The free-running property of circadian clocks is needed to tolerate changing photoperiods

Summary:

A defining feature of circadian rhythms is an internal oscillator that is self-sustaining in constant conditions, but the utility of this free-running property is not clear¹. In cyanobacteria, two alternative timing systems are found, a canonical circadian clock and an hourglass-like system incapable of free-running². By swapping genetic elements, we engineer a pathway to convert a circadian clock into an hourglass. We show that the performance of these systems is similar in a balanced light-dark cycle, but the hourglass shows dysregulated transcription in long photoperiod days and fails to provide resistance to midday UV exposure. A minimal mathematical model shows that inability to adapt to a changing photoperiod is a generic limitation of these hourglass systems that free-running clocks can overcome. We conclude that the ability to occupy niches far from the equator where daylength is highly variable demands a self-sustaining circadian rhythm, consistent with the observed geographical range of cyanobacterial species³. Our work establishes a genetic model system to study how environmental pressures led to the evolution of circadian rhythms.

Blurb:

Schober et al. reveal a genetic pathway for converting the model circadian clock of S. elongatus from a free-running oscillator into a damped hourglass timer. The authors use a combination of modeling and experiment to show that hourglasses do not correctly time UV resistance in long days.

Results

Many organisms respond to the daily rotation of the Earth not through simple stimulus-response but through entrainment of an internal oscillator known as a circadian rhythm⁴. A definitional property of these systems is that they can free-run for many days in constant laboratory conditions with high precision^5–7. However, since constant conditions never occur in nature, a foundational question is why free-running rhythms exist, whether the free-running property is evolutionarily adaptive, and, if so, what environments select for it¹.

Here we develop an experimental approach to study this question using bacterial circadian systems. In cyanobacteria, the circadian oscillator is generated by the KaiABC proteins⁸, but natural variants exist where the free-running property of the circadian clock is absent, concomitant with the loss of KaiA^2,9. By swapping elements of the kai genes between species, we identify a region of KaiC sufficient to convert the clock into an hourglass-like system that can be driven by light-dark cycles but is unable to produce more than a single cycle in free-running conditions. Comparing gene expression dynamics and stress resistance between these systems along with mathematical modeling reveals a simple principle: free-running clocks are needed for niches that encounter a broad range of seasonally changing photoperiods.

Replacing the KaiC C-terminus converts the circadian clock into a KaiA-independent hourglass

Circadian rhythms were discovered in cyanobacteria as metabolic and transcriptional rhythms that persist in constant light^10,11. In the genetically tractable freshwater isolate Synechococcus elongatus PCC 7942, the origin of the rhythm was traced to a cluster of three genes named kaiABC⁸. It was subsequently shown by Takao Kondo’s group and others that a mixture of the three purified Kai proteins was sufficient to reconstitute a circadian rhythm in a test tube manifest as a multisite phosphorylation cycle on KaiC¹². At the heart of the free-running property of this purified oscillator is a post-translational feedback loop: KaiA is required to stimulate KaiC phosphorylation¹³, and sufficiently phosphorylated KaiC then inactivates KaiA through the formation of KaiABC complexes¹⁴ (Figure 1A).

Figure 1. Reconstructing an hourglass phenotype in S. elongatus using homologous sequence from P. marinus.

(A) Simplified phylogenetic tree showing how Kai-gene context diverges between the Synechococcus and Prochlorococcus genera. Prochlorococcus is characterized by an either fragmentary or entirely absent kaiA gene². (B) Cartoon illustrating the C-terminal swap of homologous sequence from P. marinus MED4 KaiC into an S. elongatus PCC7942 background. The swapped region is indicated in teal on a ribbon structure of the CII domain from S. elongatus KaiC (T482A/S481A; PDB ID: 7X1Y). Unresolved residues at the end of the C-termini are displayed as helices predicted by AlphaFold^30,31. Structural features important for KaiA-mediated CII nucleotide exchange and autophosphorylation are labeled. The chimeric KaiC variant resulting from this homologous sequence fusion is referred to here as the “Kaimera.”. (C) Western blot quantification showing Kai variants of S. elongatus incubated in a light-dark cycle followed by continuous light. The Kaimera construct was transformed as a KaiBC cassette into a ΔkaiABC background of 7942 to produce a reduced KaiBC system resembling P. marinus. (D) Average bioluminescence traces (PpsbAI::luxABCDE) of S. elongatus Kai variants in two light-dark cycles followed by continuous light. (E) Average YFP fluorescence (black; PkaiBC::eyfp) of Kai-variants in two light-dark cycles followed by continuous light. Colored traces represent timeseries of individual cells. See also Figures S1 and S2.

Most cyanobacterial genomes contain kaiABC clusters, though an important exception is the clade Prochlorococcus. These are abundant marine cyanobacteria found in the open ocean that are characterized by submicron cell sizes and are important players in the global carbon cycle^15–17. In Prochlorococcus, the kaiA gene is either completely absent or truncated². Because KaiC phosphorylation feeds back to regulate KaiA activity is used in the canonical KaiABC system¹⁴, a natural hypothesis is that Prochlorococcus cells will lack free-running rhythms. Indeed, bulk rhythms in gene expression and DNA replication do not persist in constant conditions². However, we previously observed that Prochlorococcus KaiC phosphorylation is highly rhythmic in light-dark cycles⁹. Thus, we hypothesized that the Prochlorococcus kaiBC genes retains an important timing function despite being unable to free-run.

The existence of alternative time-keeping mechanisms (free-running vs. non-free-running) in nature based on homologous sets of genes presents a unique opportunity to experimentally isolate both the underlying mechanism and the importance of the free-running property. We thus sought to engineer minimally altered cyanobacterial strains that convert between “clock” (free-running) and “hourglass” (not free-running) phenotypes.

S. elongatus KaiC phosphorylation depends on KaiA, implying that Prochlorococcus KaiC has acquired KaiA-independent function. To isolate regions of KaiC involved in this transition, we were guided by previous structural and molecular dynamics analysis of the KaiA-KaiC interaction. KaiA binds to the KaiC C-terminal tail¹⁸ stabilizing exposure of the A-loops, whose exposure has been shown to be involved in regulating KaiC autokinase activity and nucleotide exchange^19,20 (Fig 1B). The A-loop interacts with the 422-loop which is itself coupled to the phosphorylation sites²¹. Further, the C-terminal tail of Prochlorococcus KaiC diverges substantially from KaiC in cyanobacteria in a full KaiABC cluster (Figure S1). Since the KaiC N-terminus interacts with output pathways to control transcription, we excluded it from consideration²². Based on this sequence analysis, we identified the KaiC amino acid sequence extending from the 422-loop to the C-terminus (388–519) as a target for transplantation with the goal of creating KaiA-independent function.

Transplanting the C-terminus from Prochlorococcus KaiC creates hourglass phosphorylation cycles

We created a chimeric kaiC gene in S. elongatus by replacing the C-terminal region with its counterpart from Prochlorococcus MED4 kaiC. To mimic the Prochlorococcus gene structure, we also deleted kaiA resulting in a strain we dubbed “Kaimera”. In the Kaimera, KaiC phosphorylation is highly rhythmic in light-dark cycles, with peak phosphorylation occurring near the end of the light period, similar to Prochlorococcus cells. However, unlike the Synechococcus wildtype, phosphorylation rhythms in the Kaimera are completely dependent on the cycling environment, suggesting hourglass function similar to what we previously observed in Prochlorococcus cells. These high amplitude phosphorylation cycles are independent of kaiA, in contrast to the very weak KaiC phosphorylation observed when kaiA is deleted in the wildtype system (Figures 1C and S2).

We constructed a bioluminescent reporter strain to study the dynamics of gene expression in cycling environments followed by release into constant light. As expected, rhythms in the Kaimera disappear rapidly under constant illumination but the gene expression output produced in 12 hours light:12 hours dark cycles by the Kaimera is remarkably similar to the wildtype clock (Figure 1D).

One possible alternative explanation for a loss of bulk gene expression rhythms in the Kaimera is desynchronization among single cell oscillators. In this scenario, the Prochlorococcus-like system would not be a true hourglass but rather a noisy clock. To evaluate this scenario, we analyzed gene expression in single cells in both WT and Kaimera backgrounds carrying a YFP reporter of KaiC-driven transcription. While WT cells showed coherent single cell oscillations in constant light, each cell carrying chimeric KaiC showed a deterministic relaxation to a non-oscillating steady state, rather than stochastic oscillations (Figure 1E). Thus, we conclude that replacing the KaiC C-terminus with its Prochlorococcus equivalent causes a true loss of free-running and recapitulates an hourglass timekeeper in single cells that relies on daily input from the environment.

Gene expression driven by the hourglass becomes dysfunctional in long photoperiod days

Because of the Earth’s axial tilt, regions away from the equator experience seasonal changes in the length of the day (photoperiod). We previously showed that the cyanobacterial clock can adapt its phase to the photoperiod through an entrainment process²³, but such mechanisms may not apply to a system with hourglass dynamics. To test this, we grew cells in many photoperiods (Figure 2A, S3) and compared the amplitude and peak time of gene expression between the wildtype clock and the Kaimera hourglass strain. Consistent with previous reports, the entrained phase of the WT circadian clock scales with photoperiod, allowing gene expression timing to vary smoothly as the length of the day changes while maintaining amplitude.

Figure 2. Characterization of clock and hourglass timing across varying photoperiods.

(A) Average bioluminescence traces from select photoperiods for wild-type clock (WT), Kaimera (as a KaiBC cassette transformed into ΔkaiABC S. elongatus), and clock-null variants. Data were shifted on the y-axis such that minimum luminescence after day 2 is zero for ease of visual comparison. Photoperiods are labeled in an hours-light : hours-dark format. (B-C) Quantification of bioluminescence timing (B) and amplitude (C) across an array of photoperiods interpolating between continuous darkness and continuous light. Error bars represent standard measurement error across days 3–6 for triplicate cultures.

The dynamics of the hourglass and clock systems are similar in short photoperiod and balanced days, producing clear rhythms compared to the arrhythmic kaiBC-null. However, the chimeric hourglass system is unable to adjust its peak time when days become long, while the WT system continues to move the phase of peak reporter expression later into the day relative to dawn. Further, amplitude of gene expression rhythms in the Kaimera increases as photoperiod increases, peaking around a balanced 12:12 day, but then ultimately collapses in long photoperiods. In contrast, the free-running behavior of the WT circadian clock allows high amplitude output in these conditions (Figure 2B–C).

