With the development of hight-throughput technologies, the investigation of the topologies and the functioning of genetic regulatory networks have become an important research topic in recent years. Most of the studies concentrate on reconstructing the local architecture of genetic regulatory networks and the determination of the corresponding interaction parameters. The preferred data sources are time series expression data. However, inevitably one or more important members of the regulatory network will remain unknown. The absence of important members of the genetic circuit leads to incorrectly inferred network topologies and control mechanisms. In this thesis we propose a method to infer the connection and expression pattern of these “missing genes”. In order to make the problem tractable, we have to make further simplifying assumptions. We assume that the interactions within the network are described by Hill-functions. We then approximate these functions by power-law functions. We show that this simplification still captures the dynamic regulatory behaviors of the network. The genetic control system can now be converted to linear model by using a logarithm transformation. In another word, we can analyze the genetic regulatory networks by linear approaches. In the logarithmic space, we propose a procedure for extracting the expression profile of a missing gene within the otherwise defined genetic regulatory network. The algorithm also determines the regulatory connections of this missing gene to the rest of the regulation network. The inference algorithm is based on Factor Analysis, a well-developed multivariate statistical analysis approach that is used to investigate unknown, underlying features of an ensemble of data, in our case the promoter activities and intracellular concentrations of the known genes. We also explore a second blind sources separation method, “Independent Component Analysis”, which is also commonly used to estimate hidden signals. Once the expression profile of the missing gene has been derived, we investigate possible connections of this gene to the remaining network by methods of search space reduction. The proposed method of inferring the expression profile of a missing gene and connecting it to a known network structure is applied to artificial genetic regulatory networks, as well as a real biologicial network studied in the laboratory: the acs regulatory network of Escherichia coli. In these applications we confirm that power-law functions are a good approximation of Hill-functions. Factor Analysis predicts the expression profiles of missing genes with a high accuracy of 80% in small artificial genetic regulatory networks. The accuracy of Factor Analysis of predicting the expression profiles of missing genes of large artificial genetic regulatory networks is 60%. In contrast, Independent Component Analysis is less powerful than Factor Analysis in extracting the expression profiles of missing components in small, as well as large, artificial genetic regulatory networks. Both Factor Analysis and Independent Component suggest that only one missing gene is sufficient to explain the observed expression profiles of Acs, Fis and Crp. The expression profiles of the missing genes in the △cya strain and in the △cya strain supplemented with cAMP estimated by Factor Analysis and Independent Component Analysis are very similar. Factor Analysis suggests that fis is regulated by the missing genes, while Independent Component Analysis suggests that crp is controlled by the missing gene.
