Robustness Analysis of MAPK Signaling Cascades

The MAPK cascade is responsible for transmitting information in the cytoplasm of the cell and regulating important fate decisions like cell division and apoptosis. Due to scarce experimental data and limited knowledge about many complex biochemical processes, existing MAPK pathway models, which exhibit bistability, have a significant structural uncertainty. Often, small perturbations of network interactions or components can reduce the bistable region significantly or make it even disappear and small fluctuations of the input can make the system switch back, which reflects its low robustness. However, real biological systems have developed significant robustness through evolution and this robustness should be reflected by the models. The main goal of the present thesis is the development of a methodology for increasing the robustness of biochemical models, which exhibit bistability. Based on modifying existing network interactions or introducing new interactions to the system, several methods for both internal and external robustification are proposed. Internal robustness is addressed through a sensitivity analysis, which deals with a linearization of the model and can be used sequentially to introduce multiple modifications to the model. The methods for external robustness improvement are based on eigenvalue placement and slope modification (drawing on the linear model) and on the identification of feedback structures (nonlinear model). Further, a way to integrate static interaction changes to the nonlinear model, so that these perturbations have only a local impact on its behavior, is proposed. The application of the methods to existing MAPK models shows that, by introducing small modifications, the internal and external robustness of models can be increased significantly and thus provides knowledge about complex dynamics and interactions that play a key role for the inherent robustness of real biological systems. Furthermore, by employing a robustness analysis, stable steady-state branches can be recovered and bistability can be induced