The molecular genetics of circadian rhythms in Arabidopsis

Deciphering the Dynamics of Interlocked Feedback Loops in a Model of the Mammalian Circadian Clock

Mathematical models of fundamental biological processes play an important role in consolidating theory and experiments, especially if they are systematically developed, thoroughly characterized, and well tested by experimental data. In this work, we report a detailed bifurcation analysis of a mathematical model of the mammalian circadian clock network developed by Relógio et al., noteworthy for its consistency with available data. Using one- and two-parameter bifurcation diagrams, we explore how oscillations in the model depend on the expression levels of its constituent genes and the activities of their encoded proteins. These bifurcation diagrams allow us to decipher the dynamics of interlocked feedback loops by parametric variation of genes and proteins in the model. Among other results, we find that REV-ERB, a member of a subfamily of orphan nuclear receptors, plays a critical role in the intertwined dynamics of Relógio's model. The bifurcation diagrams reported here can be used for predicting how the core clock network responds-in terms of period, amplitude and phases of oscillations-to different perturbations.

RNA around the clock - regulation at the RNA level in biological timing

The circadian timing system in plants synchronizes their physiological functions with the environment. This is achieved by a global control of gene expression programs with a considerable part of the transcriptome undergoing 24-h oscillations in steady-state abundance. These circadian oscillations are driven by a set of core clock proteins that generate their own 24-h rhythm through periodic feedback on their own transcription. Additionally, post-transcriptional events are instrumental for oscillations of core clock genes and genes in clock output. Here we provide an update on molecular events at the RNA level that contribute to the 24-h rhythm of the core clock proteins and shape the circadian transcriptome. We focus on the circadian system of the model plant Arabidopsis thaliana but also discuss selected regulatory principles in other organisms.

Tuning the mammalian circadian clock: robust synergy of two loops

The circadian clock is accountable for the regulation of internal rhythms in most living organisms. It allows the anticipation of environmental changes during the day and a better adaptation of physiological processes. In mammals the main clock is located in the suprachiasmatic nucleus (SCN) and synchronizes secondary clocks throughout the body. Its molecular constituents form an intracellular network which dictates circadian time and regulates clock-controlled genes. These clock-controlled genes are involved in crucial biological processes including metabolism and cell cycle regulation. Its malfunction can lead to disruption of biological rhythms and cause severe damage to the organism. The detailed mechanisms that govern the circadian system are not yet completely understood. Mathematical models can be of great help to exploit the mechanism of the circadian circuitry. We built a mathematical model for the core clock system using available data on phases and amplitudes of clock components obtained from an extensive literature search. This model was used to answer complex questions for example: how does the degradation rate of Per affect the period of the system and what is the role of the ROR/Bmal/REV-ERB (RBR) loop? Our findings indicate that an increase in the RNA degradation rate of the clock gene Period (Per) can contribute to increase or decrease of the period--a consequence of a non-monotonic effect of Per transcript stability on the circadian period identified by our model. Furthermore, we provide theoretical evidence for a potential role of the RBR loop as an independent oscillator. We carried out overexpression experiments on members of the RBR loop which lead to loss of oscillations consistent with our predictions. These findings challenge the role of the RBR loop as a merely auxiliary loop and might change our view of the clock molecular circuitry and of the function of the nuclear receptors (REV-ERB and ROR) as a putative driving force of molecular oscillations.

Consistent robustness analysis (CRA) identifies biologically relevant properties of regulatory network models

BACKGROUND

A number of studies have previously demonstrated that "goodness of fit" is insufficient in reliably classifying the credibility of a biological model. Robustness and/or sensitivity analysis is commonly employed as a secondary method for evaluating the suitability of a particular model. The results of such analyses invariably depend on the particular parameter set tested, yet many parameter values for biological models are uncertain.

RESULTS

Here, we propose a novel robustness analysis that aims to determine the "common robustness" of the model with multiple, biologically plausible parameter sets, rather than the local robustness for a particular parameter set. Our method is applied to two published models of the Arabidopsis circadian clock (the one-loop [1] and two-loop [2] models). The results reinforce current findings suggesting the greater reliability of the two-loop model and pinpoint the crucial role of TOC1 in the circadian network.

CONCLUSIONS

Consistent Robustness Analysis can indicate both the relative plausibility of different models and also the critical components and processes controlling each model.

Constitutive expression of CIR1 (RVE2) affects several circadian-regulated processes and seed germination in Arabidopsis

Circadian clocks are endogenous auto-regulatory mechanisms that allow organisms, from bacteria to humans, to advantageously time a wide range of activities within 24 h environmental cycles. Here we report the identification and characterization of an MYB-related gene, designated Circadian 1 (CIR1), that is involved in circadian regulation in Arabidopsis. Expression of CIR1 is transiently induced by light and oscillates with a circadian rhythm. The rhythmic expression of CIR1 is controlled by the central oscillator. Constitutive expression of CIR1 resulted in a shorter period length for the rhythms of four central oscillator components, and much lower amplitude for the rhythms of central oscillator components CCA1 and LHY. Furthermore, CIR1 over-expression severely affected the circadian rhythms of its own RNA and those of the slave oscillator EPR1 and effector genes Lhcb and CAT3. Plants that constitutively expressed CIR1 displayed delayed flowering, longer hypocotyls and reduced seed germination in the dark. These results suggest that CIR1 is possibly part of a regulatory feedback loop that controls a subset of the circadian outputs and modulates the central oscillator.

Evolutionary mechanisms of circadian clocks

An intriguing question in biology is to know how circadian molecular networks could have evolved their particular topologies to adjust to a daily period. We analyze the mechanism of the evolution of such networks by using a computational design strategy that allows for the generation of synthetic networks with a targeted 24 hours oscillation. We have performed a systematic analysis of all possible two-gene network topologies based on a core activator-repressor frequently found in circadian mechanisms. We have considered transcriptional and post-translational regulations to implement this core. We have applied our analysis to both, eukaryotic and prokaryotic circadian machinery. Finally, we conjecture a possible mechanism for the evolution of circadian clocks.

Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.

Toward a detailed computational model for the mammalian circadian clock

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression.

Dual role of TOC1 in the control of circadian and photomorphogenic responses in Arabidopsis

To examine the role of the TOC1 (TIMING OF CAB EXPRESSION1) gene in the Arabidopsis circadian system, we generated a series of transgenic plants expressing a gradation in TOC1 levels. Silencing of the TOC1 gene causes arrhythmia in constant darkness and in various intensities of red light, whereas in blue light, the clock runs faster in silenced plants than in wild-type plants. Increments in TOC1 gene dosage delayed the pace of the clock, whereas TOC1 overexpression abolished rhythmicity in all light conditions tested. Our results show that TOC1 RNA interference and toc1-2 mutant plants displayed an important reduction in sensitivity to red and far-red light in the control of hypocotyl elongation, whereas increments in TOC1 gene dosage clearly enhanced light sensitivity. Furthermore, the red light-mediated induction of CCA1/LHY expression was decreased in TOC1 RNA interference and toc1-2 mutant plants, indicating a role for TOC1 in the phytochrome regulation of circadian gene expression. We conclude that TOC1 is an important component of the circadian clock in Arabidopsis with a crucial function in the integration of light signals to control circadian and morphogenic responses.