Summary paragraph
Predicting a multicellular organism’s phenotype quantitatively from its genotype is challenging, as genetic effects must propagate up time and length scales. Circadian clocks are intracellular regulators that control temporal gene expression patterns and hence metabolism, physiology and behaviour, from sleep/wake cycles in mammals to flowering in plants1–3. Clock genes are rarely essential but appropriate alleles can confer a competitive advantage4,5 and have been repeatedly selected during crop domestication3,6. Here we quantitatively explain and predict canonical phenotypes of circadian timing in a multicellular, model organism. We used metabolic and physiological data to combine and extend mathematical models of rhythmic gene expression, photoperiod-dependent flowering, elongation growth and starch metabolism within a Framework Model for growth of Arabidopsis thaliana7–9. The model predicted the effect of altered circadian timing upon each particular phenotype in clock-mutant plants. Altered night-time metabolism of stored starch accounted for most but not all of the decrease in whole-plant growth rate. Altered mobilisation of a secondary store of organic acids explained the remaining defect. Our results link genotype through specific processes to higher-level phenotypes, formalising our understanding of a subtle, pleiotropic syndrome at the whole-organism level, and validating the systems approach to understand complex traits starting from intracellular circuits.
Small networks of “clock genes” drive 24-hour, biological rhythms in eukaryotic model species1. A few among thousands of downstream, clock-regulated genes are known to mediate physiological phenotypes, such as the metabolic syndrome of clock mutant animals10. Identifying such causal links cannot predict whole-organism phenotypes quantitatively: formal, mathematical models are required. Predictive modelling in multicellular organisms has best succeeded for phenotypes that closely map the intracellular behaviour of gene circuits11, metabolic12 or signalling pathways13. Circadian clocks in contrast integrate multiple environmental inputs and affect disparate, potentially interacting biological processes, up to organismal growth and lifecycle traits4,14. Mis-timed mutant organisms suffer a syndrome of mild, environment-dependent effects akin to a chronic disease1,4,10.
The Arabidopsis clock mechanism1 comprises dawn-expressed transcription factors LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK-ASSOCIATED 1 (CCA1), which inhibit the expression of evening genes such as GIGANTEA (GI) (Fig.1a). LHY and CCA1 expression is inhibited by PSEUDO-RESPONSE REGULATOR (PRR) proteins. Removing the earliest-expressed PRR genes in prr7prr9 mutants slows the clock15 by delaying the decline of LHY and CCA1 expression and the subsequent rise of their targets (Fig.1b). Mathematical models of this circuit16 have been extended to intermediate transcription factors, including factors that regulate flowering time and organ elongation7. We therefore tested whether these causal links were sufficient to understand (explain and predict) the multiple phenotypes of a clock mutant genotype.
The Arabidopsis Framework Model (FMv1)9 represents the interacting physiological components of whole-organism phenotypes, in a simple, modular fashion. Flowering time in Arabidopsis is commonly scored by the number of rosette leaves, for example. Predicting leaf number involves the FM’s clock and photoperiod7, phenology17 and functional-structural sub-models18. Adding a clock sub-model that explicitly represents PRR7, PRR9 and output pathways (see Supplementary Methods; Fig.2) was sufficient to match the published, late-flowering phenotype19 of prr7prr9 compared to wild-type Columbia (Col) plants under long photoperiods (Fig.1c). Under short photoperiods, the mutant phenotype is weaker (Extended Data Fig.1a). The model also matched the observed20, photoperiodic regulation of hypocotyl elongation in wild-type plants and qualitatively matched the longer hypocotyls of prr7prr9 (Extended Data Fig.1b).
