Title: The clock gene circuit in <i>Arabidopsis</i> includes a repressilator with additional feedback loops
Abstract: Article6 March 2012Open Access The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops Alexandra Pokhilko Alexandra Pokhilko School of Biological Sciences, University of Edinburgh, Edinburgh, UK Search for more papers by this author Aurora Piñas Fernández Aurora Piñas Fernández School of Biological Sciences, University of Edinburgh, Edinburgh, UK Search for more papers by this author Kieron D Edwards Kieron D Edwards School of Biological Sciences, University of Edinburgh, Edinburgh, UKPresent address: Advanced Technologies Cambridge, 210 Cambridge Science Park, Cambridge CB4 0WA, UK Search for more papers by this author Megan M Southern Megan M Southern Department of Biological Sciences, University of Warwick, Coventry, UK Search for more papers by this author Karen J Halliday Karen J Halliday School of Biological Sciences, University of Edinburgh, Edinburgh, UK SynthSys Edinburgh, University of Edinburgh, Edinburgh, UK Search for more papers by this author Andrew J Millar Corresponding Author Andrew J Millar School of Biological Sciences, University of Edinburgh, Edinburgh, UK SynthSys Edinburgh, University of Edinburgh, Edinburgh, UK Search for more papers by this author Alexandra Pokhilko Alexandra Pokhilko School of Biological Sciences, University of Edinburgh, Edinburgh, UK Search for more papers by this author Aurora Piñas Fernández Aurora Piñas Fernández School of Biological Sciences, University of Edinburgh, Edinburgh, UK Search for more papers by this author Kieron D Edwards Kieron D Edwards School of Biological Sciences, University of Edinburgh, Edinburgh, UKPresent address: Advanced Technologies Cambridge, 210 Cambridge Science Park, Cambridge CB4 0WA, UK Search for more papers by this author Megan M Southern Megan M Southern Department of Biological Sciences, University of Warwick, Coventry, UK Search for more papers by this author Karen J Halliday Karen J Halliday School of Biological Sciences, University of Edinburgh, Edinburgh, UK SynthSys Edinburgh, University of Edinburgh, Edinburgh, UK Search for more papers by this author Andrew J Millar Corresponding Author Andrew J Millar School of Biological Sciences, University of Edinburgh, Edinburgh, UK SynthSys Edinburgh, University of Edinburgh, Edinburgh, UK Search for more papers by this author Author Information Alexandra Pokhilko1, Aurora Piñas Fernández1, Kieron D Edwards1, Megan M Southern2, Karen J Halliday1,3 and Andrew J Millar 1,3 1School of Biological Sciences, University of Edinburgh, Edinburgh, UK 2Department of Biological Sciences, University of Warwick, Coventry, UK 3SynthSys Edinburgh, University of Edinburgh, Edinburgh, UK *Corresponding author. SynthSys Edinburgh, University of Edinburgh, CH Waddington Building, Kings Buildings, Mayfield Road, Edinburgh EH9 3JD, UK. Tel.: +44 131 651 3325; Fax: +44 131 651 9068; E-mail: >[email protected] Molecular Systems Biology (2012)8:574https://doi.org/10.1038/msb.2012.6 PDFDownload PDF of article text and main figures. Peer ReviewDownload a summary of the editorial decision process including editorial decision letters, reviewer comments and author responses to feedback. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info Circadian clocks synchronise biological processes with the day/night cycle, using molecular mechanisms that include interlocked, transcriptional feedback loops. Recent experiments identified the evening complex (EC) as a repressor that can be essential for gene expression rhythms in plants. Integrating the EC components in this role significantly alters our mechanistic, mathematical model of the clock gene circuit. Negative autoregulation of the EC genes constitutes the clock's evening loop, replacing the hypothetical component Y. The EC explains our earlier conjecture that the morning gene PSEUDO-RESPONSE REGULATOR 9 was repressed by an evening gene, previously identified with TIMING OF CAB EXPRESSION1 (TOC1). Our computational analysis suggests that TOC1 is a repressor of the morning genes LATE ELONGATED HYPOCOTYL and CIRCADIAN CLOCK ASSOCIATED1 rather than an activator as first conceived. This removes the necessity