Abundant clock proteins point to missing molecular regulation in the plant circadian clock

  1. Uriel Urquiza-García
  2. Nacho Molina
  3. Karen J Halliday
  4. Andrew J Millar

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Abstract

Understanding the biochemistry behind whole-organism traits such as flowering time is a longstanding challenge, where mathematical models are critical. Very few models of plant gene circuits use the absolute units required for comparison to biochemical data. We refactor two detailed models of the plant circadian clock from relative to absolute units. Using absolute RNA quantification, a simple model predicted abundant clock protein levels in Arabidopsis thaliana , up to 100,000 proteins per cell. NanoLUC reporter protein fusions validated the predicted levels of clock proteins in vivo. Recalibrating the detailed models to these protein levels estimated their DNA-binding dissociation constants ( K d ). We estimate the same K d from multiple results in vitro, extending the method to any promoter sequence. The detailed models simulated the K d range estimated from LUX DNA-binding in vitro but departed from the data for CCA1 binding, pointing to further circadian mechanisms. Our analytical and experimental methods should transfer to understand other plant gene regulatory networks, potentially including the natural sequence variation that contributes to evolutionary adaptation.

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  1. Version published to 10.1038/s44320-025-00086-5
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    Reply to the reviewers

    1. General Statements

    We are very grateful for the three reviewers’ positive and considered comments. We copy specific comments below in bold font, and address them in turn including quotations from the revised manuscript in italics.

    2. Description of the planned revisions

    One Supplementary Figure could be copied from an earlier manuscript to show the model circuits, please see Reviewer 3 comment 1, below.

    3. Description of the revisions that have already been incorporated in the transferred manuscript

    Reviewer 1

    __Major

    1. In this work, the authors observed discrepancies between the estimated and actual values of DNA-binding dissociation constant (Kd). Such inconsistencies may arise if the model used to simulate Kd omits certain regulatory mechanisms. For example, previous studies (____https://doi.org/10.1371/journal.pcbi.1008340____, ____https://doi.org/10.1098/rsfs.2021.0084____) showed that when specific gene regulatory mechanisms are missing, the dissociation constant required for generating oscilla-tions can be underestimated. Thus, the inconsistency between the estimated and ac-tual Kd values might result from missing mechanisms in the model. It would be benefi-cial if the authors could discuss this possibility. __

    We thank the reviewer for these examples, which illustrate the relevant point that multiple biochemical processes can contribute to the non-linearity required to simulate a particular clock behaviour within biochemically-reasonable parameter values. We now cite both, along with the original Buchler & Louis paper on the titration mechanism in general, as follows:

    “It is possible that the measured, bulk clock protein levels might over-estimate the protein available for promoter binding due to mechanisms absent from the model, such as protein partitioning outside the nucleus (Yakir et al, 2009), protein titration (Buchler & Louis, 2008), clustering of proteins within the nucleus, a processing step akin to the formation of a smaller EC pool from a fraction of the bulk LUX protein or any combination of these mechanisms (Jeong et al, 2022b; Yao et al, 2022).”

    __ Minor

    1. The order in which the figures are mentioned does not match the order of the figures. Please adjust the sequence of the figures accordingly. __
    • The amalgamated PDF for review presented the Figures and Supplementary Figures in the order of citation, which we intended for the reviewers’ convenience. As this didn’t help two of the reviewers, they are now in numerical sequence.

    __ In the last paragraph of Introduction, the authors state, 'The absolute numbers of proteins directly constrain their possible biochemical activities (Kim & Forger, 2012)'. It would be helpful to also cite Jeong et al. (____https://doi.org/10.1073/pnas.2113403119____), who showed that two circadian neuronal groups in Drosophila, containing different amount of clock proteins, exhibit distinct molecular properties within the circadian clock. __

    • Added a citation to this relevant example later in that sentence.

