A Compact Model for the Complex Plant Circadian Clock

Decoding the plant clock: a review of mathematical models for the circadian regulatory network

Most organisms have evolved specific mechanisms to respond to changes in environmental conditions such as light and temperature over the course of day. These periodic changes in the physiology and behaviour of organisms, referred to as circadian rhythms, are a consequence of intricate molecular mechanisms in the form of transcription and translational feedback loops. The plant circadian regulatory network is a complex web of interconnected feedback loops involving various transcription factors such as CCA1, LHY, PRRs, TOC1, LUX, ELF3, ELF4, RVE8, and more. This network enables plants to adapt and thrive in diverse environmental conditions. It responds to entrainment signals, including light, temperature, and nutrient concentrations and interacts with most of the physiological functions such as flowering, growth and stress response. Mathematical modelling of these gene regulatory networks enables a deeper understanding of not only the function but also the perturbations that may affect the plant growth and function with changing climate. Over the years, numerous mathematical models have been developed to understand the diverse aspects of plant circadian regulation. In this review, we have delved into the systematic development of these models, outlining the model components and refinements over time. We have also highlighted strengths and limitations of each of the models developed so far. Finally, we conclude the review by describing the prospects for investigation and advancement of these models for better understanding of plant circadian regulation.

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacemaker yield an internal representation of season. Output pathways of the circadian clock regulate photoperiodic responses such as flowering time in plants or hibernation in mammals. Here, we review the concepts of seasonal entrainment and photoperiodic encoding. We introduce conceptual phase oscillator models as their high level of abstraction, but, yet, intuitive interpretation of underlying parameters allows for a straightforward analysis of principles that determine entrainment characteristics. Results from this class of models are related and discussed in the context of more complex conceptual amplitude-phase oscillators as well as contextual molecular models that take into account organism, tissue, and cell-type-specific details.

Complex epistatic interactions between ELF3, PRR9, and PRR7 regulate the circadian clock and plant physiology

Circadian clocks are endogenous timekeeping mechanisms that coordinate internal physiological responses with the external environment. EARLY FLOWERING3 (ELF3), PSEUDO RESPONSE REGULATOR (PRR9), and PRR7 are essential components of the plant circadian clock and facilitate entrainment of the clock to internal and external stimuli. Previous studies have highlighted a critical role for ELF3 in repressing the expression of PRR9 and PRR7. However, the functional significance of activity in regulating circadian clock dynamics and plant development is unknown. To explore this regulatory dynamic further, we first employed mathematical modeling to simulate the effect of the prr9/prr7 mutation on the elf3 circadian phenotype. These simulations suggested that simultaneous mutations in prr9/prr7 could rescue the elf3 circadian arrhythmia. Following these simulations, we generated all Arabidopsis elf3/prr9/prr7 mutant combinations and investigated their circadian and developmental phenotypes. Although these assays could not replicate the results from the mathematical modeling, our results have revealed a complex epistatic relationship between ELF3 and PRR9/7 in regulating different aspects of plant development. ELF3 was essential for hypocotyl development under ambient and warm temperatures, while PRR9 was critical for root thermomorphogenesis. Finally, mutations in prr9 and prr7 rescued the photoperiod-insensitive flowering phenotype of the elf3 mutant. Together, our results highlight the importance of investigating the genetic relationship among plant circadian genes.

Diurnal Rhythms in the Red Seaweed Gracilariopsis chorda are Characterized by Unique Regulatory Networks of Carbon Metabolism

Cellular and physiological cycles are driven by endogenous pacemakers, the diurnal and circadian rhythms. Key functions such as cell cycle progression and cellular metabolism are under rhythmic regulation, thereby maintaining physiological homeostasis. The photoreceptors phytochrome and cryptochrome, in response to light cues, are central input pathways for physiological cycles in most photosynthetic organisms. However, among Archaeplastida, red algae are the only taxa that lack phytochromes. Current knowledge about oscillatory rhythms is primarily derived from model species such as Arabidopsis thaliana and Chlamydomonas reinhardtii in the Viridiplantae, whereas little is known about these processes in other clades of the Archaeplastida, such as the red algae (Rhodophyta). We used genome-wide expression profiling of the red seaweed Gracilariopsis chorda and identified 3,098 rhythmic genes. Here, we characterized possible cryptochrome-based regulation and photosynthetic/cytosolic carbon metabolism in this species. We found a large family of cryptochrome genes in G. chorda that display rhythmic expression over the diurnal cycle and may compensate for the lack of phytochromes in this species. The input pathway gates regulatory networks of carbon metabolism which results in a compact and efficient energy metabolism during daylight hours. The system in G. chorda is distinct from energy metabolism in most plants, which activates in the dark. The green lineage, in particular, land plants, balance water loss and CO2 capture in terrestrial environments. In contrast, red seaweeds maintain a reduced set of photoreceptors and a compact cytosolic carbon metabolism to thrive in the harsh abiotic conditions typical of intertidal zones.