Biomass growth is mediated by the metabolic network, the development of sink and source organs and resource partitioning amongst them. Here, we test the importance of one of many potential circadian effects on biomass, via the nightly, clock-limited rate of sugar mobilisation from storage in transient starch21. To understand these carbon dynamics in prr7prr9, we first extended the metabolic sub-model. Daytime starch accumulation in wild-type plants under short photoperiods was underestimated in the FMv19,22. Partitioning of photoassimilate towards starch in the model was therefore updated using the measured activity of the key biosynthetic enzyme, AGPase, which partitions more carbon to starch under short photoperiods than is allowed for in the FMv1 (Supplementary Methods; Extended Data Fig.2a). At night, starch is mobilised (degraded) at a constant rate to provide sugar until dawn, as anticipated by the circadian clock21,23. We therefore linked the starch degradation rate to the clock sub-model8 (Supplementary Methods). Simulation of the revised model closely matched end-of-day starch levels under photoperiods of 12h or less (Fig.1e). Finally, the organic acids malate and fumarate also accumulate significantly during the day in Arabidopsis, are mobilised at night and have been proposed as secondary carbon stores24. At the end of the day, levels of malate and fumarate were two-fold higher in prr7prr9 than wild-type, with a smaller elevation of citrate, aconitate and iso-citrate (Figs.1d, Extended Data Fig.3). Malate and fumarate were therefore included as an organic acid pool with dynamics similar to starch, in an extended model termed the FMv2 (Fig.2). The FMv2 predicts the gain of carbon biomass directly and other major biomass components indirectly. For example, the 3.3-fold increase in protein synthesis rates from night to day predicted by the model was very close to the observed 3.1-fold increase25(see Supplementary Methods). If altered starch mobilisation in the clock mutant was sufficient to affect its biomass, the FMv2 should also predict that phenotype.
We first tested whether the FMv2 could explain the phenotypes caused by a direct change in starch degradation, in mutants of LIKE SEX FOUR 1 (LSF1). LSF1 encodes a phosphatase homologue necessary for normal starch mobilisation26. lsf1 mutants grown under 12L:12D have mildly elevated starch levels and reduced biomass26, similar to the prr7prr9 clock mutant (Fig.3b). Reducing the relative starch degradation rate alone in the FMv2 recapitulated the lsf1 starch excess observed in published studies26 (Extended Data Fig.1c) and new datasets (Figs.3g,3i). The higher baseline starch level arises naturally if the plant is close to a steady state, where the absolute amount of starch degraded nightly in lsf1 equals the daily synthesis. Absolute starch synthesis in lsf1 is wild-type (Fig.3g,3i). To degrade the same amount of starch as wild-type at a lower relative rate, the lsf1 mutant must have a higher baseline starch level. The assumption of a lower relative degradation rate in lsf1 is therefore functionally equivalent to but conceptually simpler than the previous assumption of an altered ‘starch set point’ baseline level23,26.
A minimal model calibration workflow (Extended Data Fig.4) allowed comparison of simulations of the FMv2 with measurements from multiple experiments on prr7prr9 and lsf1 mutants. Measured photosynthetic and metabolic variables (Extended Data Fig.5) calibrated up to 4 model parameters (Extended Data Table 1), and the genotype-specific water content9. Reducing the relative starch degradation rate in the calibrated model accurately predicted the reduced biomass of lsf1 mutant plants in each case (Figs.3c,3e), despite the apparent paradox that the mutants mobilised the same absolute amount of starch as the wild type. The explanation supported by the model is that lsf1 mutant plants accumulate large, unused starch pools as well as new biomass, whereas wild-type plants produce biomass more efficiently, leaving only a minimum of carbon in starch. The coefficient of variation of the Root-Mean-Square Error (cvRMSE) provides a normalised error metric for all biomass data9, showing a good fit to both lsf1 and wild-type genotypes (10.1%, 15.3% Col and 13.7%, 15.4% lsf1 in experiments 1 and 2 respectively). Altering the relative starch degradation rate therefore explained both the lsf1 mutant’s modest starch excess and its reduced biomass, validating the model.
prr7prr9 mutants showed slower relative starch degradation (Fig.3a) and higher starch levels at both dawn and dusk (Extended Data Fig.1d) than the wild type. Simulating prr7prr9 mutations in the clock sub-model matched these phenotypes for plants grown in Norwich (Figs.3a, Extended Data 1e) and Edinburgh (Fig.3h), indicating that the mutant clock’s later estimate of subjective dawn explained the starch degradation defect. prr7 single mutants27 fully mobilised starch and grew normally, as predicted (Extended Data Fig.6). Although model calibration data showed that photosynthesis, starch synthesis and leaf production rates were unaffected by the mutations (Extended Data Fig.5), biomass of prr7prr9 mutant plants was strongly reduced relative to wild-type plants in independent studies (by 40% and 31% at 38 days in experiments 1 and 2 respectively). However, the calibrated FMv2 predicted much smaller reductions in biomass in prr7prr9 due to accumulating starch (26% and 18% in experiments 1 and 2 respectively). Neither 1 S.D. variation in the mutant’s simulated water content, the most sensitive parameter in our model (Extended Data Fig.7), nor any measured water content value allowed the model with only a starch defect to match the mutant biomass (Extended Data Fig.8). The poor model fits (cvRMSE = 41%, 45% in experiments 1 and 2 respectively) indicated that process(es) additional to starch degradation limited the growth of prr7prr9 but not of lsf1 plants.
