Domain-oriented reduction of rule-based network models

Abstract

The coupling of membrane-bound receptors to transcriptional regulators and other effector functions is mediated by multi-domain proteins that form complex assemblies. The modularity of protein interactions lends itself to a rule-based description, in which species and reactions are generated by rules that encode the necessary context for an interaction to occur, but also can produce a combinatorial explosion in the number of chemical species that make up the signalling network. The authors have shown previously that exact network reduction can be achieved using hierarchical control relationships between sites/domains on proteins to dissect multi-domain proteins into sets of non-interacting sites, allowing the replacement of each 'full' (progenitor) protein with a set of derived auxiliary (offspring) proteins. The description of a network in terms of auxiliary proteins that have fewer sites than progenitor proteins often greatly reduces network size. The authors describe here a method for automating domain-oriented model reduction and its implementation as a module in the BioNetGen modelling package. It takes as input a standard BioNetGen model and automatically performs the following steps: 1) detecting the hierarchical control relationships between sites; 2) building up the auxiliary proteins; 3) generating a raw reduced model and 4) cleaning up the raw model to provide the correct mass balance for each chemical species in the reduced network. The authors tested the performance of this module on models representing portions of growth factor receptor and immunoreceptor-mediated signalling networks and confirmed its ability to reduce the model size and simulation cost by at least one or two orders of magnitude. Limitations of the current algorithm include the inability to reduce models based on implicit site dependencies or heterodimerisation and loss of accuracy when dynamics are computed stochastically.

Fig. 1. Multiplicity of the states of receptor and receptor-adapter complexes

The state of the receptor molecule R is characterized by a vector (r₁, r₂, r₃, r₄), where r₁ stands for the ligand (L)-binding site, r₂ depicts the dimerization site, and r₃ and r₄ specify the state of docking sites for adapter proteins. The adapter protein B is a scaffold that possesses three sites (site b₁ for binding to the receptor, and tyrosine residues b₂ and b₃).

Fig. 2

A flowchart of operations for the domain-oriented reduction algorithm.