Controlling circadian rhythms by dark-pulse perturbations in Arabidopsis thaliana

An extended Hilbert transform method for reconstructing the phase from an oscillatory signal

Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian's theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.

Application of time lags between light and temperature cycles for growth control based on the circadian clock of Lactuca sativa L. seedlings

The circadian clock plays an important role in agriculture, especially in highly controlled environments, such as plant factories. However, multiple environmental factors have an extremely high degree of freedom, and it is difficult to experimentally search for the optimal design conditions. A recent study demonstrated that the effect of time lags between light and temperature cycles on plant growth could be predicted by the entrainment properties of the circadian clock in Arabidopsis thaliana. Based on this prediction, it was possible to control plant growth by adjusting the time lag. However, for application in plant factories, it is necessary to verify the effectiveness of this method using commercial vegetables, such as leaf lettuce. In this study, we investigated the entrainment properties of the circadian clock and the effect of the time lag between light and temperature cycles on circadian rhythms and plant growth in Lactuca sativa L. seedlings. For evaluation of circadian rhythms, we used transgenic L. sativa L. with a luciferase reporter in the experiment and a phase oscillator model in the simulation. We found that the entrainment properties for the light and temperature stimuli and the effects of time lags on circadian rhythm and growth were similar to those of A. thaliana. Moreover, we demonstrated that changes in growth under different time lags could be predicted by simulation based on the entrainment properties of the circadian clock. These results showed the importance of designing a cultivation environment that considers the circadian clock and demonstrated a series of methods to achieve this.

Restoring circadian gene profiles in clock networks using synthetic feedback control

The circadian system-an organism's built-in biological clock-is responsible for orchestrating biological processes to adapt to diurnal and seasonal variations. Perturbations to the circadian system (e.g., pathogen attack, sudden environmental change) often result in pathophysiological responses (e.g., jetlag in humans, stunted growth in plants, etc.) In view of this, synthetic biologists are progressively adapting the idea of employing synthetic feedback control circuits to alleviate the effects of perturbations on circadian systems. To facilitate the design of such controllers, suitable models are required. Here, we extend our recently developed model for the plant circadian clock-termed the extended S-System model-to model circadian systems across different kingdoms of life. We then use this modeling strategy to develop a design framework, based on an antithetic integral feedback (AIF) controller, to restore a gene's circadian profile when it is subject to loss-of-function due to external perturbations. The use of the AIF controller is motivated by its recent successful experimental implementation. Our findings provide circadian biologists with a systematic and general modeling and design approach for implementing synthetic feedback control of circadian systems.

Universality in kinetic models of circadian rhythms in A r a b i d o p s i s t h a l i a n a

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.

Unstable Phase Response Curves Shown by Spatiotemporal Patterns in the Plant Root Circadian Clock

Phase response curves (PRCs) play important roles in the entrainment of periodic environmental cycles. Measuring the PRC is necessary to elucidate the relationship between environmental cues and the circadian clock. Conversely, the PRCs of plant circadian clocks are unstable due to multiple factors such as biotic/abiotic noise, individual differences, changes in amplitude, growth stage, and organ/tissue specificity. However, evaluating the effect of each factor is important because PRCs are commonly obtained by determining the response of many individuals, which include different amplitude states and organs. The plant root circadian clock spontaneously generates a spatiotemporal pattern called a stripe pattern, whereby all phases of the circadian rhythm exist within an individual root. Therefore, stimulating a plant root expressing this pattern enables phase responses at all phases to be measured using an individual root. In this study, we measured PRCs for thermal stimuli using this spatiotemporal pattern method and found that the PRC changed asymmetrically with positive and negative temperature stimuli. Individual differences were observed for weak but not for strong temperature stimuli. The root PRC changed depending on the amplitude of the circadian rhythm. The PRC in the young root near the hypocotyl was more sensitive than those in older roots or near the tip. Simulation with a phase oscillator model revealed the effect of measurement and internal noises on the PRC. These results indicate that instability in the entrainment of the plant circadian clock involves multiple factors, each having different characteristics. These results may help us understand how plant circadian clocks adapt to unstable environments and how plant circadian clocks with different characteristics, such as organ, age, and amplitude, are integrated within individuals.

Time Lag Between Light and Heat Diurnal Cycles Modulates CIRCADIAN CLOCK ASSOCIATION 1 Rhythm and Growth in Arabidopsis thaliana

Plant growth responses to cues such as light, temperature, and humidity enable the entrainment of the circadian rhythms with diurnal cycles. For example, the temperature variations between day and night affect plant growth and accompany the time lag to light cycle. Despite its importance, there has been no systematic investigation into time lags, and the mechanisms behind the entrainment of the circadian rhythms with multiple cycles remain unknown. Here, we investigated systemically the effects of the time lag on the circadian rhythm and growth in Arabidopsis thaliana. To investigate the entrainment status of the circadian clock, the rhythm of the clock gene CIRCADIAN CLOCK ASSOCIATION 1 (CCA1) was measured with a luciferase reporter assay. As a result, the rhythm was significantly modulated by the time lag with +10°C heating for 4 h every day but not -10°C cooling. A model based on coupled cellular oscillators successfully described these rhythm modulations. In addition, seedling growth depended on the time lag of the heating cycle but not that of the cooling cycle. Based on the relationship between the CCA1 rhythms and growth, we established an estimation method for the effects of the time lag. Our results found that plant growth relates to the CCA1 rhythm and provides a method by which to estimate the appropriate combination of light-dark and temperature cycles.

