Introduction

The circadian clock, a timekeeping mechanism with an ~24 h period, helps organisms coordinate functions over the diel light cycle. Many of the mechanisms of the cyanobacterial clock are now characterized at the molecular level [1, 2] and the fitness benefit has been demonstrated experimentally [3]. Despite this, the mechanism(s) by which the circadian clock increases fitness is unknown and fundamental questions in ecology and evolution, e.g., why some cyanobacteria have a circadian clock and some do not, remain unanswered. Connecting across these scales of biological organization, from molecular biology to ecology, is a challenge common to many areas of the biological sciences.

In Synechococcus, the circadian clock controls gene expression at the genome scale [4,5,6], so its role in the biology and fitness is expected to be multifaceted and complex. Recent evidence suggests the clock plays a role in the metabolism of glycogen (GLG) [7,8,9]. In general, GLG is synthesized during the day as an energy reserve, and then broken down at night to support cellular functions. Several of the genes involved in this mechanism are under the control of the circadian clock. The (relatively) well-understood intracellular function of GLG and clock control make the GLG metabolism mechanism a good candidate to begin to investigate the role of the clock on fitness.

The circadian clock may play a role in the biogeography of the two most abundant marine cyanobacteria; Prochlorococcus, which dominates in the low-latitude open ocean, and Synechococcus, which dominates in high-latitude and coastal waters [10, 11]. The geographic distribution of these cyanobacteria depends on many factors, including their response to temperature and light [11], but they also have different timekeeping mechanisms. Synechococcus has a bona fide circadian clock that exhibits free-running rhythms. Prochlorococcus does not have a circadian clock, rather an hourglass timing mechanism that does not free-run [2, 12,13,14].

Here we explore the ecological role of the cyanobacterial circadian clock using mechanistic modeling. We develop a model of Synechococcus, which includes a molecular-level representation of the circadian clock, including genes, transcripts, proteins (incl. phosphorylation state), and metabolites, as well as GLG metabolism. We calibrate the model to laboratory observations, which shows it reproduces the main observed pattern for wild type and no-clock mutant strains. Then we integrate it into a global ocean model and compare with field observations, including clock gene (kaiABC) and photosynthesis (psbA) transcript levels. We simulate wild type and no-clock mutants and compute the spatial pattern of fitness benefit (selection coefficient) conferred by the circadian clock, which is generally consistent with the observed biogeography of marine cyanobacteria Synechococcus and Prochlorococcus.

Model overview

The dynamic gene-level model of Synechococcous is based on a previous version [15] that was expanded to include glycogen metabolism and integrated into a global ocean circulation model. A complete model description, following the ODD (Overview, Design concepts, and Details) model documentation standard [16] is provided in Section S1 (Figs. S1–14, Tables S1–24). The remainder of this section presents an overview of the model (following the Overview part of the ODD protocol).

The purpose of the model is to explore how the circadian clock acts and interacts with other intracellular mechanisms (i.e., glycogen metabolism) to produce cellular behavior, and how it ultimately affects the ecological fitness of cyanobacteria. The basic entities in the model are individual cells, which are simulated using an agent-based modeling approach to resolve population heterogeneity (i.e., cell cycle phasing [17]) and allow for comparison to single-cell observations [15]. Each cell has a number of state variables, including genes, transcripts, proteins (incl. phosphorylation level), and metabolites. The model simulates a select number of representative genes using a coarse-grained modeling approach [18]. For example, glgP is representative of all genes involved in the degradation of GLG to G3P. The model resolves the diel light cycle and is applied at a number of temporal and spatial scales, ranging from a few days in a zero-dimensional laboratory beaker to a year in the three-dimensional global ocean.

The model includes a number of intracellular processes that are resolved at the gene or molecular level (Fig. 1a). Genes are transcribed by the RNA polymerase (RNAP) to produce transcripts (mRNA), which are translated by the ribosome (RPT) to yield proteins that perform various functions. For example, the photosynthetic unit (PSU, Fig. 1A1) produces energy (G3P), which is then converted to biomass (m).

