A Symmetric Dual Feedback System Provides a Robust and Entrainable Oscillator

Many organisms have evolved molecular clocks to anticipate daily changes in their environment. The molecular mechanisms by which the circadian clock network produces sustained cycles have extensively been studied and transcriptional-translational feedback loops are common structures to many organisms. Although a simple or single feedback loop is sufficient for sustained oscillations, circadian clocks implement multiple, complicated feedback loops. In general, different types of feedback loops are suggested to affect the robustness and entrainment of circadian rhythms. To reveal the mechanism by which such a complex feedback system evolves, we quantify the robustness and light entrainment of four competing models: the single, semi-dual, dual, and redundant feedback models. To extract the global properties of those models, all plausible kinetic parameter sets that generate circadian oscillations are searched to characterize their oscillatory features. To efficiently perform such analyses, we used the two-phase search (TPS) method as a fast and non-biased search method and quasi-multiparameter sensitivity (QMPS) as a fast and exact measure of robustness to uncertainty of all kinetic parameters. So far the redundant feedback model has been regarded as the most robust oscillator, but our extensive analysis corrects or overcomes this hypothesis. The dual feedback model, which is employed in biology, provides the most robust oscillator to multiple parameter perturbations within a cell and most readily entrains to a wide range of light-dark cycles. The kinetic symmetry between the dual loops and their coupling via a protein complex are found critically responsible for robust and entrainable oscillations. We first demonstrate how the dual feedback architecture with kinetic symmetry evolves out of many competing feedback systems.