Modelling temperature dependence in the Arabidopsis thaliana circadian clock

The circadian clock is the mechanism responsible for generating and controlling the biological rhythms that occur with 24 h periodicity in most living organisms. This clock allows organisms to anticipate the environmental variation caused by the rotation of the Earth such as the daily light and temperature cycles, providing them adaptive advantages. The circadian clock is a complex network of genes interacting with each other in regulatory processes which have been represented by mathematical models. In the plant Arabidopsis thaliana, the mechanisms by which light regulates the circadian clock have been widely modelled mathematically and implemented computationally permitting to explain experimental observations and to generate hypotheses, which have led experimental investigation. However, the role of temperature and the mechanisms of adaptation to temperature variation are poorly understood, and especially in the scenario of global climate change, modelling a temperature responsive plant clock is of increasing importance. Here we present a framework of temperature dependence for the Arabidopsis circadian clock by applying Arrhenius equations to the most predominant models for the plant system and we additionally propose three minimal models via random parameterisations to explore design principles underlying temperature compensation. By numerical investigation, we conclude that temperature compensation is especially sensitive to degradation processes, and that the combined effect of light and temperature favors the robustness of the clock. We also propose to analyse the plant clock as a whole system and under that perspective we suggest that context graph-theoretic approaches could be a powerful tool to uncover the design principles for temperature mechanisms.