Fig. 1
figure 1

Model schematic. From genes to ecosystems. a Cell with basic intracellular mechanisms including (A1) photosynthesis system, (A2) glycogen metabolism, and (A3) Posttranslational oscillator (PTO). I irradiance, PSU photosynthetic unit (a = open, b = closed, c = damaged), D1′ free photosystem II reaction center protein, G3P internal stored energy, m = cell size/mass, and GLG glycogen. Gene/protein: rpoMH/RNAP RNA polymerase, rptMH/RPT ribosome, psuMH/PSU photosynthetic unit, psbAI/D1 PSII reaction center, luxAB/Lux luciferase, polMH/Pol DNA polymerase, ftsMH/Fts cell division, dumMH/−, dummy (accounts for genes not explicitly considered), kaiA/KaiA, kaiB/KaiB, kaiC/KaiC (UKaiC unphosphorylated, SKaiC phosphorylated only on serine 431, TKaiC phosphorylated only on threonine 432, DKaiC phosphorylated on both sites), circadian clock, and glgC/GlgC glycogen synthesis. glgP/GlgP glycogen degradation. Schematic is simplified and not all processes are shown for clarity (see Section S1, Figs. S1–S14, Tables S1–24 for model details). b Population. An agent-based approach is used to scale up from individual cells to the population. c Light regime. Diel light pattern based on sunset/sunrise calculations, seasonal, and horizontal based on monthly MODIS photosynthetically available radiation (PAR) and vertical attenuation based on MODIS Chlorophyll a. d Circulation model grid. 2° × 2° resolution in the horizontal, 22 layers in the vertical, transport based on OFES model [20]. Green points marked O13 is Lagrangian track of transcriptomics survey off Californian coast from ref. [32], see Fig. 3c. e Global scale

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The model incorporates a GLG pool, genes responsible for synthesis (glgC) and degradation (glgP), and the associated metabolic cost, based on recent evidence demonstrating the role of the circadian clock in GLG metabolism [7, 8, 19] (Fig. 1A2). The energy pool (G3P) serves as substrate and breakdown product for GLG. In the dark, G3P is removed by respiration and supplied by GLG breakdown, and when the cell runs out of G3P it dies (referred to here as “dark death”).

The circadian clock is encoded by the kaiABC genes and consists of two parts, including posttranslational oscillator (PTO, Fig. 1A3) and transcriptional/translational feedback loop. The model can reproduce the major observed features of the clock in laboratory experiments, including entrainment to light/dark (LD) cycles, free-running rhythms, phase shifts by dark pulses, and KaiC protein dynamics. The model proceeds in discrete time steps using an explicit finite difference solution to the intracellular differential equations (e.g., protein mass balances).

The Synechococcus model is integrated into a global ocean circulation model [20], which was aggregated in the horizontal onto a 2° × 2° grid [21]. Incident light intensity (photosynthetically available radiation, PAR) is based on MODIS satellite observations, which was spread out over the diel cycle and attenuated vertically based on MODIS Chlorophyll a [22]. Individual cells are transported based on output from the circulation model (e.g., velocities). The population grows as a result of individual cells dividing (cell growth is based on the net effect of photosynthesis and respiration) and dying (intrinsic death when the cell runs out of G3P, i.e., dark death). Nutrients are not included and to constrain the population, an extrinsic death process that accounts for grazing and viral lysis is additionally included. Specifically, the extrinsic death rate is adjusted spatially and dynamically to produce total population patterns consistent with observed horizontal Chlorophyll a concentrations from MODIS, which is based on formulations used in previous ocean models [23, 24]. The total population size is therefore imposed and not an emergent output from the model, which is acceptable in this case because the focus is on the relative fitness of various Synechococcus strains. Additional discussion of imposed vs. emergent patterns, including a classification of all model output, is presented in Section S1 and Table S1.

Glycogen metabolism of the wild type in the lab

In the wild type, the GLG synthesis rate is light- and clock-controlled and the GLG level fluctuates in L:D and this fluctuation continues when transferred to LL (Fig. 2a, the mutants are discussed in the next section). The sustained rhythm in continuous light is clear evidence for the control of the circadian clock on GLG synthesis, but this is of little ecological relevance since cells do not live in this light regime in the wild. In L:D cycles, the circadian clock functions to suppress GLG synthesis early in the light period, which is evident in the time course of GLG level, especially when compared with the no-clock mutant. This feature has an important effect on the fitness difference between the wild type and mutant strains, as discussed in detail later.

Fig. 2
figure 2

Model-data comparison for glycogen metabolism in Synechococcus elongatus strain PCC 7942. Blue: Wildtype (wt1), Red and green: No-clock mutants (nc1, nc2). a GLG level in cells grown in L:D 12:12 and transferred to LL at 0 day. Data from a ref. [7] and b ref. [8]. b Probability of death by an 18 h dark pulse applied at different points in the circadian cycle and GLG level. Data from ref. [19]. See ref. [15]. and Section S2 for additional model-data comparisons and discussion

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The model was designed and calibrated to reproduce these data, i.e., by making the GLG synthesis rate light- and clock-controlled and calibrating various parameters (e.g., the GlgC rate constant, see Section S1), and this is therefore not an emergent pattern or independent prediction. Nonetheless, the model-data comparison serves as a check and supports the mechanistic realism of the model.

Glycogen serves as a substrate for nighttime respiration [25] and mutants of Synechocystis defective in GLG synthesis are not viable in L:D light regimes [26]. We included this effect by killing cells that run out of G3P, which happens in cells without a GLG reserve in the dark. This is consistent with recent observations that show cells are more susceptible to killing by a dark pulse (referred to here as “dark death”) at dawn, because they haven’t synthesized enough GLG to survive the dark period [19] (Fig. 2b, dawn corresponds to times 0 and 1 days). The probability of dark death is generally lower at dusk when the GLG level is highest (Fig. 2b, dusk corresponds to time 0.5 days). Experiments [8] also show that energy (ATP/(ATP + ADP)) is maintained at a higher level when a dark pulse is administered at dusk (time of higher GLG). This general pattern is consistent with the model, although the model uses G3P as an energy currency.

In addition to the primary pattern, which shows lower probability of death at dusk, there is a secondary minimum at ~0.3 days. The model reproduces this pattern, despite the lower GLG level at that time, because the clock-controlled respiration (which consumes G3P) rate is also lower at this time (illustrated in Fig. S15). The susceptibility to dark death is not only a function of the GLG level, but also how fast it is used up.

The circadian clock controls the timing of respiration and that affects the G3P level and susceptibility to dark death. Model predictions suggest that this constitutes an important fitness benefit of the circadian clock in the wild type over the no-clock mutant at the global scale, as discussed in more detail later.

The model was designed and calibrated to reproduce the observed pattern of dark death probability. First, cells that run out of G3P are killed, which results in a probability inverse to GLG (which supports G3P in the dark), i.e., the primary pattern in Fig. 2b. Second, the respiration rate was made clock-controlled, which produces the secondary minimum, as discussed above. As for the diel pattern in GLG level, this model-data comparison serves as a check and shows the model accurately represents the effect of GLG on the susceptibility to dark death.

Additional model-data comparisons are presented in the SI (see Section S2, Figs. S15–26 for additional model results and discussion). This includes GlgC and GlgP protein levels, which are relatively constant in L:D cycles [27]. Observations for the corresponding transcript levels are inconsistent [4, 28]. The clock control of GLG synthesis (Fig. 2a) is included in the model by making the GlgC enzyme activity clock-controlled. Allosteric activation of GlgC has been demonstrated [7]. The model is also compared with growth and photosynthesis rates of wild type and glgA and glgC mutants [25], which shows that photosynthesis is enhanced in the presence of GLG. This effect was suggested to be related to electron transfer efficiency [25] and is included in the photosynthesis component of the model. Overall, the model reproduces the main observed patterns of GLG metabolism in Synechococcus.

Glycogen metabolism and fitness of the no-clock mutant in the lab

To investigate the fitness advantage of clock-controlled GLG synthesis we construct a model strain that has clock output functions fixed at a constant value (no clock, nc1). Driven only by light, this strain produces GLG accumulation that is rhythmic in LD and relatively constant in continuous light (LL), a pattern consistent with observations [7, 8] (Fig. 2a). The GLG level is unnecessarily high and the growth rate in L:D 12:12 is substantially lower than the wild type. The selection coefficient (s = growth rate of wild type (wt1)/growth rate of no-clock mutant (nc1) − 1) is 30%, which is of similar magnitude as the 20% difference quantified for the long period mutant (P28 [15],). The larger difference here suggests that having no clock is worse than having a slow clock.

