Quantitative Analysis of Robustness in Systems Biology: Combining Global and Local Approaches

To characterize the behavior and robustness of cellular circuits is a major challenge for Systems Biology. Many of the published methods that address this question quantify the local robustness of the models. In this thesis, I tried to underpin the inappropriateness of such local measures and proposed an alternative solution: a glocal measure for robustness that combines both global and local aspects. It comprises a broad exploration of the parameter space and a further refinement based on different local measures. The method is general and such glocal analysis could be applied to many problems. Along with the theoretical and formal aspects of this new analysis method, I developed sampling algorithms that efficiently investigate the generally high-dimensional parameter space of models. To show the usefulness of my method, I applied it on different models of cyclic systems such as the circadian clock and the mitotic cycle. I first considered two models of the cyanobacterial circadian clock and compared their robustness properties. Also in the context of circadian rhythms, I studied the effect of additional feedback loops on the robustness properties in relation with entrainment. Models of the mitotic cycle are also used to assess the effect of an additional positive feedback loop on circuit robustness to parameter changes and molecular noise. Finally, I established some principles for the design of a synthetic circuit based on robustness. The thesis carries on with a discussion that emphasizes the advantages of the glocal method for robustness analysis: in all works, correlations between parameter values and local robustness can be found. Such results facilitate our understanding of the biochemical systems and can be a guide for new experiments to discriminate models or give directions for altering the robustness of the systems. I conclude by discussing potential applications for my method and possible improvements.

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