Bayesian Parameter Identification and Uncertainty Quantification in Systems Biology: A case study for the Drosophila Gap Gene System

Systems biology is a growing discipline that combines experimental techniques and computational methods in order to construct predictive models. The mathematical modeling of gene regulatory networks is particularly challenging, because their biology is incompletely understood, implying that a large number of potentially irrelevant regulatory links has to be considered in the fitting process. One of the major challenges in systems biology is the pruning of gene regulatory network structures based on experimental data, known as reverse engineering. Such inverse problems are typically ill-conditioned (discretely ill-posed) because the solution (in the least-squares sense) depends extremely sensitively on the measurement data. That is, small measurement errors lead to large error propagation from the data to the solution and hence poor parameter estimates. The ill-posedness becomes more dominant with increasing number of unknown parameters, and for problems with many parameters it is necessary to apply some form of regularization. Our long term goal is to provide a general framework for ODE-based models that yields such a regularization strategy for the stable estimation of unknown model parameters and for the derivation of a minimal measurement-compliant network topology. At the same time the algorithm should be capable of assessing the reliability of the parameter estimates. The latter aspect has so far been widely neglected in the biological literature, possibly due to extensive computational complexity. With our study we hope to contribute both, an efficient parallel implementation of a versatile novel regularization strategy, as well as a mathematical justification of the underlying numerical method. In the present project, we plan to further evolve a strategy in the framework of Bayesian inverse problems, combining sparsity promoting regularization and subsequent uncertainty quantification. This strategy has been developed recently at the Institute of Mathematics, and then applied to a particular parameter identification problem arising from inverse modeling of the Drosophila gap gene system. This biological system has been characterized in detail by quantitative experimental measurements and received a great amount of attention in the field of systems biology. Biological expertise is crucial for the performance of this method, hence the project is to be continued in close collaboration with Dr. S. Legewie's group from the Institute of Molecular Biology. Independent of the Drosophila case study there exists a strong interest on the part of Dr. Legewie’s group to use the new strategy in the context of reverse engineering problems in systems biology, e.g., for gene regulatory networks controlling cell migration and for signaling pathways deregulated in colon cancer. In order to cope with the computational complexity of large-scale studies, the primary focus during the funding period will lie on the development of a parallel implementation and on a thorough evaluation of this implementation by comparing it with established approaches for the Drosophila gap gene system test case.