An allosteric model of KaiC phosphorylation

Abstract

In a recent series of ground-breaking experiments, Nakajima et al. [Science 308, 414-415 (2005)] 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 synchronisation 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.

8 pages, 6 figures. Accepted for publication in PNAS

Cited by in corpus (35)

• Spatio-temporal correlations can drastically change the response of a MAPK pathway
• Nonequilibrium Physics in Biology
• Sloppiness, robustness, and evolvability in systems biology
• Cost and Precision of Brownian Clocks
• Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization
• Robust circadian clocks from coupled protein modification and transcription-translation cycles
• Generic temperature compensation of biological clocks by autonomous regulation of catalyst concentration
• Spatial partitioning improves the reliability of biochemical signaling
• Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology
• A Thermodynamically consistent model of the post-translational Kai circadian clock
• Discrete gene replication events drive coupling between the cell cycle and circadian clocks
• Phase transition in thermodynamically consistent biochemical oscillators
• Mechanism of robust circadian oscillation of KaiC phosphorylation in vitro
• Topology protects chiral edge currents in stochastic systems
• Reciprocity Between Robustness of Period and Plasticity of Phase in Biological Clocks
• Energy Dissipation Bounds for Autonomous Thermodynamic Cycles
• Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations
• Entropy production limits all fluctuation oscillations
• High chemical affinity increases the robustness of biochemical oscillations
• Quantifying fluctuations in reversible enzymatic cycles and clocks
• Robustness of clocks to input noise
• A topological mechanism for robust and efficient global oscillations in biological networks
• Optimal entrainment of circadian clocks in the presence of noise
• Oscillations in feedback driven systems: thermodynamics and noise
• An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions
• Synchronization and phase redistribution in self-replicating populations of coupled oscillators and excitable elements
• Arnol'd Tongues in Oscillator Systems with Nonuniform Spatial Driving
• Topological phases in discrete stochastic systems
• The macroscopic effects of microscopic heterogeneity
• Topological phase locking in stochastic oscillators
• Computational modeling of protein interactions and phosphoform kinetics in the KaiABC cyanobacterial circadian clock
• Physical Constraints on the Rhythmicity of the Biological Clock
• Simple post-translational circadian clock models from selective sequestration
• Single-molecular and Ensemble-level Oscillations of Cyanobacterial Circadian Clock
• Optimization of multisite reactions in complex compartmentalized media