Bayesian Inference of Gene Regulatory Networks : From Parameter Estimation to Experimental Design

Abstract

To learn the structure of gene regulatory networks is an interesting and important topic in systems biology. This structure could be used to specify key regulators and this knowledge may be used to develop new drugs which affect the expression of these regulators. However, the inference of gene regulatory networks, especially from time-series data is a challenging task. This is due to the limited amount of given data which additionally contain a lot of noise. These data cause from the technical point of view for the parameter estimation procedure problems like the non-identifiability and sloppiness of parameters. To address these difficulties, in these thesis new methods for both, the parameter estimation task and the experimental design for gene regulatory networks, are developed for a non-linear ordinary differential equations model, which use a Bayesian procedure and generate samples of the underlying distribution of the parameters. These distributions are of high interest, since they do not provide only one network structure but give all network structures that are consistent with the given data. And all of these structures can then be examined in more detail. The proposed method for Bayesian parameter estimation uses smoothing splines to circumvent the numerical integration of the underlying system of ordinary differential equations, which is usually used for parameter estimation procedures in systems of ordinary differential equations. An iterative Hybrid Monte Carlo and Metropolis-Hastings algorithm is used to sample the model parameters and the smoothing factor. This new method is applied to simulated data, which shows that it is able to reconstruct the topology of the underlying gene regulatory network with high accuracy. The approach was also applied to real experimental data, a synthetic designed 5-gene network (the DREAM 2 Challenge #3 data) and outperforms other methods. For the Bayesian experimental design step, a full Bayesian approach was used which does not use any parametric assumption of the posterior distribution, nor linearizes around a point estimate. To make the full Bayesian approach computationally manageable, maximum entropy sampling is used together with a population-based Markov chain Monte Carlo algorithm. The approach was applied to simulated and real experimental data, the DREAM 2 Challenge #3 data, and outperforms the usage of random experiments and a classical experimental design method.