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Low light intensity elongates period and defers peak time of photosynthesis: a computational approach to circadian-clock-controlled photosynthesis in tomato

Photosynthesis is involved in the essential process of transforming light energy into chemical energy. Although the interaction between photosynthesis and the circadian clock has been confirmed, the mechanism of how light intensity affects photosynthesis through the circadian clock remains unclear. Here, we propose a first computational model for circadian-clock-controlled photosynthesis, which consists of the light-sensitive protein P, the core oscillator, photosynthetic genes, and parameters involved in the process of photosynthesis. The model parameters were determined by minimizing the cost function ( [Formula: see text]), which is defined by the errors of expression levels, periods, and phases of the clock genes (CCA1, PRR9, TOC1, ELF4, GI, and RVE8). The model recapitulates the expression pattern of the core oscillator under moderate light intensity (100 μmol m -2 s-1). Further simulation validated the dynamic behaviors of the circadian clock and photosynthetic outputs under low (62.5 μmol m-2 s-1) and normal (187.5 μmol m-2 s-1) intensities. When exposed to low light intensity, the peak times of clock and photosynthetic genes were shifted backward by 1-2 hours, the period was elongated by approximately the same length, and the photosynthetic parameters attained low values and showed delayed peak times, which confirmed our model predictions. Our study reveals a potential mechanism underlying the circadian regulation of photosynthesis by the clock under different light intensities in tomato.

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.

Circadian autonomy and rhythmic precision of the Arabidopsis female reproductive organ

The plant circadian clock regulates essential biological processes including flowering time or petal movement. However, little is known about how the clock functions in flowers. Here, we identified the circadian components and transcriptional networks contributing to the generation of rhythms in pistils, the female reproductive organ. When detached from the rest of the flower, pistils sustain highly precise rhythms, indicating organ-specific circadian autonomy. Analyses of clock mutants and chromatin immunoprecipitation assays showed distinct expression patterns and specific regulatory functions for clock activators and repressors in pistils. Genetic interaction studies also suggested a hierarchy of the repressing activities that provide robustness and precision to the pistil clock. Globally, the circadian function in pistils primarily governs responses to environmental stimuli and photosynthesis and controls pistil growth and seed weight and production. Understanding the circadian intricacies in reproductive organs may prove useful for optimizing plant reproduction and productivity.

COP1 dynamics integrate conflicting seasonal light and thermal cues in the control of Arabidopsis elongation

As the summer approaches, plants experience enhanced light inputs and warm temperatures, two environmental cues with an opposite morphogenic impact. Key components of this response are PHYTOCHROME B (phyB), EARLY FLOWERING 3 (ELF3), and CONSTITUTIVE PHOTOMORPHOGENIC 1 (COP1). Here, we used single and double mutant/overexpression lines to fit a mathematical model incorporating known interactions of these regulators. The fitted model recapitulates thermal growth of all lines used and correctly predicts thermal behavior of others not used in the fit. While thermal COP1 function is accepted to be independent of diurnal timing, our model shows that it acts at temperature signaling only during daytime. Defective response of cop1-4 mutants is epistatic to phyB-9 and elf3-8, indicating that COP1 activity is essential to transduce phyB and ELF3 thermosensory function. Our thermal model provides a unique toolbox to identify best allelic combinations enhancing climate change resilience of crops adapted to different latitudes.

Data-driven dynamical modelling of a pathogen-infected plant gene regulatory network: A comparative analysis

Recent advances in synthetic biology have enabled the design of genetic feedback control circuits that could be implemented to build resilient plants against pathogen attacks. To facilitate the proper design of these genetic feedback control circuits, an accurate model that is able to capture the vital dynamical behaviour of the pathogen-infected plant is required. In this study, using a data-driven modelling approach, we develop and compare four dynamical models (i.e. linear, Michaelis-Menten with Hill coefficient (Hill Function), standard S-System and extended S-System) of a pathogen-infected plant gene regulatory network (GRN). These models are then assessed across several criteria, i.e. ease of identifying the type of gene regulation, the predictive capability, Akaike Information Criterion (AIC) and the robustness to parameter uncertainty to determine its viability of balancing between biological complexity and accuracy when modelling the pathogen-infected plant GRN. Using our defined ranking score, we obtain the following insights to the modelling of GRN. Our analyses show that despite commonly used and provide biological relevance, the Hill Function model ranks the lowest while the extended S-System model ranks highest in the overall comparison. Interestingly, the performance of the linear model is more consistent throughout the comparison, making it the preferred model for this pathogen-infected plant GRN when considering data-driven modelling approach.

Genome-wide TCP transcription factors analysis provides insight into their new functions in seasonal and diurnal growth rhythm in Pinus tabuliformis

BACKGROUND

Pinus tabuliformis adapts to cold climate with dry winter in northern China, serving as important commercial tree species. The TEOSINTE BRANCHED 1, CYCLOIDEA, and PROLIFERATING CELL FACTOR family(TCP)transcription factors were found to play a role in the circadian clock system in Arabidopsis. However, the role of TCP transcription factors in P. tabuliformis remains little understood.

RESULTS

In the present study, 43 TCP genes were identified from P. tabuliformis genome database. Based on the phylogeny tree and sequence similarity, the 43 TCP genes were classified into four groups. The motif results showed that different subfamilies indeed contained different motifs. Clade II genes contain motif 1, clade I genes contain motif 1, 8, 10 and clade III and IV contain more motifs, which is consistent with our grouping results. The structural analysis of PtTCP genes showed that most PtTCPs lacked introns. The distribution of clade I and clade II on the chromosome is relatively scattered, while clade III and clade IV is relatively concentrated. Co-expression network indicated that PtTCP2, PtTCP12, PtTCP36, PtTCP37, PtTCP38, PtTCP41 and PtTCP43 were co-expressed with clock genes in annual cycle and their annual cycle expression profiles both showed obvious seasonal oscillations. PtTCP2, PtTCP12, PtTCP37, PtTCP38, PtTCP40, PtTCP41, PtTCP42 and PtTCP43 were co-expressed with clock genes in diurnal cycle. Only the expression of PtTCP42 showed diurnal oscillation.