A generic mathematical model shows that hourglass systems cannot adapt to extreme photoperiods

To address whether these features are specific to this engineered system or general results, we turned to a mathematical model of the circadian rhythm that can transition from a clock to an hourglass. The dynamics of this model live in a two-dimensional state space where the clock dynamics are represented by an attracting cycle (see SI text). The environment is coupled to the system by shifting the position of the cycle when conditions switch between light and dark. An entrained oscillation can then be visualized as a trajectory that follows the attracting cycle as it moves between daytime and nighttime (Figure 3A). The phase of this trajectory relative to dawn and dusk depends on the magnitude of the shift in cycle position caused by the transition from light to dark, and this parameter allows smooth tuning of the phase-photoperiod curve²³.

Figure 3. Mathematical modeling of clock-hourglass bifurcation.

A single parameter $\mu$ controls whether the system (A) exhibits a stable limit cycle, analogous to a clock, or (B) goes to a fixed point in a constant environment, like the hourglass. Sample trajectories x(t) under short or long photoperiodic driving conditions are shown (white bars represent day, gray bars represent night). Environmental driving is modeled as shifting the origin of the limit cycle (dashed circle) or fixed point (black dot) in phase space, with systems trajectories shown in blue or red. (C) Time of maximum amplitude for a clock-like model ($\mu =10$; blue trace) and hourglass-like model ($\mu =-10$; red trace) across a range of photoperiods. (D) Timing of maximum amplitude versus photoperiod across a range of $\mu$ interpolating from very damped hourglass-like (dark blue) to very strong limit cycle (dark red). As in the data, peak timing has a slope of 1 for small photoperiods which tapers off to a slope near 0 for longer days. The slope for clocks is constant and less than 1, approaching 1/2 for large $\mu$.

As an alternative to the free-running oscillator, we represent the hourglass system by a shifting point attractor, where the position in state-space represents the phosphorylation state of KaiC. KaiC reaches a highly phosphorylated steady state in constant light, and a weakly phosphorylated steady state in constant dark⁹. In the model, trajectories relax into the steady state point, so that free-running oscillations cannot occur (Figure 3B). The transition between these two extremes can be described mathematically by changing the bifurcation parameter $\mu$ in the normal form of a Hopf bifurcation, a generic description of oscillations that are created by increasing amplitude while holding period constant. When $\mu >0$, the system has a stable limit cycle corresponding to a free-running clock. When $\mu <<0$, trajectories monotonically decay to a fixed point under constant conditions, corresponding to hourglass dynamics.

This general, unified framework for modeling both clocks and hourglasses allows us to compare phase relationships between the external light-dark cycle and the internal response in these two systems. A clock comprised of sufficiently strong limit cycle dynamics shifts linearly with photoperiod with a slope of 1/2 (Figure 3C), consistent with prior measurements of the Kai clock^23,24. In contrast, we find that hourglass timing saturates past a photoperiod threshold, what we find experimentally in our engineered Kaimera system (compare Figure 2B). These results suggest that the difference in amplitude timing emerges from general properties of clocks and hourglasses, rather than the specific details of the Kai system. Thus, free-running clocks are a general solution to the problem of scheduling events in days of different lengths, a goal that cannot be achieved by the minimal hourglass system. These calculations from a minimal model are consistent with in silico evolution of regulatory networks that suggests that photoperiodic change is a condition of fitness needed to generate a selective advantage for free-running clocks²⁵.

The hourglass system has mistimed UV resistance in long days

We turn to the question of what specific events are scheduled by the cyanobacterial clock in days of varying photoperiod and whether the hourglass incurs a fitness penalty relative to the clock. The clock plays a key role in allowing cells to tolerate ultraviolet (UV) radiation, and kaiBC-null mutants have been shown to highly susceptible to UV damage²⁶. Since UV from solar radiation is most likely in the middle of the day, this means that as the photoperiod lengthens, the time of maximal UV damages changes relative to dawn.

We grew cultures in long photoperiod days and found that, in wildtype cells carrying a circadian clock, the time of peak UV resistance allows protection during midday hours when UV exposure should be highest (Figure 4A–B). In wildtype cells, UV resistance is low at the beginning of the day and then increases as the middle of the day approaches (Figure 4C). While the hourglass system is able to provide UV resistance relative to the kaiBC-null (P < 0.01 in 12:12 cycles, paired $t$-test), the timing of resistance is incorrect, with peak resistance occurring late in the day. (Figure 4C). In a balanced photoperiod, the Kaimera strain shows glycogen storage similar to WT but with reduced diurnal difference, suggesting that the metabolic cycling shown to be needed for UV resistance is intact (Figure S3)²⁶. Thus, we suggest that a key function of the free-running clock is to predict midday based on light-dark signals in a wide range of photoperiods, a task which the hourglass system cannot achieve, resulting in decreased survival in long photoperiod days with midday UV exposure.

Figure 4. Alteration of UV resistance rhythms in hourglass variant of S. elongatus.

(A) Schematic of the experimental schedule for constructing UV resistance timeseries in 12-hour day (12:12), 15-hourr day (15:9), and 18-hour day (18:6) photoperiods. Cells were spotted in serial dilution and synchronized to two cycles of the specified photoperiod. Quadruplicate time points from the following light incubation were given UV irradiation, followed by a 6-hour incubation in darkness, and finally outgrowth in continuous light before quantification. (B) Representative spotting assay of wild-type (WT) and Kaimera cells irradiated with UV-C at dawn (top) and midday (bottom) in the 18:6 photoperiodic condition. (C) UV resistance rhythms of the wild-type clock, Kaimera hourglass, and clock-null (ΔkaiBC) variants across three photoperiods. Growth was quantified relative to UV(−) controls across all serial dilutions (see STAR Methods). Error bars represent standard error of measurement. Color bar along the top of each plot indicates the timing of UV irradiance (relative to maximum) experienced in a typical day in each photoperiod, calculated from a reference location at ~58°N. (D). Relative abundance of marine Synechococcus and Prochlorococcus cyanobacteria plotted against the maximum photoperiod experienced annually at the latitude of each sampling site. Abundances are normalized to the sum of all averages across all photoperiodic bins. Data represent a reanalysis of prior work by Flombaum et al³. See also Figure S3.

