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Bioinformatics Advance Access published online on March 26, 2008
Bioinformatics, doi:10.1093/bioinformatics/btn107
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© The Author (2008). Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Linear time-varying models can reveal nonlinear interactions of biomolecular regulatory networks using multiple time-series data

Jongrae Kim a,d, Declan G. Bates b,d, Ian Postlethwaite b,d, Pat Heslop-Harrison c,d and Kwang-Hyun Cho e,*

aDepartment of Aerospace Engineering, University of Glasgow, Glasgow G12 8QQ, UK, bDepartment of Engineering, University of Leicester, Leicester LE1 7RH, UK, cDepartment of Biology, University of Leicester, Leicester, LE1 7RH, UK, dSystems Biology Lab, University of Leicester, Leicester, LE1 7RH, UK, eDepartment of Bio and Brain Engineering and KI for the BioCentury, Korea Advanced Institute of Science and Technology (KAIST), 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Republic of Korea

*To whom correspondence should be addressed. Prof. Kwang-Hyun Cho, E-mail: ckh{at}kaist.ac.kr


  Abstract

Motivation: Inherent nonlinearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear timeinvariant models will have fundamental limitations in their capability to infer certain nonlinear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given data set, there may be many different possible networks which generate the same time-series expression profiles.

Results: A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a nonlinear optimisation problem. In order to systematically reduce the set of possible solutions for the optimisation problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady-state, of using time-series profiles which have been generated by a single experiment, and of allowing nonlinear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a nonlinear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale nonlinear model of a group of synchronised Dictyostelium cells.

Availability: The software used in this paper is available from http://sbie.kaist.ac.kr/software.

Contact: ckh{at}kaist.ac.kr

Supplementary Information: Supplementary Material is available at Bioinformatics online.

Associate Editor: Prof. Martin Bishop

Received on January 16, 2008; revised on March 7, 2008; accepted on March 22, 2008

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