‘Glocal’ Robustness Analysis and Model Discrimination for Circadian Oscillators

To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a high-dimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This ‘global’ analysis is then supplemented by a ‘local’ analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the two-sites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our ‘glocal’ combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and different parameter sets.Author Summary: Robustness is an intrinsic property of many biological systems. To quantify the robustness of a model that represents such a system, two approaches exist: global methods assess the volume in parameter space that is compliant with the proper functioning of the system; and local methods, in contrast, study the model for a given parameter set and determine its robustness. Local methods are fundamentally biased due to the a priori choice of a particular parameter set. Our ‘glocal’ analysis combines the two complementary approaches and provides an objective measure of robustness. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator. Our results allow discriminating the two models based on this analysis: both global and local measures of robustness favor one of the two models. The ‘glocal’ method also identifies key factors that influence robustness. For instance, we find that in both models the most fragile reactions are the ones that affect the concentration of the feedback component.