Considering malate and fumarate as a secondary carbon store24, the amount of carbon mobilised from malate and fumarate at night in the wild type was up to 19% of the carbon mobilised from starch. prr7prr9 but not lsf1 plants accumulated excess malate and fumarate, representing further ‘wasted’ carbon that did not contribute to subsequent growth (Figs.3k-n). We therefore reduced the relative malate and fumarate mobilisation rate in the FMv2 simulation of prr7prr9, to reproduce the observed organic acid excess (Figs.3l,n). Together, the simulated defects in starch and organic acid mobilisation quantitatively accounted for the mutant’s reduced biomass (Figs.3d,3f; cvRMSE = 14.4%, 20.1% in experiments 1 and 2 respectively).
The FMv2 built upon delayed gene expression patterns in prr7prr9 mutants to predict canonical clock phenotypes: altered hypocotyl elongation, flowering time, starch metabolism and hence most (58-65%) of the mutants’ reduced biomass. Unused malate and fumarate accounted for their remaining biomass defect, and might similarly affect arrhythmic prr5prr7prr9 mutants28. Carbon supply limited growth in our well-watered, nutrient-rich growth conditions22, though carbon limitation was milder than in conditions that reduced the chlorophyll content of clock mutants4 or triggered sugar signals to alter timing27. Future extensions of the model could address the nutrient and water limitations that prevail in field conditions, test further aspects of circadian regulation and critical functions of plant biology with daily regulation, such as photosynthesis. Our results suggest a broader proof of principle, that the contributions of dynamic gene regulation and metabolism to whole-organism physiology will also be understood (explained and predicted) quantitatively in other multicellular species29, for example using clock and metabolic models in animals and humans to understand body composition10.
Methods
Experimental methods
Plant materials and growth conditions
Arabidopsis thaliana of the Columbia (Col-0) accession, prr7-3/prr9-119 and lsf1-126 were used in this study. Seeds were first sown on half strength Murashige and Skoog (MS) solution and stratified in darkness at 4°C for 5 days before being exposed to white light at the desired photoperiod and temperature. Four-day-old seedlings were then transferred to soil containing Levington seed and modular compost (plus sand). The growth and treatment conditions for each experiment are shown in the figure legends. For the experiment in Fig.1d and Extended Data Fig.3 only, seeds were sown on wet soil in pots and transferred directly to experimental conditions. Plants were thinned after a week and treated with Nematodes after two weeks as a biological pest control.
Leaf number and plant assay
The total number of leaves (including the cotyledons) was recorded every 3-4 days from seedling emergence. Only leaves exceeding 1 mm2 in size (by eye) were considered in the total leaf count. Plants were harvested for biomass at different time points and for metabolite measurement at 3 weeks (Extended Data Fig.3) and 4 weeks (other data). For metabolite measurement, rosettes were harvested and immediately submerged in liquid nitrogen, half an hour before lights off (end of day, ED) or lights on (end of night, EN) and stored at -80°C until extraction. For dry biomass, dissected plants were oven-dried at 80°C for 7 days. Area analysis was conducted using ImageJ 31. Each image was first processed with colour thresholding to isolate the green region, which was next converted into binary format. The area was then determined using the Analyze Particles tool.
Gas exchange measurement
An EGM-4 Environmental Gas Monitor for CO2 (PP Systems, US) was used for CO2 flux measurement. A Plexiglass cylindrical chamber (12 cm in diameter x 3 cm sealed height, with a 6 cm tall support) was used (Extended Data Fig.5f). Rubber rings around the lid and the hole for the pot ensured an airtight seal. The chamber was connected to the EGM-4 with two butyl tubes for closed-loop measurement.
Each individual measurement was taken by placing an individual plant pot in the chamber for approximately 60 seconds, during which the EGM-4 recorded CO2 concentration (μmol mol-1 or ppm) every 4.6 seconds. We covered the soil surface of the pots with black opaque plastic, leaving only a small hole in the middle for the plants. Plants were measured when they were 37 days old. Dark respiration was measured one hour before lights-on while daytime assimilation was measured one hour before lights-off.
