Abstract
A cyanobacterial protein KaiC shows a stable oscillation in its phosphorylation level with approximately one day period when three proteins, KaiA, KaiB, and KaiC, are incubated in the presence of ATP in vitro. During this oscillation, KaiC hydrolyzes more ATP molecules than required for phosphorylation. Here, in this report, a theoretical model of the KaiABC oscillator is developed to elucidate the role of this ATP consumption by assuming multifold feedback relations among reactions and structural transition in each KaiC molecule and the structure-dependent binding reactions among Kai proteins. Results of numerical simulation showed that ATP hydrolysis is a driving mechanism of the phosphorylation oscillation in the present model, and that the frequency of ATP hydrolysis in individual KaiC molecules is correlated to the frequency of oscillation in the ensemble of many Kai molecules, which indicates that the coherent oscillation is generated through the coupled microscopic intramolecular and ensemble-level many-molecular regulations.
Highlights
How is the coherent oscillation in biological system generated and how is it regulated by structures and reactions of constituent molecules? The system comprised of three cyanobacterial proteins, KaiA, KaiB, and KaiC, provides a unique opportunity to examine these problems[1,2,3]
ATP molecules can bind on CI-CI and CII-CII interfaces of KaiC subunits; with slow ATPase activity, about 10 molecules of ATP are hydrolyzed per each CI domain and several ATP molecules per each CII domain in 24 hours[16,17]
A striking feature is the strong correlation between the ATPase activity and the phosphorylation rhythm: When the KaiC sequence is mutated, the induced modulation of frequency of ATP hydrolysis observed in the absence of KaiA and KaiB, which is the non-oscillatory condition, is correlated to the modulation of frequency of the phosphorylation rhythm observed in the oscillatory condition[16,17]
Summary
How is the coherent oscillation in biological system generated and how is it regulated by structures and reactions of constituent molecules? The system comprised of three cyanobacterial proteins, KaiA, KaiB, and KaiC, provides a unique opportunity to examine these problems[1,2,3]. KaiA forms a dimer[10] and binds to the CII ring of KaiC hexamer[11] to promote the autophosphorylation of KaiC12 We write this KaiCA complex as C6A2. The ATPase activity of the truncated CI ring shows correlation to the oscillation frequency of the phosphorylation rhythm[17] These observations suggested the intrinsic relation between ATP hydrolysis in the CI and phosphorylation rhythm in the CII16,18. The discovery of the correlation between the ATPase activity and the phosphorylation rhythm has indicated that the ensemble-level regulation but the regulation within individual KaiC molecules through the interplay between the ATP hydrolysis and P/dP reactions should be important for determining the oscillation features. Detailed molecular-level model of this interplay has been recently developed by Paijmans et al.[28], and the further development of a comprehensive model that bridges between the molecular and ensemble levels is necessary
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