A high-throughput delayed fluorescence method reveals underlying differences in the control of circadian rhythms in Triticum aestivum and Brassica napus

Background A robust circadian clock has been implicated in plant resilience, resource-use efficiency, competitive growth and yield. A huge number of physiological processes are under circadian control in plants including: responses to biotic and abiotic stresses; flowering time; plant metabolism; and mineral uptake. Understanding how the clock functions in crops such as Triticum aestivum (bread wheat) and Brassica napus (oilseed rape) therefore has great agricultural potential. Delayed fluorescence (DF) imaging has been shown to be applicable to a wide range of plant species and requires no genetic transformation. Although DF has been used to measure period length of both mutants and wild ecotypes of Arabidopsis, this assay has never been systematically optimised for crop plants. The physical size of both B. napus and T. aestivum led us to develop a representative sampling strategy which enables high-throughput imaging of these crops. Results In this study, we describe the plant-specific optimisation of DF imaging to obtain reliable circadian phenotypes with the robustness and reproducibility to detect diverging periods between cultivars of the same species. We find that the age of plant material, light regime and temperature conditions all significantly effect DF rhythms and describe the optimal conditions for measuring robust rhythms in each species. We also show that sections of leaf can be used to obtain period estimates with improved throughput for larger sample size experiments. Conclusions We present an optimized protocol for high-throughput phenotyping of circadian period specific to two economically valuable crop plants. Application of this method revealed significant differences between the periods of several widely grown elite cultivars. This method also identified intriguing differential responses of circadian rhythms in T. aestivum compared to B. napus; specifically the dramatic change to rhythm robustness when plants were imaged under constant light versus constant darkness. This points towards diverging networks underlying circadian control in these two species. Electronic supplementary material The online version of this article (10.1186/s13007-019-0436-6) contains supplementary material, which is available to authorized users.


