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A thermodynamically consistent model of the post-translational Kai circadian clock
Fig 2
KaiA regulates the fraction of ATP in the CII binding pockets by increasing the nucleotide dissociation rates, in combination with the ATPase activity in the CII domain.
A) Without KaiA bound to CII, the nucleotide dissociation rates are identically zero, and there is no nucleotide exchange with the bulk. Since ATP is hydrolyzed at a constant rate, 
, eventually all the binding pockets will be occupied by ADP. B) When KaiA is bound to the CII domain, it increases the dissociation rates of ADP and ATP, 
and 
, respectively, while leaving the affinities for ATP and ADP unchanged. Now, ADP in the CII domain is replaced by ATP at a rate that is faster than that at which ATP is hydrolyzed; this indeed increases the fraction of ATP in the binding pockets. For simplicity, we assumed equal diffusion limited association rates for ATP and ADP, such that the probability of binding ATP after ADP has dissociated is equal to αATP. The rate of the reverse pathway is proportional to the bulk ADP fraction, 1 − αATP.
doi: https://doi.org/10.1371/journal.pcbi.1005415.g002