Enumeration and Online Library of Mass-Action Reaction Networks

Background The aim of this work is to make available to the community a large collection of mass-action reaction networks of a given size for further research. The set is limited to what can be computed on a modern multicore desktop in reasonable time (< 20 days). Results We have currently generated over 47 million unique reaction networks. All currently generated sets of networks are available and as new sets are completed they will also be made available. Also provided are programs for translating them into different formats, along with documentation and examples. Source code and binaries for all the programs are included. These can be downloaded from http://www.sys-bio.org/ networkenumeration. Conclusions This library of networks will allow for thorough studies of the reaction network space. Additionally, these methods serve as an example for future work on enumerating other types of biological networks, such as genetic regulatory networks and mass-action networks that include regulation. Background In this paper we describe the enumeration of a significant number of reaction networks that follow massaction kinetics. The aim of this work is to make available to the community a database of reaction networks for further research. In previous work we developed methods for evolving reaction networks in silico with specific functional capabilities such as oscillators, bistable switches, and frequency filters [1, 2]. However, this work sampled only a very small proportion of all networks with a given functionality and we were intrigued by the possibility of enumerating the entire space of all networks. In this first paper we describe the approach we took to enumerate all reaction networks up to a given size. We begin by defining reactions networks, representing reaction networks using graph theory, followed by a detailed description of the algorithm used and a summary of the results. In the discussion we give one small application of the data involving the identification of network that can show oscillatory behavior. Reaction Networks A reaction network is described by a set of reactions and associated molecular species. The simplest reaction networks are governed by mass-action kinetics, where the reaction rate of any particular reaction is proportional to the product of participating species, each raised to a corresponding kinetic order. Such reactions are also termed elementary reactions because they cannot be described in terms of simpler reactions. Given the elementary nature of the reactions, the kinetic orders will often correspond to the stoichiometries of the participating reactants, although in reality this need not be the case depending on the exact kinetic mechanism. In this work we assume that the kinetic orders correspond exactly to the stoichiometries. Given a generalized reaction such as: n1A + n2B + . . . −→ where A and B are reactants with corresponding stoichiometries n1 and n2. We assume, without loss of generality, that all reactions are irreversible and that the rate law (as found through empirical observation) has the form: