  The principal pacemaker of the circadian clock of the cyanobacterium S.
elongatus is a protein phosphorylation cycle consisting of three proteins,
KaiA, KaiB and KaiC. KaiC forms a homohexamer, with each monomer consisting of
two domains, CI and CII. Both domains can bind and hydrolyze ATP, but only the
CII domain can be phosphorylated, at two residues, in a well-defined sequence.
While this system has been studied extensively, how the clock is driven
thermodynamically has remained elusive. Inspired by recent experimental
observations and building on ideas from previous mathematical models, we
present a new, thermodynamically consistent, statistical-mechanical model of
the clock. At its heart are two main ideas: i) ATP hydrolysis in the CI domain
provides the thermodynamic driving force for the clock, switching KaiC between
an active conformational state in which its phosphorylation level tends to rise
and an inactive one in which it tends to fall; ii) phosphorylation of the CII
domain provides the timer for the hydrolysis in the CI domain. The model also
naturally explains how KaiA, by acting as a nucleotide exchange factor, can
stimulate phosphorylation of KaiC, and how the differential affinity of KaiA
for the different KaiC phosphoforms generates the characteristic temporal order
of KaiC phosphorylation. As the phosphorylation level in the CII domain rises,
the release of ADP from CI slows down, making the inactive conformational state
of KaiC more stable. In the inactive state, KaiC binds KaiB, which not only
stabilizes this state further, but also leads to the sequestration of KaiA, and
hence to KaiC dephosphorylation. Using a dedicated kinetic Monte Carlo
algorithm, we show that the model can describe a wealth of experimental data.
