Robustness of minimal biochemical oscillators

Robustness-the insensitivity to perturbations-is a hallmark of biological systems and it could provide a key to understanding design principles of complex cellular networks. However, current methods for the characterization of parametric robustness in (dynamic models of) biological systems are insufficient because of their local nature and the high dimensionality of the corresponding parameter spaces. Here, we propose first methods for a quantitative characterization of geometries in parameter space that are related to qualitative systems behavior. Using minimal biochemical oscillators as examples, we show that such approaches can provide detailed insight into relations between network structures, behavior, and robustness properties, which is not possible with traditional sampling-based methods. We expect that scaling and resolution of the algorithms could be vastly improved by using more advanced concepts from computational geometry.