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Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks

Sootla, Aivar and Anderson, James (2017) Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks. IEEE Transactions on Automatic Control, 62 (11). pp. 5554-5566. ISSN 0018-9286.

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The chemical master equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason, simpler approximations to the CME have been proposed. In this paper, we focus on one such model, the linear noise approximation (LNA). Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced-order LNA converges to the full-order model in the mean square sense. Using this as motivation, we derive a network structure-preserving reduction algorithm based on structured projections. We discuss when these structured projections exist and we present convex optimization algorithms that describe how such projections can be computed. The algorithms are then applied to a linearized stochastic LNA model of the yeast glycolysis pathway.

Item Type:Article
Related URLs:
URLURL TypeDescription
Sootla, Aivar0000-0003-4666-4454
Anderson, James0000-0002-2832-8396
Additional Information:© 2017 IEEE. Manuscript received July 21, 2016; revised February 25, 2017; accepted March 19, 2017. Date of publication April 5, 2017; date of current version October 25, 2017. The work of A. Sootla was supported in part by the EPSRC Grant EP/J014214/1 and Grant EP/G036004/1, in part by the Wallonia-Brussels Federation through the F.R.S.-FNRS Fellowship, and in part by EPSRC Grant EP/M002454/1. The work of J. Anderson was supported by a Junior Research Fellowship from St. John’s College, Oxford, U.K. Recommended by Associate Editor S. Anderson. (Corresponding Author: James Anderson.) The authors would like thank Prof. B. Jayawardhana and Prof. S. Rao for kindly providing the kinetic model of yeast glycolysis.
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)EP/J014214/1
Engineering and Physical Sciences Research Council (EPSRC)EP/G036004/1
Wallonia-Brussels FederationUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EP/M002454/1
St. John's College, OxfordUNSPECIFIED
Subject Keywords:Chemical master equation (CME), linear noise approximation (LNA), model reduction, stochastic differential equations, structured model reduction
Issue or Number:11
Record Number:CaltechAUTHORS:20170405-152041219
Persistent URL:
Official Citation:A. Sootla and J. Anderson, "Structured Projection-Based Model Reduction With Application to Stochastic Biochemical Networks," in IEEE Transactions on Automatic Control, vol. 62, no. 11, pp. 5554-5566, Nov. 2017. doi: 10.1109/TAC.2017.2691315. URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75751
Deposited By: Kristin Buxton
Deposited On:05 Apr 2017 22:54
Last Modified:03 Oct 2019 16:53

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