Stochastic Simulation and System Identification of large Signal Transduction Networks in Cells

New approaches are required for the mathematical modelling and system identification of complex networks, which are characterized by a large number of unknown parameters, uncertain network topologies, partially poorly understood mechanisms and significant stochastic effects. Networks with such properties are ubiquitous in many fields of science, especially in molecular cell biology, where, for example, large signal transduction networks are formed, by which cells transfer and process information, based on the biochemical interactions between signal transduction molecules. Complexity arises from the high number of different molecule species involved and the diversity of sub-processes interacting with each other. Previous attempts to model signal transduction were often limited to small systems or based on qualitative data only. One goal of this thesis is to reduce the complexity to enable system identification on the basis of experimental data. The concept of ’Sensitivity of Sensitivities’, which is presented here for the first time and which is based on the evaluation of stochastically generated parameter set ensembles, reveals two important inherent system properties: high robustness and modular structures of the dependency between state variables and parameters. This is the key to drastically reduce the dimensionality of the parameter identification problem. The approach is applied to the signalling pathway of CD95-induced apoptosis, also called programmed cell death. Defects in the regulation of apoptosis result in a number of serious diseases such as cancer. Despite the ever-increasing number of studies of the molecular mechanisms of apoptotic signalling, a systemic understanding of this complex pathway is still missing. With the model and the estimated parameters of this thesis, it becomes possible to reproduce the observed system behaviour and to predict important system properties. The predictions have been experimentally confirmed and are used for the planning of further experiments. Thereby, a novel regulatory mechanism was revealed, i.e. a threshold between cell death and cell survival. High fluctuations and extremely low particle numbers of crucial molecule species require exact stochastic simulations. Computational problems arise from the huge differences among the timescales on which the reactions occur. Therefore, a stochastic hybrid algorithm is developed by combining the exact Gillespie algorithm with a system of stochastic differential equations. This enables stochastically accurate and highly efficient simulations for large reaction systems and for any other kind of Markov processes. In summary, this thesis provides a methodology specifically suited for highly underdetermined networks. This is of high relevance for the newly emerging field of systems biology going far beyond the present application of programmed cell death