CONCLUSIONS

The TCP gene family, especially clade II, may play an important role in the regulation of the season and circadian rhythm of P. tabuliformis. In addition, the low temperature in winter may affect the diurnal oscillations.

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.

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.

Dynamic physiological and transcriptome changes reveal a potential relationship between the circadian clock and salt stress response in Ulmus pumila

Despite the important role the circadian clock plays in numerous critical physiological responses in plants, such as hypocotyl elongation, leaf movement, stomatal opening, flowering, and stress responses, there have been no investigations into the effect of the circadian clock on physiological and transcriptional networks under salt stress. Ulmus pumila L. has been reported to tolerate 100-150 mM NaCl treatment. We measured the diurnal variation in photosynthesis and chlorophyll fluorescence parameters and performed a time-course transcriptome analysis of 2-years-old U. pumila seedlings under salt treatment to dissect the physiological regulation and potential relationship between the circadian network and the salt stress response. Seedlings in 150 mM NaCl treatment exhibited salt-induced physiological enhancement compared to the control group. A total of 7009 differentially expressed unigenes (DEGs) were identified under salt stress, of which 16 DEGs were identified as circadian rhythm-related DEGs (crDEGs). Further analysis of dynamic expression changes revealed that DEGs involved in four crucial pathways-photosynthesis, thiamine metabolism, abscisic acid synthesis and metabolism, and the hormone-MAPK signal crosstalk pathway-are closely related to the circadian clock. Finally, we constructed a co-expression network between the circadian clock and these four crucial pathways. Our results help shed light on the molecular link between the circadian network and salt stress tolerance in U. pumila.

Systems scale characterization of circadian rhythm pathway in Camellia sinensis

Tea (Camellia sinensis) is among the most valuable commercial crops being a non-alcoholic beverage having antioxidant properties. Like in other plants, circadian oscillator in tea modulates several biological processes according to earth's revolution dependent variations in environmental cues like light and temperature. In the present study, we report genome wide identification and characterization of circadian oscillator (CO) proteins in tea. We first mined the genes (24, in total) involved in circadian rhythm pathway in the 56 plant species having available genomic information and then built their hidden Markov models (HMMs). Using these HMMs, 24 proteins were identified in tea and were further assessed for their functional annotation. Expression analysis of all these 24 CO proteins was then performed in 3 abiotic (A) and 3 biotic conditions (B) stress conditions and co-expressed as well as differentially expressed genes in the selected 6 stress conditions were elaborated. A methodology to identify the differentially expressed genes in specific types of stresses (A or B) is proposed and novel markers among CO proteins are presented. By mapping the identified CO proteins against the recently reported genome wide interologous protein-protein interaction network of tea (TeaGPIN), an interaction sub-network of tea CO proteins (TeaCO-PIN) is developed and analysed. Out of 24 CO proteins, structures of 4 proteins could be successfully predicted and validated using consensus of three structure prediction algorithms and their stability was further assessed using molecular dynamic simulations at 100 ns. Phylogenetic analysis of these proteins is performed to examine their molecular evolution.

ODE (Ordinary Differential Equation) Models for Plant Circadian Networks: What the Models Are and How They Should Be Used

ODE models have been used for decades to help circadian biologists understand the rhythmic phenomena they observe and to predict the behavior of plant circadian rhythms under changed conditions such as genetic mutations or novel environments. The models vary in complexity, and for good reasons, but they share the same mathematical ingredients in their construction and the same computational methods in their solution. Here we explain the fundamental concepts which define ODE models. We sketch how ODE models can be understood, how they can be solved mathematically and computationally, and the important distinction between autonomous and non-autonomous phenomena. The concepts are illustrated with examples which illustrate the basic concepts and which may help to describe the strengths and limitations of these models and the computational investigations of their properties.

A framework of artificial light management for optimal plant development for smart greenhouse application

Smart greenhouse farming has emerged as one of the solutions to global food security, where farming productivity can be managed and improved in an automated manner. While it is known that plant development is highly dependent on the quantity and quality of light exposure, the specific impact of the different light properties is yet to be fully understood. In this study, using the model plant Arabidopsis, we systematically investigate how six different light properties (i.e., photoperiod, light offset, intensity, phase of dawn, duration of twilight and period) would affect plant development i.e., flowering time and hypocotyl (seedling stem) elongation using an established mathematical model of the plant circadian system relating light input to flowering time and hypocotyl elongation outputs for smart greenhouse application. We vary each of the light properties individually and then collectively to understand their effect on plant development. Our analyses show in comparison to the nominal value, the photoperiod of 18 hours, period of 24 hours, no light offset, phase of dawn of 0 hour, duration of twilight of 0.05 hour and a reduced light intensity of 1% are able to improve by at least 30% in days to flower (from 32.52 days to 20.61 days) and hypocotyl length (from 1.90 mm to 1.19mm) with the added benefit of reducing energy consumption by at least 15% (from 4.27 MWh/year to 3.62 MWh/year). These findings could provide beneficial solutions to the smart greenhouse farming industries in terms of achieving enhanced productivity while consuming less energy.