Background
A circadian clock is an endogenous oscillator entrained by external temporal cues. Circadian control of gene expression is a ubiquitous feature which appears to have arisen independently in bacteria, fungi, plants and animals [1]. Since the discovery of the first Arabidopsis circadian mutant in 1995 [2], the significance of the circadian clock in plants has become increasingly evident. Approximately 30% of genes in Arabidopsis are predicted to be under circadian control, regulating photosynthetic, metabolic and developmental pathways [3,4]. Moreover, a selective advantage resulting from a clock which is matched to the exogenous day-length has been demonstrated in mammals, insects, bacteria and plants [5][6][7][8][9].
The most recent model for the molecular control of the Arabidopsis clock is comprised of a series of interlocking negative transcriptional feedback loops regulated by key activators which control the oscillation of clock gene expression [10]. To ascertain the underlying nature of circadian rhythms, a clock-controlled output representing the pace of the clock must be measured in constant (free-running) conditions. Previously, this research has been conducted by studying leaf movement rhythms or by following luciferase gene expression under the control of a circadian regulated promoter [11][12][13]. Delayed fluorescence (DF) imaging provides an alternative to these methods that does not require plant transformation. It has previously been shown to work in a variety of plants for which leaf movement assays are not feasible [14,15]. Delayed fluorescence occurs when excited electrons in photosystem II (PSII) undergo spin-conversion to a triplet excited state before charge recombination allows them to return to their ground state releasing light energy [16]. Measurements of DF have been correlated with the photosynthetic state of PSII [17] and the amount of DF production is regulated by the circadian clock. DF can be measured with a low-light imaging system identical to that used for luciferase imaging and output rhythms have been shown to oscillate with a comparable period to those estimated from luciferase reporter experiments [14]. The output from a DF experiment is a waveform which has parameters that can be mathematically defined and therefore quantified. These parameters include 'period' (the time taken to complete one cycle), 'phase' (the time of day at which this peaks) and 'amplitude' (the distance between the peak and the baseline of the oscillation). Important to circadian dynamics is also the idea of 'rhythm robustness' i.e. whether these parameters change over time. In this paper, rhythm robustness was assessed by: the percentage of samples classified as rhythmic; the relative amplitude error (RAE); the period coefficient of variation (CV) and the average period error threshold (all defined in Additional file 1). Together, these parameters allow the effects of different imaging conditions to be quantified.
As DF measurement is correlated with the oscillations in photosynthetic status of PSII, leaf material is the logical choice for a representative sample. Rhythms have been shown to persist in excised leaves in several species [18][19][20][21][22]. However, previous research has demonstrated that independent clocks run at different periods throughout the plant under constant conditions, coordinated by a degree of intercellular coupling [23][24][25][26][27]. The extent to which the clock is affected by dissecting leaf material into small segments is investigated in this paper.
Alongside these spatial differences, the clock has also been shown to be temporally dynamic and is affected by the life history of the plant. Both the systemic age of the plant and the 'emergence age' of the individual leaves on a plant have been reported to effect the clock in Arabidopsis, with increasing age associated with period reduction [28]. Conversely, the timing of leaf senescence has also been shown to be directly regulated by core circadian genes [29].
In addition to this endogenous entrainment, the clock is also responsive to external stimuli; the most well characterized of which are light and temperature cues. Increasing light intensity causes a shortening of period in free-running conditions [30][31][32] and these rhythms rapidly dampen in amplitude under continuous darkness [33]. Circadian systems are relatively buffered against temperature changes compared to other biochemical reactions but are not completely independent of it [34]. Period shortening of 1.8-4.2 h have been reported following temperature increases from 17 to 27 °C determined by both leaf-movement assays and luciferase reporters under circadian regulation in Arabidopsis [31,35,36]. Seedlings grown at 17 °C also have rhythms with lower period variability and RAE values than plants grown at 27 °C [35,37]. The extent to which rhythms are temperature compensated is described using the inverse of the temperature coefficient Q10; the change in the rate of a process over a temperature change of 10 °C [38].
Here we present an optimized protocol for highthroughput phenotyping of circadian period using two crop plant models; Triticum aestivum (bread wheat) and Brassica napus (oilseed rape). B. napus (AACC) and T. aestivum (AABBDD) are both recent polyploids still undergoing genomic rearrangements. The contribution of each genome to clock function remains to be investigated. B. napus is a dicot recently diverged from Arabidopsis [39] and so is likely to have clock homologs with similar functions. T. aestivum is a monocot with an incompletely understood clock mechanism [40]. These species therefore provide interesting insights into two genetically diverse families. Both T. aestivum and B. napus have been influenced by human domestication, genome duplication events and geographical speciation as the use of these crops became globalized. The specific and combined effects of these factors on the control of the clock is yet to be investigated.
Within this paper we show that both the age of the plant and the developmental age of leaves have significant effects on period with older material displaying shorter rhythms. To make our method high-throughput whilst still providing reliable rhythms, tissues were segmented into various sizes and compared to whole leaf samples. We identify regions of the plant leaves which are the most robustly rhythmic and give the most consistent period estimates. Both the light regime and temperature conditions also had large effects on period estimation and we describe conditions optimal for each species.
Finally, we applied our optimized, high-throughput DF method to investigate differences between elite cultivars in both B. napus and T. aestivum and demonstrate it to be a useful tool for assaying circadian rhythms in these crop species.

