An allosteric model of circadian KaiC phosphorylation.
In a recent series of ground-breaking experiments, Nakajima et al. [Nakajima M, Imai K, Ito H, Nishiwaki T, Murayama Y, Iwasaki H, Oyama T, Kondo T (2005) Science 308:414-415] showed that the three cyanobacterial clock proteins KaiA, KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of KaiC. Here, we present a mathematical model of the Kai system. At its heart is the assumption that KaiC can exist in two conformational states, one favoring phosphorylation and the other dephosphorylation. Each individual KaiC hexamer then has a propensity to be phosphorylated in a cyclic manner. To generate macroscopic oscillations, however, the phosphorylation cycles of the different hexamers must be synchronized. We propose a novel synchronization mechanism based on differential affinity: KaiA stimulates KaiC phosphorylation, but the limited supply of KaiA dimers binds preferentially to those KaiC hexamers that are falling behind in the oscillation. KaiB sequesters KaiA and stabilizes the dephosphorylating KaiC state. We show that our model can reproduce a wide range of published data, including the observed insensitivity of the oscillation period to variations in temperature, and that it makes nontrivial predictions about the effects of varying the concentrations of the Kai proteins.
van Zon
Jeroen S
JS
Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
Lubensky
David K
DK
Altena
Pim R H
PR
ten Wolde
Pieter Rein
PR
D000494:Allosteric Regulation; D001426:Bacterial Proteins / Q000235:genetics / Q000378:metabolism*; D002940:Circadian Rhythm / Q000502:physiology*; D056925:Circadian Rhythm Signaling Peptides and Proteins; D008954:Models, Biological; D010766:Phosphorylation; D011485:Protein Binding; D013696:Temperature
D001426:Bacterial Proteins; D056925:Circadian Rhythm Signaling Peptides and Proteins; C114269:KaiA protein, cyanobacteria; C114270:KaiB protein, cyanobacteria; C114271:KaiC protein, cyanobacteria