Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

Authors:
Fang-Xiang Wu;Lei Mu;Zhong-Ke Shi
Affiliations:
Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada,Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada;Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada;College of Automatic Control, Northwestern Polytechnical University, Shaanxi, China
Venue:
International Journal of Systems Science - Dynamics Analysis of Gene Regulatory Networks
Year:
2010

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Abstract

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.