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

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.

Unlocking Nature's Rhythms: Insights into Secondary Metabolite Modulation by the Circadian Clock

Plants, like many other living organisms, have an internal timekeeper, the circadian clock, which allows them to anticipate photoperiod rhythms and environmental stimuli to optimally adjust plant growth, development, and fitness. These fine-tuned processes depend on the interaction between environmental signals and the internal interactive metabolic network regulated by the circadian clock. Although primary metabolites have received significant attention, the impact of the circadian clock on secondary metabolites remains less explored. Transcriptome analyses revealed that many genes involved in secondary metabolite biosynthesis exhibit diurnal expression patterns, potentially enhancing stress tolerance. Understanding the interaction mechanisms between the circadian clock and secondary metabolites, including plant defense mechanisms against stress, may facilitate the development of stress-resilient crops and enhance targeted management practices that integrate circadian agricultural strategies, particularly in the face of climate change. In this review, we will delve into the molecular mechanisms underlying circadian rhythms of phenolic compounds, terpenoids, and N-containing compounds.

The distribution of fitness effects during adaptive walks using a simple genetic network

The tempo and mode of adaptation depends on the availability of beneficial alleles. Genetic interactions arising from gene networks can restrict this availability. However, the extent to which networks affect adaptation remains largely unknown. Current models of evolution consider additive genotype-phenotype relationships while often ignoring the contribution of gene interactions to phenotypic variance. In this study, we model a quantitative trait as the product of a simple gene regulatory network, the negative autoregulation motif. Using forward-time genetic simulations, we measure adaptive walks towards a phenotypic optimum in both additive and network models. A key expectation from adaptive walk theory is that the distribution of fitness effects of new beneficial mutations is exponential. We found that both models instead harbored distributions with fewer large-effect beneficial alleles than expected. The network model also had a complex and bimodal distribution of fitness effects among all mutations, with a considerable density at deleterious selection coefficients. This behavior is reminiscent of the cost of complexity, where correlations among traits constrain adaptation. Our results suggest that the interactions emerging from genetic networks can generate complex and multimodal distributions of fitness effects.

Unlocking allelic variation in circadian clock genes to develop environmentally robust and productive crops

MAIN CONCLUSION

Molecular mechanisms of biological rhythms provide opportunities to harness functional allelic diversity in core (and trait- or stress-responsive) oscillator networks to develop more climate-resilient and productive germplasm. The circadian clock senses light and temperature in day-night cycles to drive biological rhythms. The clock integrates endogenous signals and exogenous stimuli to coordinate diverse physiological processes. Advances in high-throughput non-invasive assays, use of forward- and inverse-genetic approaches, and powerful algorithms are allowing quantitation of variation and detection of genes associated with circadian dynamics. Circadian rhythms and phytohormone pathways in response to endogenous and exogenous cues have been well documented the model plant Arabidopsis. Novel allelic variation associated with circadian rhythms facilitates adaptation and range expansion, and may provide additional opportunity to tailor climate-resilient crops. The circadian phase and period can determine adaptation to environments, while the robustness in the circadian amplitude can enhance resilience to environmental changes. Circadian rhythms in plants are tightly controlled by multiple and interlocked transcriptional-translational feedback loops involving morning (CCA1, LHY), mid-day (PRR9, PRR7, PRR5), and evening (TOC1, ELF3, ELF4, LUX) genes that maintain the plant circadian clock ticking. Significant progress has been made to unravel the functions of circadian rhythms and clock genes that regulate traits, via interaction with phytohormones and trait-responsive genes, in diverse crops. Altered circadian rhythms and clock genes may contribute to hybrid vigor as shown in Arabidopsis, maize, and rice. Modifying circadian rhythms via transgenesis or genome-editing may provide additional opportunities to develop crops with better buffering capacity to environmental stresses. Models that involve clock gene‒phytohormone‒trait interactions can provide novel insights to orchestrate circadian rhythms and modulate clock genes to facilitate breeding of all season crops.

