Bayesian Modeling Reveals Ultrasensitivity Underlying Metabolic Compensation in the Cyanobacterial Circadian Clock

Mathematical models can enable a predictive understanding of mechanism in cell biology by quantitatively describing complex networks of interactions, but such models are often poorly constrained by available data. Owing to its relative biochemical simplicity, the core circadian oscillator in Synechococcus elongatus has become a prototypical system for studying how collective dynamics emerge from molecular interactions. The oscillator consists of only three proteins, KaiA, KaiB, and KaiC, and near-24-h cycles of KaiC phosphorylation can be reconstituted in vitro. Here, we formulate a molecularly-detailed but mechanistically agnostic model of the KaiA-KaiC subsystem and fit it directly to experimental data within a Bayesian parameter estimation framework. Analysis of the fits consistently reveals an ultrasensitive response for KaiC phosphorylation as a function of KaiA concentration, which we confirm experimentally. This ultrasensitivity primarily results from the differential affinity of KaiA for competing nucleotide-bound states of KaiC. We argue that the ultrasensitive stimulus-response relation is critical to metabolic compensation by suppressing premature phosphorylation at nighttime. SynopsisThis study takes a data-driven kinetic modeling approach to characterizing the interaction between KaiA and KaiC in the cyanobacterial circadian oscillator and understanding how the oscillator responds to changes in cellular metabolic conditions. O_LIAn extensive dataset of KaiC autophosphorylation measurements was gathered and fit to a detailed yet mechanistically agnostic kinetic model within a Bayesian parameter estimation framework. C_LIO_LIKaiA concentration tunes the sensitivity of KaiC autophosphorylation and the period of the full oscillator to %ATP. C_LIO_LIThe model reveals an ultrasensitive dependence of KaiC phosphorylation on KaiA concentration as a result of differential KaiA binding affinity to ADP- vs. ATP-bound KaiC. C_LIO_LIUltrasensitivity in KaiC phosphorylation contributes to metabolic compensation by suppressing premature phosphorylation at nighttime. C_LI