Circadian variability due to leaf development and age of plant
We tested the effect of both plant and leaf aging on period estimates from Brassica and wheat seedlings. Previous studies in Arabidopsis have reported that the pace of the clock increases as the plant ages and that earlier emerged leaves have a shorter period than those which emerge later within the same individual [28]. Our results mirror these findings for young wheat and Brassica plants, however this association was lost for older material (Fig. 1a). For wheat we calculated period estimates from the second leaf of plants at 18, 25, 32 and 39 days after sowing and show that between 18 and 32 days period decreases linearly at a rate of approximately half an hour per week while maintaining a near constant relative amplitude error (RAE) (Fig. 1a, b). However, in leaves from 39 day old plants there was an increase in both average period and relative amplitude error, potentially due to metabolic changes as a leaf changes from a source to a sink tissue or due to the onset of senescence in these samples. A one-way analysis of variance yielded a significant effect of wheat age on both period and RAE (F(3,90) = 12.13, p < 0.001) and (F(3,90) = 7.018, p < 0.001) respectively. Based on our investigation, we recommend using plants between 25 and 32 days after sowing. At 25 days 100% of samples were classified as rhythmic and period CV was 1.52 h. 32 day old samples were also robust, having the lowest RAE (0.15) and period error (0.43) averages (see Additional file 1: Supplementary material S1).
In a separate experiment, we analyzed 4 leaves from 25 day old wheat plants as is shown in Fig. 1c, where leaves 1 and 3 were the oldest leaves and leaves 2 and 4 the second oldest leaves from the main and secondary tiller, respectively. There was a statistically significant difference between the mean periods at each leaf age (one-way ANOVA (F(3,83) = 7.434, p < 0.001). Within each tiller pair, the older leaf had a shorter period than the younger leaf and had higher RAE averages (Fig. 1d, e). The mean period for leaf 4 (24.50 h) was found to be significantly longer than both leaf 1 (23.15 h) and leaf 3 (23.32 h) (Tukey HSD). We recommend using leaf 2 as it had the best overall circadian robustness with regards to the % samples returned (100%), RAE (0.18) and period error (0.50) (Additional file 1: Supplementary material S2).
For Brassica seedlings, plants were grown to 4 different ages: 20, 25, 30 and 35 days after sowing and leaf 1, 3 and 5 were sampled in the same experiment with leaf 1 being the earliest emerged leaf and leaf 5 the most recently emerged leaf (Fig. 2). We conducted a nested ANOVA to test the effects of both plant age and within-plant leafage on period. We found that variation in plant-age had a significant effect on period, with increasing age causing a shortening of period (F(3,53) = 8.48, p < 0.001). The nested effect of leaf age within each plant age-group was also found to be significant (F(8,53) = 5.45, p < 0.001). The largest difference between leaves in each age-group was seen for 20 day old plants where a difference of 3.14 h was observed between leaf 1 and 5 (p < 0.001, Tukey HSD) (Fig. 2a). Brassica plant-age was also found to have a significant effect on RAE averages with younger plants having a lower mean RAE (F(3,53) = 5.953, p < 0.01) (Fig. 2b). Additional file 1: Supplementary material S3 shows robustness statistics for all plant ages and leafages tested. We recommend using leaf 1 from 20 day old plants as they had the lowest RAE (0.15) and period error threshold (0.47).
To approximate the period shortening due to plant aging in Brassica we followed the changes in average period in leaf 5 across plant ages from 20 days after sowing to 30 days after sowing. Our analysis revealed that period shortened by approximately 3 h per week from a mean of 26.50 h (SD 1.17) to 22.38 h (SD 0.62).

Finding an optimal size of leaf sample
We needed to identify representative leaf sections which allowed a sufficient number of samples to be analyzed on one plate without compromising the robustness of rhythms for period estimation. For wheat, we selected leaf 2 from 25 day old plants and analyzed the periods and circadian robustness given by whole leaves compared to leaves cut into 10 cm sections and leaves cut into 4 cm sections as shown in Fig. 3a. By taking 4 cm samples from 2 regions on the same leaf (5 or 15 cm down from the tip) we could investigate changes in period across the length of the leaf. For Brassica seedlings we selected leaf 1 from 21 day old plants and then kept them whole, took 3 cm square samples from the centre or quartered them (Fig. 3b). This helped inform whether any changes in circadian characteristics were a result of size reduction or from sub-sectioning regions of the leaf. Our data showed that period and RAE averages were not significantly affected by cutting samples in wheat (Fig. 3c, d) (F(3,75) = 2.066, p > 0.1, one-way ANOVA). However, cutting Brassica leaves did significantly affect period estimates; quartered Period (hours) 18 Plant age (days) 25 32 39 18 Plant age (days) Brassica seedlings were grown to 4 different ages: 20, 25, 30 and 35 days after sowing. Leaves 1, 3 and 5 were sampled from each plant in the experiment with leaf 1 being the earliest emerged leaf and leaf 5 the most recently emerged leaf. Boxplots show differences in period (a) and RAE (b) for each leaf age within each plant age. Colour scales reflect an ageing gradient with lighter colours representing younger material. Periods and RAE estimates were calculated using FFT NLLS (BAMP dtr, 24-120 h cut-off ). Data represents results from two imaging cabinets run in parallel as technical replicates and normalised for the between-cabinet effects. Age 20: leaf 1 (N = 6/6), leaf 3 (N = 6/6), leaf 5 (N = 6/6). Age 25: leaf 1 (N = 4/6), leaf 3 (N = 6/6), leaf 5 (N = 6/6). Age 30: leaf 1 (N = 2/6), leaf 3 (N = 5/6), leaf 5 (N = 6/6). Age 35: leaf 1 (N = 6/6), leaf 3 (N = 6/6), leaf 5 (N = 6/6). Significance codes: ***p < 0.001, **p < 0.01 *p < 0.05, all significance markers are relative to leaf 1 at each age segments had a slightly longer period than whole samples (F(2,113) = 5.46, p < 0.01, one-way ANOVA, Tukey HSD (Whole-Quarter p < 0.01) but RAE means were similar (Fig. 3e, f ) (Additional file 1: Supplementary material S4). From this data we recommend using 10 cm segments for wheat and 3 cm square sections for Brassica imaging as these gave similar results to whole leaves and increased throughput by 44% for Brassica and 100% for wheat. We next wanted to investigate whether period estimates changed across the axis of the leaf. We selected only the whole leaf images and digitally sectioned them into 10 or 5 regions of interest for wheat and Brassica leaves respectively (Fig. 3g, h). Using this approach we observed an average within-leaf variance of 0.45 h in wheat and 0.42 h in Brassica leaves. This variation was larger than the leaf-to-leaf variation determined for wheat (0.04 h) and Brassica (0.3 h) leaves. The mean period and RAE for each section across these leaves was calculated and plotted (Fig. 3g, h). No significant difference was observed between the period of wheat or Brassica segments; however the RAE was significantly different across wheat leaves (F(9,139) = 6.077, p < 0.001, One-way ANOVA). The middle segments (4, 5, 6, 7 and 8) had significantly lower RAE averages compared to the tip (segment 1) suggesting that this middle region may give the most robust DF rhythms.

