach, we used data from a mathematical model of cell cycle control in budding yeast that realistically reproduces the complexity of a cellular system. We evaluated the ability of the networks to describe the dynamics of cellular systems and their precision in reconstructing the true underlying causal relationships between variables. We also tested the robustness of the results by analyzing the effect of noise on the data, and the impact of a different sampling time.ConclusionThe results confirmed that DBNs with Gaussian models can be effectively exploited for a first level analysis of data from complex cellular systems. The inferred models are parsimonious and have a satisfying goodness of fit. Furthermore, the networks not only offer a phenomenological description of the dynamics of cellular systems, but are also able to suggest hypotheses concerning the causal interactions between variables. The proposed nonlinear generalization of Gaussian models yielded models characterized by a slightly lower goodness of fit than the linear model, but a better ability to recover the true underlying connections between variables.

Highlights

  • Reverse engineering cellular networks is currently one of the most challenging problems in systems biology

  • The results confirmed that dynamic Bayesian network (DBN) with Gaussian models can be effectively exploited for a first level analysis of data from complex cellular systems

  • The networks offer a phenomenological description of the dynamics of cellular systems, but are able to suggest hypotheses concerning the causal interactions between variables

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Summary

Introduction

Reverse engineering cellular networks is currently one of the most challenging problems in systems biology. The various reverse engineering methods proposed in the literature range from highly detailed models, such as those based on differential equations, to highly abstract models, such as Boolean networks The former describe the molecular reactions taking place in a cell, and the latter represent cellular components as binary variables that are linked to each other by logical relationships [1,2]. Like BNs, when applied to cellular networks, DBNs describe cellular entities (i.e. mRNA or protein concentrations) by means of random variables and model the relationships between these variables both at qualitative and quantitative level [5]. The dependence relationships are described by means of conditional probability distributions Because of their probabilistic framework, BNs and DBNs can automatically take into account the variability of biological systems, as well as the possible presence of experimental noise in the data

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