Insights from Mathematical Modeling/Simulations of the In Vitro KaiABC Clock

Abstract

This chapter discusses mathematical modeling of the in vitro KaiABC clock, focusing on various potential insights into mechanisms of synchrony and attempts by different groups to reproduce various experimental properties of observed clock dynamics. It is separated into a discussion of modeling the dynamics of population phosphoform state transitions to generate limit cycles, and in simulating the dynamics of KaiC hexamers and protein-protein interactions, including allosteric transitions. The latter models include both phenomenological simplified state transition models between various hexameric complexes and protein-protein interactions, and direct numerical simulations of biochemical reactions which incorporate thousands of combinatorial states and their transitions, including the effects of stochasticity (noise) on the simulated dynamics.