The observations for the no-clock strains in Fig. 2a are from lab-generated mutants and the high GLG synthesis rate is unlikely representative of wild-type no-clock strains. In other words, we would expect that such a mutant (Fig. 2a, nc1) would probably acquire some secondary/compensatory mutation(s) to reduce the GLG synthesis rate if it is to survive in the wild. The laboratory knockout mutant strain may not have acquired such mutations. To allow for a fairer comparison of the clock-controlled and light-controlled GLG synthesis strategies, we construct a no-clock strain with lower GlgC rate, which produces GLG levels comparable to the wild type (nc2) (Fig. 2a). Despite the similar GLG levels, the mutant synthesizes more GLG early in the light phase compared with the wild type. In the wild type, the clock suppresses GLG synthesis early in the light phase. In the mutant, GLG synthesis is controlled only by light and there is no mechanism to slow it down early in the light phase. This timing difference in GLG synthesis affects the relative fitness of the strains. Specifically, rapid GLG synthesis early in the light phase lowers energy, which reduces synthesis of the photosynthesis apparatus and that lowers photosynthesis overall (illustrated in Fig. S18). The net effect is that the no-clock mutant strain grows a little slower than the wild type (s = 4.0%).

As for the wild type, the temporal pattern of GLG level in the mutant, i.e., synthesis in light and degradation in dark, and no rhythm in continuous light, is a direct and obvious consequence of the model design and calibration, and therefore not an emergent pattern. However, the absolute and relative growth rates (selection coefficient) are independent predictions and emergent model output.

Marine wild type and no-clock mutants

The model was developed based on observations from a freshwater strain and for the ocean application several photosynthesis parameters were recalibrated. Additional model-data comparisons for the marine strain in the laboratory, including growth rate at various light intensities [29] and GLG content vs. time in LD cycle [30] are presented in the SI (Figs. S19, S20). In addition, parameters were calibrated against observed Synechococcus levels at Hawaii (see next section). To allow for a fair comparison between the clock and no-clock strategies, the GlgC rate for the ocean wild type (wt3) and no-clock mutant (nc3) were optimized to yield maximum growth at Hawaii (Fig. S4 presents results of optimization).

Growth and gene expression of the wild type in the ocean

Comparison to field data shows the model reproduces many of the observed features (Fig. 3). The observed Synechococcus concentration at Hawaii is higher near the surface and shows a weak subsurface maximum at 75 m (Fig. 3A1). The model reproduces this feature as a result of calibration. Therefore, although the model accurately reproduces the vertical distribution of cells, this is not an emergent output. Observations show a relatively weak seasonal pattern of Synechococcus concentration, which is related to increased vertical mixing and nitrate availability in the winter [31]. The model population follows the satellite Chlorophyll a, which shows a weaker seasonal signal (Fig. S6).

Fig. 3
figure 3

Model-data comparison. a, b Synechococcus cell concentration, psbA mRNA, and GLG at Hawaii Ocean Time-series (HOT) Station ALOHA (hahana.soest.hawaii.edu/hot, see Fig. 1e for location). Cell concentration normalized to mean, psbA mRNA: 10−8 mol molC−1, GLG: 10−1 molC molC−1. Data for vertical profile and time series (0–200 m) are average for all available years (1990–2014). c Synechococcus transcripts, total and phosphorylated KaiC protein, and GLG levels off the coast of northern California (see Fig. 1d, e for location). Transcript levels are percent of Synechococcus transcripts, scaled to arbitrary units (a.u.). Model at 24 m. Data at 23 m from ref. [32]. All data except PAR are averages over two days in mid-September. See Fig. S21 for comparison for 2-day time series, and Fig. S22 for results at different location and depth. See also Movie S1 for an animation of various model outputs

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Comparison to in situ observations of gene expression illustrate that the model captures the main observed pattern in Synechococcus clock and photosynthesis genes [32] (Fig. 3c). The observed transcript levels for the clock genes (kaiABC) peak around 18:00. The model predicts a slightly earlier peak and a faster decline following the peak. Observed photosynthesis gene (psbA) transcripts peak earlier, around 16:00. The model also predicts an earlier peak, but predicts no expression at night. Overall, the observed gene expression appears more damped than the model, which may be a consequence of the higher genetic diversity in the field compared with the laboratory experiments used to support the model development. Further, the circadian clock model was developed based on observations from experiments with freshwater Synechococcus and exclusively for continuous light conditions.