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.

DE-ETIOLATED1 has a role in the circadian clock of the liverwort Marchantia polymorpha

Previous studies of plant circadian clock evolution have often relied on clock models and genes defined in Arabidopsis. These studies identified homologues with seemingly conserved function, as well as frequent gene loss. In the present study, we aimed to identify candidate clock genes in the liverwort Marchantia polymorpha using a more unbiased approach. To identify genes with circadian rhythm we sequenced the transcriptomes of gemmalings in a time series in constant light conditions. Subsequently, we performed functional studies using loss-of-function mutants and gene expression reporters. Among the genes displaying circadian rhythm, a homologue to the transcriptional co-repressor Arabidopsis DE-ETIOLATED1 showed high amplitude and morning phase. Because AtDET1 is arrhythmic and associated with the morning gene function of AtCCA1/LHY, that lack a homologue in liverworts, we functionally studied DET1 in M. polymorpha. We found that the circadian rhythm of MpDET1 expression is disrupted in loss-of-function mutants of core clock genes and putative evening-complex genes. MpDET1 knock-down in turn results in altered circadian rhythm of nyctinastic thallus movement and clock gene expression. We could not detect any effect of MpDET1 knock-down on circadian response to light, suggesting that MpDET1 has a yet unknown function in the M. polymorpha circadian clock.

Evolutionary conservations, changes of circadian rhythms and their effect on circadian disturbances and therapeutic approaches

The circadian rhythm is essential for the interaction of all living organisms with their environments. Several processes, such as thermoregulation, metabolism, cognition and memory, are regulated by the internal clock. Disturbances in the circadian rhythm have been shown to lead to the development of neuropsychiatric disorders, including attention-deficit hyperactivity disorder (ADHD). Interestingly, the mechanism of the circadian rhythms has been conserved in many different species, and misalignment between circadian rhythms and the environment results in evolutionary regression and lifespan reduction. This review summarises the conserved mechanism of the internal clock and its major interspecies differences. In addition, it focuses on effects the circadian rhythm disturbances, especially in cases of ADHD, and describes the possibility of recombinant proteins generated by eukaryotic expression systems as therapeutic agents as well as CRISPR/Cas9 technology as a potential tool for research and therapy. The aim is to give an overview about the evolutionary conserved mechanism as well as the changes of the circadian clock. Furthermore, current knowledge about circadian rhythm disturbances and therapeutic approaches is discussed.

Stochastic simulation of a model for circadian rhythms in plants

Circadian clocks allow living organisms to anticipate and adapt to the daily variations of the environment. The interlocked feedback loops of the transcription factors network in the plant clock generate oscillations with expression peaks at specific times of the day. In this work, we explore the effect of molecular noise on the behavior of the plant circadian clock through numerical simulations. The influence of system size, photoperiod, and mutations of clock genes on the robustness of the oscillations are discussed. Our simulations show that the oscillations remain robust when the mRNA and protein levels are in the range of a few hundreds molecules. Entrainment by light-dark cycles enhances the robustness compared to constant conditions. Multiple light inputs and inter-cellular coupling also contribute to the robustness of the oscillations. The comparison between deterministic and stochastic simulations of single and double mutants shows that stochasticity does not qualitatively affect the behaviour of mutants but that they do not have the same robustness to noise. Finally, the model shows that noise can induce transitions between two limit cycles in a birhythmic clock mutant.

Layers of crosstalk between circadian regulation and environmental signalling in plants

Circadian regulation has a pervasive influence upon plant development, physiology and metabolism, impacting upon components of fitness and traits of agricultural importance. Circadian regulation is inextricably connected to the responses of plants to their abiotic environments, from the cellular to whole plant scales. Here, we review the crosstalk that occurs between circadian regulation and responses to the abiotic environment from the intracellular scale through to naturally fluctuating environments. We examine the spatial crosstalk that forms part of plant circadian regulation, at the subcellular, tissue, organ and whole-plant scales. This includes a focus on chloroplast and mitochondrial signalling, alternative splicing, long-distance circadian signalling and circadian regulation within natural environments. We also consider mathematical models for plant circadian regulation, to suggest future areas for advancing understanding of roles for circadian regulation in plant responses to environmental cues.

Magnesium maintains the length of the circadian period in Arabidopsis

The circadian clock coordinates the physiological responses of a biological system to day and night rhythms through complex loops of transcriptional/translational regulation. It can respond to external stimuli and adjust generated circadian oscillations accordingly to maintain an endogenous period close to 24 h. However, the interaction between nutritional status and circadian rhythms in plants is poorly understood. Magnesium (Mg) is essential for numerous biological processes in plants, and its homeostasis is crucial to maintain optimal development and growth. Magnesium deficiency in young Arabidopsis thaliana seedlings increased the period of circadian oscillations of the CIRCADIAN CLOCK-ASSOCIATED 1 (CCA1) promoter (pCCA1:LUC) activity and dampened their amplitude under constant light in a dose-dependent manner. Although the circadian period increase caused by Mg deficiency was light dependent, it did not depend on active photosynthesis. Mathematical modeling of the Mg input into the circadian clock reproduced the experimental increase of the circadian period and suggested that Mg is likely to affect global transcription/translation levels rather than a single component of the circadian oscillator. Upon addition of a low dose of cycloheximide to perturb translation, the circadian period increased further under Mg deficiency, which was rescued when sufficient Mg was supplied, supporting the model's prediction. These findings suggest that sufficient Mg supply is required to support proper timekeeping in plants.