Intolerance of extreme photoperiods is consistent with the geographical range of KaiA-less cyanobacteria

The length of the maximum photoperiod near the solstice increases with distance from the equator. We therefore expect the discrepancy in transcriptional dynamics between the clock and hourglass systems to depend on latitude. Previous work has estimated the geographical range of Prochlorococcus (lacking kaiA) and Synechococcus (full kaiABC gene cluster) species in the global oceans using metagenomic data³. Consistent with the hypothesis that a free-running clock is needed to adjust to changing photoperiod, we find a strong correlation between the relative abundance of clock and hourglass systems at the maximum photoperiod experienced at a sampling site (Figure 4D).

Discussion

The rotation of the Earth presents a regular pattern of environmental challenges to organisms living near the surface. Circadian clocks can be used to anticipate future environmental changes, but, in fact, stimulus-response systems, such as an hourglass, can also anticipate when they operate on an appropriate timescale. The limitation of these systems is that anticipation is limited to a fixed time following the previous cue—e.g. triggering a response 6 hours after dawn—while a free-running clock can adjust timing flexibly in different photoperiods because it maintains an internal memory of phase. In the case of clock-mediated stress tolerance, such as the UV resistance phenotype we consider here, the timing cues of dawn and dusk are distinct from the times when environmental conditions are harshest at midday. Here, the free-running circadian clock is capable of performing a computation to predict midday from only dawn and dusk inputs.

Nevertheless, some organisms, such as Prochlorococcus, do not use the free-running oscillator mechanism. These tiny cyanobacteria are apparently under selective pressure to reduce both cell size and genome size. We previously showed that as internal noise due to low copy number increases, hourglass dynamics become more reliable than circadian clocks^9,27. Further, the elimination of kaiA from the genome likely reduces the cost of DNA replication. Overall, the picture that emerges is that Prochlorococcus has found a niche in near-equatorial waters where the biosynthetic costs of a free-running clock can be abandoned in favor of a hourglass system with little drawback to timing in balanced day-night cycles. Since kaiB and kaiC appear to have a more ancient origin than kaiA, this system may represent the function of a primordial timing system before the emergence of a true circadian clock^28,29. As the oceans warm, one expectation is that Prochlorococcus may be able to expand its range into higher latitudes with implications for global carbon fixation³. However, this scenario may not occur if Prochlorococcus is unable to tolerate variable photoperiods due to its alternative kai system.

Finally, we consider a phylogenetic perspective. kaiA is apparently limited to the cyanobacteria while kaiB and kaiC homologs are found much more broadly in prokaryotes²⁸. Since it is needed in extant systems for free-running phosphorylation oscillations, this suggests that an ancestral form of the system was hourglass-like²⁹. The approach shown here to transplant elements of the kai system between species may open the door to understanding the evolutionary pathway that allowed free-running oscillation to originally emerge. This development may have been linked historically to the appearance of cyanobacterial species that could thrive across the global oceans.

RESOURCE AVAILABILITY

Lead Contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Michael Rust (mrust@uchicago.edu)

Materials Availability

All strains and plasmids generated in this study are available upon request.

Data and Code Availability

• All data generated in this study will be shared by the lead contact upon request.

• Analysis code used for this study is hosted at https://github.com/afschober/. All other data and are available upon request.

• Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

STAR Methods

EXPERIMENTAL MODEL AND STUDY PARTICIPANT DETAILS

Cloning and strain construction

The Synechococcus elongatus PCC 7942 lab strain was originally obtained from the American Type Culture Collection (ATCC). All other model strains were derived from this background using standard molecular cloning and transformation techniques. Knockout plasmids (ΔkaiA::Gm^r, ΔkaiABC::Gm^r) were constructed in the pBlueScript II SK (+) backbone (Addgene). Plasmids for recombination at neutral site 1 (NS1) are derivatives of pAM2314³². The Kaimera construct was made by Gibson assembly³³ of S. elongatus operon fragment PkaiBC::kaiB^synC^syn:1-388 with 125 amino acid P. marinus MED4 gene fragment kaiC^pro:385-509 to produce the chimeric PkaiBC::kaiB^synC^{syn:1-388,pro:389-513} in the pAM2314 vector backbone (pMR0307). A second variant of this plasmid (pMR0308) with an additional noncoding sequence for potential use as an NGS amplicon was also made. The reporter-less Kaimera strain was made by transforming pMR0308 into a ΔkaiABC background of S. elongatus to produce MRC1322. The plasmid pMR0307 was transformed into a KaiABC-null luciferase reporter background (ΔkaiABC, PpsbAI::luxABCDE) and fluorescent reporter background (ΔkaiABC, PkaiBC::eyfp) to produce strains MRC1325 and MRC1327 respectively.