for the unknown component X (or TOC1mod) from previous clock models. As well as matching timeseries and phase-response data, the model provides a new conceptual framework for the plant clock that includes a three-component repressilator circuit in its complex structure. Synopsis Recent findings are incorporated into a new mathematical model of the plant circadian clock, revealing a complex circuit structure comprised of multiple negative feedback loops, and predicting a repressive role for a key regulator, TOC1, which the authors confirm experimentally. The feedback structure of the plant clock's evening loop was reconstructed based on multiple data, and is now represented by the evening complex (ELF3-ELF4-LUX), which represses transcription from the ELF4 and LUX promoters. Computational analysis of timeseries data from mutant plants predicts that TOC1 is a repressor of the key morning genes LHY and CCA1, not an activator. Analysis of LHY and CCA1 expression in TOC1 gain- and loss-of-function plants confirms this prediction. Light induction of LHY and CCA1 expression is predicted to determine the clock's response to brief light pulses, matching the observed phase-response curve. The evening complex controls LHY and CCA1 expression by a double-negative connection, rather than direct activation, forming part of a three-component repressilator circuit, which is itself only part of the more complex circuit of the clock system. Introduction Circadian clocks are found widely among organisms, ranging from cyanobacteria to mammals (Dong and Golden, 2008; Zhang and Kay, 2010). These internal time-keepers generate ~24 h rhythms of expression of multiple genes even in the absence of any environmental cues, allowing the organism to anticipate each new day. Circadian rhythms can enhance growth and survival (Dodd et al, 2005; Harmer, 2009; Zhang and Kay, 2010). In order to understand the behaviour, mechanisms and properties of the system, we previously built a mathematical model of the plant circadian clock (Pokhilko et al, 2010). The clock was represented by a three-loop structure of interconnected morning and evening loops (Figure 1, upper right). The morning loop included MYB-related transcription factors LHY (LATE ELONGATED HYPOCOTYL) and CCA1 (CIRCADIAN CLOCK ASSOCIATED 1), which activate the expression of PRR9, PRR7 and PRR5/NI (PSEUDO-RESPONSE REGULATORs 9, 7, 5/night inhibitor) (Farre et al, 2005; Nakamichi et al, 2010). Transcriptional co-regulators PRR9, PRR7 and PRR5 inhibit LHY and CCA1 expression in the model, and in data that showed binding to their promoters (Nakamichi et al, 2010). The evening loop was represented by TIMING OF CAB EXPRESSION1 (TOC1), which inhibited the expression of its unknown activator Y. The hypothetical gene Y was introduced in the model by Locke et al (2005) to describe the observed autonomous oscillations of TOC1 expression in lhy/cca1 double-mutant plants. GIGANTEA (GI), a large plant-specific protein, accelerated the degradation of TOC1 protein through stabilisation of the F box protein ZTL (ZEITLUPE) in the model, as in the data (Kim et al, 2007). Figure 1.The revised outline of the Arabidopsis circadian clock. Elements of the morning and evening loops are shown in yellow and grey, respectively. Proteins are shown only for EC, ZTL and COP1 for simplicity. Transcriptional regulation is shown by solid lines. EC protein complex formation is denoted by a dashed black line. Post-translational regulation of TOC1 and the EC by GI, ZTL and COP1 are shown by red dashed lines. Acute light responses in gene transcription are shown by flashes. Post-translational regulation by light is shown by small yellow circles. The previous outline circuit (Pokhilko et al, 2010) is shown on the upper right. Download figure Download PowerPoint The connections between morning and evening loops were represented in the model by the inhibition of evening gene expression by LHY/CCA1 protein, which was well documented, and by activation of LHY/CCA1 expression by TOC1. Previous models required unknown substances TOC1mod or X to match the observed ~12 h delay between TOC1 expression and LHY/CCA1 induction (Locke et al, 2005; Pokhilko et al, 2010). Pokhilko et al (2010) introduced an