Date of Award


Document Type

Thesis open access



First Advisor

Orrin Shindell

Second Advisor

Kelvin Cheng

Third Advisor

Nirav Mehta


Adapting to the 24-hour periodic environment on the Earth, plants have evolved sets of chemical reactions that regulate their circadian rhythms. A number of research groups studying these circadian reactions in the common laboratory plant Arabidopsis thaliana have developed eleven, increasingly elaborate, chemical kinetic models based on genetic feedback loops. Each model consists of a system of coupled nonlinear ordinary differential equations. We find these models are all situated near a Hopf bifurcation in parameter space. This suggests that there may be some biological significance corresponding to this mathematical property.

To study the properties of these systems related to the Hopf bifurcation, we first numerically compute the solutions to the kinetic models for Arabidopsis thaliana. At the whole plant scale, we perform a weakly nonlinear analysis, the Reductive Perturbation Method, on each model near bifurcation to predict the amplitude and frequency of the oscillating concentration of chemical species from the Stuart-Landau amplitude equation. By scaling the numerical frequencies and amplitudes by our theoretical predictions, we show that the solutions to all these models collapse into a universal parameter-free form. Then, we implement Gillespie’s Stochastic Simulation Algorithm to simulate the system at the single-cell level and account for random fluctuations in molecule numbers. We relate the two approaches and discuss some implications of our results for improving future modeling efforts to ensure that the models are consistent with each other and with the dynamics of the Arabidopsis thaliana circadian rhythms. Finally, we comment on the possible biological significance of the models' mathematical features.

Creative Commons License

Creative Commons Attribution-NonCommercial 4.0 International License
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