A Computational Model for the Cold Response Pathway in Plants

Understanding the mechanism by which plants respond to cold stress and strengthen their tolerance to low temperatures is an important and challenging task in plant sciences. Experiments have established that the first step in the perception and transduction of the cold stress signal consists of a transient influx of Ca²⁺. This Ca²⁺ influx triggers the activation of a cascade of phosphorylation-dephosphorylation reactions that eventually affects the expression of C-repeat-binding factors (CBFs, notably CBF3), which were shown in many plants to control resistance to cold stress by regulating the expression of cold-regulated (COR) genes. Based on experimental observations mostly made on Arabidopsis thaliana, we build a computational model for the cold response pathway in plants, from the transduction of the cold signal via the transient influx of Ca²⁺ to the activation of the phosphorylation cascade leading to CBF3 expression. We explore the dynamics of this regulatory network by means of numerical simulations and compare the results with experimental observations on the dynamics of the cold response, both for the wild type and for mutants. The simulations show how, in response to cold stress, a brief Ca²⁺ influx, which is over in minutes, is transduced along the successive steps of the network to trigger the expression of cold response genes such as CBF3 within hours. Sometimes, instead of a single Ca²⁺ spike the decrease in temperature brings about a train of high-frequency Ca²⁺ oscillations. The model is applied to both types of Ca²⁺ signaling. We determine the dynamics of the network in response to a series of identical cold stresses, to account for the observation of desensitization and resensitization. The analysis of the model predicts the possibility of an oscillatory expression of CBF3 originating from the negative feedback exerted by ZAT12, a factor itself controlled by CBF3. Finally, we extend the model to incorporate the circadian control of CBF3 expression, to account for the gating of the response to cold stress by the plant circadian clock.

Early Detection of Daylengths with a Feedforward Circuit Coregulated by Circadian and Diurnal Cycles

Light-entrained circadian clocks confer rhythmic dynamics of cellular and molecular activities to animals and plants. These intrinsic clocks allow stable anticipations to light-dark (diel) cycles. Many genes in the model plant Arabidopsis thaliana are regulated by diel cycles via pathways independent of the clock, suggesting that the integration of circadian and light signals is important for the fitness of plants. Previous studies of light-clock signal integrations have focused on moderate phase adjustment of the two signals. However, dynamical features of integrations across a broad range of phases remain elusive. Phosphorylation of ribosomal protein of the small subunit 6 (eS6), a ubiquitous post-translational modification across kingdoms, is influenced by the circadian clock and the light-dark (diel) cycle in an opposite manner. To understand this striking phenomenon and its underlying information processing capabilities, we built a mathematical model for the eS6 phosphorylation (eS6-P) control circuit. We found that the dynamics of eS6-P can be explained by a feedforward circuit with inputs from both circadian and diel cycles. Furthermore, the early day response of this circuit with dual rhythmic inputs is sensitive to the changes in daylength, including both transient and gradual changes observed in realistic light intervals across a year, because of weather and seasons. By analyzing published gene expression data, we found that the dynamics produced by the eS6-P control circuit can be observed in the expression profiles of a large number of genes. Our work provides mechanistic insights into the complex dynamics of a ribosomal protein, and it proposes a previously underappreciated function of the circadian clock, which not only prepares organisms for normal diel cycles but also helps to detect both transient and seasonal changes with a predictive power.

Genome-wide analysis of PRR gene family uncovers their roles in circadian rhythmic changes and response to drought stress in Gossypium hirsutum L

BACKGROUND

The circadian clock not only participates in regulating various stages of plant growth, development and metabolism, but confers plant environmental adaptability to stress such as drought. Pseudo-Response Regulators (PRRs) are important component of the central oscillator (the core of circadian clock) and play a significant role in plant photoperiod pathway. However, no systematical study about this gene family has been performed in cotton.

METHODS

PRR genes were identified in diploid and tetraploid cotton using bioinformatics methods to investigate their homology, duplication and evolution relationship. Differential gene expression, KEGG enrichment analysis and qRT-PCR were conducted to analyze PRR gene expression patterns under diurnal changes and their response to drought stress.

RESULTS

A total of 44 PRR family members were identified in four Gossypium species, with 16 in G. hirsutum, 10 in G. raimondii, and nine in G. barbadense as well as in G. arboreum. Phylogenetic analysis indicated that PRR proteins were divided into five subfamilies and whole genome duplication or segmental duplication contributed to the expansion of Gossypium PRR gene family. Gene structure analysis revealed that members in the same clade are similar, and multiple cis-elements related to light and drought stress response were enriched in the promoters of GhPRR genes. qRT-PCR results showed that GhPRR genes transcripts presented four expression peaks (6 h, 9 h, 12 h, 15 h) during 24 h and form obvious rhythmic expression trend. Transcriptome data with PEG treatment, along with qRT-PCR verification suggested that members of clade III (GhPRR5a, b, d) and clade V (GhPRR3a and GhPRR3c) may be involved in drought response. This study provides an insight into understanding the function of PRR genes in circadian rhythm and in response to drought stress in cotton.