For the global simulation there was some recalibration of photosynthesis and glycogen metabolism components in the model (see previous section), but the circadian clock part was not changed. Although the pattern can be considered imposed, because the model was designed and calibrated to reproduce the general observed diel patterns of psbA and kaiABC gene expression, the application to a different environment and comparison to new data can be considered a validation. Overall, the model captures the main observed patterns and can reproduce the functioning of the circadian clock in the ocean.

The model also computes other parameters that were not measured in the field study [32], such as total and phosphorylated KaiC protein and GLG levels (Fig. 3C5 and 3C6), and it generates output at different locations, depths, and times (see Fig. S22), illustrating the capability of the model to provide information and fill data gaps in various dimensions.

Spatial patterns of clock fitness benefit in the ocean

To understand the fitness benefit conferred by the circadian clock, we simulate wild type and “no-clock” strains in the global ocean model. Both strains grow well with higher growth rates at the sunnier low latitude and less turbid open ocean (Fig. S23). The wild type grows faster everywhere, which is mostly due to the diel rhythm in respiration and effect on G3P and dark death (the same mechanism responsible for the secondary minimum in Fig. 2b), as follows. In the model, respiration constitutes a loss of energy and the beneficial function of respiration is not explicitly considered (a common approach in phytoplankton ecosystem models). This means respiration is a fitness cost. The overall respiration rates are similar, but slightly lower for the mutant (Fig. 4B2). Therefore, the fitness benefit for the wild type does not arise from simply respiring less across the board. Rather, it is due to the timing of respiration, which is repressed early in the dark period by the clock in the wild type. This shifts respiration to later in the dark period and allows the cell to maintain a higher G3P level and consequently experience less dark death (Fig. 4b). The fitness benefit (selection coefficient) is generally larger at darker locations (Fig. 5), because dark death is a more significant factor there, which amplifies the fitness advantage of the wild type.

Fig. 4
figure 4

Fitness benefit of circadian clock in the global ocean. a Global pattern of selection coefficient (s = net growth rate of wildtype [wt3]/no-clock mutant [nc3] − 1). Blue lines are mean annual latitudinal extent of Synechococcus (circadian clock) and Prochlorococcus (only a reduced clock) from ref. [11]. b Comparison of select variables at HOT, south Indian (SOIN), north Atlantic (NOAT), and Amazon River (AMAZ) locations (see Fig. S24 for time series). Filled boxes are for the wild-type, while white boxes are for the no-clock mutant. All values are averaged over model water column and 1 year (2010) simulation period

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Fig. 5
figure 5

Selection coefficient vs. light experienced by the population. Each point corresponds to one model grid box. Note axis scales. Some outliers (<0.1%) fall outside of plot range

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This is a testable prediction coming out of the model, and we attempted to validate this pattern experimentally, using laboratory experiments with wild type and laboratory no-clock mutant strains. These experiments were unsuccessful, in that they showed a stronger fitness benefit at higher light intensities (Section S3, Figs. S27, 28 which presents methods and results of this experiment). These results suggest the model is incomplete, but the discrepancy may also be due to differences between the mutant strains used for the model development (Fig. 2, kaiC, kaiBC, and cikA mutants) and experiment (kaiABC mutant), optimization of GlgG rate in the ocean environment, different light regimes in the ocean and lab, and neither strain may be a good representative of the wild type no-clock strain.

Interestingly, the fitness map (Fig. 4a) shows more structure than a simple low-to-high latitude gradient. That is because a number of factors affect the light experienced by the population, including (in order of significance), incoming radiation (R2 = 0.78, also lower at the cloudier equator, Fig. S11), vertical mixing (R2 = 0.37, highest in Southern Ocean, Fig. S8), light extinction (R2 = 0.096, higher in turbid coastal areas and to lesser extent equator and northern latitudes), and vertical advection (R2 = 0.046, positive at Equator and coastal upwelling areas, Fig. S9).

