Parameter optimization of linear ordinary differential equations with application in gene regulatory network inference problems

Sammanfattning: In this thesis we analyze parameter optimization problems governed by linear ordinary differential equations (ODEs) and develop computationally efficient numerical methods for their solution. In addition, a series of noise-robust finite difference formulas are given for the estimation of the derivatives in the ODEs. The suggested methods have been employed to identify Gene Regulatory Networks (GRNs). GRNs are responsible for the expression of thousands of genes in any given developmental process. Network inference deals with deciphering the complex interplay of genes in order to characterize the cellular state directly from experimental data. Even though a plethora of methods using diverse conceptual ideas has been developed, a reliable network reconstruction remains challenging. This is due to several reasons, including the huge number of possible topologies, high level of noise, and the complexity of gene regulation at different levels. A promising approach is dynamic modeling using differential equations. In this thesis we present such an approach to infer quantitative dynamic models from biological data which addresses inherent weaknesses in the current state-of-the-art methods for data-driven reconstruction of GRNs. 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 but due to data limitations; the challenge is a huge number of possible topologies. Therefore we embed a filtration step into the method to reduce the number of free parameters before simulating dynamical behavior. The latter is used to produce more information about the network’s structure. We evaluate our method on simulated data, and study its performance with respect to data set size and levels of noise on a 1565-gene E.coli gene regulatory network. We show the computation time over various network sizes and estimate the order of computational complexity. Results on five networks in the benchmark collection DREAM4 Challenge are also presented. Results on five networks in the benchmark collection DREAM4 Challenge are also presented and show our method to outperform the current state of the art methods on synthetic data and allows the reconstruction of bio-physically accurate dynamic models from noisy data.