A gene regulatory network critical for axillary bud dormancy directly controlled by Arabidopsis BRANCHED1

The Arabidopsis thaliana transcription factor BRANCHED1 (BRC1) plays a pivotal role in the control of shoot branching as it integrates environmental and endogenous signals that influence axillary bud growth. Despite its remarkable activity as a growth inhibitor, the mechanisms by which BRC1 promotes bud dormancy are largely unknown. We determined the genome-wide BRC1 binding sites in vivo and combined these with transcriptomic data and gene co-expression analyses to identify bona fide BRC1 direct targets. Next, we integrated multi-omics data to infer the BRC1 gene regulatory network (GRN) and used graph theory techniques to find network motifs that control the GRN dynamics. We generated an open online tool to interrogate this network. A group of BRC1 target genes encoding transcription factors (BTFs) orchestrate this intricate transcriptional network enriched in abscisic acid-related components. Promoter::β-GLUCURONIDASE transgenic lines confirmed that BTFs are expressed in axillary buds. Transient co-expression assays and studies in planta using mutant lines validated the role of BTFs in modulating the GRN and promoting bud dormancy. This knowledge provides access to the developmental mechanisms that regulate shoot branching and helps identify candidate genes to use as tools to adapt plant architecture and crop production to ever-changing environmental conditions.

The 1972 Meadows report: A wake-up call for plant science

The 1972 Meadows report, 'the limits to growth', predicted a global socio-economic tipping point during the twenty-first century. Now supported by 50 years of empirical evidence, this work is a tribute to systems thinking and an invitation to take the current environmental crisis for what it is: neither a transition nor a bifurcation, but an inversion. For instance, we used matter (e.g., fossil fuel) to save time; we will use time to preserve matter (e.g., bioeconomy). We were exploiting ecosystems to fuel production; production will feed ecosystems. We centralised to optimise; we will decentralise to support resilience. In plant science, this new context calls for new research on plant complexity (e.g., multiscale robustness and benefits of variability), also extending to new scientific approaches (e.g., participatory research, art and science). Taking this turn reverses many paradigms and becomes a new responsibility for plant scientists as the world becomes increasingly turbulent.

Localization of Noise in Biochemical Networks

Noise, or uncertainty in biochemical networks, has become an important aspect of many biological problems. Noise can arise and propagate from external factors and probabilistic chemical reactions occurring in small cellular compartments. For species survival, it is important to regulate such uncertainties in executing vital cell functions. Regulated noise can improve adaptability, whereas uncontrolled noise can cause diseases. Simulation can provide a detailed analysis of uncertainties, but parameters such as rate constants and initial conditions are usually unknown. A general understanding of noise dynamics from the perspective of network structure is highly desirable. In this study, we extended the previously developed law of localization for characterizing noise in terms of (co)variances and developed noise localization theory. With linear noise approximation, we can expand a biochemical network into an extended set of differential equations representing a fictitious network for pseudo-components consisting of variances and covariances, together with chemical species. Through localization analysis, perturbation responses at the steady state of pseudo-components can be summarized into a sensitivity matrix that only requires knowledge of network topology. Our work allows identification of buffering structures at the level of species, variances, and covariances and can provide insights into noise flow under non-steady-state conditions in the form of a pseudo-chemical reaction. We tested noise localization in various systems, and here we discuss its implications and potential applications. Results show that this theory is potentially applicable in discriminating models, scanning network topologies with interesting noise behavior, and designing and perturbing networks with the desired response.

AGENT for Exploring and Analyzing Gene Regulatory Networks from Arabidopsis

Gene regulatory networks (GRNs) are important for determining how an organism develops and how it responds to external stimuli. In the case of Arabidopsis thaliana, several GRNs have been identified covering many important biological processes. We present AGENT, the Arabidopsis GEne Network Tool, for exploring and analyzing published GRNs. Using tools in AGENT, regulatory motifs such as feed-forward loops can be easily identified. Nodes with high centrality-and hence importance-can likewise be identified. Gene expression data can also be overlaid onto GRNs to help discover subnetworks acting in specific tissues or under certain conditions.

WRKY2 and WRKY10 regulate the circadian expression of PIF4 during the day through interactions with CCA1/LHY and phyB