Culture conditions

S. elongatus cultures were generally grown and maintained in a Percival incubator (Percival Scientific) at 30°C in BG11 medium supplemented with 20 mM HEPES (pH 8.0), with shaking at 180 rpm and a constant illumination of $~68\mu \text{mol}$ photons m⁻²s⁻¹ cool white fluorescent light. Culture conditions for specific experiments are explained under their respective sections.

METHOD DETAILS

Western blotting of KaiC phosphorylation rhythms

S. elongatus strains (WT, MRC1321, MRC1322) were back diluted into duplicate 100 mL cultures with an OD₇₅₀ of approximately 0.05 before entrainment. Strain replicates were entrained to disparate 12 hours light : 12 hours dark cycles exactly 12 hours out of phase with one another to enable simultaneous sampling of day and night circadian times. Entrainment proceeded for 3 days, followed by 12 hours of sampling in light-dark (LD) and 12 hours of sampling in continuous light (LL). The final time series was constructed by stitching together data from the alternating cultures at dawn, dusk, and subjective dusk breakpoints.

Samples were collected every 3 hours by harvesting 10 mL of cell culture which was pelleted at $3000g$, flash frozen in liquid nitrogen, and stored at −80°C until ready to use. Frozen cell pellets were resuspended in lysis buffer (8M urea, 20mM HEPES pH 8.0, 1 mM MgCl₂), then lysed through 10 cycles of vortex bead beating using 0.1 mm glass beads. Finally, samples were mixed with 3x SDS-PAGE sample buffer (150 mM Tris-Cl pH 6.8, 6% SDS, 300 mM DTT, 30% glycerol, 0.1% bromophenol blue), heated to 95°C for 5 minutes, and loaded onto 10% acrylamide gels (37.5:1 acrylamide:bis-acrylamide) for analysis. Each gel was run at a 30 mA constant current and 12°C for 4.5 hours. Transfer to PVDF membranes (Bio-Rad) was achieved through a semi-dry transfer apparatus (Bio-Rad) run at 90 mA for 1 hour.

Membranes were blocked for 1 hour in TBST (137 mM NaCl, 2.7 mM KCl, 20 mM Tris, 0.05% Tween-20, pH 7.4) + 2.5 % nonfat milk powder, then incubated overnight at 4°C with an affinity-purified polyclonal antibody against KaiC. Two dilution factors (1:5000 for wild-type KaiC, 1:1000 for chimeric KaiC) of primary antibody were used to account for likely differences in gene expression and antibody affinity. After thorough washing in TBST, blots were probed with a 1:10,000 dilution of HRP-conjugated goat anti-rabbit antibody (Bio-Rad) and visualized with SuperSignal West Pico Substrate (ThermoFisher Scientific). The relative intensity of unphosphorylated and phosphorylated KaiC was estimated by densitometry in ImageJ³⁴ (Figure 1C, S2).

Bioluminescent measurement of gene expression rhythms

S. elongatus cultures expressing the luciferase reporter (MRC1005, MRC1323, MRC1324, MRC1325) were back diluted to an OD₇₅₀ of approximately 0.05 and synchronized with three LD12:12 cycles leading up to the experiment. Cultures were back diluted once more to a starting OD₇₅₀ of 0.2 immediately prior to bioluminescence measurement. A black 96-well plate was filled with $250\mu \text{L}$ of BG-11 + 0.9% Gelzan (Sigma-Aldrich) per well and given enough time for the Gelzan to solidify. Wells were then seeded with $30\mu \text{L}$ of cell culture and the plate was sealed with a transparent UniSeal (Cytiva). Holes were punched above each well with a 16G1½ needle (BD) to allow gas exchange. To simulate light-dark cycles of varying photoperiod, the plate was mounted under a custom-built Arduino-controlled LED array, as described previously^23,35. Custom Arduino scripts were written to provide every well the same light intensity (1.8 V across each LED) during the light portion of the day. The plate was held at 30°C and bioluminescence was measured every 30 min using a TopCount scintillation counter (PerkinElmer) for 1 s per measurement.

Time-lapse microscopy

S. elongatus cultures expressing the YFP reporter (MRC1006, MRC1326, MRC1327) were back diluted to an OD₇₅₀ of approximately 0.025 and synchronized with three LD12:12 cycles leading up to the experiment. Prior to the experiment, cultures were back diluted again to an OD₇₅₀ of 0.05 and $1\mu \text{L}$ of of culture was spotted on a 6-well glass-bottom plate (MatTek Corporation). Each spot was covered with a square pad (~ 5 mm × 5 mm × 1 mm) of BG11 + 2% Low Melting Point Agarose (LMPA; ThermoFisher Scientific). Pads were then covered with 6 mL of molten BG11 + 2% LMAP and left to cool and solidify. Time-lapse microscopy was conducted with an Olympus IX-71 inverted microscope with a motorized stage and focus control. Automated image acquisition was accomplished using the μManager software package³⁶. Images were captured with a 100x NA=1.3 oil-immersion objective (Olympus) and an Andor Luca EMCCD camera (Oxford Instruments).

After transfer to the microscope, cells were grown in three cycles of LD12:12 with a red light source ($~10\mu \text{mol}$ photons m⁻²s⁻¹) before release into 48 hours of continuous light. Images were collected in brightfield, chlorophyll (excitation bandpass filter: 542 − 582 nm, dichroic filter: 593 nm, emission long-pass filter: 593 nm), and EYFP (487 − 513 nm excitation bandpass filter, a 520 nm dichroic filter, and a 528 –556 nm emission bandpass filter) channels using an LED illumination source every hour.