    __ In the title of the first section of Results, 'Predicting clock proteins levels' should be revised to 'Predicting clock protein levels.' __

    • Done

    __ The description of the results in Figure 4 is unclear. Please, refer to the color and shape of the points when explaining the results for better clarity.__

    • The legend of Figure 4 now refers to both characteristics. Reviewer 2

    __2.1. Limited Generalizability of Some Assumptions: __

    __The translation and degradation rate assumptions are based on data from specific temperature and light conditions, which may not generalize well to other growth conditions. The authors could address this point by explicitly stating this limitation and explaining how variable conditions would affect the model's underlying assumptions. __

    • To address this point, we now note in Discussion: “For example, the reporter assays could quickly test protein numbers under different conditions from those reported here, to understand the biochemical mechanisms for the canonical ‘temperature compensation’ of circadian period in constant conditions (as modelled in Gould et al, 2013) and/or the adaptation to fluctuating, natural conditions (see Future perspectives: models informed by genome sequence, below).”

    __2.5. Simplified Model for Translational Efficiency: __

    __The model simplifies translational efficiency, which may not fully capture the complexity of clock protein synthesis. A more comprehensive approach, considering factors like ribosome density variation across transcripts, would add depth to the protein quantification model. Experiments are not required here. But it'd be nice to explain how a more complex model involving differential ribosomal density per transcript could affect the overall conclusions. __

    • The ‘simple model’ is intentionally simple. We note in the Results that it even ignores the published light/dark-regulation of translation rate, both generally in Arabidopsis and specifically for LHY. To address this point, we have added in Discussion, “In other words, the bulk levels of these clock proteins might be rather simply regulated. The simple model’s approach could justifiably be repeated to estimate the levels of other proteins, and extended to test where more complex biochemical mechanisms, such as translational regulation, are functionally significant.”

    __ Minor Points __

    __- Figure Legends: Several figures lack sufficient detail in legends, particularly Figures 3 and 5, where the methodology for generating the predicted protein levels and Kd values could be described a bit more, without majorly elongating the caption length. __

    • Both legends have been updated. However, the methods are described in detail in the Supplementary Information, which provides much more space. - Unclear Units in Supplementary Table 1: Some units in Supplementary Table 1 for translation and degradation rates are not clearly specified.

    • Units seem clear in the column headings, as follows:

    s (proteins per mRNA per hour)

    k or klight (per hour)

    kdark (per hour)

    The reviewer might be highlighting that some values of kdark were given as “-“ because that protein did not have light-regulated degradation in the simple model, so degradation rate was just k rather than *klight *and kdark. This notation has been updated to NA, with an explanatory note in the supplementary table legend.

    Reviewer 3

    1. __ I would have appreciated inclusion of an additional figure describing the U2019 and U2020 that were previously published by this group in 2021, along with a brief clarification of the differences between the simple and full versions of these models (Beyond the small summary presented in Figure 8). __ Supplementary Figure 3 of Urquiza and Millar 2021 shows simplified circuit diagrams of the two models and could be added as a new Supplementary Figure in this manuscript, as the editor prefers. To address this point, we added an introduction to the detailed models in the Results: “Our detailed models of the clock gene circuit (see Introduction) are not driven by rhythmic data input like the simple model, but rather use ordinary differential equations to recapitulate the dynamics of each RNA and protein component in the clock circuit, along with their interconnected feedback loops and their regulation by light signals. The models autonomously generate rhythmic patterns of RNA and protein expression that match the rhythmic data. The gene circuits in models U2019 and U2020 differ only in the regulation of daytime processes, involving LHY/CCA1 and the PRR genes (Urquiza-García & Millar, 2021). The circuit of U2019 is closer to its antecedent model P2011 (Pokhilko et al, 2011), using gene activation, whereas U2020 uses repression (for circuit diagrams, see Supplementary Figure 3 of (Urquiza-García & Millar, 2021). Repression is better supported by molecular data but U2020 simulations fit the data no better than, or slightly worse than, the activation-based model U2019 (consistent with Fogelmark & Troein, 2014), so we use both circuits here.”

