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

Kim, J., Bates, D.G. and Postlethwaite, I. (2008) Evaluation of stochastic effects on biomolecular networks using the generalised Nyquist stability criterion. IEEE Transactions on Automatic Control, 53(8), pp. 1937-1941. (doi: 10.1109/TAC.2008.929463)

Abstract

Abstract—Stochastic differential equations are now commonly used to model biomolecular networks in systems biology, and much recent 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: Articles
• Keywords: Dictyostelium, cAMP oscillations, stochastic noise, Nyquist stability criterion
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kim, Dr Jongrae
• Authors: Kim, J., Bates, D.G., and Postlethwaite, I.
• Subjects: T Technology > TL Motor vehicles. Aeronautics. Astronautics; T Technology > T Technology (General)
• College/School: College of Science and Engineering > School of Engineering > Biomedical Engineering; College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Journal Name: IEEE Transactions on Automatic Control
• Publisher: IEEE
• ISSN: 0018-9286
• Copyright Holders: Copyright © 2008 Institute of Electrical and Electronics Engineers
• First Published: First published in IEEE Transactions on Automatic Control 53(8):1937-1941
• Publisher Policy: Reproduced with permission of the publisher.