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Mathematical modelling and parameter inference of genetic regulatory networks
thesisposted on 2017-02-27, 05:44 authored by Wu, Qianqian
Mathematical modelling opens the door to a rich pathway to study the dynamic properties of biological systems. Among the many biological systems that would benefit from mathematical modelling, improving our understanding of gene regulatory networks has received much attention from the fields of computational biology and bioinformatics. To understand system dynamics of biological networks, mathematical models need to be constructed and studied. In spite of the efforts that have been given to explore regulatory mechanisms among gene net- works, accurate description of chemical events with multi-step chemical reactions still remains a challenge in biochemistry and biophysics. This dissertation is aimed at developing several novel methods for describing dynamics of multi-step chemical reaction systems. The main idea is introduced by a new concept for the location of molecules in the multi-step reactions, which is used as an additional indicator of system dynamics. Additionally, novel idea in the stochastic simulation algorithm is used to calculate time delay exactly, which shows that the value of time delay depends on the system states. All of these innovations alter the focus of originally complex multi-step structures towards defining novel simplified structures, which simplifies the modelling process significantly. Research results yield substantially more accurate results than published methods. Apart from the well-established knowledge for modelling techniques, there are still significant challenges in understanding the dynamics of systems biology. One of the major challenges in systems biology is how to infer unknown parameters in mathematical models based on experimental datasets, in particular, when data are sparse and networks are stochastic. To tackle this challenge, parameters estimation techniques using Approximate Bayesian Computation (ABC) for chemical reaction system and inference method for dynamic network have been investigated. This dissertation discusses developed ABC methods that have been tested on two stochastic systems. Results on artificial data show certain promising approximations for the unknown parameters in the systems. While unknown parameters are difficult and sometimes even impossible to measure with biological experiments, instead we can study the influence of parameter variation on system properties. Robustness and sensitivity are two major measurements to describe the dynamic properties of a system against the variation of model parameters. For stochastic models of discrete chemical reaction systems, although these two properties have been studied separately, no work has been done so far to investigate these two properties together. In this dissertation, An integrated framework has been proposed to study these two properties for the Nanog gene network simultaneously. It successfully identifies key coefficients that have more impacts on the network dynamics than the others. The proposed inference method to infer dynamic protein-gene interactions is applied to a case study of the human P53 protein, which is a well-known biological network for cancer study. Investigating the dynamics for such regulatory networks through high throughput experimental data has become more popular. To tackle the hindrances with large number of unknown parameters when building detailed mathematical models, a new integrated method is proposed by combining a top-down approach using probability graphical models and a bottom-up approach using differential equation models. Model simulation error, Akaike’s information criterion, parameter identifiability and robustness properties are used as criteria to select the optimal network. Results based on random permutations of input gene network structures provide accurate prediction and robustness property. In addition, a comparison study suggests that the proposed approach has better simulation accuracy and robustness property than the earlier one. In particular, the computational cost is significantly reduced. Overall, the new integrated method is a promising approach for investigating the dynamics of genetic regulations.