System identification algorithms and techniques for systems biology

Abstract

Mathematical models for revealing the dynamics and interaction properties of biological systems play an important role in computational systems biology. This PhD work is motivated by the current difficulty in system identification of dynamic biochemical pathways, given limited highly noisy and spare time-course experimental data. In this thesis, the inverse problem of identifying unknown parameters of dynamical biological systems, which are modelled by ordinary differential equations (ODEs) or delay-differential equations (DDEs), is treated using experimental data. In some cases, even the model can sufficiently describe the measured data, it is still important to infer how well the model parameters are determined by the amount and quality of the available experimental data, which is essential for investigation of model prediction. For this reason, another key topic in this thesis is identifiability analysis. The main contributions of this PhD work are summarized as follows: 1. In many cases, bio-system models are autonomous systems, which are linear in parameters. For this type of models, an optimization-based parameter estimation approach is proposed. Spline and numerical differentiation methods are used to smooth noisy observations and to estimate the time derivative of the underlying dynamical system, respectively. Subsequently, the parameter estimation problem can be reduced to a Least-Squares Parameter Estimation (LSPE) or a Linear Programming Parameter Estimation (LPPE) problem, which can then be efficiently solved by many global optimization algorithms. 2. For general bio-system models, a parameter estimation method combining spline theory with Nonlinear Programming (NLP) is developed. This method removes the need for ODE solvers during the identification process. Our analysis shows that the augmented cost function surface used in the proposed method is smoother; which can ease the optimal searching process and hence enhance the robustness and speed of the search algorithm. Moreover, the core of our algorithms is NLP based, which is flexible and where consequently additional constraints can be embedded/removed easily. 3. In practice, time-delay feedback pathways exist in many biological systems, which can be modelled by continuous delay-differential equations (DDEs). In this work, a two-stage approach is adopted for parameter estimation: first, by combining spline theory and NLP, the parameter estimation problem is formulated as an optimization problem with only algebraic constraints; then, a new differential evolution (DE) algorithm is proposed to find a feasible solution. The approach is designed to handle problems of realistic sizes with noisy observation data. 4. Identifiability analysis of the so-called S-system is given. The basic theory is developed and the structural identifiability of the S-system is proved. This work also analyzes the limitation of existing structural identification approaches, revealing that these approaches face the risk of the overfitting/underfitting problem.

Date of Award	15 Feb 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Lam Fat YEUNG (Supervisor)