    __Minor comments __

    __Supplemental figure 2 is partially cut off __

    • Corrected. Only the edge of a label was affected. It would be useful if figures/supplemental figures were provided in order.

    • Corrected, see reviewer 1 above.

    4. Description of analyses that authors prefer not to carry out

    Reviewer 1

    N/A

    Reviewer 2

    __2.2. Discrepancies in CCA1 Binding Affinity: __

    __The model's simulated Kd values for CCA1 largely deviate from empirical measurements, suggesting missing mechanisms that may impact protein binding affinity. This might be due to some structural or environmental factors influencing CCA1 binding. No experiments are needed here but some plausible explanations would enhance the manuscript. __

    • This point is addressed in the section ‘Future perspectives: investigating Kd in vivo’, now enhanced by our response to reviewer 1’s major comment, as noted above. __2.3. Limited Data for Evening Complex Proteins: __

    __The model assumptions for ELF3, ELF4, and LUX rely on estimated degradation rates, which could introduce inaccuracies in the predictions. Empirical quantification of these rates would strengthen the reliability of these protein dynamics in the model. If these experiments are too resource and time intensive, then include some explanation of how changing these estimated degradation rates would affect the overall result. __

    • We assume that the reviewer is referring to the k parameters of the simple model driven by RNA data, as in Figure 2, which gives the predicted protein levels that we compare to measured protein levels in Table 1. Both the prior degradation rate data and our NanoLUC reporter measurements are strongest for LHY, CCA1, PRR7 and TOC1, so these are our focus. New measurements of degradation rate for ELF3, ELF4 and LUX are indeed beyond our scope. Our reporter methods might facilitate future measurement of such parameters by other researchers. In the Supplementary Information, we outline the estimation of degradation rates k, which returned biologically plausible protein half-lives for LUX = 3.7 h, ELF4 = 1.3 h and ELF3 8.7 h. We have no data for ELF4 and we highlight the specific limitations of our ELF3 and LUX data in the Results and Discussion text, Table 1, Methods and Supplementary Information. Taking the *in vivo *data for ELF3 for example (Table 1), the protein levels predicted by the simple model using that degradation rate were within 6% to 7% of the measured levels at the peak and at the trough under LD. This independent result supports the estimated degradation rate: varying the estimated degradation rate for ELF3 would not maintain a prediction so remarkably close to the data.

    __2.4. Unexplained Variability in Reporter Data: __

    __The NanoLUC reporter assays show some variability that the model does not account for, possibly due to factors like differential protein stability or folding in vivo. Further tests across different expression contexts, or including protein stability measurements, would clarify these inconsistencies. If these experiments are too resource and time intensive, then include some explanation of how changing these estimated degradation rates would affect the overall result. __

    • This comment cannot be addressed without knowing which of the many possible data series the reviewer is referring to, and whether the variability of interest is in level, timing or a higher-order dynamic behaviour. For example, we discuss three specific instances where reporter and model behaviour differs, in detail, in Discussion section ‘Refining the modelled protein profiles’ (726 words).

    Reviewer 3

    __ It would have been useful to quantify the mRNA expression levels in the rescued transgenic lines to enable direct comparison to WT. The use of multiple independent transgenic lines supports the authors' conclusions but this characterisation would aid future research. __

    The proposed study most directly addresses whether RNA from the reporter transgene is functionally equivalent to wild-type RNA, whereas the focus of this article is at the protein level. As the reviewer notes, the proposed study would principally be an aid to future research, so we prefer not to start that additional experimental work.

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    Referee #3

    Evidence, reproducibility and clarity

    Summary

    This is a valuable manuscript that begins to factorise the plant circadian model according to estimated protein translation and degradation rates. These models are iterative by nature, but the latest models provide a significant advance in our understanding and highlight avenues for future exploration. The use of Nanoluc protein:reporter fusions enables estimation of protein abundance, providing additional support for the modelled biological process.

