A thermodynamically consistent model of the post-translational Kai circadian clock
Fig 9
Model correctly predicts the ATP fractions in KaiC nucleotide binding pockets and the phase difference between this fraction and the phosphorylation level.
Figures A-D show the fraction ATP/(ATP+ADP) in the nucleotide binding pockets of the CI domain (orange), the CII domain (green) and their sum (blue), in a 100% ATP solution, for different scenarios: KaiC initially unphosphorylated, no KaiA and KaiB present (A), KaiC initially phosphorylated, no KaiA and KaiB (B), initially unphosphorylated KaiC + KaiA (C) and KaiC + KaiA + KaiB (D). (A) The ATP levels drop monotonically due to the slow hydrolysis in both the CI and CII domain. (B) ATP fractions in dephosphorylating KaiC shows a clear trough in the ATP fraction of the CI domain due to the peak in the number of monomers in the S state (Fig 6A), which temporarily decreases the ADP-off-rate in the CI domain. (C) For a system with KaiC and KaiA, the ATP fraction is higher in the CII domain and lower in the CI domain. KaiA increases the nucleotide exchange rate in the CII domain, and the resultant high phosphorylation level decreases the ADP dissociation rate in CI, which decreases the ATP fraction in this domain. (D) Full system with KaiA, KaiB and KaiC shows oscillations in the ATP fractions of both the CI and CII domains. (E) The phase difference and amplitude of the ATP fraction (% ATP, blue line) and the phosphorylation level (% phosphorylated monomers, black line) agree well with experimental results in [39]. (F) ATPase levels of the KaiC domains show oscillations proportional to the ATP fractions in the respective domains.