Deng Yue: Parameter optimization of linear Ordinary Differential Equations in the Gene Regulatory Network Reconstruction Problem

In this thesis we analyze parameter optimization problems governed by linear Ordinary Differential Equations (ODEs) and develop computationally efficient numerical methods for the solution. In addition, a series of noise-robust finite difference formulas are given for estimation of the derivatives in the ODEs.

The Gene Regulatory Networks (GRNs) are largely responsible for the process of organisms, such as metabolism and cell differentiation and a good prediction of the regulatory networks from experimental data has an important interest in biotechnology. The GRNs can be characterized by dynamical models, so we apply the parameter optimization method to reconstruct large gene regulatory networks with a ODEs model from the dynamical (time-series) data set. The method is tested on a 1565-gene E.coli gene regulatory network.

Although the method is computationally cheap such that the size of the network (model complexity) is no longer a main concern with respect to the computational cost, the data availability for determining large number of parameters is still a problem. We introduce a filtration technique to reduce the the number of free parameters before the ODEs model is applied. After ODEs model is fitted into the data, it is used to simulate dynamical behaviors to produce more information about the network’s structure. The combination of pre-filtration, ODEs optimization and post-modelling is called a pipeline.

The pipeline method is test on five 100-gene networks presented in DREAM4 network inference challenge in 2009, and the performance could have ranked first out of 19 participant teams. The effects on the performance of choosing finite difference schemes and other parameters in the pipeline are discussed.