    The latest models highlight discrepancies between protein abundance predicted in the model compared to the experimental evidence, and sensible suggestions are discussed to prioritise experiments to enable greater biological understanding.

    Major comments

    1. I would have appreciated inclusion of an additional figure describing the U2019 and U2020 that were previously published by this group in 2021, along with a brief clarification of the differences between the simple and full versions of these models (Beyond the small summary presented in Figure 8).
    2. It would have been useful to quantify the mRNA expression levels in the rescued transgenic lines to enable direct comparison to WT. The use of multiple independent transgenic lines supports the authors' conclusions but this characterisation would aid future research.

    Minor comments

    Supplemental figure 2 is partially cut off

    It would be useful if figures/supplemental figures were provided in order.

    Significance

    This work extends models of the plant circadian system to assess absolute protein numbers. This enables the biological 'plausibility' of the model to be assessed and also highlights where the model diverges from experimental data, indicating where additional understanding is required.

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    Referee #2

    Evidence, reproducibility and clarity

    1. Summary of this work

    This manuscript delves into the Arabidopsis circadian clock by addressing a major gap in plant gene circuit models-particularly, the lack of absolute units for protein quantification, which has historically hindered comparisons to biochemical data. By recalibrating two mathematical models of Arabidopsis thaliana's circadian clock from relative to absolute units, the authors introduce a framework that allows protein levels to be quantified in terms of copies per cell. This approach facilitates more direct comparisons between model predictions and empirical measurements.

    The core of the study involves both analytical predictions and experimental validation to quantify protein levels for key clock proteins (such as LHY, CCA1, PRR7, and TOC1) using RNA data and luciferase reporter protein fusions. The simple model predicts the abundance of clock proteins, suggesting that the protein concentration may reach up to 100,000 copies per cell, which was then verified through experiments involving NanoLUC reporters. The recalibration of detailed mathematical models enabled the calculation of DNA-binding dissociation constants (Kd) based on empirical data, establishing a bridge between theoretical and experimental insights for understanding plant circadian rhythms.

    The authors further explore how recalibrated models align with data by focusing on Kd values associated with DNA binding, particularly with LUX and CCA1 proteins. In vitro binding assays validated these predictions, while certain discrepancies emerged for CCA1 binding, implying other mechanisms could be influencing the observed results. Importantly, the recalibrated models provide a more realistic representation of protein-DNA interactions within the circadian clock, and the framework can be applied to understand other plant gene regulatory networks.

    Overall, the authors demonstrate how absolute protein quantification can advance our understanding of circadian rhythm dynamics in Arabidopsis. This study highlights the broader applicability of their methods, suggesting potential adaptations for investigating gene regulation across plant species and evolutionary contexts. The integration of empirical data with mathematical models introduces a new standard for rigor in plant gene circuit modeling and opens up avenues for exploring gene regulation in crop species and adaptive evolution in plants.

    1. Major points

    2.1. Limited Generalizability of Some Assumptions:

    The translation and degradation rate assumptions are based on data from specific temperature and light conditions, which may not generalize well to other growth conditions. The authors could address this point by explicitly stating this limitation and explaining how variable conditions would affect the model's underlying assumptions.

    2.2. Discrepancies in CCA1 Binding Affinity:

    The model's simulated Kd values for CCA1 largely deviate from empirical measurements, suggesting missing mechanisms that may impact protein binding affinity. This might be due to some structural or environmental factors influencing CCA1 binding. No experiments are needed here but some plausible explanations would enhance the manuscript.

    2.3. Limited Data for Evening Complex Proteins:

    The model assumptions for ELF3, ELF4, and LUX rely on estimated degradation rates, which could introduce inaccuracies in the predictions. Empirical quantification of these rates would strengthen the reliability of these protein dynamics in the model. If these experiments are too resource and time intensive, then include some explanation of how changing these estimated degradation rates would affect the overall result.