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

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.

Basal leakage in oscillation: Coupled transcriptional and translational control using feed-forward loops

The circadian clock is a complex system that plays many important roles in most organisms. Previously, many mathematical models have been used to sharpen our understanding of the Arabidopsis clock, which brought to light the roles of each transcriptional and post-translational regulations. However, the presence of both regulations, instead of either transcription or post-translation, raised curiosity of whether the combination of these two regulations is important for the clock’s system. In this study, we built a series of simplified oscillators with different regulations to study the importance of post-translational regulation (specifically, 26S proteasome degradation) in the clock system. We found that a simple transcriptional-based oscillator can already generate sustained oscillation, but the oscillation can be easily destroyed in the presence of transcriptional leakage. Coupling post-translational control with transcriptional-based oscillator in a feed-forward loop will greatly improve the robustness of the oscillator in the presence of basal leakage. Using these general models, we were able to replicate the increased variability observed in the E3 ligase mutant for both plant and mammalian clocks. With this insight, we also predict a plausible regulator of several E3 ligase genes in the plant’s clock. Thus, our results provide insights into and the plausible importance in coupling transcription and post-translation controls in the clock system.

For circadian clocks, several current models had successfully captured the essential dynamic behavior of the clock system mainly with transcriptional regulation. Previous studies have shown that the 26S proteasome degradation controls are important in maintaining the stability of circadian rhythms. However, how the loss-of-function or over-expression mutant of this targeted degradations lead to unstable oscillation is still unclear. In this work, we investigate the importance of coupled transcriptional and post-translational feedback loop in the circadian oscillator. With general models our study indicate that the unstable behavior of degradation mutants could be caused by the increase in the basal level of the clock genes. We found that coupling a non-linear degradation control into this transcriptional based oscillator using feed-forward loop improves the robustness of the oscillator. Using this finding, we further predict some plausible regulators of Arabidopsis’s E3 ligase protein such as COP1 and SINAT5. Hence, our results provide insights on the importance of coupling transcription and post-translation controls in the clock system.

Shade signals alter the expression of circadian clock genes in newly-formed bioenergy sorghum internodes

Stem internodes of bioenergy sorghum inbred R.07020 are longer at high plant density (shade) than at low plant density (control). Initially, the youngest newly-formed subapical stem internodes of shade-treated and control plants are comparable in length. However, full-length internodes of shade-treated plants are three times longer than the internodes of the control plants. To identify the early molecular events associated with internode elongation in response to shade, we analyzed the transcriptome of the newly-formed internodes of shade-treated and control plants sampled between 4 and 6 hr after the start of the light period (14 hr light/10 hr dark). Sorghum genes homologous to the Arabidopsis shade marker genes ATHB2 and PIL1 were not differentially expressed. The results indicate that shade signals promote internode elongation indirectly because sorghum internodes are not illuminated and grow while enclosed with leaf sheaths. Sorghum genes homologous to the Arabidopsis morning-phased circadian clock genes LHY, RVE, and LNK were downregulated and evening-phased genes such as TOC1, PRR5, and GI were upregulated in young internodes in response to shade. We hypothesize that a change in the function or patterns of expression of the circadian clock genes is the earliest molecular event associated with internode elongation in response to shade in bioenergy sorghum. Increased expression of CycD1, which promotes cell division, and decreased expression of cell wall-loosening and MBF1-like genes, which promote cell expansion, suggest that shade signals promote internode elongation in bioenergy sorghum in part through increasing cell number by delaying transition from cell division to cell expansion.

A simplified modelling framework facilitates more complex representations of plant circadian clocks

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach-and the concomitant problem of robustly identifying regulation types-has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits.

Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this "presumably transient" dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock.

Heat the Clock: Entrainment and Compensation in Arabidopsis Circadian Rhythms

The circadian clock is a biological mechanism that permits some organisms to anticipate daily environmental variations. This clock generates biological rhythms, which can be reset by environmental cues such as cycles of light or temperature, a process known as entrainment. After entrainment, circadian rhythms typically persist with approximately 24 hours periodicity in free-running conditions, i.e. in the absence of environmental cues. Experimental evidence also shows that a free-running period close to 24 hours is maintained across a range of temperatures, a process known as temperature compensation. In the plant Arabidopsis, the effect of light on the circadian system has been widely studied and successfully modelled mathematically. However, the role of temperature in periodicity, and the relationship between entrainment and compensation, are not fully understood. Here we adapt recent models to incorporate temperature dependence by applying Arrhenius equations to the parameters of the models that characterize transcription, translation, and degradation rates. We show that the resulting models can exhibit thermal entrainment and temperature compensation, but that these phenomena emerge from physiologically different sets of processes. Further simulations combining thermal and photic forcing in more realistic scenarios clearly distinguish between the processes of entrainment and compensation, and reveal temperature compensation as an emergent property which can arise as a result of multiple temperature-dependent interactions. Our results consistently point to the thermal sensitivity of degradation rates as driving compensation and entrainment across a range of conditions.

