Temperature robustness in Arabidopsis circadian clock models is facilitated by repressive interactions, autoregulation, and three-node feedbacks

•Temperature dependence is incorporated in a range of circadian clock models.•Key network features allowing temperature compensation are identified.•These features are tested via a set of simple randomly parameterised networks. The biological interactions underpinning the Arabidopsis circadian clock have been systematically uncovered and explored by biological experiments and mathematical models. This is captured by a series of published ordinary differential equation (ODE) models, which describe plant clock dynamics in response to light/dark conditions. However, understanding the role of temperature in resetting the clock (entrainment) and the mechanisms by which circadian rhythms maintain a near-24 h period over a range of temperatures (temperature compensation) is still unclear. Understanding entrainment and temperature compensation may elucidate the principles governing the structure of the circadian clock network. Here we explore the design principles of the Arabidopsis clock and its responses to changes in temperature. We analyse published clock models of Arabidopsis, spanning a range of complexity, and incorporate temperature-dependent dynamics into the parameters of translation rates in these models, to discern which regulatory patterns may best explain clock function and temperature compensation. We additionally construct three minimal clock models and explore what key features govern their rhythmicity and temperature robustness via a series of random parameterisations. Results show that the highly repressive interactions between the components of the plant clock, together with autoregulation patterns and three-node feedback loops, are associated with circadian function of the clock in general, and enhance its robustness to temperature variation in particular. However, because the networks governing clock function vary with time due to light and temperature conditions, we emphasise the importance of studying plant clock functionality in its entirety rather than as a set of discrete regulation patterns.