Constant free-running conditions: dark versus light
Two light regimes were tested which allowed free-running DF rhythms to be recorded. We entrained plants for 4  RAE ratios reflected the accuracy seen in period estimation between the regimes (Fig. 4c).

Finding an optimum free-running temperature
To investigate the effect of temperature on period and rhythm robustness we tested Brassica and wheat seedlings at a range of constant temperatures. We used the optimal conditions from the variables so far tested and entrained each batch of plants at the imaging temperature for 4 days prior to imaging (see Methods). Both Brassica and wheat experienced an acceleration of the clock at higher temperatures, with the rate increasing most dramatically at lower temperatures (Fig. 5a) ). Q10 was found to be 1.12 for wheat and 1.14 for Brassica indicating a degree of thermal compensation, but to a lesser extent than has been previously reported in Arabidopsis [36]. We next looked at which temperatures gave the best rhythmicity in each crop. Rhythms were most robust in wheat grown at 27 °C: 100% of period estimates were returned, the average RAE ratio was 0.15, period CV was 2.48% and period error threshold was 0.48 (Additional file 1: Supplementary material S6). There was a clear negative trend in period CV as the temperature increased in wheat from 13.63% at 17 °C to 1.38% at 32 °C. Mean RAE at each temperature can be seen in Fig. 5b.
Across the temperatures tested Brassica rhythm robustness remained consistent; all samples were returned from FFT-NLLS and RAE, period CV and Period error were similar (Fig. 5b, Additional file 1: Supplementary material S6). We recommend 22 °C for DF using Brassica as it had the lowest period CV of 2.24%.

An optimized DF method can be used in circadian analysis for crops
To see whether the optimized method could be used to investigate circadian differences between cultivars of For the B. napus lines, seeds were obtained from 3 different harvest years to see whether period was constant between batches. The optimized imaging parameters we used for these elite cultivars is outlined in Table 1.
There was significant variation in the periods of the wheat lines tested as shown in Fig. 6a (F(6,152) Figure 6b shows the variation in period across three Brassica lines taken from three seed batches. We conducted a two-way analysis of variance to compare cultivar ID and seed batch effects as well as the interaction between the two factors. The cultivar ID was found to have a significant effect on period (F(2,60) = 25.47, p < 0.001) but batch year did not significantly account for any variation in period either as a main effect (F(2,60) = 1.73, p > 0.1) or as an interaction with the cultivar ID (F(4,60) = 2.27, p = 0.72). This suggests that the observed differences in period are due to heritable genetic differences. The Brassica cultivar Norin had the shortest overall period of 22.29 h (SD 0.34); shorter than either Cabriolet (23.32 h, SD 0.57) or Chuanyou II (23.18 h, SD 0.72) (p < 0.001, Tukey HSD).
DF oscillations in both Brassica and wheat remained rhythmic throughout the experiment allowing confident period estimation over 4 days (24-120 h following T 0 ). The average DF oscillations for the two most divergent wheat lines is shown in Fig. 6c; the other lines have been omitted for clarity. DF expression from all 3 years was averaged to make the oscillation plots for the Brassica lines as shown in Fig. 6d. The percentage of DF rhythms returned from period estimation was high for both Brassica (96.3%) and wheat (98.8%) proving that the method is both efficient and reliable.
The overall throughput of this assay is dependent on the expected exclusion rate from period analysis and on the number of imaging cabinets available. Designs with 3 replicates per plate allow 10 independent lines to be assayed per cabinet over one experiment allowing for an expected 5% loss of samples. If rhythms are expected to be less robust, for example in a mutant screen, we suggest using a larger number of replicates. The scaling-up of this imaging assay to multiple cabinets is also becoming increasingly affordable as the CCD camera technology progresses.

