Exact maximal reduction of stochastic reaction networks by species lumping

TL;DR

This paper introduces an exact species lumping method for stochastic reaction networks that reduces model complexity while preserving key dynamics, applicable to biological systems with noise, demonstrated on signaling and epidemic models.

Contribution

The paper presents a novel exact lumping technique for stochastic reaction networks that identifies maximal species equivalences, including parameter-independent cases, with an efficient algorithm and software implementation.

Findings

Effective reduction of complex models demonstrated on biological networks.

Maximal lumping preserves stochastic dynamics exactly.

Algorithm scales well to large networks.

Abstract

Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete state-space representation hinders analytical tractability and makes numerical simulations expensive. Reduction methods can lower complexity by computing model projections that preserve dynamics of interest to the user. Results: We present an exact lumping method for stochastic reaction networks with mass-action kinetics. It hinges on an equivalence relation between the species, resulting in a reduced network where the dynamics of each macro-species is stochastically equivalent to the sum of the original species in each equivalence class, for any choice of the initial state of the system. Furthermore, by an appropriate encoding of kinetic parameters as additional species, the method can establish equivalences that do not depend on specific values of the parameters. The method is supported by an efficient algorithm to compute the largest species equivalence, thus the maximal lumping. The effectiveness and scalability of our lumping technique, as well as the physical interpretability of resulting reductions, is demonstrated in several models of signaling pathways and epidemic processes on complex networks. Availability: The algorithms for species equivalence have been implemented in the software tool ERODE, freely available for download from https://www.erode.eu.