CO2 enrichment of the atmosphere in the growth chambers due to the experimenters’ breathing was avoided by using a breath-scrubbing device during measurement. Hourly CO2 concentration at leaf level was also monitored by connecting the EGM-4 to a computer for automated data logging. The average hourly CO2 level was used as input to the model.
Extraction and determination of metabolite content
Rosettes were harvested as described above and ground in liquid nitrogen. Around 20mg of ground material was aliquoted in screw-cap tubes (Micronic). Ethanolic extraction was performed using 80% ethanol v/v with 10mM MES (pH 5.9) and 50% ethanol v/v with 10mM MES (pH 5.9). During extraction, the successive supernatants obtained were combined into 96-deep well plates. The supernatant was used for spectrophotometric determination of chlorophylls, soluble carbohydrates, amino acids and organic acids as described32. The pellet remaining after the ethanolic extraction was used for the determination of starch and total protein content as described33.
Modelling methods
Development of the FMv2 in Matlab (Mathworks, Cambridge, UK), model equations, experimental data for model calibration and simulation procedures are described in the Supplementary Methods section.
Data and model availability
A simulator to run the FMv2 in multiple conditions is publicly accessible online at http://turnip.bio.ed.ac.uk/fm/. Numerical data and model files will be available from the University of Edinburgh DataShare www.datashare.ed.ac.uk [insert doi].
Author Contributions
YHC, AS, MS and AJM designed the study. YHC, VM, AF, SM, AS and MS performed the experiments and analysed the experimental data. YHC and DDS performed the modelling and analysed the simulation results. YHC, DDS and AJM wrote the paper with input from all authors.
Supplementary methods-modelling
1 Updating the circadian clock, starch, and photoperiod response models
1.1 Photoperiod response model
The circadian clock controls the timing of flowering by regulating the expression of the FT gene through the photoperiod pathway. The photoperiod response was previously modelled in the Arabidopsis Framework Model version 1 (FMv1) 1 by including the model from Salazar et al 2009 2. However, this model includes an older circadian clock model 3 that does not explicitly represent the relevant clock components PRR9 and PRR7. We therefore replaced the Salazar model with our most recent, Seaton-Smith model of the photoperiod pathway 4. This brings several advantages. First, the Seaton-Smith model includes additional understanding of the photo period response mechanism, such as the regulation of CO protein stability by FKF1 5. Second, it is based upon the same circadian clock model 6 as the clock-starch model that we introduce in Section 1.2, below. Third, the clock model includes PRR9 and PRR7, allowing explicit simulation of the prr9prr7 mutation (see section 1.2.2). Fourth, the Seaton-Smith model represents circadian regulation of hypocotyl elongation via the PIF transcription factors, allowing the FMv2 to represent this canonical clock phenotype.
As in the Salazar and FMv1 models, the photoperiod response model in the FMv2 interacts with the phenology model through the control of FT transcript expression. The important characteristic is 'FTarea', the integrated FT level over the course of a 24h day. FTarea controls the Photoperiod component of the phenology model through the expression:
In order to utilise this connection with the new circadian clock model, the parameters b, c and n were chosen so that this function matched the original photoperiod function given by Chew et al 2012 7, as was done previously for the connection from the older clock model in Chew et al 2014 1.
1.2 Circadian control of starch turnover
The circadian clock controls the rate of starch degradation during the night in light: dark cycles 8,9. The molecular mechanisms responsible for this control have not been identified, but our recent work identified simple, plausible mechanisms 10. These were formalised in mathematical models that were evaluated by comparison to a wide range of experimental data (e.g. the change in starch turnover when dusk arrives ~4 hours early). In Seaton et al 2014 10, three models were described in detail, named Model Variants 1, 2 and 3. Of these, Model Variants 2 and 3 provided the best match to experimental data, while Model Variant 1 was shown to have several limitations. Since Model Variants 2 and 3 provided quantitatively similar predictions over a range of conditions, and Model Variant 2 is simpler (6 fewer parameters and 2 fewer regulatory links from the circadian clock), we chose to integrate Model 2 with the FMv2.
