Coordinated circadian timing through the integration of local inputs in Arabidopsis thaliana.

Individual plant cells have a genetic circuit, the circadian clock, that times key processes to the day-night cycle. These clocks are aligned to the day-night cycle by multiple environmental signals that vary across the plant. How does the plant integrate clock rhythms, both within and between organs, to ensure coordinated timing? To address this question, we examined the clock at the sub-tissue level across Arabidopsis thaliana seedlings under multiple environmental conditions and genetic backgrounds. Our results show that the clock runs at different speeds (periods) in each organ, which causes the clock to peak at different times across the plant in both constant environmental conditions and light-dark (LD) cycles. Closer examination reveals that spatial waves of clock gene expression propagate both within and between organs. Using a combination of modeling and experiment, we reveal that these spatial waves are the result of the period differences between organs and local coupling, rather than long-distance signaling. With further experiments we show that the endogenous period differences, and thus the spatial waves, can be generated by the organ specificity of inputs into the clock. We demonstrate this by modulating periods using light and metabolic signals, as well as with genetic perturbations. Our results reveal that plant clocks can be set locally by organ-specific inputs but coordinated globally via spatial waves of clock gene expression.

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.

PeTTSy: a computational tool for perturbation analysis of complex systems biology models.

BACKGROUND: Over the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary. RESULTS: Here we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems. To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters. CONCLUSIONS: PeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.

Network balance via CRY signalling controls the Arabidopsis circadian clock over ambient temperatures.

Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature-dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature-compensated clock model by adding passive temperature effects into only the light-sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature-dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems-level understanding of period control in the plant circadian oscillator.

The interaction graph structure of mass-action reaction networks.

Behaviour of chemical networks that are described by systems of ordinary differential equations can be analysed via the associated graph structures. This paper deals with observations based on the interaction graph which is defined by the signs of the Jacobian matrix entries. Some of the important graph structures linked to network dynamics are signed circuits and the nucleus (or Hamiltonian hooping). We use mass-action chemical reaction networks as an example to showcase interesting observations about the aforementioned interaction graph structures. We show that positive circuits and specific nucleus structures (associated to multistationarity) are always present in a great generic class of mass-action chemical and biological networks. The theory of negative circuits remains poorly understood, but there is some evidence that they are indicators of stable periodicity. Here we introduce the concept of non-isolated circuits which indicate the presence of a negative circuit.

Fine tuning of hormonal signaling is linked to dormancy status in sweet cherry flower buds.

In temperate trees, optimal timing and quality of flowering directly depend on adequate winter dormancy progression, regulated by a combination of chilling and warm temperatures. Physiological, genetic and functional genomic studies have shown that hormones play a key role in bud dormancy establishment, maintenance and release. We combined physiological and transcriptional analyses, quantification of abscisic acid (ABA) and gibberellins (GAs), and modeling to further investigate how these signaling pathways are associated with dormancy progression in the flower buds of two sweet cherry cultivars. Our results demonstrated that GA-associated pathways have distinct functions and may be differentially related with dormancy. In addition, ABA levels rise at the onset of dormancy, associated with enhanced expression of ABA biosynthesis PavNCED genes, and decreased prior to dormancy release. Following the observations that ABA levels are correlated with dormancy depth, we identified PavUG71B6, a sweet cherry UDP-GLYCOSYLTRANSFERASE gene that up-regulates active catabolism of ABA to ABA glucosyl ester (ABA-GE) and may be associated with low ABA content in the early cultivar. Subsequently, we modeled ABA content and dormancy behavior in three cultivars based on the expression of a small set of genes regulating ABA levels. These results strongly suggest the central role of ABA pathway in the control of dormancy progression and open up new perspectives for the development of molecular-based phenological modeling.

Bistability and oscillations in chemical reaction networks.

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461-3470, 1987; Clarke and Jiang in J Chem Phys 99:4464-4476, 1993; Gatermann et al. in J Symb Comput 40:1361-1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks.

Coordination of robust single cell rhythms in the Arabidopsis circadian clock via spatial waves of gene expression.

The Arabidopsis circadian clock orchestrates gene regulation across the day/night cycle. Although a multiple feedback loop circuit has been shown to generate the 24-hr rhythm, it remains unclear how robust the clock is in individual cells, or how clock timing is coordinated across the plant. Here we examine clock activity at the single cell level across Arabidopsis seedlings over several days under constant environmental conditions. Our data reveal robust single cell oscillations, albeit desynchronised. In particular, we observe two waves of clock activity; one going down, and one up the root. We also find evidence of cell-to-cell coupling of the clock, especially in the root tip. A simple model shows that cell-to-cell coupling and our measured period differences between cells can generate the observed waves. Our results reveal the spatial structure of the plant clock and suggest that unlike the centralised mammalian clock, the Arabidopsis clock has multiple coordination points.

Phytochromes function as thermosensors in Arabidopsis.

Plants are responsive to temperature, and some species can distinguish differences of 1°C. In Arabidopsis, warmer temperature accelerates flowering and increases elongation growth (thermomorphogenesis). However, the mechanisms of temperature perception are largely unknown. We describe a major thermosensory role for the phytochromes (red light receptors) during the night. Phytochrome null plants display a constitutive warm-temperature response, and consistent with this, we show in this background that the warm-temperature transcriptome becomes derepressed at low temperatures. We found that phytochrome B (phyB) directly associates with the promoters of key target genes in a temperature-dependent manner. The rate of phyB inactivation is proportional to temperature in the dark, enabling phytochromes to function as thermal timers that integrate temperature information over the course of the night.

Using constraints and their value for optimization of large ODE systems.

We provide analytical tools to facilitate a rigorous assessment of the quality and value of the fit of a complex model to data. We use this to provide approaches to model fitting, parameter estimation, the design of optimization functions and experimental optimization. This is in the context where multiple constraints are used to select or optimize a large model defined by differential equations. We illustrate the approach using models of circadian clocks and the NF-κB signalling system.

ELF3 controls thermoresponsive growth in Arabidopsis.

Plant development is highly responsive to ambient temperature, and this trait has been linked to the ability of plants to adapt to climate change. The mechanisms by which natural populations modulate their thermoresponsiveness are not known. To address this, we surveyed Arabidopsis accessions for variation in thermal responsiveness of elongation growth and mapped the corresponding loci. We find that the transcriptional regulator EARLY FLOWERING3 (ELF3) controls elongation growth in response to temperature. Through a combination of modeling and experiments, we show that high temperature relieves the gating of growth at night, highlighting the importance of temperature-dependent repressors of growth. ELF3 gating of transcriptional targets responds rapidly and reversibly to changes in temperature. We show that the binding of ELF3 to target promoters is temperature dependent, suggesting a mechanism where temperature directly controls ELF3 activity.

Balance equations can buffer noisy and sustained environmental perturbations of circadian clocks.

We present a new approach to understanding how regulatory networks such as circadian clocks might evolve robustness to environmental fluctuations. The approach is in terms of new balance equations that we derive. We use it to describe how an entrained clock can buffer the effects of daily fluctuations in light and temperature levels. We also use it to study a different approach to temperature compensation where instead of considering a free-running clock, we study temperature buffering of the phases in a light-entrained clock, which we believe is a more physiological setting.