The Annals of Statistics

Stochastic kinetic models: Dynamic independence, modularity and graphs

Clive G. Bowsher

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Abstract

The dynamic properties and independence structure of stochastic kinetic models (SKMs) are analyzed. An SKM is a highly multivariate jump process used to model chemical reaction networks, particularly those in biochemical and cellular systems. We identify SKM subprocesses with the corresponding counting processes and propose a directed, cyclic graph (the kinetic independence graph or KIG) that encodes the local independence structure of their conditional intensities. Given a partition [A, D, B] of the vertices, the graphical separation AB|D in the undirected KIG has an intuitive chemical interpretation and implies that A is locally independent of B given A ∪ D. It is proved that this separation also results in global independence of the internal histories of A and B conditional on a history of the jumps in D which, under conditions we derive, corresponds to the internal history of D. The results enable mathematical definition of a modularization of an SKM using its implied dynamics. Graphical decomposition methods are developed for the identification and efficient computation of nested modularizations. Application to an SKM of the red blood cell advances understanding of this biochemical system.

Article information

Source
Ann. Statist., Volume 38, Number 4 (2010), 2242-2281.

Dates
First available in Project Euclid: 11 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1278861248

Digital Object Identifier
doi:10.1214/09-AOS779

Mathematical Reviews number (MathSciNet)
MR2676889

Zentralblatt MATH identifier
1203.92033

Subjects
Primary: 62P10: Applications to biology and medical sciences 62-09: Graphical methods
Secondary: 60G55: Point processes 92C37: Cell biology 92C40: Biochemistry, molecular biology 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]

Keywords
Stochastic kinetic model kinetic independence graph counting and point processes dynamic and local independence graphical decomposition reaction networks systems biology

Citation

Bowsher, Clive G. Stochastic kinetic models: Dynamic independence, modularity and graphs. Ann. Statist. 38 (2010), no. 4, 2242--2281. doi:10.1214/09-AOS779. https://projecteuclid.org/euclid.aos/1278861248


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