Abstract
BackgroundThe inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation.ResultsWe claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP), therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining 'true' reaction structures are generally not enough without additional prior information.ConclusionsThe inference of biological networks can be an extremely challenging problem even in the utopian case of perfect experimental information. Unfortunately, the practical situation is often more complex than that, since the measurements are typically incomplete, noisy and sometimes dynamically not rich enough, introducing further obstacles to the structure/parameter estimation process. In this paper, we show how the structural uniqueness and identifiability of the models can be guaranteed by carefully adding extra constraints, and that these important properties can be checked through appropriate computation methods.
Highlights
The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology
DREAM tries to address two fundamental questions: (i) how can we assess how well we are describing the networks of interacting molecules that underlie biological systems? and (ii) how can we know how well we are predicting the outcome of previously unseen experiments from our models? Interestingly, one of the main conclusions of the DREAM3 event was that the vast majority of the teams’ predictions were statistically equivalent to random guesses
We consider the widely used reaction kinetic formalism, where dynamic models of biological networks are described by a set of ordinary differential equations
Summary
The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. Many methods have been developed to solve the network-inference In this context, it is worth mentioning the DREAM initiative (Dialogue for Reverse Engineering Assessments and Methods) [26], which targeted the problems of cellular network inference and quantitative model building in systems biology. The use of a performance profiling framework with the DREAM3 benchmark problems revealed that current inference methods are affected by different types of systematic prediction errors [6]. These authors conclude that reliable network inference from gene expression data remains an unsolved problem. We consider the central question of the identifiability of such a network as understood in the systems and control area [31,32]
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