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.

Hilbert transform-based time-series analysis of the circadian gene regulatory network

In this work, the authors propose the Hilbert transform (HT)‐based numerical method to analyse the time series of the circadian rhythms. They demonstrate the application of HT by taking both deterministic and stochastic time series that they get from the simulation of the fruit fly model Drosophila melanogaster and show how to extract the period, construct phase response curves, determine period sensitivity of the parameters to perturbations and build Arnold tongues to identify the regions of entrainment. They also derive a phase model that they numerically simulate to capture whether the circadian time series entrains to the forcing period completely (phase locking) or only partially (phase slips) or neither. They validate the phase model, and numerics with the experimental time series forced under different temperature cycles. Application of HT to the circadian time series appears to be a promising tool to extract the characteristic information about circadian rhythms.

Multicellularity enriches the entrainment of Arabidopsis circadian clock

The phase response curve (PRC) of the circadian clock provides one of the most significant indices for anticipating entrainment of outer cycles, despite the difficulty of making precise PRC determinations in experiments. We characterized the PRC of the Arabidopsisthaliana circadian clock on the basis of its phase-locking property to variable periodic pulse perturbations. Experiments revealed that the PRC changed remarkably from continuous to discontinuous fashion, depending on the oscillation amplitude. Our hypothesis of amplitude-dependent adaptability to outer cycles was successfully clarified by elucidation of this transition of PRC as a change in the collective response of the circadian oscillator network. These findings provide an essential criterion against which to evaluate the precision of PRC measurement and an advanced understanding of the adaptability of plant circadian systems to environmental conditions.

Circadian Oscillation of the Lettuce Transcriptome under Constant Light and Light-Dark Conditions

Although, the circadian clock is a universal biological system in plants and it orchestrates important role of plant production such as photosynthesis, floral induction and growth, there are few such studies on cultivated species. Lettuce is one major cultivated species for both open culture and plant factories and there is little information concerning its circadian clock system. In addition, most of the relevant genes have not been identified. In this study, we detected circadian oscillation in the lettuce transcriptome using time-course RNA sequencing (RNA-Seq) data. Constant light (LL) and light-dark (LD) conditions were used to detect circadian oscillation because the circadian clock has some basic properties: one is self-sustaining oscillation under constant light and another is entrainment to environmental cycles such as light and temperature. In the results, 215 contigs were detected as common oscillating contigs under both LL and LD conditions. The 215 common oscillating contigs included clock gene-like contigs CCA1 (CIRCADIAN CLOCK ASSOCIATED 1)-like, TOC1 (TIMING OF CAB EXPRESSION 1)-like and LHY (LATE ELONGATED HYPOCOTYL)-like, and their expression patterns were similar to those of Arabidopsis. Functional enrichment analysis by GO (gene ontology) Slim and GO Fat showed that the GO terms of response to light stimulus, response to stress, photosynthesis and circadian rhythms were enriched in the 215 common oscillating contigs and these terms were actually regulated by circadian clocks in plants. The 215 common oscillating contigs can be used to evaluate whether the gene expression pattern related to photosynthesis and optical response performs normally in lettuce.

Phase response of the Arabidopsis thaliana circadian clock to light pulses of different wavelengths

Light is known as one of the most powerful environmental time cues for the circadian system. The quality of light is characterized by its intensity and wavelength. We examined how the phase response of Arabidopsis thaliana depends on the wavelength of the stimulus light and the type of light perturbation. Using transgenic A. thaliana expressing a luciferase gene, we monitored the rhythm of the bioluminescence signal. We stimulated the plants under constant red light using 3 light perturbation treatments: (1) increasing the red light intensity, (2) turning on a blue light while turning off the red light, and (3) turning on a blue light while keeping the red light on. To examine the phase response properties, we generated a phase transition curve (PTC), which plots the phase after the perturbation as a function of the phase before the perturbation. To evaluate the effect of the 3 light perturbation treatments, we simulated PTCs using a mathematical model of the plant circadian clock and fitted the simulated PTCs to the experimentally measured PTCs. Among the 3 treatments, perturbation (3) provided the strongest stimulus. The results indicate that the color of the stimulus light and the type of pulse administration affect the phase response in a complex manner. Moreover, the results suggest the involvement of interaction between red and blue light signaling pathways in resetting of the plant circadian clock.

