The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, Linear Mapping Approximation, and state-space lumping. Despite the success of these techniques, they appear to be rather disparate, and at present, no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper, we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimizing a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimization approaches. In addition, we derive general expressions for propensities of a reduced system that generalize those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system, and a genetic oscillator.

Model reduction for the Chemical Master Equation: An information-theoretic approach / Ocal, Kaan; Sanguinetti, Guido; Grima, Ramon. - In: JOURNAL OF CHEMICAL PHYSICS ONLINE. - ISSN 1089-7690. - 158:11(2023), pp. 1-27. [10.1063/5.0131445]

Model reduction for the Chemical Master Equation: An information-theoretic approach

Sanguinetti, Guido;
2023-01-01

Abstract

The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, Linear Mapping Approximation, and state-space lumping. Despite the success of these techniques, they appear to be rather disparate, and at present, no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper, we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimizing a well-known information-theoretic quantity between the full model and its reduction, the Kullback-Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimization approaches. In addition, we derive general expressions for propensities of a reduced system that generalize those found using classical methods. We show that the Kullback-Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis-Menten enzyme system, and a genetic oscillator.
2023
158
11
1
27
114113
10.1063/5.0131445
https://arxiv.org/abs/2210.05329
Ocal, Kaan; Sanguinetti, Guido; Grima, Ramon
File in questo prodotto:
File Dimensione Formato  
2210.05329.pdf

accesso aperto

Descrizione: preprint
Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 1.07 MB
Formato Adobe PDF
1.07 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/132230
Citazioni
  • ???jsp.display-item.citation.pmc??? 0
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact