Emergence of Bistability in Circadian Clock Temperature Response

Faculty Mentors: Michael Rust (University of Chicago) and Aaron Dinner (University of Chicago)

Abstract: A defining feature of biological time-keeping is temperature compensation, in which the amplitude of an oscillation varies such that the frequency is nearly invariant to temperature. Temperature compensation enables circadian rhythms to anticipate the length of the day correctly even as temperature varies. Because individual enzymatic reactions are typically sensitive to temperature, temperature compensation is thought to be an emergent property of a reaction network. What features of a reaction network can enable temperature compensation is an open mathematical question.

In cyanobacteria, interactions of the proteins KaiA, KaiB, and KaiC give rise to near-24-hour oscillations in phosphorylation of KaiC. KaiA binding to KaiC promotes phosphorylation of KaiC, while KaiB binding to KaiC promotes dephosphorylation. Preliminary work indicates that, as temperature decreases, KaiC phosphorylation can occur in a KaiA-independent manner, which can be viewed as modulating the feedback in the network. Furthermore, multiple steady states that depend on initial conditions appear at low temperatures.

A computational approach based on algebraic geometry will be used to map the fixed points and bifurcations of models of the Kai system at various temperatures and, in turn, to elucidate general principles about the role of feedback in temperature compensation. The computational results will be tested experimentally using mutants of the Kai proteins that alter the KaiA-KaiC interaction. By revealing how feedback in a reaction network is related to the fixed-point and bifurcation structure elucidated by the approach based on algebraic geometry, the project will advance dynamical systems theory.