An extended mathematical model for reproducing the phase response of Arabidopsis thaliana under various light conditions

The circadian clock of the bacterium B. subtilis evokes properties of complex, multicellular circadian systems

Circadian clocks are pervasive throughout nature, yet only recently has this adaptive regulatory program been described in nonphotosynthetic bacteria. Here, we describe an inherent complexity in the Bacillus subtilis circadian clock. We find that B. subtilis entrains to blue and red light and that circadian entrainment is separable from masking through fluence titration and frequency demultiplication protocols. We identify circadian rhythmicity in constant light, consistent with the Aschoff's rule, and entrainment aftereffects, both of which are properties described for eukaryotic circadian clocks. We report that circadian rhythms occur in wild isolates of this prokaryote, thus establishing them as a general property of this species, and that its circadian system responds to the environment in a complex fashion that is consistent with multicellular eukaryotic circadian systems.

Red Light Resets the Expression Pattern, Phase, and Period of the Circadian Clock in Plants: A Computational Approach

Simple Summary

Progress in computational biology has provided a comprehensive understanding of the dynamics of the plant circadian clock. Previously proposed models of the plant circadian clock have intended to model its entrainment using white-light/dark cycles. However, these models have failed to take into account the effect of light quality on circadian rhythms, which has been experimentally observed. In this work, we developed a computational approach to characterizing the effects of light quality on plant circadian rhythms. The results demonstrated that red light can reset the expression patterns, phases, and periods of clock component genes. The circadian period, amplitude, and phase can be co-optimized for high-quality and efficient breeding.

Abstract

Recent research in the fields of biochemistry and molecular biology has shown that different light qualities have extremely different effects on plant development, and optimizing light quality conditions can speed up plant growth. Clock-regulated red-light signaling, can enhance hypocotyl elongation, and increase seedling height and flower and fruit productivity. In order to investigate the effect of red light on circadian clocks in plants, a novel computational model was established. The expression profiles of the circadian element CCA1 from previous related studies were used to fit the model. The simulation results were validated by the expression patterns of CCA1 in Arabidopsis, including wild types and mutants, and by the phase shifts of CCA1 after red-light pulse. The model was used to further explore the complex responses to various photoperiods, such as the natural white-light/dark cycles, red/white/dark cycles, and extreme 24 h photoperiods. These results demonstrated that red light can reset the expression pattern, period, and phase of the circadian clock. Finally, we identified the dependence of phase shifts on the length of red-light pulse and the minimum red-light pulse length required for producing an observable phase shift. This work provides a promising computational approach to investigating the response of the circadian clock to other light qualities.

Modelling of plant circadian clock for characterizing hypocotyl growth under different light quality conditions

To meet the ever-increasing global food demand, the food production rate needs to be increased significantly in the near future. Speed breeding is considered as a promising agricultural technology solution to achieve the zero-hunger vision as specified in the United Nations Sustainable Development Goal 2. In speed breeding, the photoperiod of the artificial light has been manipulated to enhance crop productivity. In particular, regulating the photoperiod of different light qualities rather than solely white light can further improve speed breading. However, identifying the optimal light quality and the associated photoperiod simultaneously remains a challenging open problem due to complex interactions between multiple photoreceptors and proteins controlling plant growth. To tackle this, we develop a first comprehensive model describing the profound effect of multiple light qualities with different photoperiods on plant growth (i.e. hypocotyl growth). The model predicts that hypocotyls elongated more under red light compared to both red and blue light. Drawing similar findings from previous related studies, we propose that this might result from the competitive binding of red and blue light receptors, primarily Phytochrome B (phyB) and Cryptochrome 1 (cry1) for the core photomorphogenic regulator, CONSTITUTIVE PHOTOMORPHOGENIC 1 (COP1). This prediction is validated through an experimental study on Arabidopsis thaliana. Our work proposes a potential molecular mechanism underlying plant growth under different light qualities and ultimately suggests an optimal breeding protocol that takes into account light quality.

