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

Liu, F., Burrage, K and Hamilton, N. A. (2013) Some novel techniques of parameter estimation of dynamical models in biological systems. IMA Journal of Applied Mathematics, 78 2: 235-260. doi:10.1093/imamat/hxr046


Author Liu, F.
Burrage, K
Hamilton, N. A.
Title Some novel techniques of parameter estimation of dynamical models in biological systems
Language of Title eng
Journal name IMA Journal of Applied Mathematics   Check publisher's open access policy
Language of Journal Name eng
ISSN 1464-3634
0272-4960
Publication date 2013-04
Year available 2011
Sub-type Article (original research)
DOI 10.1093/imamat/hxr046
Volume 78
Issue 2
Start page 235
End page 260
Total pages 26
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Collection year 2012
Language eng
Formatted 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.
Keyword Parameter estimation
Inverse problems
Non-linear dynamical models
Picard contraction mapping
Collage methods
Grid approximation method
Simplex search method
Particle swarm optimization
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article published online ahead of print December 2, 2011.

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2012 Collection
Institute for Molecular Bioscience - Publications
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 2 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 2 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Wed, 07 Mar 2012, 14:32:06 EST by Susan Allen on behalf of Institute for Molecular Bioscience