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Identifiability of stochastically modelled reaction networks

Part of: Chemistry Physiological, cellular and medical topics Markov processes Controllability, observability, and system structure Inference from stochastic processes

Published online by Cambridge University Press:  15 February 2021

GERMAN ENCISO ,
RADEK ERBAN Open the ORCID record for RADEK ERBAN [Opens in a new window]  and
JINSU KIM
GERMAN ENCISO
Affiliation:
Department of Mathematics, University of California, Irvine, CA92697, USA e-mail: enciso@uci.edu
RADEK ERBAN
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK e-mail: erban@maths.ox.ac.uk
JINSU KIM
Affiliation:
NSF-Simons Center for Multiscale Cell Fate Research, University of California, Irvine, CA92697, USA e-mail: jinsu.kim@uci.edu
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Abstract

Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations.

Keywords

Chemical reaction networksidentifiabilitystochastic simulationnetwork inferenceGillespie algorithm

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 62M10: Time series, auto-correlation, regression, etc. 92C42: Systems biology, networks 92E20: Classical flows, reactions, etc. 93B30: System identification
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 5: 30th Anniversary Special Issue , October 2021 , pp. 865 - 887
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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