Multiobjective Optimization for Inverse Problems and Design of Biochemical Systems

• Main Authors: Pang-Kai Liu, 劉邦凱
• Other Authors: Feng-Sheng Wang
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/30443425248160421817

博士 === 國立中正大學 === 化學工程所 === 97 === The mathematical modeling and dynamic simulation of genetic networks, metabolic networks, and signal transduction cascades is a central theme in systems biology. There are often many alternative models of a biochemical system, but no single mathematical model can fully meet the requirements for a rational explanation and prediction of system behavior. Traditionally, researchers have used Michaelis-Menten type kinetic models to biochemical systems, but these may not yield saturation curve expressions. An alternative is Biological Systems Theory, which uses power law kinetic expressions. The GMA model, a variant of the power law model, is able to capture realistic reaction information such as branched and reversed pathways. Little has been reported on determining rate constants and kinetic orders in the GMA model, by given measurement information. Given a model structure, parameter estimation remains the limiting step in the modeling of biological systems, due to the high-dimensional search space involved and the lack of accurate data. However, there is no unique method to estimate model parameters for nonlinear dynamic models. Therefore, this dissertation first introduces a multiobjective optimization technique to determine the kinetic parameter values of biochemical reaction systems. This technique converts the multiobjective parameter estimation into a minimax problem through the satisfying trade-off method. This approach assigns the aspiration value as the minimum solution to the corresponding single objective estimation. The aim of this trade-off estimation is to obtain a compromised result by simultaneously minimizing both concentration and slope error criteria. A hybrid differential evolution method can solve the minimax problem and yield a global estimation. The S-system model, another variant of the power law model, is more amenable to the black-box model where no topology information is available. To infer a realizable S-system structure, most articles have applied the sums of magnitude of kinetic orders as a penalty term in the fitness evaluation. Tuning a penalty weight to yield a realizable model structure is the main issue in inverse problems. No guideline has yet been published on tuning a suitable penalty weight to infer a suitable model structure in biochemical networks. Therefore, this dissertation also introduces an interactive inference algorithm to infer a realizable S-system structure for biochemical networks. The inference problem is formulated as a multiobjective optimization problem to simultaneously minimize the concentration error, slope error, and interaction measure to find a suitable S-system model structure and its corresponding model parameters. This Pareto optimality estimation solve the multiobjective optimization problem by the ε-constraint method to minimize the interaction measure subject to the expectation constraints for the concentration and slope error criteria. By making use of contradictory arguments guarantee the minimum solution for ε-constrained problems and achieve the minimum interaction network for the inference problem. This approach can avoid assigning a penalty weight to the sums of magnitude of kinetic orders. Many inverse problems or process optimization problems for biochemical reactions have large parameter search spaces. When an optimization problem is defined on a wide parameter search space, very few evolutionary algorithms can find a global solution to the large parameter search problem. Therefore, this dissertation also discusses embedding a geometric mean mutation strategy in a hybrid differential evolution algorithm to replace a gene of the selected individual outside the assigned region. The replaced individuals are then applied to a differential mutation strategy to yield a perturbed individual. The results of this study show that the proposed algorithm outperforms other algorithms. Further, this approach offers the benefit of using a wide parameter search space in an inverse problem, reducing the kinetic model complexity to yield a more compact formulation.