Some novel techniques of parameter estimation for the dynamical models in biological systems

Liu, F., Hamilton, N., & Burrage, K. (2011) Some novel techniques of parameter estimation for the dynamical models in biological systems. IMA Journal of Numerical Analysis, 78(2), pp. 235-260.

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Abstract

Inverse problems based on using experimental data to estimate unknown parameters of a system often arise in biological and chaotic systems. In this paper, we consider parameter estimation in systems biology involving linear and non-linear complex dynamical models, including the Michaelis–Menten enzyme kinetic system, a dynamical model of competence induction in Bacillus subtilis bacteria and a model of feedback bypass in B. subtilis bacteria. We propose some novel techniques for inverse problems. Firstly, we establish an approximation of a non-linear differential algebraic equation that corresponds to the given biological systems. Secondly, we use the Picard contraction mapping, collage methods and numerical integration techniques to convert the parameter estimation into a minimization problem of the parameters. We propose two optimization techniques: a grid approximation method and a modified hybrid Nelder–Mead simplex search and particle swarm optimization (MH-NMSS-PSO) for non-linear parameter estimation. The two techniques are used for parameter estimation in a model of competence induction in B. subtilis bacteria with noisy data. The MH-NMSS-PSO scheme is applied to a dynamical model of competence induction in B. subtilis bacteria based on experimental data and the model for feedback bypass. Numerical results demonstrate the effectiveness of our approach.

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ID Code: 45865
Item Type: Journal Article
Refereed: Yes
Additional URLs:
DOI: 10.1093/imamat/hxr046
ISSN: 1464-3642
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 12 Sep 2011 01:33
Last Modified: 04 Nov 2013 00:50

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