WRKY transcription factors are known mostly for their function in plant defense, abiotic stress responses, senescence, seed germination, and development of the pollen, embryo, and seed. Here, we report the regulatory functions of two WRKY proteins in photomorphogenesis and PIF4 expression. PIF4 is a critical signaling hub in light, temperature, and hormonal signaling pathways. Either its expression or its accumulation peaks in the morning and afternoon. WRKY2 and WRKY10 form heterodimers and recognize their target site in the PIF4 promoter near the MYB element that is bound by CCA1 and LHY under red and blue light. WRKY2 and WRKY10 interact directly with CCA1/LHY to enhance their targeting but interact indirectly with SHB1. The two WRKY proteins also interact with phyB, and their interaction enhances the targeting of CCA1 and LHY to the PIF4 promoter. SHB1 associates with the WRKY2 and WRKY10 loci and enhances their expression in parallel with the PIF4 expression peaks. This forward regulatory loop further sustains the accumulation of the two WRKY proteins and the targeting of CCA1/LHY to the PIF4 locus. In summary, interactions of two WRKY proteins with CCA1/LHY and phyB maintain an optimal expression level of PIF4 toward noon and afternoon, which is essential to sketch the circadian pattern of PIF4 expression.

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.

Noise suppression in stochastic genetic circuits using PID controllers

Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. We investigate the effectiveness of proportional, integral and derivative (PID) based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as PID controllers are discussed, with particular focus on individual controllers separately, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances, particularly when the disturbance comes at low frequencies. Counter-intuitively, integral feedback is found to amplify external disturbances at intermediate frequencies. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis using both analytical methods and Monte Carlo simulations reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

In the noisy cellular environment, biochemical species such as genes, RNAs and proteins that often occur at low molecular counts, are subject to considerable stochastic fluctuations in copy numbers over time. How cellular biochemical processes function reliably in the face of such randomness is an intriguing fundamental problem. Increasing evidence suggests that random fluctuations (noise) in protein copy numbers play important functional roles, such as driving genetically identical cells to different cell fates. Moreover, many disease states have been attributed to elevated noise levels in specific proteins. Here we systematically investigate design of biochemical systems that function as proportional, integral and derivative-based feedback controllers to suppress protein count fluctuations arising from bursty expression of the protein and external disturbance in protein synthesis. Our results show that different controllers are effective in buffering different noise components, and identify ranges of feedback gain for minimizing deleterious fluctuations in protein levels.

A KMT2A-AFF1 gene regulatory network highlights the role of core transcription factors and reveals the regulatory logic of key downstream target genes

Regulatory interactions mediated by transcription factors (TFs) make up complex networks that control cellular behavior. Fully understanding these gene regulatory networks (GRNs) offers greater insight into the consequences of disease-causing perturbations than can be achieved by studying single TF binding events in isolation. Chromosomal translocations of the lysine methyltransferase 2A (KMT2A) gene produce KMT2A fusion proteins such as KMT2A-AFF1 (previously MLL-AF4), causing poor prognosis acute lymphoblastic leukemias (ALLs) that sometimes relapse as acute myeloid leukemias (AMLs). KMT2A-AFF1 drives leukemogenesis through direct binding and inducing the aberrant overexpression of key genes, such as the anti-apoptotic factor BCL2 and the proto-oncogene MYC However, studying direct binding alone does not incorporate possible network-generated regulatory outputs, including the indirect induction of gene repression. To better understand the KMT2A-AFF1-driven regulatory landscape, we integrated ChIP-seq, patient RNA-seq, and CRISPR essentiality screens to generate a model GRN. This GRN identified several key transcription factors such as RUNX1 that regulate target genes downstream of KMT2A-AFF1 using feed-forward loop (FFL) and cascade motifs. A core set of nodes are present in both ALL and AML, and CRISPR screening revealed several factors that help mediate response to the drug venetoclax. Using our GRN, we then identified a KMT2A-AFF1:RUNX1 cascade that represses CASP9, as well as KMT2A-AFF1-driven FFLs that regulate BCL2 and MYC through combinatorial TF activity. This illustrates how our GRN can be used to better connect KMT2A-AFF1 behavior to downstream pathways that contribute to leukemogenesis, and potentially predict shifts in gene expression that mediate drug response.

How Retroactivity Affects the Behavior of Incoherent Feedforward Loops

An incoherent feedforward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. It remains an open question to understand the behavior of IFFLs in contexts with high levels of retroactivity, where an upstream transcription factor binds to numerous downstream binding sites. Here we study the behavior of IFFLs by simulating and comparing ODE models with different levels of retroactivity. We find that increasing retroactivity in an IFFL can increase, decrease, or keep the network's response time and pulse amplitude constant. This suggests that increasing retroactivity, traditionally considered an impediment to designing robust synthetic systems, could be exploited to improve the performance of IFFLs. In contrast, we find that increasing retroactivity in a negative autoregulated circuit can only slow the response. The ability of an IFFL to flexibly handle retroactivity may have contributed to its significant abundance in both bacterial and eukaryotic regulatory networks.