Evaluation of UV resistance by spot assay

The UV resistance spot assay largely follows prior work by Kawasaki et al²⁶. First, each S. elongatus strain (WT, MRC1002, MRC1322) was back diluted to an OD₇₅₀ of 0.1 to serve as the starting point for serial dilution. Each aliquot was diluted 1:10 four times to produce an array of serial dilutions spanning 10⁰ to 10⁻⁴, then $4\mu \text{L}$ of each dilution was spotted onto solid BG-11 + 20 mM HEPES (pH 8.0) + 0.9% Gelzan plates. Dilution series were spotted twice on each plate across 4 plates per condition per timepoint for a total of 8 technical repeats. Plates were synchronized with two cycles of their experimental condition, LD12:12, LD15:9, or LD18:6, then released into continuous light until their designated time of UV-irradiation. Illumination was provided by cool white fluorescent bulbs at a photon synthetic flux density of $~27\mu \text{mol}$ photons m⁻²s⁻¹, and incubation temperature was set at 30°C. UV-C irradiation was conducted with a UVP crosslinker CL-1000 (Analytic Jena AG) fitted with a 254 nm discharge tube. The Irradiation intensity was programmed to 500 J/m². Immediately following UV stress, plates were wrapped with aluminum foil and incubated in darkness at 30°C for 6 hours before an outgrowth period lasting 3 days in continuous light. Finally, plates were imaged on a white tray in a ChemiDoc MP Imaging System (Bio-Rad) set to auto rapid-exposure.

Measurement of glycogen content

S. elongatus strains (WT, MRC1322) were back diluted into triplicate 200 mL cultures at an OD₇₅₀ of approximately 0.1 before synchronization to three LD12:12 cycles. Illumination was provided by cool white fluorescent bulbs at a photon synthetic flux density of $~27\mu \text{mol}$ photons m⁻²s⁻¹. At dawn and dusk (12 hour) timepoints, cultures had reached an OD₇₅₀ ≈ 0.4 – 0.8 and 4 mL of cells were harvested by pelleting at $3000g$, flash frozen in liquid nitrogen, and stored at −80°C until ready to use.

Quantification of glycogen from cell pellets was carried out as described by Bandyopadhyay et al³⁷, with a few minor modifications. Sample pellets were resuspended in 1 mL methanol and incubated at room temperature for 1 hour in order to extract chlorophyll. After spinning down at $\mathrm{16,1000}g$ for 5 minutes, chlorophyll content was measured by calculating the absorbance of the supernatant at 665 nm (chlorophyll a). At this stage, a calibration curve of bovine glycogen (500, 300, 200, 100, 50, 25, 5, $0\mu \text{g}$) was introduced in parallel with the sample pellets. Samples were resuspended in $600\mu \text{L}$ 40% KOH then incubated at 95°C for 90 minutes. Two volumes of 100% ethanol were added to each sample and glycogen was precipitated overnight at −20°C. The next day, glycogen was pelleted by spinning samples for 60 minutes at 16,1000 g and 4°C. Sample pellets were watched twice with 100% ethanol, then resuspended in $200\mu \text{L}$ of 2N HCL to digest glycogen into glucose. Samples were incubated at 95°C for 30 minutes before neutralization with $400\mu \text{L}$ pH 7 phosphate buffer, $200\mu \text{L}$ ddH2O, and $200\mu \text{L}$ 2N NaOH.

Samples were analyzed with a Glucose (HK) kit (Sigma) by mixing $75\mu \text{l}$ of sample extract with $200\mu \text{l}$ of enzyme solution in a 96-well plate (Costar, ultraviolet light proof) and incubating for 30 minutes at 25°C. The resulting product of NADPH was measured at 340 nm using a microplate reader (Tecan Spark).

QUANTIFICATION AND STATISTICAL ANALYSIS

Protein sequence alignment

S. elongatus PCC 7942 and P. marinus MED4 KaiC sequences were downloaded from UniProt³⁸ and aligned with Protein BLAST³⁹. When designing the C-terminal homology swap, residues 388–513 of KaiC^syn were found to align with residues 385–509 of the KaiC^pro protein sequence (Figure S1).

Structural visualization of KaiC homology swap

Visualization of the KaiC hexamer and CII domains (Figure 1B) were accomplished through the ChimeraX software^40,41 and cryo-EM structure with rcsb ID: 7X1Y⁴². Residues 485–519 in the ribbon cartoon of CII were modeled through the ColabFold^30,31 extension of ChimeraX.

Quantification of bioluminescence peak timing and amplitude

The timing properties of bioluminescence rhythms were assessed with a custom written Python script. In order to account for increase in the average level of the luminescence signal due to growth of the culture, 6 days of measurements in a given condition were fit to the logistic function:

$$y(t)=\frac{L}{1+e^{-k\left(t-t_0\right)}}+b$$

where $L$ describes the carrying capacity of the population, $k$ is the logistic growth rate, $t_0$ is the midpoint of growth, and $b$ is the floor. Luminescence traces were detrended in a piecewise fashion one LD cycle at a time by determining the scalar offset that minimizes the residuals of $y\left(t\right)$ within each window and dividing the luminescence traces by $y\left(t\right)$ plus the offset. The resulting traces give an approximation of the relative luminescence oscillation per cell. It is known that the bacterial luciferase reporter exhibits masking effects upon entry into darkness and immediately following transition into light. As such, all dark samples and the first 2 hours after the lights turn on for a given cycle were excluded from the analysis. Relative luminescence oscillations were fit to a spline function which was differentiated to find extrema within a window. In cases where a trough was observed during daylight hours, peak time was defined as the maximum relative luminescence occurring after the trough. Amplitude was defined as the additive difference between the relative luminescence at peak time and the minimum relative luminescence preceding it. Peak time and amplitude were estimated for 3 LD cycles (days 3–6) and triplicate technical repeats totaling 9 observations per condition.