additional connection from the evening loop to the morning loop, based on timeseries data, through inhibition of PRR9 expression by TOC1. This improved the model's description of plant rhythms but left open questions about core parts of the clock mechanism. Loss-of-function mutants in each of the genes represented in previous clock models remained rhythmic, albeit with varying rhythmic properties. This was problematic, because the model required a hypothetical component Y to explain the rhythms observed in the lhy/cca1 double mutant. GI, the first gene proposed as a candidate for Y, was known not to perform all of the required functions (Locke et al, 2005), so the biological identity of the missing components was unknown. Conversely, three mutants that did cause striking, arrhythmic phenotypes could not be integrated into the model, because the functions of the plant-specific proteins ELF3 (EARLY FLOWERING 3), ELF4 (EARLY FLOWERING 4) and the GARP transcription LUX (LUX ARRHYTHMO) (also known as PCL1) were unclear (Hicks et al, 1996; Covington et al, 2001; Doyle et al, 2002; Hazen et al, 2005). Recent results demonstrate that ELF3, ELF4 and LUX are the key regulators of clock gene expression at night (Onai and Ishiura, 2005; Kolmos et al, 2009; Dixon et al, 2011; Helfer et al, 2011). ELF3, ELF4 and LUX proteins were shown to form a complex, the EC (evening complex), which binds to the promoters of target genes (Nusinow et al, 2011). Although only LUX protein binds directly to promoters, both ELF3 and ELF4 proteins are important for EC function (Nusinow et al, 2011). The binding of the EC to the promoters of target genes, such as PRR9 and LUX itself, suppresses their expression (Dixon et al, 2011; Helfer et al, 2011). The importance of the ELF3/ELF4/LUX complex for free-running rhythms in constant light, and for entrainment of both wild-type (WT) and the lhy/cca1 double mutant (Hazen et al, 2005; Onai and Ishiura, 2005; Kolmos et al, 2009; Dixon et al, 2011), suggested that ELF3, ELF4 and LUX (the EC genes) are the major elements of the evening loop of the clock. However, the evening loop's structure and integration with the rest of the clock circuit remained unclear. To create the new clock structure, we first recast the evening loop to include the EC genes, together with post-translational regulation of ELF3 protein by the ubiquitin E3 ligase COP1 (CONSTITUTIVE PHOTOMORPHOGENIC 1) (Yu et al, 2008) (Figure 1, see Results for further detail). The oscillatory mechanism of the evening loop was analysed using data from the lhy/cca1 double mutant, where only the evening loop sustains rhythmicity. We explored the function of GI in the new circuit, using data from the lhy/cca1/gi triple mutant. Second, we connected the evening loop to the rest of the clock and explored a new mechanism connecting the clock's evening components to the morning genes. In the context of the whole clock circuit, the observed repression of PRR9 by the EC (Dixon et al, 2011; Helfer et al, 2011) creates a three-negative feedback ring structure, termed the repressilator. Another prediction relates to the regulation of LHY and CCA1 expression by TOC1. Although the molecular details remain to be elucidated, our computational analysis revealed that timeseries data on the ztl and prr7/prr9 mutants (Farre et al, 2005; Baudry et al, 2010) are more consistent with TOC1 being an inhibitor instead of an activator of LHY and CCA1 expression. Besides, our new experiments with the toc1 mutant and TOC1-overexpressing (TOC1-ox) plants further supported the negative role of TOC1 in regulation of LHY and CCA1 genes inside the morning loop. The proposed clock circuit integrates both positive and negative connections, including the repressilator, into a complex, multi-loop structure. Our model of this circuit includes significantly more experimental data and explains the clock's responses to multiple genetic and environmental perturbations, now including the canonical response to short light pulses at various times (the phase-response curve (PRC)). Results Qualitative analysis leading to revision of the clock gene circuit in Arabidopsis Figure 1 shows the principal scheme of the new clock model. We justify the new components