1.2.1 Starch model structure
In order to incorporate this control of starch turnover with the FM, we treat the starch component S as a measure of starch concentration (rather than absolute quantity per plant). Thus, this is taken as:
Where S(t) is starch concentration variable used in the model of starch turnover, Cstarch(t) and Cshoot(t) are the carbon in starch and in the shoot biomass respectively, and r is a scaling factor used to bring S(t) to a similar range of concentrations to those used in the original model construction10. Note, the control of starch synthesis by the species Y is disregarded, as starch synthesis is modelled as a fixed fraction of photoassimilate (see Section 1.2).
This model runs on an hourly basis throughout the day, but controls starch turnover only during the night. The starch concentration (i.e. S(t)) is calculated at the start of the timestep, and the change in starch levels by the end of the hour is then given by:
Where ∆S(t) denotes the change in starch concentration across the hour of simulation. Total starch carbon at the following timepoint is then updated according to:
1.2.2 Simulating lsf1 and prr7prr9 mutant genotypes
In order to simulate the circadian clock mutant prr7prr9, we set to 0 the clock parameters q3, n4, n7, n8, and n9, which control the multiple aspects of the transcription rate of PRR7 and PRR9. Model simulations predicted ~70% turnover of starch in the mutant, in agreement with experimental data (Fig. 3a and Extended Data Figure 1d).
All other parameter values were calibrated as described in Section 4, below (Extended Data Fig.4), and are shown in Extended Data Table 1. The starch degradation rate parameter in FMv1 (sta_turnover) is not used in FMv2, because the starch degradation rate is computed bythe clock-regulated starch model. In order to simulate the lsf1 mutant, the parameters kd,S and kd,T,2 in this model were set to 10 and 0.018, respectively, calibrating simulated starch to our experimental data. This allowed the model to match the experimentally observed starch turnover in our experiment 1 (Fig. 3g) and in literature data 11 (Extended Data Figure 1c). Where prr7prr9 showed a mild starch phenotype in experiment 2, sta_turnover was calibrated as described in Extended Data Fig.4; the same model was used to compare all genotypes in the experiment.
2. Revision of Starch synthesis
In the original Carbon Dynamic Model (CDM) 1,12, starch is synthesised at a rate that is the sum of a baseline rate and an ‘overflow’ rate. The baseline rate is a fixed proportion of the photoassimilate. The rest of the photoassimilate is first converted into soluble sugars which are used for growth and respiration. As growth demand is limited to a maximum value, any excess photoassimilate is converted into starch, through the ‘overflow’ rate.
Our previous work 1,13 showed that the ‘overflow’ mechanism is not always applicable, especially when plants are grown in short-day conditions (Figure 1e). Results suggested that starch is synthesised at a photoperiod-dependent fixed rate that is much higher than the baseline, and any excess photoassimilate remains as sugars. This ensures that plants store sufficient starch to last the night. We therefore re-routed the carbon flow based on this finding.
To determine the photoperiod-dependent starch synthesis rate, we first calculated the fraction of measured net assimilate partitioned to starch using our previous data13 and the equation below:
where
FS = Fraction partitioned to starch
SED = Starch level at ED
SEN = Starch level at EN
AN = Net assimilation rate per hour
P = Photoperiod
It has been reported that under low light conditions, most of the flux control through the pathway of starch synthesis resides in the reaction catalysed by AGPase 14. Since most lab experiments are conducted under low light, we therefore also tested the relation between the fraction partitioned to starch and AGPase activity. If the total amount of starch accumulated over the light period is proportional to daily AGPase activity (averaged between ED and EN), the fraction is given by:
where k is the proportional constant. We determined the value of k using data from 12-hr photoperiod as the reference. We found a strong linear relation between the fraction of measured net assimilate and photoperiod (Extended Data Figure 2). This relation is therefore used in the FMv2 to determine starch synthesis rate, StaSyn, as follows:
3. Addition of carbon pool for malate and fumarate
Malate and fumarate can be interconverted in the tricarboxylic acid cycle, so they are considered together in a single pool. The dynamics of this pool is modelled in a manner similar to starch except for the regulation of degradation rate by the clock. In the daytime, a fixed proportion of the photoassimilate is converted to starch, malate and fumarate, while sugar level is allow to fluctuate depending on the carbon excess. At night, malate and fumarate are consumed with a linear rate, while starch degradation rate is controlled by the clock sub-model (see Extended Data Figure 2 and Section 1.2). For simplicity, we model a direct conversion of carbon from malate and fumarate into sugar at night, omitting the intermediate metabolic reactions.