Single cell image processing and data analysis

Cell segmentation, signal detection, and data analysis of microscopy images were performed using custom MATLAB and Python scripts following prior studies by Liao and Rust^43,44. Briefly, Otsu thresholding was applied to the chlorophyll image of a region of interest (ROI) to create a binary mask in which the foreground pixels were considered candidates for being part of a cell. Next, the transport of intensity equation (TIE) method was applied to brightfield images of the same ROI to produce an image with significantly improved contrast⁴⁵. Finally, the watershed algorithm was used to segment cells within the enhanced brightfield image. Objects outside the foreground of the chlorophyll mask were eliminated and erroneous detection results were corrected manually by adjusting segmentation parameters.

Cell lineages were constructed by matching each segmented cell of a frame to the previous frame based on the size of a pixel overlap. Cell division events were determined from cases in which 2 cells in the current frame matched with the same cell from the previous frame.

Quantification of relative survival following UV stress

Raw images taken with the ChemiDoc were first quantified by densitometry in ImageJ following the work of Takeuchi et al⁴⁶. Pixels were transformed into absorbances using the equation $-{\text{log}}_{10}\left(I_{\mathit{\text{pixel}}}/I_{\mathit{\text{agar}}}\right)$ before cell spots were segmented from their background using the Triangle Threshold with a cutoff of 0.035. Integrated densities were further analyzed with a custom Python script to assess the relative growth of each UV stress timepoint normalized to non-irradiated controls in the same condition. To synthesize the information provided by the dilution series, relative growth $RG\left(x\right)$ was modeled as a dose response curve where the independent variable $x$ represents the dilution factor at the time of spotting:

$$RG(x)=\frac{L}{1+e^{-k\left(x-x_0\right)}}+b$$

The total relative growth score (Figure 4C) was defined as the integral of $RG\left(x\right)$ across the dilution ranges included in this assay, rescaled such that a total growth of 1 would mean that UV irradiation resulted in no difference in cell mass relative to the control plates. Uncertainty was estimated through a bootstrapping process $(N=100)$ in which each column of the dilution series (sample and control) was resampled with replacement. Some technical replicates had to be excluded from analysis due to handling error, but each timepoint was represented by a minimum of 2 plates with 2 rows for a total of 4 observations.

The color bar at the top of each plot in Fig 4C shows the relative UV irradiance (280–400 nm) expected in a typical day with the same photoperiod. Kodiak, Alaska was chosen as a reference point since it’s at a sufficient latitude (~58°N) to experience all three photoperiods each year. Solar irradiance measurements taken every 30 minutes from 1998–2024 were downloaded from the National Solar Radiation Database (NSRDB)⁴⁷. Daylight hours were defined as having a solar zenith angle less than or equal to 90°. Average UV irradiance time series were computed from this dataset in Python.

Reanalysis of marine cyanobacteria abundance

The plot of marine Synechococcus and Prochlorococcus sp. abundance (Fig 4D) was produced through a reanalysis of prior work by Flombaum et al³. Each sample in their dataset is annotated with a latitude, longitude, and estimated abundance of Synechococcus and Prochlorococcus. Using a custom Python script, latitudes were transformed onto a new axis reflecting the maximum photoperiod experienced during the year using the Brock model⁴⁸. Maximum photoperiods were divided into 1-hour bins and samples that lack both Synechococcus and Prochlorococcus were excluded from the analysis. Average abundances and standard errors of abundance were calculated within each photoperiodic bin.

Mathematical model interpolating between clock and hourglass

We model the cyanobacterial circadian clock as a simple system that can exist either in an oscillating regime or operating with a single fixed point in a constant environment. We describe the system mathematically as the normal form of a Hopf bifurcation which generically describes the behavior of a dynamical system close to a condition where oscillations are born from the loss of stability of a fixed point:

$$\dot{r}=\mu r-\alpha r^3$$

$$\dot{\theta }=\omega +\beta r^2$$

As in Chew et al. 2018⁹, we set $\beta =0$ to capture the constant period of a circadian clock, independent of amplitude, and we will describe the driving by the external light source as moving the origin along the x axis: x → x−L(t), where L(t) is the time-varying light signal. When $\alpha <0$, the bifurcation will exhibit the two regimes we are interested in: a stable fixed point that represents an hourglass, and a stable limit cycle. We can set $\alpha =1$ to make these equations dimensionless. For $\mu <0$, the system will be attracted to a fixed point at the origin with perturbations decaying with timescale $1/\left|\mu \right|$. For $\mu >0$, the system will have a limit cycle at $r=\sqrt{\mu }$. We set L(t) = L for $0<\text{t}<\tau$, and L(t) = 0 for $\tau <\text{t}<24$. Our system can be rewritten as

$$\dot{r}=\mu r-r^3$$

$$\dot{\theta }=\omega$$

with the single parameter $\mu$ describing the transition between limit cycle and stable fixed point dynamics. An illustration of the dynamics is shown in Figure 3A. Here, we will take the value of $x=r\text{cos}\theta$ as the amplitude of the circadian clock.