Detection of Diurnal Variation of Tomato Transcriptome through the Molecular Timetable Method in a Sunlight-Type Plant Factory

The timing of measurement during plant growth is important because many genes are expressed periodically and orchestrate physiological events. Their periodicity is generated by environmental fluctuations as external factors and the circadian clock as the internal factor. The circadian clock orchestrates physiological events such as photosynthesis or flowering and it enables enhanced growth and herbivory resistance. These characteristics have possible applications for agriculture. In this study, we demonstrated the diurnal variation of the transcriptome in tomato (Solanum lycopersicum) leaves through molecular timetable method in a sunlight-type plant factory. Molecular timetable methods have been developed to detect periodic genes and estimate individual internal body time from these expression profiles in mammals. We sampled tomato leaves every 2 h for 2 days and acquired time-course transcriptome data by RNA-Seq. Many genes were expressed periodically and these expressions were stable across the 1st and 2nd days of measurement. We selected 143 time-indicating genes whose expression indicated periodically, and estimated internal time in the plant from these expression profiles. The estimated internal time was generally the same as the external environment time; however, there was a difference of more than 1 h between the two for some sampling points. Furthermore, the stress-responsive genes also showed weakly periodic expression, implying that they were usually expressed periodically, regulated by light-dark cycles as an external factor or the circadian clock as the internal factor, and could be particularly expressed when the plant experiences some specific stress under agricultural situations. This study suggests that circadian clock mediate the optimization for fluctuating environments in the field and it has possibilities to enhance resistibility to stress and floral induction by controlling circadian clock through light supplement and temperature control.

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

Experimental studies showed that light qualities such as color and strength influence the phase response properties of plant circadian systems. These effects, however, have yet to be properly addressed in theoretical models of plant circadian systems. To fill this gap, the present paper develops a mathematical model of a plant circadian clock that takes into account the intensity and wavelength of the input light. Based on experimental knowledge, we model three photoreceptors, Phytochrome A, Phytochrome B, and Cryptochrome 1, which respond to red and/or blue light, in Arabidopsis thaliana. The three photoreceptors are incorporated into a standard mathematical model of the plant system, in which activator and repressor genes form a single feedback loop. The model capability is examined by a phase response curve (PRC), which plots the phase shifts elicited by the light perturbation as a function of the perturbation phase. Numerical experiments demonstrate that the extended model reproduces the essential features of the PRCs measured experimentally under various light conditions. Particularly, unlike conventional models, the model generates the inherent shape of the PRC under dark pulse stimuli. The outcome of our modeling approach may motivate future theoretical and experimental studies of plant circadian rhythms.

Nondestructive and intuitive determination of circadian chlorophyll rhythms in soybean leaves using multispectral imaging

The circadian clock, synchronized by daily cyclic environmental cues, regulates diverse aspects of plant growth and development and increases plant fitness. Even though much is known regarding the molecular mechanism of circadian clock, it remains challenging to quantify the temporal variation of major photosynthesis products as well as their metabolic output in higher plants in a real-time, nondestructive and intuitive manner. In order to reveal the spatial-temporal scenarios of photosynthesis and yield formation regulated by circadian clock, multispectral imaging technique has been employed for nondestructive determination of circadian chlorophyll rhythms in soybean leaves. By utilizing partial least square regression analysis, the determination coefficients R(2), 0.9483 for chlorophyll a and 0.8906 for chlorophyll b, were reached, respectively. The predicted chlorophyll contents extracted from multispectral data showed an approximately 24-h rhythm which could be entrained by external light conditions, consistent with the chlorophyll contents measured by chemical analyses. Visualization of chlorophyll map in each pixel offers an effective way to analyse spatial-temporal distribution of chlorophyll. Our results revealed the potentiality of multispectral imaging as a feasible nondestructive universal assay for examining clock function and robustness, as well as monitoring chlorophyll a and b and other biochemical components in plants.

Circadian rhythms of hydraulic conductance and growth are enhanced by drought and improve plant performance

Circadian rhythms enable plants to anticipate daily environmental variations, resulting in growth oscillations under continuous light. Because plants daily transpire up to 200% of their water content, their water status oscillates from favourable during the night to unfavourable during the day. We show that rhythmic leaf growth under continuous light is observed in plants that experience large alternations of water status during an entrainment period, but is considerably buffered otherwise. Measurements and computer simulations show that this is due to oscillations of plant hydraulic conductance and plasma membrane aquaporin messenger RNA abundance in roots during continuous light. A simulation model suggests that circadian oscillations of root hydraulic conductance contribute to acclimation to water stress by increasing root water uptake, thereby favouring growth and photosynthesis. They have a negative effect in favourable hydraulic conditions. Climate-driven control of root hydraulic conductance therefore improves plant performances in both stressed and non-stressed conditions.

Circadian rhythms allow plants to respond to diurnal fluctuations in the environment. Here Caldeira et al. find that circadian control of hydraulic conductance, aquaporin expression and leaf growth are entrained by oscillations of plant water status and promote water uptake in drought-stressed plants.