Temperature Dependence in Stochastic and Deterministic Models of the Circadian Rhythm of Cyanobacteria

The chemical reactions that lead to circadian rhythms in organisms are deterministically described in the limit where the number of cells is large. However, for each individual cell these reactions are stochastic as the number of molecules involved in them is small. Here, the circadian rhythms of cyanobacteria are considered. Using mathematical models of biochemical oscillations, we analyze the characteristic behavior of the deterministic system near a non-equilibrium phase transition. The control parameter that drives the transition is the temperature, which must be high enough for any biochemical oscillations to occur. We analyze the same set of reactions near the transition temperature in the stochastic limit and discuss features that emerge in the probability distributions of oscillation amplitudes and frequencies. We also comment on the thermodynamic connection between the small and large scale descriptions.