Experimental innovations starting in the 1990’s leading to the advent of high-throughput experiments in cellular biology have made it possible to measure thousands of genes simultaneously at a modest cost. This enables the discovery of new unexpected relationships between genes in addition to the possibility of falsify existing. To benefit as much as possible from these experiments the new inter disciplinary research field of systems biology have materialized. Systems biology goes beyond the conventional reductionist approach and aims at learning the whole system under the assumption that the system is greater than the sum of its parts. One emerging enterprise in systems biology is to use the high-throughput data to reverse engineer the web of gene regulatory interactions governing the cellular dynamics. This relatively new endeavor goes further than clustering genes with similar expression patterns and requires the separation of cause of gene expression from the effect. Despite the rapid data increase we then face the problem of having too few experiments to determine which regulations are active as the number of putative interactions has increased dramatic as the number of units in the system has increased. One possibility to overcome this problem is to impose more biologically motivated constraints. However, what is a biological fact or not is often not obvious and may be condition dependent. Moreover, investigations have suggested several statistical facts about gene regulatory networks, which motivate the development of new reverse engineering algorithms, relying on different model assumptions. As a result numerous new reverse engineering algorithms for gene regulatory networks has been proposed. As a consequent, there has grown an interest in the community to assess the performance of different attempts in fair trials on “real” biological problems. This resulted in the annually held DREAM conference which contains computational challenges that can be solved by the prosing researchers directly, and are evaluated by the chairs of the conference after the submission deadline.

This thesis contains the evolution of regularization schemes to reverse engineer gene networks from high-throughput data within the framework of ordinary differential equations. Furthermore, to understand gene networks a substantial part of it also concerns statistical analysis of gene networks. First, we reverse engineer a genome-wide regulatory network based solely on microarray data utilizing an extremely simple strategy assuming sparseness (LASSO). To validate and analyze this network we also develop some statistical tools. Then we present a refinement of the initial strategy which is the algorithm for which we achieved best performer at the DREAM2 conference. This strategy is further refined into a reverse engineering scheme which also can include external high-throughput data, which we confirm to be of relevance as we achieved best performer in the DREAM3 conference as well. Finally, the tools we developed to analyze stability and flexibility in linearized ordinary differential equations representing gene regulatory networks is further discussed.