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Chemical oscillations are a universal feature of living systems. In plants, for example, the daily periodicity of many functions is regulated by the oscillatory expression of circadian gene networks present in each cell. We analyze the chemically reacting system that controls the circadian rhythms in cells of the plant Arabidopsis thaliana by numerically solving a continuous kinetic model whose parameters were deduced from experimental data [1]. We find that the model exhibits slowly decaying oscillations and is situated near a Hopf bifurcation in parameter space. Then we implement Gillespie’s Stochastic Simulation Algorithm to simulate the system at the single-cell level and account for random fluctuations in particle numbers [2]. Finally, we comment on the relationship between the two approaches and on the possible biological significance of the model’s mathematical features.

[1] Locke et al. Stochastic Simulations of Single-Cell Circadian Oscillations in Arabidopsis thaliana. J. Theor. Bio. 234 (2005) 383.
[2] Gillespie, Daniel T. Exact Stochastic Simulations of Coupled Chemical Reactions. J. Phys. Chem. Vol. 81, No. 25, 1977. 2340-2361.