Evaluation of stochastic effects on biomolecular networks using the generalized Nyquist stability criterion

Kim, Jongrae, Bates, Declan and Postlethwaite, Ian (2008) Evaluation of stochastic effects on biomolecular networks using the generalized Nyquist stability criterion. IEEE Transactions on Automatic Control, 53 (8). pp. 1937-1941. ISSN 0018-9286

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Abstract

Stochastic differential equations are now commonly used to model biomolecular networks in systems biology, and much research has been devoted to the development of methods to analyse their stability properties. Stability analysis of such systems may be performed using the Laplace transform, which requires the calculation of the exponential matrix involving time symbolically. However, the calculation of the symbolic exponential matrix is not feasible for problems of even moderate size, as the required computation time increases exponentially with the matrix order. To address this issue, we present a novel method for approximating the Laplace transform which does not require the exponential matrix to be calculated explicitly. The calculation time associated with the proposed method does not increase exponentially with the size of the system, and the approximation error is shown to be of the same order as existing methods. Using this approximation method, we show how a straightforward application of the generalized Nyquist stability criterion provides necessary and sufficient conditions for the stability of stochastic biomolecular networks. The usefulness and computational efficiency of the proposed method is illustrated through its application to the problem of analysing a model for limit-cycle oscillations in cAMP during aggregation of Dictyostelium cells.

Item Type:	Article
Uncontrolled Keywords:	Dictyostelium, cAMP oscillations, stochastic noise
Subjects:	H600 Electronic and Electrical Engineering
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Sarah Howells
Date Deposited:	24 Oct 2012 11:11
Last Modified:	13 Oct 2019 00:24
URI:	http://nrl.northumbria.ac.uk/id/eprint/9918

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