Stochastic simulation of a model for circadian rhythms in plants

Noise-induced entrainment of the circadian clock by thermoperiods in tomato: A computational approach

The endogenous circadian rhythm (approximately 24 h) allows plants to adapt to daily light and temperature variations. Although the mechanism of photoperiod entrainment has been studied extensively, entrainment to diurnal temperature rhythms remains poorly understood. Here we investigate the stochastic entrainment of the circadian clock in the model crop tomato, subject to different thermoperiods. We first proposed the deterministic model of the thermoresponsive circadian clock. The expressions of the circadian clock genes under constant warm temperature (29 ℃) were quantified by RT-qPCR for basal parameters estimation through minimizing the cost function. Model simulations by the stochastic simulation algorithm showed warm temperatures resulting in an advanced phase for approximately 3-4 h. A few hundred molecules for the system size of the stochastic model were sufficient to engage the robust oscillations. Multiple temperature inputs and abnormal temperature cycles similarly showed the invariant robustness of the oscillations. In addition, phases of the core circadian elements were remarkably correlated linearly with periods under temperature cycles. Whereas, the phases were correlated with the duration of daily warm temperature stimuli in a polynomial mode.

Adaptive Diversification in the Cellular Circadian Behavior of Arabidopsis Leaf- and Root-Derived Cells

The plant circadian system is based on self-sustained cellular oscillations and is utilized to adapt to daily and seasonal environmental changes. The cellular circadian clocks in the above- and belowground plant organs are subjected to diverse local environments. Individual cellular clocks are affected by other cells/tissues in plants, and the intrinsic circadian properties of individual cells remain to be elucidated. In this study, we monitored bioluminescence circadian rhythms of individual protoplast-derived cells from leaves and roots of a CCA1::LUC Arabidopsis transgenic plant. We analyzed the circadian properties of the leaf- and root-derived cells and demonstrated that the cells with no physical contact with other cells harbor a genuine circadian clock with ∼24-h periodicity, entrainability and temperature compensation of the period. The stability of rhythm was dependent on the cell density. High cell density resulted in an improved circadian rhythm of leaf-derived cells while this effect was observed irrespective of the phase relation between cellular rhythms. Quantitative and statistical analyses for individual cellular bioluminescence rhythms revealed a difference in amplitude and precision of light/dark entrainment between the leaf- and root-derived cells. Circadian systems in the leaves and roots are diversified to adapt to their local environments at the cellular level.

A spatial model of the plant circadian clock reveals design principles for coordinated timing

Individual plant cells possess a genetic network, the circadian clock, that times internal processes to the day-night cycle. Mathematical models of the clock are typically either "whole-plant" that ignore tissue or cell type-specific clock behavior, or "phase-only" that do not include molecular components. To address the complex spatial coordination observed in experiments, here we implemented a clock network model on a template of a seedling. In our model, the sensitivity to light varies across the plant, and cells communicate their timing via local or long-distance sharing of clock components, causing their rhythms to couple. We found that both varied light sensitivity and long-distance coupling could generate period differences between organs, while local coupling was required to generate the spatial waves of clock gene expression observed experimentally. We then examined our model under noisy light-dark cycles and found that local coupling minimized timing errors caused by the noise while allowing each plant region to maintain a different clock phase. Thus, local sensitivity to environmental inputs combined with local coupling enables flexible yet robust circadian timing.