Inferring Gene Regulatory Networks from Multiple Datasets

Gaussian process dynamical systems (GPDS) represent Bayesian nonparametric approaches to inference of nonlinear dynamical systems, and provide a principled framework for the learning of biological networks from multiple perturbed time series measurements of gene or protein expression. Such approaches are able to capture the full richness of complex ODE models, and can be scaled for inference in moderately large systems containing hundreds of genes. Related hierarchical approaches allow for inference from multiple datasets in which the underlying generative networks are assumed to have been rewired, either by context-dependent changes in network structure, evolutionary processes, or synthetic manipulation. These approaches can also be used to leverage experimentally determined network structures from one species into another where the network structure is unknown. Collectively, these methods provide a comprehensive and flexible platform for inference from a diverse range of data, with applications in systems and synthetic biology, as well as spatiotemporal modelling of embryo development. In this chapter we provide an overview of GPDS approaches and highlight their applications in the biological sciences, with accompanying tutorials available as a Jupyter notebook from https://github.com/cap76/GPDS .

Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

A major bottleneck in the modelling of biological networks is the parameter explosion problem - the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently - reducing the number of parameters - whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.

ELONGATED HYPOCOTYL 5 mediates blue light signalling to the Arabidopsis circadian clock

Circadian clocks are gene networks producing 24-h oscillations at the level of clock gene expression that are synchronized to environmental cycles via light signals. The ELONGATED HYPOCOTYL 5 (HY5) transcription factor is a signalling hub acting downstream of several photoreceptors and is a key mediator of photomorphogenesis. Here we describe a mechanism by which light quality could modulate the pace of the circadian clock through governing abundance of HY5. We show that hy5 mutants display remarkably shorter period rhythms in blue but not in red light or darkness, and blue light is more efficient than red to induce accumulation of HY5 at transcriptional and post-transcriptional levels. We demonstrate that the pattern and level of HY5 accumulation modulates its binding to specific promoter elements of the majority of clock genes, but only a few of these show altered transcription in the hy5 mutant. Mathematical modelling suggests that the direct effect of HY5 on the apparently non-responsive clock genes could be masked by feedback from the clock gene network. We conclude that the information on the ratio of blue and red components of the white light spectrum is decoded and relayed to the circadian oscillator, at least partially, by HY5.

An incoherent feed-forward loop switches the Arabidopsis clock rapidly between two hysteretic states

In higher plants (e.g., Arabidopsis thaliana), the core structure of the circadian clock is mostly governed by a repression process with very few direct activators. With a series of simplified models, we studied the underlying mechanism and found that the Arabidopsis clock consists of type-2 incoherent feed-forward loops (IFFLs), one of them creating a pulse-like expression in PRR9/7. The double-negative feedback loop between CCA1/LHY and PRR5/TOC1 generates a bistable, hysteretic behavior in the Arabidopsis circadian clock. We found that the IFFL involving PRR9/7 breaks the bistability and moves the system forward with a rapid pulse in the daytime, and the evening complex (EC) breaks it in the evening. With this illustration, we can intuitively explain the behavior of the clock under mutant conditions. Thus, our results provide new insights into the underlying network structures of the Arabidopsis core oscillator.

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.

Circadian Rhythms and Redox State in Plants: Till Stress Do Us Part

A growing body of evidence demonstrates a significant relationship between cellular redox state and circadian rhythms. Each day these two vital components of plant biology influence one another, dictating the pace for metabolism and physiology. Diverse environmental stressors can disrupt this condition and, although plant scientists have made significant progress in re-constructing functional networks of plant stress responses, stress impacts on the clock-redox crosstalk is poorly understood. Inter-connected phenomena such as redox state and metabolism, internal and external environments, cellular homeostasis and rhythms can impede predictive understanding of coordinated regulation of plant stress response. The integration of circadian clock effects into predictive network models is likely to increase final yield and better predict plant responses to stress. To achieve such integrated understanding, it is necessary to consider the internal clock not only as a gatekeeper of environmental responses but also as a target of stress syndromes. Using chlorophyll fluorescence as a reliable and high-throughput probe of stress coupled to functional genomics and metabolomics will provide insights on the crosstalk across a wide range of stress severity and duration, including potential insights into oxidative stress response and signaling. We suggest the efficiency of photosystem II in light conditions (Fv'/Fm') to be the most dynamic of the fluorescence variables and therefore the most reliable parameter to follow the stress response from early sensing to mortality.

Photosynthetic Entrainment of the Circadian Clock Facilitates Plant Growth under Environmental Fluctuations: Perspectives from an Integrated Model of Phase Oscillator and Phloem Transportation

Plants need to avoid carbon starvation and resultant growth inhibition under fluctuating light environments to ensure optimal growth and reproduction. As diel patterns of carbon metabolism are influenced by the circadian clock, appropriate regulation of the clock is essential for plants to properly manage their carbon resources. For proper adjustment of the circadian phase, higher plants utilize environmental signals such as light or temperature and metabolic signals such as photosynthetic products; the importance of the latter as phase regulators has been recently elucidated. A mutant of Arabidopsis thaliana that is deficient in phase response to sugar has been shown, under fluctuating light conditions, to be unable to adjust starch turnover and to realize carbon homeostasis. Whereas, the effects of light entrainment on growth and survival of higher plants are well studied, the impact of phase regulation by sugar remains unknown. Here we show that endogenous sugar entrainment facilitates plant growth. We integrated two mathematical models, one describing the dynamics of carbon metabolism in A. thaliana source leaves and the other growth of sink tissues dependent on sucrose translocation from the source. The integrated model predicted that sugar-sensitive plants grow faster than sugar-insensitive plants under constant as well as changing photoperiod conditions. We found that sugar entrainment enables efficient carbon investment for growth by stabilizing sucrose supply to sink tissues. Our results highlight the importance of clock entrainment by both exogenous and endogenous signals for optimizing growth and increasing fitness.