and circuit structure in outline below, and examine its dynamic behaviour in the following sections. As in all previous models, CCA1 and LHY were treated as a single component (CCA1/LHY). The model consists of 28 ordinary differential equations and 104 parameters. Values of 43 parameters were constrained based on the available data and 61 parameters were fitted to multiple timeseries data sets (see Supplementary Table S1). The value of the six Hill coefficients was set to two. A detailed description of the model is presented in the Supplementary information, together with a discussion of the model's limitations and its robustness to parameter variations (Supplementary Figures S3 and S4). The evening loop of the clock was fundamentally revised in order to include the ELF3, ELF4 and LUX genes (EC genes). The model includes the formation of the triple ELF3-ELF4-LUX protein complex, the EC (Figure 1), which was shown to be important for clock function (Nusinow et al, 2011). Multiple data show that the EC genes have repressive effects on clock gene expression, so that expression of LUX, ELF4, GI, TOC1 and PRR9 was derepressed in elf3, lux and elf4 mutants (Fowler et al, 1999; Kikis et al, 2005; Kolmos et al, 2009; Dixon et al, 2011; Helfer et al, 2011). The model assumes that the EC suppresses the expression of these five target genes (Figure 1). To define the minimal structure of the evening loop that remains in the lhy/cca1 mutant, we analysed data on triple mutants lhy/cca1/elf3, lhy/cca1/gi and lhy/cca1/toc1. The data showed that clock entrainment is completely disrupted in the lhy/cca1/elf3 mutant (Dixon et al, 2011), although the remnant circuit is still entrained in lhy/cca1/toc1 (Ding et al, 2007) and lhy/cca1/gi (Locke et al, 2006). This suggested that the EC genes represent a core structure of the evening loop (Figure 1), which drives oscillations in the lhy/cca1 mutant as described below, whereas TOC1 and GI have different roles. Because the remnant circuit in lhy/cca1 is entrained by light signals, we included light-dependent, post-translational regulation of the EC component ELF3 through its observed interactions with COP1 and GI, as detailed below. The new structure of the evening loop allowed us to describe our new data on the lhy/cca1 and lhy/cca1/gi mutants without the hypothetical component Y. Next, we connected the evening circuit to the rest of the clock. The connection from the morning to the evening loop was described through the suppression of TOC1, LUX, ELF4, ELF3 and GI expression by CCA1 and LHY proteins (Harmer and Kay, 2005; Hazen et al, 2005; Kikis et al, 2005; Locke et al, 2005; Dixon et al, 2011; Li et al, 2011). The connections from the evening loop to the morning loop include the inhibition of PRR9 expression by evening components. Based on indirect observations, we previously suggested the inhibition of PRR9 by TOC1 (Pokhilko et al, 2010). Recent biochemical work demonstrated that PRR9 expression is more likely to be inhibited by the EC (Dixon et al, 2011; Helfer et al, 2011) (Figure 1). Another important connection from the evening to the morning genes is related to the regulation of LHY and CCA1 expression by TOC1 protein (Alabadi et al, 2001; Makino et al, 2002; Mas et al, 2003b; Baudry et al, 2010). Below we changed the sign of TOC1 function in the regulation of LHY and CCA1 expression from an activator to an inhibitor, which improved the model's description of the existing data on the ztl and prr7/prr9 mutants. This revision of TOC1 function removed the need for the hypothetical components X and TOC1mod of our previous models (Locke et al, 2005, 2006; Pokhilko et al, 2010), the most recent of which is hereafter referred to as the P2010 model. To further verify the proposed negative role of TOC1, we measured the level of LHY and CCA1 expression in the toc1 mutant and TOC1-ox plants. Our results showed that LHY and CCA1 mRNA levels were reduced in the TOC1-ox plants and increased in the toc1 mutant, which confirmed our model prediction about the negative regulation of LHY and CCA1 genes by TOC1. Moreover, data published during revision of this manuscript further demonstrated the direct suppressive effect of TOC1 on LHY and CCA1 expression (Gendron