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      Parameter estimation methods for biological systems

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      MSc_thesis_LeiMU.pdf (503.0Kb)
      Date
      2010-03
      Author
      Mu, Lei
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      The inverse problem of modeling biochemical processes mathematically from measured time course data falls into the category of system identification and parameter estimation. Analyzing the time course data would provide valuable insights into the model structure and dynamics of the biochemical system. Based on the types of biochemical reactions, such as metabolic networks and genetic networks, several modeling frameworks have been proposed, developed and proved effective, including the Michaelis-Menten equation, the Biochemical System Theory (BST), etc. One bottleneck in analyzing the obtained data is the estimation of parameter values within the system model. As most models for molecular biological systems are nonlinear with respect to both parameters and system state variables, estimation of parameters in these models from experimental measurement data is thus a nonlinear estimation problem. In principle, all algorithms for nonlinear optimization can be used to deal with this problem, for example, the Gauss-Newton iteration method and its variants. However, these methods do not take the special structures of biological system models into account. When the number of parameters to be determined increases, it will be challenging and computationally expensive to apply these conventional methods. In this research, several methods are proposed for estimating parameters in two classes of widely used biological system models: the S-system model and the linear fractional model (LFM), by utilizing their structure specialties. For the S-system, two estimation methods are designed. 1) Based on the two-term structure (production and degradation) of the model, an alternating iterative least squares method is proposed. 2) A separation nonlinear least squares method is proposed to deal with the partially linear structure of the model. For the LFM, two estimation methods are provided. 1) The separation nonlinear least squares method can also be adopted to treat the partially linear structure of the LFM, and moreover a modified iterative version is included. 2) A special strategy using the separation principle and the weighted least squares method is implemented to turn the cost function into a quadratic form and thus the estimates for parameters can be analytically solved. Simulation results have demonstrated the effectiveness of the proposed methods, which have shown better performance in terms of estimation accuracy and computation time, compared with those conventional nonlinear estimation methods.
      Degree
      Master of Science (M.Sc.)
      Department
      Mechanical Engineering
      Program
      Mechanical Engineering
      Supervisor
      Wu, FangXiang
      Committee
      Shi, Yang; Dolovich, Allan; Bugg, James; Chen, Li
      Copyright Date
      March 2010
      URI
      http://hdl.handle.net/10388/etd-03302010-140138
      Subject
      parameter estimation
      least squares
      optimization
      linear fractional model (LFM)
      separation method
      nonlinear biological system
      S-system
      time course data
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