Exploring candidate biological functions by Boolean Function Networks for Saccharomyces cerevisiae

The great amount of gene expression data has brought a big challenge for the discovery of Gene Regulatory Network (GRN). For network reconstruction and the investigation of regulatory relations, it is desirable to ensure directness of links between genes on a map, infer their directionality and explore candidate biological functions from high-throughput transcriptomic data. To address these problems, we introduce a Boolean Function Network (BFN) model based on techniques of hidden Markov model (HMM), likelihood ratio test and Boolean logic functions. BFN consists of two consecutive tests to establish links between pairs of genes and check their directness. We evaluate the performance of BFN through the application to S. cerevisiae time course data. BFN produces regulatory relations which show consistency with succession of cell cycle phases. Furthermore, it also improves sensitivity and specificity when compared with alternative methods of genetic network reverse engineering. Moreover, we demonstrate that BFN can provide proper resolution for GO enrichment of gene sets. Finally, the Boolean functions discovered by BFN can provide useful insights for the identification of control mechanisms of regulatory processes, which is the special advantage of the proposed approach. In combination with low computational complexity, BFN can serve as an efficient screening tool to reconstruct genes relations on the whole genome level. In addition, the BFN approach is also feasible to a wide range of time course datasets.

Early evolution of the land plant circadian clock

While angiosperm clocks can be described as an intricate network of interlocked transcriptional feedback loops, clocks of green algae have been modelled as a loop of only two genes. To investigate the transition from a simple clock in algae to a complex one in angiosperms, we performed an inventory of circadian clock genes in bryophytes and charophytes. Additionally, we performed functional characterization of putative core clock genes in the liverwort Marchantia polymorpha and the hornwort Anthoceros agrestis. Phylogenetic construction was combined with studies of spatiotemporal expression patterns and analysis of M. polymorpha clock gene mutants. Homologues to core clock genes identified in Arabidopsis were found not only in bryophytes but also in charophytes, albeit in fewer copies. Circadian rhythms were detected for most identified genes in M. polymorpha and A. agrestis, and mutant analysis supports a role for putative clock genes in M. polymorpha. Our data are in line with a recent hypothesis that adaptation to terrestrial life occurred earlier than previously expected in the evolutionary history of charophyte algae. Both gene duplication and acquisition of new genes was important in the evolution of the plant circadian clock, but gene loss has also contributed to shaping the clock of bryophytes.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.

Kinetics of the LOV domain of ZEITLUPE determine its circadian function in Arabidopsis

A LOV (Light, Oxygen, or Voltage) domain containing blue-light photoreceptor ZEITLUPE (ZTL) directs circadian timing by degrading clock proteins in plants. Functions hinge upon allosteric differences coupled to the ZTL photocycle; however, structural and kinetic information was unavailable. Herein, we tune the ZTL photocycle over two orders of magnitude. These variants reveal that ZTL complexes with targets independent of light, but dictates enhanced protein degradation in the dark. In vivo experiments definitively show photocycle kinetics dictate the rate of clock component degradation, thereby impacting circadian period. Structural studies demonstrate that photocycle dependent activation of ZTL depends on an unusual dark-state conformation of ZTL. Crystal structures of ZTL LOV domain confirm delineation of structural and kinetic mechanisms and identify an evolutionarily selected allosteric hinge differentiating modes of PAS/LOV signal transduction. The combined biochemical, genetic and structural studies provide new mechanisms indicating how PAS/LOV proteins integrate environmental variables in complex networks.

Diurnal Transcriptome and Gene Network Represented through Sparse Modeling in Brachypodium distachyon

We report the comprehensive identification of periodic genes and their network inference, based on a gene co-expression analysis and an Auto-Regressive eXogenous (ARX) model with a group smoothly clipped absolute deviation (SCAD) method using a time-series transcriptome dataset in a model grass, Brachypodium distachyon. To reveal the diurnal changes in the transcriptome in B. distachyon, we performed RNA-seq analysis of its leaves sampled through a diurnal cycle of over 48 h at 4 h intervals using three biological replications, and identified 3,621 periodic genes through our wavelet analysis. The expression data are feasible to infer network sparsity based on ARX models. We found that genes involved in biological processes such as transcriptional regulation, protein degradation, and post-transcriptional modification and photosynthesis are significantly enriched in the periodic genes, suggesting that these processes might be regulated by circadian rhythm in B. distachyon. On the basis of the time-series expression patterns of the periodic genes, we constructed a chronological gene co-expression network and identified putative transcription factors encoding genes that might be involved in the time-specific regulatory transcriptional network. Moreover, we inferred a transcriptional network composed of the periodic genes in B. distachyon, aiming to identify genes associated with other genes through variable selection by grouping time points for each gene. Based on the ARX model with the group SCAD regularization using our time-series expression datasets of the periodic genes, we constructed gene networks and found that the networks represent typical scale-free structure. Our findings demonstrate that the diurnal changes in the transcriptome in B. distachyon leaves have a sparse network structure, demonstrating the spatiotemporal gene regulatory network over the cyclic phase transitions in B. distachyon diurnal growth.