et al, 2012). Next, after connecting the loops, we tested the effects of the EC's repressive function on the dynamics of the whole system by comparing the simulated elf3 mutant with WT, and also investigated the sensitivity of the new clock structure to light. New structure of the evening loop accounts for data on the lhy/cca1 and lhy/cca1/gi mutants The EC as the main element of the evening loop Based on the published data, we revised the structure of the evening loop, which supports oscillations in the lhy/cca1 double mutant. It is represented by the formation of the EC by ELF3, ELF4 and LUX proteins (Nusinow et al, 2011). Inhibition of ELF4 and LUX expression by the EC creates a negative feedback loop (Kikis et al, 2005; Helfer et al, 2011). To verify the new structure, we studied clock gene expression in the lhy/cca1 double mutant computationally and experimentally under various light conditions. Expression peaks of the evening genes TOC1 and GI were first shown to be advanced to a morning phase in RT-qPCR assays of the lhy/cca1 mutant compared with WT plants grown under LD cycles (Figure 2A and B) (Alabadi et al, 2001; Mizoguchi et al, 2002; Locke et al, 2005). Transcriptome data from the lhy/cca1 mutant identified GI as the most LHY/CCA1-responsive, evening-expressed gene (Supplementary Figure S2C). However, ELF3, ELF4 and LUX were shown to be similarly affected (Supplementary Figure S2; Hazen et al, 2005; Kikis et al, 2005; Dixon et al, 2011; Li et al, 2011). We therefore extended the inhibitory action of LHY/CCA1 to all evening genes in our model, and the resulting simulations agreed with these data (Figure 2C): the early expression is caused by the loss of transcriptional inhibition by LHY/CCA1 in the morning. LHY/CCA1 regulation in WT delays the rising phase of evening gene expression, as in previous models. Figure 2.Regulation of TOC1 and LUX expression in the evening circuit of the clock. The phase advance of TOC1 (A) and LUX (B) expression in the lhy/cca1 double mutant (black line) compared with WT (grey line) was measured by qRT-PCR assays of plants grown under 12L:12D cycles, as described in Supplementary information. (C) Model simulations demonstrate that in both WT and lhy/cca1 plants, the increase in EC (grey lines) coincides with the time of the fall in the expression of the EC's target genes (such as TOC1, black lines). Data are double-plotted to facilitate comparison to simulations. Light conditions are shown by open and filled bars below the figure. Download figure Download PowerPoint TOC1 is also repressed by the EC in the model, which is based on the data on the high level of TOC1 expression in the elf3 and elf4 mutants (Kolmos et al, 2009; Dixon et al, 2011) and the presence of two consensus LUX-binding sites, GAT(A/T)CG, in the TOC1 promoter (Helfer et al, 2011). Simulated TOC1 RNA levels fall after dusk as EC levels rise, demonstrating that negative feedback from the EC is an important determinant of the falling phase of the evening genes‘ expression in the WT (Figure 2C). In the lhy/cca1 mutant, this feedback is the only cause of oscillation in the model, so the profile of TOC1 RNA level almost mirrors the EC profile (Figure 2C). The mutant's observed short period in constant conditions (17-18 h; Locke et al, 2005, 2006) reflects the lack of the additional delays from LHY and CCA1 inhibitor proteins (Supplementary Figure S5), which accelerates the expression of the EC genes. Formation of the EC then leads to autoinhibition of EC gene expression. Regulation of EC activity by COP1 and GI The lhy/cca1 mutant retained light entrainment (Alabadi et al, 2001; Mizoguchi et al, 2002; Locke et al, 2005), so light inputs must target at least one component of the evening loop. We therefore included the regulation of EC activity by light through targeted degradation of the EC component ELF3 by the COP1 ubiquitin E3 ligase, which was shown to be important for clock function (Millar et al, 1995b; Yu et al, 2008). To describe the kinetics of COP1 in diel cycles, we used the recent observation that COP1 protein exists in two different forms (Chen et al, 2010). Similarly to Pokhilko et al (2011), we assumed that light/dark transitions switch between the activities