Universality in kinetic models of circadian rhythms in [Formula: see text]

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

The singularity response reveals entrainment properties of the plant circadian clock

Circadian clocks allow organisms to synchronize their physiological processes to diurnal variations. A phase response curve allows researchers to understand clock entrainment by revealing how signals adjust clock genes differently according to the phase in which they are applied. Comprehensively investigating these curves is difficult, however, because of the cost of measuring them experimentally. Here we demonstrate that fundamental properties of the curve are recoverable from the singularity response, which is easily measured by applying a single stimulus to a cellular network in a desynchronized state (i.e. singularity). We show that the singularity response of Arabidopsis to light/dark and temperature stimuli depends on the properties of the phase response curve for these stimuli. The measured singularity responses not only allow the curves to be precisely reconstructed but also reveal organ-specific properties of the plant circadian clock. The method is not only simple and accurate, but also general and applicable to other coupled oscillator systems as long as the oscillators can be desynchronized. This simplified method may allow the entrainment properties of the circadian clock of both plants and other species in nature.

Phase response curves reveal how biological clocks respond to stimuli applied during different circadian phases but can be costly to produce. Here Masuda et al. show that phase response curves for plants can be reconstructed by monitoring how a desynchronized population responds to a single stimulus.

Gene regulatory network models in response to sugars in the plant circadian system

Circadian entrainment is the process by which internal circadian oscillators staying in synchronization with the local environmental rhythms. Circadian clocks are entrained by adjusting phase and period in response to environmental and metabolic signals. In Arabidopsis thaliana, light and sugar signals differentially affect the circadian phase; the former advances the phase in the late of the subjective night and delays around dusk, while the latter advances the phase mainly in the morning, which is optimal to maintain sucrose homeostasis. We have proposed that the phase adjustment of the A. thaliana circadian oscillator by sugar signals contributes to the realization of carbon homeostasis and the increase of plant growth under fluctuating day-night cycles. However, which genes in the circadian oscillator are targets of sucrose signals and how the potential target genes should be regulated by sucrose to realize sucrose homeostasis has not been studied from the theoretical perspective. Here we investigate the effect of sugar on the phase response property of the plant circadian oscillator using clock gene-regulatory network models. We simulated phase response curves (PRCs) to sucrose pulses, which were compared with an experimental PRC. Our analyses of the gene-regulatory network model demonstrated that target genes of the sugar signal could be members of the PSEUDO-RESPONSE REGULATOR gene family and the evening complex components. We also examined the phase response property using a single feedback-loop model and elucidated how phase advance is induced in the subjective morning under certain conditions of a target clock gene of sucrose and its regulatory property.

High-Throughput Growth Prediction for Lactuca sativa L. Seedlings Using Chlorophyll Fluorescence in a Plant Factory with Artificial Lighting

Poorly grown plants that result from differences in individuals lead to large profit losses for plant factories that use large electric power sources for cultivation. Thus, identifying and culling the low-grade plants at an early stage, using so-called seedlings diagnosis technology, plays an important role in avoiding large losses in plant factories. In this study, we developed a high-throughput diagnosis system using the measurement of chlorophyll fluorescence (CF) in a commercial large-scale plant factory, which produces about 5000 lettuce plants every day. At an early stage (6 days after sowing), a CF image of 7200 seedlings was captured every 4 h on the final greening day by a high-sensitivity CCD camera and an automatic transferring machine, and biological indices were extracted. Using machine learning, plant growth can be predicted with a high degree of accuracy based on biological indices including leaf size, amount of CF, and circadian rhythms in CF. Growth prediction was improved by addition of temporal information on CF. The present data also provide new insights into the relationships between growth and temporal information regulated by the inherent biological clock.

A Compact Model for the Complex Plant Circadian Clock

The circadian clock is an endogenous timekeeper that allows organisms to anticipate and adapt to the daily variations of their environment. The plant clock is an intricate network of interlocked feedback loops, in which transcription factors regulate each other to generate oscillations with expression peaks at specific times of the day. Over the last decade, mathematical modeling approaches have been used to understand the inner workings of the clock in the model plant Arabidopsis thaliana. Those efforts have produced a number of models of ever increasing complexity. Here, we present an alternative model that combines a low number of equations and parameters, similar to the very earliest models, with the complex network structure found in more recent ones. This simple model describes the temporal evolution of the abundance of eight clock gene mRNA/protein and captures key features of the clock on a qualitative level, namely the entrained and free-running behaviors of the wild type clock, as well as the defects found in knockout mutants (such as altered free-running periods, lack of entrainment, or changes in the expression of other clock genes). Additionally, our model produces complex responses to various light cues, such as extreme photoperiods and non-24 h environmental cycles, and can describe the control of hypocotyl growth by the clock. Our model constitutes a useful tool to probe dynamical properties of the core clock as well as clock-dependent processes.