Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of interleukin-12 (IL-12) signaling in naïve CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo-equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics.