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A spatial model of the plant circadian clock reveals design principles for coordinated timing

2022; Springer Nature; Volume: 18; Issue: 3 Linguagem: Inglês

10.15252/msb.202010140

1744-4292

Mark Greenwood, Isao T. Tokuda, James Locke,

Light effects on plants

Article21 March 2022Open Access Transparent process A spatial model of the plant circadian clock reveals design principles for coordinated timing Mark Greenwood Mark Greenwood orcid.org/0000-0002-2652-6647 Sainsbury Laboratory, University of Cambridge, Cambridge, UK Department of Biochemistry, University of Cambridge, Cambridge, UK Contribution: Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, ​Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Isao T Tokuda Corresponding Author Isao T Tokuda [email protected] orcid.org/0000-0001-6212-0022 Department of Mechanical Engineering, Ritsumeikan University, Kusatsu, Japan Contribution: Conceptualization, Resources, Software, Formal analysis, Supervision, Funding acquisition, Validation, ​Investigation, Visualization, Methodology, Project administration, Writing - review & editing Search for more papers by this author James C W Locke Corresponding Author James C W Locke [email protected] orcid.org/0000-0003-0670-1943 Sainsbury Laboratory, University of Cambridge, Cambridge, UK Contribution: Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Mark Greenwood Mark Greenwood orcid.org/0000-0002-2652-6647 Sainsbury Laboratory, University of Cambridge, Cambridge, UK Department of Biochemistry, University of Cambridge, Cambridge, UK Contribution: Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, ​Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Isao T Tokuda Corresponding Author Isao T Tokuda [email protected] orcid.org/0000-0001-6212-0022 Department of Mechanical Engineering, Ritsumeikan University, Kusatsu, Japan Contribution: Conceptualization, Resources, Software, Formal analysis, Supervision, Funding acquisition, Validation, ​Investigation, Visualization, Methodology, Project administration, Writing - review & editing Search for more papers by this author James C W Locke Corresponding Author James C W Locke [email protected] orcid.org/0000-0003-0670-1943 Sainsbury Laboratory, University of Cambridge, Cambridge, UK Contribution: Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review & editing Search for more papers by this author Author Information Mark Greenwood1,2,4, Isao T Tokuda *,3 and James C W Locke *,1 1Sainsbury Laboratory, University of Cambridge, Cambridge, UK 2Department of Biochemistry, University of Cambridge, Cambridge, UK 3Department of Mechanical Engineering, Ritsumeikan University, Kusatsu, Japan 4Present address: Whitehead Institute for Biomedical Research, Cambridge, MA, USA *Corresponding author. Tel: +81 775612832; E-mail: [email protected] *Corresponding author. Tel: +44 1223761110; E-mail: [email protected] Molecular Systems Biology (2022)18:e10140https://doi.org/10.15252/msb.202010140 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 Abstract Individual plant cells possess a genetic network, the circadian clock, that times internal processes to the day-night cycle. Mathematical models of the clock are typically either “whole-plant” that ignore tissue or cell type-specific clock behavior, or “phase-only” that do not include molecular components. To address the complex spatial coordination observed in experiments, here we implemented a clock network model on a template of a seedling. In our model, the sensitivity to light varies across the plant, and cells communicate their timing via local or long-distance sharing of clock components, causing their rhythms to couple. We found that both varied light sensitivity and long-distance coupling could generate period differences between organs, while local coupling was required to generate the spatial waves of clock gene expression observed experimentally. We then examined our model under noisy light-dark cycles and found that local coupling minimized timing errors caused by the noise while allowing each plant region to maintain a different clock phase. Thus, local sensitivity to environmental inputs combined with local coupling enables flexible yet robust circadian timing. Synopsis A spatial molecular model is developed to understand the design principles of plant clock coordination. The model shows that local cell-to-cell coupling combined with varied environmental signaling allows robust, yet flexible, timing. A spatial molecular model of the plant circadian clock provides a framework for understanding timing across cellular, organ, and whole-plant scales. Varied sensing of the environment by cells can explain the period differences observed within plants in experiments. Local cell-to-cell communication drives spatial waves of gene expression whereas long-distance communication can create period differences between organs. Under noisy light-dark conditions, local cell-to-cell communication improves timing accuracy yet allows regional phase differences to persist. Introduction The circadian clock is a 24-h genetic oscillator found in many organisms. The clock consists of a circuit of interlocking feedback loops of mRNAs and proteins that generate daily oscillations in circuit component levels. Signals from the environment align the timing of these oscillations to the day-night cycle (Webb et al, 2019). Once set, circadian clocks act as an internal timing signal, allowing biological processes to anticipate the external environmental cycles. The clock modulates a diverse range of processes in plants, including cell division, tissue growth, flowering time, and scent emission (Nozue et al, 2007; Fenske et al, 2018; Fung-Uceda et al, 2018; Greenwood & Locke, 2020). Altogether this daily timing provides a significant fitness advantage to the plant (Green et al, 2002; Dodd et al, 2005). Individual plant cells possess a robust circadian clock (Gould et al, 2018). However, substantial differences in the period and phase of clock rhythms across the plant have been observed. Time-lapse imaging experiments with luciferase and fluorescent reporter genes in the model plant Arabidopsis thaliana have shown that rhythms in core clock genes oscillate with different speeds in different organs under constant light (LL) (Thain et al, 2002; James et al, 2008; Yakir et al, 2011; Takahashi et al, 2015; Bordage et al, 2016; Gould et al, 2018). Further, experiments under a range of conditions have shown that differences in clock speed and phase can be caused by organs having different sensitivity to environmental signals (James et al, 2008; Bordage et al, 2016; Greenwood et al, 2019; Nimmo et al, 2020). Differences in the clock network between tissues may also contribute to generating differences in rhythms across the plant, as although the clock genes are broadly expressed (Bordage et al, 2016), some are tissue enriched (Endo et al, 2014), and mutations can affect organs differently (Takahashi et al, 2015; Lee & Seo, 2018; Nimmo et al, 2020). The observed differences in clock rhythms across the plant raise the question of how clocks in different cells and tissues remain coordinated with each other. One mechanism would be for cells to communicate their timing with their neighbors, effectively coupling their rhythms. High-resolution experiments have measured or inferred local coupling of clock rhythms between cells (Fukuda et al, 2007, 2012; Wenden et al, 2012; Endo et al, 2014; Takahashi et al, 2015; Gould et al, 2018; Greenwood et al, 2019), and local coupling can drive spatial waves of clock gene expression across the plant (Fukuda et al, 2007, 2012; Wenden et al, 2012; Gould et al, 2018; Greenwood et al, 2019). Longer distance coupling between clocks is also possible. For example, EARLY FLOWERING 4 (ELF4) communicates circadian temperature information over long distances by moving from the shoot to the root (Takahashi et al, 2015; Chen et al, 2020), and light information may be piped down the stem to entrain the root (Nimmo, 2018). Mathematical modeling has played a crucial role in gaining a mechanistic understanding of plant circadian clocks. Models of the network have increased in complexity over time in parallel with the growing number of experiments (Locke et al, 2005a, 2005b, 2006; Zeilinger et al, 2006; Pokhilko et al, 2010, 2012; Fogelmark & Troein, 2014). Recently, these detailed molecular models have been used to probe the differences between the shoot and root clock (Bordage et al, 2016). However, the coupling of clocks between cells was not considered. For this, more computationally tractable models of the clock network are necessary. Reduced models of the network have already been constructed that capture many of the features of the single-cell clock dynamics (Akman et al, 2012; De Caluwé et al, 2016; Foo et al, 2016; Tokuda et al, 2019). However, these models have not been applied to study spatial dynamics. Instead, “phase-only” models that lack any genetic network information and only consider the phases of individual cellular rhythms have been preferred (Fukuda et al, 2007, 2012; Wenden et al, 2012; Gould et al, 2018). Although these models allow the simulation of general oscillatory behavior, owing to their simplicity they are unsuitable for investigating molecular mechanisms of the clock. Recently, we used a “phase-only” Kuramoto model (Kuramoto, 1975) to propose a mechanism for whole-plant coordination of clocks (Gould et al, 2018; Greenwood et al, 2019). In order to match experimentally measured rhythms, we fixed clock periods to different speeds in each region of the plant. We assumed faster rhythms in the cotyledons, hypocotyl, and root tip, and slower rhythms in the rest of the root, as observed experimentally. With these periods fixed, cells were allowed to communicate clock phase through local cell-to-cell coupling. With these assumptions, simulations of the model generated waves of clock gene expression within and between organs, as observed experimentally (Gould et al, 2018; Greenwood et al, 2019). Thus, local cell-to-cell coupling could enable coordination between organs in plants. Multiple questions remain about how the plant clock coordinates rhythms that cannot be addressed using a “phase-only” model. For example, how are the periods set differently in different parts of the plant? What communication mechanisms allow the coupling of clock rhythms from cell-to-cell? How can the plant clock network “filter” both internal and environmental noise to robustly entrain to the environment? To begin to address these questions, in this work we developed a spatial network model of the plant circadian system. We modified a previously generated simplified network model and implemented it on a multicellular template of a seedling. In our model, the sensitivity to light varies across the plant, which can account for period differences between organs. We explore scenarios where cells communicate via local or long-distance transport of clock components. Simulations with local coupling capture the spatial waves observed under LL, demonstrating a plausible mechanism of circadian coordination. In contrast, simulations with long-distance coupling between the shoot and the root tip did not create spatial waves but could drive fast periods in the root tip. We applied our model with spatial differences in light sensitivity and local coupling to examine how plants keep time under noisy light-dark (LD) cycles. We found that regional differences persist even under LD cycles, but cell-to-cell coupling minimized the error in timing caused by the noise. Thus, the combination of regional differences in sensitivity to inputs and local cell-to-cell coupling allows for coordinated timing in noisy environments. Results A locally coupled spatial model of the plant circadian clock network We first implemented a reduced network model of the A. thaliana circadian clock, hereafter referred to as the De Caluwé model (De Caluwé et al, 2016). To decrease the complexity of the model, the authors grouped functionally similar genes into single entities (Fig 1A). The compact network model incorporates known light inputs to the network including “acute” activation of CIRCADIAN CLOCK ASSOCIATED 1 (CCA1)/LATE ELONGATED HYPOCOTYL (LHY) and PSEUDO-RESPONSE REGULATOR 9 (PRR9)/PRR7 at dawn, a constant increase in the synthesis of CCA1/LHY and ELF4/LUX ARRHYTHMO (LUX) under light, and altered degradation of several components in the light or dark (Fig 1A). The model qualitatively recapitulates clock dynamics under both LD cycles and LL, and at only 9 equations and 34 parameters is also computationally tractable for spatial simulations. We modified the De Caluwé model to include a repression rather than activation interaction between CCA1/LHY and PRR9/PRR7 and included a term for CCA1/LHY repressing its own transcription, as these interactions have recently been shown experimentally (Adams et al, 2015). We also adjusted the degradation rate of PRR5/TOC1 to be higher in the dark, as several studies have established that the degradation of both proteins is increased in the dark (Más et al, 2003; Kiba et al, 2007; Kim et al, 2007; Fujiwara et al, 2008) (Appendix Table S1, Materials and Methods). The identified parameter values were robust to at least 5% variation (Appendix Fig S1, Materials and Methods). Figure 1. The structure of the spatial circadian clock model Summary of the modified compact circadian clock model used for simulations. The original compact model (De Caluwé et al, 2016) was modified to update the regulatory interactions and light inputs (Materials and Methods). Yellow arrows represent light-induced synthesis, yellow circles light-induced degradation, and black circles dark-induced degradation. “T” arrows represent molecular repression. The network was implemented within each cell on a simplified template of a seedling, with cells classified as either cotyledon (blue), hypocotyl (yellow), root (purple), or root tip cells (green). Cells have a light sensitivity, Lsens, that depends on the region (Materials and Methods). To simulate local coupling, the level of CCA1/LHY mRNA in the focal cell (black squares) was assumed to be coupled to the average level of the cell’s neighbors (white squares). The strength of the coupling is set by the Jlocal parameter. We initially assumed coupling to occur through CCA1/LHY and also tested coupling through other components. Download figure Download PowerPoint We implemented the modified De Caluwé model on a simplified template of a seedling. The template consisted of approximately 800 cells, classified into cotyledon, hypocotyl, root, and root tip regions (Fig 1B, Materials and Methods). Although a number of studies have demonstrated local cell-to-cell coupling between clocks in A. thaliana (Fukuda et al, 2007, 2012; Wenden et al, 2012; Endo et al, 2014; Takahashi et al, 2015; Gould et al, 2018; Greenwood et al, 2019), the identity of the coupling signal, or signals, is unclear. Initially, to model the signal, the level of CCA1/LHY mRNA in one cell (Fig 1C, black squares) was assumed to be coupled to the average level of the cell’s neighbors (Fig 1C, white squares). The coupling strength, Jlocal, determines the extent that molecules are shared (Materials and Methods). Although we did not model diffusion directly, this coupling function was designed to simulate the passive movement of molecules which commonly occurs through plasmodesmata in plants (Faulkner, 2018). To simulate period variation between cells, at each time step, we multiplied the level of the mRNA and protein by a “scaling” parameter. For each cell, this parameter was randomly selected from a normal distribution to give a unique value for each cell through the simulation (Materials and Methods). This approach generates between-cell but not within-cell period differences, allowing us to focus on the one source of variation. Further, we could set the range of the distribution differently for each organ, as informed by experimental data (Appendix Fig S2). Different light sensitivities can explain organ-level differences in phase and period We next attempted to recapitulate in our model the differences in clock period and phase in different organs that have been observed in experiments using a single-cell CCA1-YFP reporter (Gould et al, 2018) and a GIGANTEA luciferase reporter (Greenwood et al, 2019). In these experiments, faster rhythms were observed in the cotyledon, hypocotyl, and root tip, with slower rhythms in the rest of the root. We first reanalyzed existing luciferase data (Greenwood et al, 2019) and confirmed that these relationships held for several of the core clock genes in our model, PSEUDO-RESPONSE REGULATOR 9 (PRR9), TIMING OF CAB EXPRESSION 1 (TOC1), and ELF4 (Fig 2A). Whereas in our previous “phase-only” model, we fixed the periods to be different in each part of the plant, with our spatial network model, we could now investigate what causes the differences in periods. Previously it has been hypothesized that varied sensitivities to light alter periods across the plant (Bordage et al, 2016; Greenwood et al, 2019; Nimmo et al, 2020). This was based on previous experiments demonstrating: (i) period differences between organs when exposed to equal amounts of light (Bordage et al, 2016; Greenwood et al, 2019); (ii) the loss of some period differences in the light-sensing mutant phyb-9 (Greenwood et al, 2019; Nimmo et al, 2020); and (iii) the spatial expression pattern of PHYB and other light-sensing genes (Somers & Quail, 1995; Bognár et al, 1999; Tóth et al, 2001). Experiments, however, are confounded by changes in metabolism and development caused by light (Nozue et al, 2011). We therefore tested the light-sensitivity hypothesis in our spatial model, by setting the sensitivity to light to differ depending on the region, and examining whether this could generate the period differences observed across the plant. Figure 2. Regional differences in light sensitivity can generate the period structure observed experimentally A. Period estimates of PRR9::LUC, TOC1::LUC, and ELF4::LUC for different organs imaged under LL. Each data point represents a period estimate from the organ of a single seedling. The horizontal black line shows the mean. B, C. Period estimates of simulated PRR9/PRR7 expression, measured from regions within the seedling template (B) or individual cells of the seedling template (C). In (B), the black line indicates the mean and the red shaded area one SD of 9 independent simulations. In (C), the color of the cell represents the periods of the individual oscillations. By assuming higher light sensitivity of cells in the cotyledon, hypocotyl, and root tip, the model approximates the period differences observed between regions in experiments. A noise parameter was set to a different value for each region, as informed by single-cell experiments (Appendix Fig S2). Simulations assumed local cell-to-cell coupling (Jlocal = 2). D–F. Times of the final peaks of simulated PRR9/PRR7 and PRR9::LUC (D), simulated PRR5/TOC1 and TOC1::LUC (E), or simulated ELF4/LUX and ELF4::LUC (F), in different organs measured under LL. Simulations assumed varied light sensitivities and local cell-to-cell coupling (Jlocal = 2). Data points represent the 25-th percentile, median, and the 75-th percentile for the peak times of oscillations scored as rhythmic, n = 9 simulations. Data information: Experimental data is an analysis of Arabidopsis time-lapse movies carried out previously (Greenwood et al, 2019). For PRR9::LUC data N = 4; TOC1::LUC data N = 3; ELF4::LUC data N = 3. For all, n = 7–18. N represents the number of independent experiments and n the total number of organs tracked. Download figure Download PowerPoint We entrained the cells in our simulations to LD cycles for 4 days before releasing them into LL for a further 6 days and measured the periods, as carried out in previous experiments (Greenwood et al, 2019). We initially set the local cell-to-cell coupling parameter, Jlocal, to 2. When assuming high sensitivity to light in the cotyledon (Lsens = 1.6) and hypocotyl (Lsens = 1.0), but lower in the root (Lsens = 0.65) and root tip (Lsens = 0.95), all regions entrained to the LD cycles (Appendix Fig S3). Upon transfer to LL, we were able to generate different periods (Fig 2B and C) and phases (Fig 2D–F and Appendix Fig S4) in each organ, matching those observed experimentally. This is due to higher light sensitivity causing the clock to run faster in our simulations (Appendix Fig S5), as expected for a diurnal organism (Aschoff & Pohl, 1978). Finally, by setting the sensitivity to light in our locally coupled model to be zero in all regions of the seedling, we were also able to simulate the loss of period differences observed in the light-sensing mutant phyb-9 (Greenwood et al, 2019) (Fig EV1A and B). Thus, our results revealed that different sensitivities to environmental inputs are sufficient to generate the experimentally observed spatial differences in period and phase across the plant. Click here to expand this figure. Figure EV1. Simulations with zero light input capture the loss of period differences observed in the phyb-9 mutant A. Period estimates of GI::LUC expression measured from different organs under red light in the light-sensing mutant phyb-9 genetic background. Each data point represents a period estimate from the organ of a single seedling and the horizontal black line shows the mean. B. Period estimates of simulated PRR9/PRR7 expression, measured from regions within the template seedling. Simulations were performed with zero light sensitivity for all cells (Lsens = 0; D = 1) and with local cell-to-cell coupling (Jlocal = 2). The horizontal black line shows the mean and the red shaded area one SD of 9 simulations. C. Representative intensity plot of GI::LUC expression across longitudinal sections of a single seedling under constant red light. Imaging was performed under red light in the light-sensing mutant phyb-9 genetic background. D. Representative intensity plot of simulated PRR9/PRR7 expression across longitudinal sections of a single seedling under LL. Simulations were performed with zero light sensitivity for all cells (Lsens = 0; D = 1) and with local cell-to-cell coupling (Jlocal = 2). E, F. Times of the final peaks of GI::LUC intensity plot (E) or simulated PRR9/PRR7 expression (F). Simulations were performed with zero light sensitivity for all cells (Lsens = 0; D = 1) and with local cell-to-cell coupling (Jlocal = 2). Data information: Experimental data is an analysis of Arabidopsis time-lapse movies carried out previously (Greenwood et al, 2019). N = 2 and n = 8–23, where N represents the number of independent experiments and n the total number of organs tracked. Download figure Download PowerPoint Local sharing of clock components can drive spatial waves of clock gene expression Previously we observed two waves of clock gene expression, one traveling up, and one down the root, in CCA1, PRR9, and GI reporters (Gould et al, 2018; Greenwood et al, 2019). These waves could be explained in a “phase-only” model by local cell-to-cell coupling (Fukuda et al, 2007, 2012; Gould et al, 2018; Greenwood et al, 2019). We next tested whether a plausible mechanism for cell-to-cell coupling, sharing of mRNA between cells (Maizel et al, 2020), can recapitulate the experimental observations. To provide a benchmark, we first analyzed the seedlings carrying transcriptional reporters for PRR9, TOC1, and ELF4 (Greenwood et al, 2019) at the sub-tissue level (Materials and Methods). As in previous studies (Fukuda et al, 2007, 2012; Wenden et al, 2012; Gould et al, 2018; Greenwood et al, 2019), space-time plots revealed spatial waves of gene expression within and between organs (Fig 3A, Appendix Fig S6A and C and Movie EV1). The direction of the waves could be clearly observed in plots of the final peaks of expression (Fig 3B and Appendix Fig S6E and G). For each gene, the wave directions appeared similar, traveling from the faster oscillating regions to the slower oscillating regions. Particularly distinct were the waves converging from the hypocotyl and root tip to the slower oscillating root region. Figure 3. Local sharing of clock components can reproduce experimentally observed spatial waves of clock gene expression