The model predicts that the fitness benefit of the circadian clock is less in the low latitude open ocean, where the light level is higher. These patterns constitute a true prediction in the sense that no parameters were calibrated to achieve these patterns. Further, they are an emergent property of the model. In other words, they result from the complex interaction of the intracellular mechanisms and are not imposed or directly defined by the model design or input. The model is based entirely on laboratory experiments with simple LD cycles (i.e., L:D 12:12) and constant light intensity, which is quite different from the light pattern in the model, which varies gradually over the diel cycle and year, and horizontally and vertically. It is entirely possible, for example, that the model would have predicted a weaker fitness benefit of the clock at higher latitudes, due to summertime increased photoperiod.

Interestingly, the global pattern is generally consistent with the observed biogeography of Prochlorococcus and Synechococcus, including latitudinal extent (blue lines in Fig. 4a) and dominance in coastal vs. open ocean domains [10], as well as laboratory experiments that show that Synechococcus is better able to survive darkness than Prochlorococcus [33]. Comparing the model no-clock Synechococcus strain to Prochlorococcus is a simplification, because although the latter does not have a bona fide circadian clock, it has an hourglass timer [2, 12,13,14]. The simplification is necessary however, because the present model does not include the Prochlorococcus timekeeping mechanism (which also has not been characterized at the molecular level). Nonetheless, we believe the comparison is meaningful, because it goes in the right direction along the dimension of timekeeping functionality, from light-induced behavior (Synechococcus no-clock mutant, model no-clock mutant) to hourglass timer (real Prochlorococcus) to bona fide circadian clock (Synechococcus wild type, model wild type).

Summary and outlook

The circadian clock manages energy over the diel cycle, and our study shows that this results in an important fitness benefit and that this benefit is weaker in the low latitude open ocean, which is consistent with observed marine microbe circadian ecology.

Several past models have combined gene-level and ecosystem processes [34,35,36], but our approach to dynamically simulate gene, transcript, protein, and metabolite levels for an entire environmental system is novel.

We investigated the role of a molecular mechanism, the circadian clock, in the fitness of cyanobacteria, and then scaled up to the global biogeography, the distribution of Synechococcus and Prochlorococcus. The scope of our study is wide and complete in the dimension of biological organization, from the molecular to the globe, but also narrow and limited in the mechanistic dimension, the role of the clock in energy management. Since the clock controls genome-wide gene expression [4, 5], we expect there to be many additional effects on cellular fitness. Even for GLG metabolism there are multiple effects, because GLG is not only an energy store, but its synthesis also serves as an electron sink during daytime [9]. In addition, there are many other factors controlling the distribution of Synechococcus and Prochlorococcus, like temperature [11]. Our choice to keep the model simple is in part based on necessity, because most other mechanisms are not as well understood as the circadian clock and its role in energy management. It was also a strategic choice, because excluding other mechanisms allows us to isolate and illustrate the effect of the included mechanism. The downside of the focus on a single mechanism is that it limits the model’s ability to comprehensively represent the fitness benefits of the clock and biogeography of marine cyanobacteria. Nonetheless, our study is proof-of-concept that a molecular mechanism can be integrated into a full-scale ecosystem model and produce meaningful and intuitive results, and the same general approach can be used to explore additional mechanisms, maybe by extending the present model.

The present model only resolves a handful of mechanisms and corresponding representative genes, but the structure permits expanding it to the genome scale, for which observations are available [4, 27, 28, 32]. Genome-scale transcription and metabolism models for cyanobacteria have been developed [37,38,39] and some of those concepts can be adopted for this effort. The model can be extended to include other cyanobacteria and heterotrophs, which also exhibit diel rhythms [32], and then integrated into biogeochemical models [40, 41]. Eventually, this methodology can be extended to include the dark ocean and closed biogeochemical cycles, and used to make climate change predictions. One major advantage of such a model would be that it can be informed by molecular-level observations, including gene, transcript, protein and metabolite levels, and single-cell observations [32, 42,43,44,45]. This would constitute a big step toward closing the growing gap between our models and observations and knowledge [46, 47].