of these two, distinguishable E3 ligases, a night-active form (COP1n) and a day-active form (COP1d). Recent data suggested that COP1d might be related with a CULLIN 4 (CUL4) complex with COP1, where COP1 acts as a scaffold for a CUL4-based ubiquitin E3 ligase (Chen et al, 2006, 2010). Here, we assumed that COP1d is more active in the targeted degradation of the EC component ELF3, which thus alters the abundance profile of the EC (Supplementary Figure S6). ELF3 levels peak in the mid-night phase in the simulated WT, as observed (Liu et al, 2001; Dixon et al, 2011), so EC levels have already fallen substantially before dawn. Light regulation of COP1 activity (Pokhilko et al, 2011) then results in ELF3 degradation to a still lower level in the morning (Figure 2C). The further fall in EC levels is predicted to derepress the EC target genes such as TOC1. Its expression increases immediately after dawn in the lhy/cca1 mutant (Figure 2; Supplementary Figures S2 and S6), though the LHY and CCA1 repressors mask this effect in WT plants. Thus, the model predicts that COP1 is important for the timing of evening gene expression in the lhy/cca1 mutant. In the WT, this regulation would most affect genes that are more strongly regulated by LUX than by LHY and CCA1. Additionally to COP1, GI protein also modulates the kinetics of the evening loop (Locke et al, 2005). Light-dependent stabilisation of ZTL by GI, and hence destabilisation of TOC1 protein (Kim et al, 2007), resulted in the simulated period lengthening in the gi mutant of the P2010 model. The short period of the most of gi mutants suggested another important function of GI in the clock (Martin-Tryon et al, 2007). Here, we added the binding of GI to ELF3 protein (Yu et al, 2008). The binding of GI to F box proteins in the presence of light suggested GI's ability to negatively regulate various protein targets (Kim et al, 2007; Sawa et al, 2007). Thus, we assumed that GI can accelerate the destruction of the EC by bringing F box proteins into its vicinity. Below we simulated computationally the possible outcomes of this role of GI and then tested the model predictions experimentally using the lhy/cca1/gi mutant. The model predicted that the absence of GI should prevent EC levels from falling to their normal trough and thus reduce the peak levels of all EC-targeted evening genes (LUX, TOC1, GI, ELF4) in the lhy/cca1/gi triple mutant compared with lhy/cca1 double mutant. Figure 3A and B show model simulations of TOC1 and LUX expression, respectively. qRT-PCR measurements of TOC1 and LUX expression confirmed this prediction (Figure 3C and D), demonstrating the indirect positive effect of GI on evening gene expression, consistent with previous reporter gene data (Locke et al, 2006). In our simulations of constant light conditions, this resulted in arrhythmia of the simulated lhy/cca1/gi mutants, in contrast to the short-period oscillations in lhy/cca1 (Supplementary Figure S7), which both are consistent with experimental observations and with previous models (Locke et al, 2006). Figure 3.The role of GI in the regulation of TOC1 expression by the evening loop. Model simulations demonstrate lower peak levels of TOC1 (A) and LUX (B) expression (black lines) in lhy/cca1/gi (dotted lines) compared with lhy/cca1 mutants under 12L:12D cycles. This results from increased EC levels (grey lines) during the morning in the lhy/cca1/gi mutant. (C, D) qRT-PCR measurements of TOC1 and LUX expression in lhy/cca1/gi and lhy/cca1 mutants under 12L:12D. Data are double-plotted to facilitate comparison to simulations. Download figure Download PowerPoint The above simulations showed that COP1 and GI regulate the level of the ELF4-ELF3-LUX complex (EC) in both lhy/cca1 mutants and WT. Despite this post-translational control of the complex, the temporal profiles of the bulk levels of ELF3, ELF4 and LUX proteins in our model mainly reflected the kinetics of the corresponding mRNAs, as shown in Supplementary Figure S8. Regulation of morning-expressed genes by the evening components of the clock TOC1—a repressor of the morning loop The importance of the evening gene TOC1 in the regulation of the morning components LHY and CCA1 has long been assumed, based on multiple