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.

Gene Regulatory Network Inference: Connecting Plant Biology and Mathematical Modeling

Plant responses to environmental and intrinsic signals are tightly controlled by multiple transcription factors (TFs). These TFs and their regulatory connections form gene regulatory networks (GRNs), which provide a blueprint of the transcriptional regulations underlying plant development and environmental responses. This review provides examples of experimental methodologies commonly used to identify regulatory interactions and generate GRNs. Additionally, this review describes network inference techniques that leverage gene expression data to predict regulatory interactions. These computational and experimental methodologies yield complex networks that can identify new regulatory interactions, driving novel hypotheses. Biological properties that contribute to the complexity of GRNs are also described in this review. These include network topology, network size, transient binding of TFs to DNA, and competition between multiple upstream regulators. Finally, this review highlights the potential of machine learning approaches to leverage gene expression data to predict phenotypic outputs.

Light Perception: A Matter of Time

Optimizing the perception of external cues and regulating physiology accordingly help plants to cope with the constantly changing environmental conditions to which they are exposed. An array of photoreceptors and intricate signaling pathways allow plants to convey the surrounding light information and synchronize an endogenous timekeeping system known as the circadian clock. This biological clock integrates multiple cues to modulate a myriad of downstream responses, timing them to occur at the best moment of the day and the year. Notably, the mechanism underlying entrainment of the light-mediated clock is not clear. This review addresses known interactions between the light-signaling and circadian-clock networks, focusing on the role of light in clock entrainment and known molecular players in this process.

Hierarchical and Dynamic Regulation of Defense-Responsive Specialized Metabolism by WRKY and MYB Transcription Factors

The plant kingdom produces hundreds of thousands of specialized bioactive metabolites, some with pharmaceutical and biotechnological importance. Their biosynthesis and function have been studied for decades, but comparatively less is known about how transcription factors with overlapping functions and contrasting regulatory activities coordinately control the dynamics and output of plant specialized metabolism. Here, we performed temporal studies on pathogen-infected intact host plants with perturbed transcription factors. We identified WRKY33 as the condition-dependent master regulator and MYB51 as the dual functional regulator in a hierarchical gene network likely responsible for the gene expression dynamics and metabolic fluxes in the camalexin and 4-hydroxy-indole-3-carbonylnitrile (4OH-ICN) pathways. This network may have also facilitated the regulatory capture of the newly evolved 4OH-ICN pathway in Arabidopsis thaliana by the more-conserved transcription factor MYB51. It has long been held that the plasticity of plant specialized metabolism and the canalization of development should be differently regulated; our findings imply a common hierarchical regulatory architecture orchestrated by transcription factors for specialized metabolism and development, making it an attractive target for metabolic engineering.

Continuous dynamic adjustment of the plant circadian oscillator

The clockwork of plant circadian oscillators has been resolved through investigations in Arabidopsis thaliana. The circadian oscillator is an important regulator of much of plant physiology, though many of the mechanisms are unclear. New findings demonstrate that the oscillator adjusts phase and period in response to abiotic and biotic signals, providing insight in to how the plant circadian oscillator integrates with the biology of the cell and entrains to light, dark and temperature cycles. We propose that the plant circadian oscillator is dynamically plastic, in constant adjustment, rather than being an isolated clock impervious to cellular events.

Dynamical differential expression (DyDE) reveals the period control mechanisms of the Arabidopsis circadian oscillator

The circadian oscillator, an internal time-keeping device found in most organisms, enables timely regulation of daily biological activities by maintaining synchrony with the external environment. The mechanistic basis underlying the adjustment of circadian rhythms to changing external conditions, however, has yet to be clearly elucidated. We explored the mechanism of action of nicotinamide in Arabidopsis thaliana, a metabolite that lengthens the period of circadian rhythms, to understand the regulation of circadian period. To identify the key mechanisms involved in the circadian response to nicotinamide, we developed a systematic and practical modeling framework based on the identification and comparison of gene regulatory dynamics. Our mathematical predictions, confirmed by experimentation, identified key transcriptional regulatory mechanisms of circadian period and uncovered the role of blue light in the response of the circadian oscillator to nicotinamide. We suggest that our methodology could be adapted to predict mechanisms of drug action in complex biological systems.