Discussion
Manipulating the circadian clock has potential for influencing crop productivity, efficiency and resilience; however research has been hindered by the lack of highthroughput circadian protocols which can be reliably applied to crop plants. Transcriptional assays, luciferase constructs and fluorescent markers have been used to investigate circadian rhythms in tobacco [13], tomato [41], potato [42,43], Brassica rapa [44], rice [45][46][47], barley [48] and wheat [49]. However, these approaches are either manually intensive, technologically expensive or require genetic modification to systematically investigate each component and so are low throughput. We have optimized a delayed fluorescence imaging method for reliable circadian phenotyping of either Brassica or wheat seedlings. Several differences between the function of these clocks have been exposed through the factors examined in this paper. The opposing robustness of clocks under D:D or L:L and the fact that DF rhythms peak with distinct phases under each condition is indicative of diverging networks underlying circadian control of each species. Lower temperatures (17 °C) also seem to have a detrimental effect on the robustness of the clock in T. aestivum but not B. napus, suggesting that temperature may be a stronger zeitgeber for wheat than for Brassica within this temperature range. The DF rhythms in both T. aestivum and B. napus have reduced temperature compensation compared to those reported for leaf movement in Arabidopsis [36,37]. However, it is important to recognize that our rhythms were measured in dissected sections of leaves and may not be truly analogous to rhythms from whole Arabidopsis individuals. The difference between intact and excised leaves has been previously reported in Hall et al. [22]. Our analysis of the homogeneity of periods across a single leaf also revealed variability of period robustness across the axis of wheat leaves but relatively little variation across Brassica leaves.
In this study, we have shown that in both Brassica and wheat there is a strong interaction between circadian period and age due to both systemic aging and leaf-specific developmental aging. Previous research in Arabidopsis has asked whether the onset of senescence is a result of a faster running clock or vice versa [28,50]. Our results suggest that the acceleration of the clock occurs in very young plants before senescence phase, raising the possibility that the clock could be artificially manipulated to moderate senescence and control timing of peak productivity in crops.
Natural variation of circadian phenotypes has been previously demonstrated in wild Arabidopsis accessions [35,36,51] revealing a selection pressure for circadian traits specific to different ecological settings. The extent to which circadian fitness has been selected-for in modern crop plants has not yet been investigated. Application of our optimized protocol in this study demonstrates that diverging rhythms are present within elite cultivars of the same species. This variation in circadian period suggests that some level of circadian diversity exists, but the question remains as to whether each cultivar is currently optimized to enhance individual plant fitness. Crop plants with 'optimized circadian clocks' may have the capacity to improve yield, efficiency and resilience potentially overlooked by traditional plant breeding methods.

Conclusions
In this study, we investigated several important factors influencing circadian rhythms in Brassica napus and Triticum aestivum and reveal intriguing differences between the two crops. We provide an optimized DF methodology which can be reliably used for high-throughput measurement of circadian rhythms. This research highlights the considerable plasticity of the circadian clock under freerunning conditions. It is our hope that these results may inform future research by showing the extent to which controllable variables can affect period estimation and how these may differ depending on the model species being studied.

Plant material and growth conditions
Brassica seedlings used were from the winter varieties Cabriolet and Norin and the semi-winter variety Chuanyou II from the OREGIN Brassica napus Diversity Fixed Foundation Set (BnDFFS) [52]. Wheat seedlings used were all hexaploid elite cultivars ordered from the Genome Resource Unit (John Innes Centre) (Additional file 1: Supplementary material S8).
Brassica plants were grown in Levington's F2 mix in FP11 pots, spaced 5 plants to a pot. They were grown in controlled greenhouse conditions, Wheat plants were imbibed at 4 °C for 6 days before being planted in Petersfield cereal mix in FP9 pots, spaced two to a pot. They were then grown in controlled greenhouse conditions (16:8 h L:D 17:12 °C). After 21 days plants were transferred to a plant growth chamber set at the cabinet conditions above. For temperature experiments, plants were entrained at the temperatures in which they would be imaged.