Representative intensity plot of PRR9::LUC expression measured from longitudinal sections of a single seedling under LL. Times of the final peaks of the PRR9::LUC intensity plot. Representative intensity plot of simulated PRR9/PRR7 expression measured from longitudinal sections of a single seedling under LL. Simulations assumed varied light sensitivities and local cell-to-cell coupling (Jlocal = 2). Times of the final peaks of the simulated PRR9/PRR7 intensity plot. Times of the final peaks of simulated PRR9/PRR7 intensity plots, each simulated under LL with increasing strengths of local cell-to-cell coupling. Data information: Experimental data is an analysis of Arabidopsis time-lapse movies carried out previously (Greenwood et al, 2019). N = 4 and n = 7–14, where N represents the number of independent experiments and n the total number of organs tracked. Data in (D) is replotted within (E) as “Jlocal = 2” and Fig EV2A as “CCA1/LHY coupled”. (E) is replotted as Fig EV3A and Appendix Fig S8A. Download figure Download PowerPoint We next analyzed at the sub-tissue level the simulations performed with varied light sensitivity and local coupling (Appendix Fig S7B, Materials and Methods), to see if they capture the spatial dynamics. For each gene, the wave patterns appeared similar to experiments, traveling from the fast oscillating regions that are more sensitive to light, into the slower regions with lower sensitivity to light (Fig 3C and D, Appendix Fig S6B, D, F and H, and Movie EV2). These waves required cell-to-cell coupling through the local sharing of clock components, as we only observed waves with coupling strengths, Jlocal, above approximately 1 (Fig 3E and Appendix Fig S8). Similar simulation results were found when keeping regional differences of light sensitivity and local cell-to-cell coupling, but assuming no cell-to-cell variability within regions (Appendix Fig S9). We also found that our simulation results were qualitatively similar when using different clock gene mRNA (Fig EV2A) or protein (Fig EV2B) as the coupling component, suggesting that any cell-to-cell sharing of clock components could explain the experimentally observed spatial dynamics. Additionally, we ran simulations assuming local coupling between 8 rather than 4 neighbor cells, and simulations assuming global (all-to-all) coupling. Increasing the local coupling to be between 8 neighbor cells gave similar results (Fig EV3A and B). However, with global coupling all cells adopted the same phase at higher coupling strengths, regardless of position in the plant (Fig EV3C). Finally, we further analyzed our simulations in which we set the sensitivity to light input to be equal in all regions of the seedling. At the sub-tissue level, we observed the loss of spatial waves (Fig EV1D and F) seen in the light-sensing mutant phyb-9 (Greenwood et al, 2019) (Fig EV1C and E). Taken together, these results show that the assumptions of local cell-to-cell coupling and differential light sensitivity between regions are the key aspects of our model that allow a match to experimental data. Click here to expand this figure. Figure EV2. Peaks of simulated expression with the local sharing of different clock molecules between cells A, B. The times of the final peaks of simulated PRR9/PRR7 intensity plots, simulated with the sharing of CCA1/LHY, PRR9/PRR7, PRR5/TOC1, or ELF4/LUX mRNA (A) or protein (B) locally between neighbor cells. Simulations were performed under LL with local cell-to-cell coupling (Jlocal = 2). Data information: Data in (A) (“CCA1/LHY coupled”) is replotted from Fig 3D and data in (B) (“ELF4/LUX coupled”) is replotted from Fig 4B. Download figure Download PowerPoint Click here to expand this figure. Figure EV3. Peaks of simulated expression under LL with different coupling rules A–C. The times of the final peaks of simulated PRR9/PRR7 intensity plots, simulated under LL with increasing strengths of local cell-to-cell coupling between the 4 nearest neighbor cells (A), 8 nearest neighbor cells (B), or globally (all-to-all; C). Data information: (A) is replotted from Fig 3E. Download figure Download PowerPoint Long-distance sharing of clock components can generate period differences In addition to local coupling, the long-distance shoot-to-root movement of ELF4 has been proposed to couple clocks in different organs (Chen et al, 2020). We simulated seedlings assuming that ELF4 protein expressed from cells in the shoot is shared with cells in the root tip region. We did this to approximate a known destination for phloem signals in plants (Oparka et al, 1994), and the location that ELF4 is observed in experiments (Chen et al, 2020). In these simulations, the peak times of cells in the root tip became closer to those in the shoot, but we did not see the spatial waves of gene expression observed in experiments (Fig 4A). We then simulated see