    2.4. Unexplained Variability in Reporter Data:

    The NanoLUC reporter assays show some variability that the model does not account for, possibly due to factors like differential protein stability or folding in vivo. Further tests across different expression contexts, or including protein stability measurements, would clarify these inconsistencies. If these experiments are too resource and time intensive, then include some explanation of how changing these estimated degradation rates would affect the overall result.

    2.5. Simplified Model for Translational Efficiency:

    The model simplifies translational efficiency, which may not fully capture the complexity of clock protein synthesis. A more comprehensive approach, considering factors like ribosome density variation across transcripts, would add depth to the protein quantification model. Experiments are not required here. But it'd be nice to explain how a more complex model involving differential ribosomal density per transcript could affect the overall conclusions.

    1. Minor Points
      • Figure Legends: Several figures lack sufficient detail in legends, particularly Figures 3 and 5, where the methodology for generating the predicted protein levels and Kd values could be described a bit more, without majorly elongating the caption length.
      • Unclear Units in Supplementary Table 1: Some units in Supplementary Table 1 for translation and degradation rates are not clearly specified.

    Significance

    1. Overall Evaluation

    The recalibration of models to absolute units for protein quantification is a novel advancement in the field, allowing more direct comparison to experimental data. The study's combination of modeling and empirical validation is robust, and the use of quantitative NanoLUC reporters adds rigor to the experimental design. The study offers a clear protocol for estimating Kd values by integrating Protein-Binding Microarray (PBM) data and Surface Plasmon Resonance (SPR) data, which is a significant methodological contribution. These approaches could become a new standard for studies aiming to link molecular and phenotypic traits in plants. Moreover, through NanoLUC reporter assays, the study provides empirical data for protein levels that align closely with the model's predictions, enhancing the validity of their model. Additionally, by creating a framework that can be adapted to other plant gene regulatory networks, the authors extend the impact of their work beyond the Arabidopsis circadian clock, hinting at potential applications in agriculture and crop science.

    I recommend this study with a minor revision, addressing the points below.

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    Referee #1

    Evidence, reproducibility and clarity

    Major

    1. In this work, the authors observed discrepancies between the estimated and actual values of DNA-binding dissociation constant (Kd). Such inconsistencies may arise if the model used to simulate Kd omits certain regulatory mechanisms. For example, previous studies (https://doi.org/10.1371/journal.pcbi.1008340, https://doi.org/10.1098/rsfs.2021.0084) showed that when specific gene regulatory mechanisms are missing, the dissociation constant required for generating oscilla-tions can be underestimated. Thus, the inconsistency between the estimated and ac-tual Kd values might result from missing mechanisms in the model. It would be benefi-cial if the authors could discuss this possibility.

    Minor

    1. The order in which the figures are mentioned does not match the order of the figures. Please adjust the sequence of the figures accordingly.
    2. In the last paragraph of Introduction, the authors state, 'The absolute numbers of proteins directly constrain their possible biochemical activities (Kim & Forger, 2012)'. It would be helpful to also cite Jeong et al. (https://doi.org/10.1073/pnas.2113403119), who showed that two circadian neuronal groups in Drosophila, containing different amount of clock proteins, exhibit distinct molecular properties within the circadian clock.
    3. In the title of the first section of Results, 'Predicting clock proteins levels' should be revised to 'Predicting clock protein levels.'
    4. The description of the results in Figure 4 is unclear. Please, refer to the color and shape of the points when explaining the results for better clarity.

    Significance

    In the manuscript by U. Urquiza-Garcia et al., entitled "Abundant clock proteins point to missing molecular regulation in the plant circadian clock," the authors refactored two models of the plant circadian clock to use absolute units, allowing direct comparison with biochemical data. This study significantly advances the integration of experimental data into computational models.

  6. Version published to 10.1101/2024.09.03.609973v1 on bioRxiv