experimental observations (Alabadi et al, 2001; Mas et al, 2003b). However, the exact mechanisms of TOC1 action are still unknown. Based on gene expression analysis with mutant plants (Alabadi et al, 2001), TOC1 was previously suggested to play the role of an activator of LHY/CCA1 expression (Alabadi et al, 2001; Locke et al, 2005; Baudry et al, 2010; Pokhilko et al, 2010). However, our analysis of the available data revealed inconsistency between the data and the activator role of TOC1. For example, the increase of TOC1 level in the ztl mutant, caused by the slowing of TOC1 protein degradation rate, leads to a substantial lengthening of the clock period (Mas et al, 2003b; Somers et al, 2004; Kevei et al, 2006). This lengthening was accompanied by a lower amplitude of LHY and CCA1 expression in ztl plants (Baudry et al, 2010). This observation cannot easily be reconciled with the activation of LHY and CCA1 expression by TOC1, which should result in a higher amplitude of LHY and CCA1 in ztl mutants, as revealed by simulation of the P2010 model (Supplementary Figure S9). In addition, recent data showed that the expression of the LHY and CCA1 inhibitors PRR9 and PRR7 is low in the ztl mutant (Baudry et al, 2010). It is hard to explain why LHY and CCA1 mRNA does not rise in the ztl mutant, despite a low level of inhibitors and a higher level of the presumed activator TOC1. On the contrary, our simulations below show that the results on ztl mutants can easily be described by assuming that TOC1 acts as a repressor of LHY/CCA1 expression. The increase of TOC1 level in the ztl mutant results in a prolonged inhibition of LHY/CCA1, which lengthens the circadian period and reduces the amplitude of LHY/CCA1 expression. As TOC1 (PRR1) belongs to the PRR gene family, the repressive function of TOC1 makes it consistent with the other PRR proteins, such as PRR9, PRR7 and PRR5 (Nakamichi et al, 2010; Pokhilko et al, 2010). Thus, we extended the wave of PRR inhibitors of LHY/CCA1 in the model by including TOC1 (Figure 1), and explored the effect of TOC1 repression on the clock's dynamics. Our simulation of the ztl mutant demonstrated that higher suppression of LHY/CCA1 by TOC1 protein resulted in longer period and lower amplitude of LHY/CCA1 in the ztl mutant compared with WT (Figure 4A and B). These results corresponded to the data (Baudry et al, 2010) and improved the description of ztl compared with the P2010 model (Supplementary Figure S9B). Figure 4A illustrates the participation of TOC1 in the wave of LHY/CCA1 inhibitors in simulations of WT plants in constant light conditions. The absence of TOC1 resulted in a 2.5 h shortening of the period in the toc1 mutant compared with WT (Supplementary Figure S10), which is close to the observed period shortening (Millar et al, 1995a; Mas et al, 2003a). LHY/CCA1 levels were slightly reduced in the simulated toc1 mutant under constant light, but this counter-intuitive result is also consistent with experimental data (Alabadi et al, 2001). The reduction was related to the higher trough level of the remaining LHY/CCA1 inhibitors—the PRR9, PRR7 and NI proteins—in the toc1 mutant (Supplementary Figure S10; please see Supplementary information for detail). Additionally to the correct description of ztl and toc1 mutants, we greatly improved the description of the prr7/prr9 double mutant compared with the P2010 model (Supplementary Figure S9C). The participation of TOC1 in LHY/CCA1 inhibition resulted in robust oscillations in the prr7/prr9 mutant under constant light with a period 30.6 h (Figure 4C), which corresponds to the experimental observations (Farre et al, 2005; Salome and McClung, 2005). In the P2010 model, the simulated period for prr7/prr9 mutants was only 27.5 h, because the only remaining inhibitor (NI) could not provide a long enough delay in LHY/CCA1 expression. Furthermore, the oscillations in the prr7/prr9 mutant simulated by the P2010 model dampened faster than observed in the data (Supplementary Figure S9C). Thus, the introduction of TOC1 repressive function improved the description of multiple mutants in the new model of the clock. Figure 4.The improved description of ztl and prr7/prr9 mutants is related to the inhibition of LHY/CCA1