Analytical approximation for an oscillator

In the limit of a strong circadian clock (large limit cycle), where $\mu >0$, we have an oscillator driven near its resonance frequency (since the period of the clock is approximately 24 hours and the period of the driving is 24 hours). For a standard damped and driven harmonic oscillator

$$m\ddot{x}+b\dot{x}+kx=F_0\text{cos}\omega t$$

If the driving frequency is very close to the resonance frequency, the phase of x will lag the driving by $\pi /2$, or approximately 6 hours. In the case of a circadian system driven by a binary light signal that is always either on or off, we can consider a similar damped driven harmonic oscillator:

$$m\ddot{x}+b\dot{x}+kx=F\left(t\right)$$

where F(t) = 1 for $\text{t}\in \left[0,\tau \right]\text{mod}\text{T}$ and F(t) = 0 for $\text{t}>\tau \text{mod}\text{T}$, where T is the external period. Then, the phase of the displacement x will lag the midpoint of the driving at $\text{t}=\tau /2$ by $\pi /2:t\left(x_{\text{max}}\right)=6\mathit{\text{hours}}+\tau /2$

Analytical approximation for an hourglass

We will refer to a ‘true hourglass’ as a system which has two possible states: either it is moving at a constant velocity (i.e., the sand is falling), or it is stationary at one of the fixed points (i.e., the sand has already entirely fallen). We can model this as a system that will move, conditioned on the input light signal. When the light is on (or, in our system, when $\text{t}\in [0,\tau ])$, $\dot{x}=v$ when $x<x_0$, and otherwise $\dot{x}=0$. Symmetrically, when $\text{t}>\tau ,\dot{x}=-v$ when x>0, and otherwise $\dot{x}=0$.

This leaves a degeneracy at $x=x_0$: when is the maximum value of x? To resolve this, we will posit that our hourglass system has some amount of internal dynamics near the final state, and the peak will be measured some time $t_2$ after the system arrives at $x_0$. In the simulations here, this $t_2$ narises from the nonzero curl—i. e. the system has some tendency to spiral into the fixed point.

Taken together, there will be two distinct regimes: one where the light input is short enough that we do not reach the fixed point, and one where we do reach that point. Specifically, when $\tau <vL+t_2$, the time at which x achieves its maximum will be exactly $\tau$, and when $\tau <vL+t_2$, the timing of the maximum will cease to increase and be fixed at $vL+t_2$. This matches precisely with our numerical simulations of the system.^49,50

Key Resources Table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Antibodies
Rabbit anti-KaiC antibody	Custom ordered (Rust lab)	N/A
Goat anti-Rabbit IgG secondary antibody, HRP	ThermoFisher Scientific	Cat# 31460
Chemicals, peptides, and recombinant proteins
UltraPure Low Melting Point Agarose	ThermoFisher Scientific	Cat# 16520050
Olympus Immersion oil type-F	ThorLabs	IMMOIL-F30CC
Critical commercial assays
Glucose (HK) Assay Kit	Sigma-Aldrich	GAHK20
Experimental models: Organisms/strains
Synecchococcus elongatus PCC 7942 (WT)	ATCC	33912
ΔkaiBC; Gmr	Pattanayak et al.40	MRC1002
ΔkaiABC; Gmr	This study	MRC1320
ΔkaiABC, PkaiBC::kaiBsynCsyn in NS1; Gmr Spr	This study	MRC1321
ΔkaiABC, PkaiBC::kaiBsynCsyn:1-388;pro:389-513 in NS1; Gmr Spr	This study	MRC1322
WT PpsbAI::luxABCDE in NS2; Cmr	Pattanayak et al.49	MRC1005
ΔkaiA, PpsbAI::luxABCDE; Gmr Cmr	This study	MRC1323
ΔkaiABC, PpsbAI::luxABCDE; Gmr Cmr	This study	MRC1324
ΔkaiABC, PkaiBC::kaiBsynCsyn:1-388;pro:389-513, PpsbAI::luxABCDE; Gmr Spr Cmr	This study	MRC1325
WT PkaiBC::eyfp in NS2; Knr	Pattanayak et al.49,50	MRC1006
ΔkaiABC, PkaiBC::eyfp; Gmr Knr	This study	MRC1326
ΔkaiABC, PkaiBC::kaiBsynCsyn:1-388;pro:389-513, PkaiBC::eyfp; Gmr Spr Knr	This study	MRC1327
Recombinant DNA
PkaiBC::kaiBsynCsyn:1-318;pro:319-448 in pAM2314	This study	pMR0307
PkaiBC::kaiBsynCsyn:1-318;pro:319-448 with additional downstream DNA barcode in pAM2314	This study	pMR0308
Software and algorithms
ChimeraX	Goddard et al.34	https://www.cgl.ucsf.edu/chimerax/
ImageJ	Schneider et al.39	https://imagej.nih.gov/ij/
Arduino IDE	Arduino SA, Chiasso, Switzerland	https://www.arduino.cc/en/software/
Python 3.13	Python Software Foundation	https://www.python.org/
μManager	Edelstein et al.41	https://micro-manager.org/
MATLAB	The MathWorks Inc.	www.mathworks.com
Custom code and scripts	This paper	https://github.com/afschober/

Highlights:

• A partial homology swap converts the S. elongatus clock into an hourglass

• Hourglasses resemble clocks in a balanced light-dark cycle, diverge in longer days

• Hourglass systems incorrectly time UV resistance in high latitude summer days