Image acquisition-standard conditions
Leaves were removed just after entrainment dawn and placed face up onto 24 cm square petri dishes (Stratlab LTD, cat no. 163-PB-007) containing 0.5% water agar (Sigma-Aldrich, SKU A1296). Unless otherwise stated, 3 cm squares were cut from the second true leaf of 21 day old B. napus seedlings. A segment of 10 cm was taken from the second leaf of the main tiller of 25 day old T. aestivum seedlings, beginning 5 cm down from the tip. A small strip of agar was placed over the ends of wheat sections to prevent leaf curling during the experiment. Plates were secured with masking tape around the periphery.
The imaging set-up is adapted from that described by Southern et al. [53]. A set-up schematic can be seen in Additional file 1: Supplementary material S10. We use Lumo Reteiga CCD cameras (QImaging, Canada), which we have found to have comparable image quality to the Orca II (Hamamatsu Photonics, Japan) without the need to run a water-cooling pump. Cameras were fitted with a Xenon 0.95/25 mm lens (Schneider-Kreuznach, Germany).
Both camera and LEDs were housed in a temperature controlled growth cabinet (Sanyo MIR-553) in a dark room. The temperature was set to 22 °C unless otherwise specified [changed for the temperature experiments (Fig. 5) and for the wheat cultivar experiment ( Fig. 6)]. Camera properties were kept the same in each experiment (Binning = 4, Gain = 1, Readout-Rate = 0.650195 MHz 16 bit) and camera exposure was initiated 500 ms after the lights were turned off. A 'L:L' script refers to a regime of 59 min of light followed by a 1 min exposure in the dark. A 'D:D' script refers to 54 min of darkness followed by 5 min light and then the 1 min exposure. BeanShell scripts run by μManager have been adapted from scripts used previously [56] and are available to view as Additional files 2 and 3. Wheat imaging used the D:D script and Brassica imaging used the L:L script with the exception of experiments in Fig. 4.

Processing in FIJI and BioDare2 parameters
Image stacks were imported into FIJI [57] and regions of interest were selected. Measurements for integrated density were taken for these regions across the stack using the Multi-measure plugin. Each region was then labeled in Excel and an offset time series added. The 'offset time' is the difference between the time of the first image (T1) and entrainment dawn (ZT) in decimal hours. Data can then be uploaded to BioDare2 as described online [58,59]. BioDare2 is an open-access web tool for analyzing timeseries data and predicting circadian parameters. For our data we found that Baseline and amplitude (BAMP) de-trending was most appropriate but recommend visual inspection of the detrending methods available to find the least intrusive method which removes any baseline trends. Period estimation was done using the Fast Fourier Transform Non-Linear Least Squares (FFT-NLLS) algorithm [60] on a data window of 24-120 h with expected periods set to 18-34 h. Manual inspection of resulting periods ensured that all arrhythmic traces were excluded from further analysis.

Rhythm Robustness analysis
We summarized rhythm robustness metrics based on several BioDare2 outputs. '% returned' is the number of samples for which periods could be estimated out of the number of samples originally imaged. The RAE (relative amplitude error) is the ratio of amplitude error to amplitude and represents amplitude robustness. A RAE of 1 indicates the most irregular waveform which can still be classified as rythmic whereas a RAE of 0 indicates a perfect sine wave with no amplitude error. The period coefficient of variation (CV) is the standard deviation of period estimates adjusted for the mean period and represents between sample variation [58,61]. Period error is the extent to which the period estimate could vary and still give a good fit to the model. Error scores close to 0 indicate a tight fit of the model to the observed data and a high within sample period robustness. See Additional file 1: Supplementary materials S1-S6 for statistic tables and further descriptions.

Normalization for experimental effects
After circadian parameters were estimated in BioDare2, data was normalized to account for the following random experimental effects. For the wheat plant age and leaf age experiments (Fig. 1), Brassica plant-leaf age experiments (Fig. 2) and the Brassica cultivar experiments (Fig. 6b) samples were split between two imaging cabinets run in parallel in a single experiment. The predicted parameters (e.g. period) for each sample from the two cabinets were adjusted so that the cabinet means were then equivalent. This was achieved by dividing the cabinet means by the overall mean to get an adjustment factor for each cabinet and then dividing each individual value by that factor to get a cabinet-normalized value. For the cutting data (Fig. 3), the experiments were replicated in two separate imaging weeks and then adjusted for