4. Parameter calibration
Results in our previous studies 1,13 suggested that carbon dynamics in plants are flexible and plants adjust processes like photosynthesis, starch synthesis and starch degradation rate depending on the environment. The aims of our study were to test if the dynamics of the different carbon pools can be quantitatively balanced over the timescale of vegetative growth, and how genetic regulation that modifies these dynamics affects plant growth. It is therefore necessary that the model first matches quantitatively the carbon pool data for wild-type plants as the reference genotype in each study. After accounting for environmental effects on all genotypes through the wild-type data, discrepancies between model simulations and data for the mutants can be attributed to genetic effects. To achieve this, we calibrated the following to the Col data (workflow illustrated in Extended Data Figure 4; parameter values in Extended Data Table 1):
photosynthesis rate was adjusted by introducing an efficiency factor relative to the default
starch synthesis rate was adjusted by introducing an efficiency factor relative to the default
Starch turnover was simulated by the clock-controlled starch submodel (Section 1.2), which reproduced experimental measurement of percentage turnover in most cases. In cases where the phenotype of starch degradation was too mild and could not be explained by the starch submodel, we used a linear degradation rate as in the previous model version (FMv1) to reproduce the turnover. We then iteratively tuned starch synthesis and photosynthesis rates to match the measured end-of-day level (Extended Data Table 1).
We next calibrated the parameter values for the new carbon pool that represents malate and fumarate (MF) using Col data as follows:
The initial level of this pool was set as 0.4 of initial starch level, based on the ratio measured in the literature 15
MF synthesis was set as a fixed fraction of starch synthesis
MF turnover was set as the fraction of dusk level consumed
Wherever possible, we used parameter values measured or calculated from our data. Mutants were simulated by changing the values of genotype-specific parameters as listed in Extended Data Table 1, notably the water content.
In each experiment, we did not find genotypic differences in photosynthesis when expressed per unit area, but there was a general increase in photosynthesis in prr7prr9 when expressed per gram fresh weight (Extended Data Figure 5). Even though we used the same photosynthesis efficiency for all genotypes, we found that the model could reproduce this increase due to the lower water content measured in prr7prr9. This suggested the importance of including water content as a genotype-specific parameter in our model, since metabolites are measured per unit fresh weight.
As expected, we found variation in photosynthesis efficiency between experiments. In particular, the photosynthesis per unit area was higher for all genotypes in Experiment 2. As a result, the model underestimated these, but reproduced the values when expressed per unit fresh weight, suggesting a difference in the specific leaf area.
5. Modelling protein synthesis, compared to literature data
The biomass prediction in the FMv2 implies minimal budgets for the nutrient constituents of biomass, which are effectively predictions that can be compared to published experimental data. For example, 13CO2 labelling has allowed quantification of the relative rates of protein synthesis in the light and dark during light:dark cycles 16, and of rates of protein turnover 17.
The model does not include protein as a distinct component of the synthesised biomass. However, since the protein fraction of biomass is relatively constant across the course of a day (for example, see Pyl et al 2012 18), and protein turnover has been measured, it is possible to calculate an implied rate of protein synthesis for a given model simulation (as done experimentally in Ishihara et al 2015 17). In particular:
where ProtSyn(t) is the calculated rate of protein synthesis at time t, in units of gProtein gFW- 1h-1. Gr(t) is the relative growth rate (= (Biomass(t)-Biomass(t-1))/Biomass(t)), in units of hr-1. Turn is the rate of protein turnover, measured as 0.0014 hr-1 (average of measurements by Pulse-Chase labelling 17). Prot is the protein content, measured as 0.0169 gProtein gFW-1 in Ishihara et al 2015 17.
Simulating the conditions used in Ishihara et al 2015 17 for wild-type plants shows that carbon biomass growth rates in the model predict a 3.3-fold increase in the rate of protein synthesis during the day, compared to during the night. This is in excellent agreement with experimental data which showed a 3.1-fold increase17, 18.
Acknowledgements
Supported by European Commission FP7 collaborative project TiMet (contract 245143) and by a BBSRC Institute Strategic Programme Grant BB/J004561/1 to the John Innes Centre.
Footnotes
↵Complete address: SynthSys, C.H. Waddington Building, University of Edinburgh, Max Born Crescent, Edinburgh EH9 3BF Scotland, UK Telephone number : +44 (0)131 651 3325 Email : Andrew.Millar{at}ed.ac.uk