Exact maximal reduction of stochastic reaction networks by species lumping

Luca Cardelli, ‪Isabel Cristina Pérez-Verona, Mirco Tribastone, Max Tschaikowski, Andrea Vandin, Tabea Waizmann

Research output: Contribution to journalJournal articleResearchpeer-review

9 Citations (Scopus)

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. Unfortunately, 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 and implementation
The algorithms for species equivalence have been implemented in the software tool ERODE, freely available for download from https://www.erode.eu.

Supplementary information
Supplementary data are available at Bioinformatics online.
Original languageEnglish
JournalBioinformatics
Volume37
Issue number15
Pages (from-to)2175–2182
ISSN1367-4803
DOIs
Publication statusPublished - 2021

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