Frequency doubling in the cyanobacterial circadian clock

Abstract

Organisms use circadian clocks to generate 24-h rhythms in gene expression. However, the clock can interact with other pathways to generate shorter period oscillations. It remains unclear how these different frequencies are generated. Here, we examine this problem by studying the coupling of the clock to the alternative sigma factor sigC in the cyanobacterium Synechococcus elongatus Using single-cell microscopy, we find that psbAI, a key photosynthesis gene regulated by both sigC and the clock, is activated with two peaks of gene expression every circadian cycle under constant low light. This two-peak oscillation is dependent on sigC, without which psbAI rhythms revert to one oscillatory peak per day. We also observe two circadian peaks of elongation rate, which are dependent on sigC, suggesting a role for the frequency doubling in modulating growth. We propose that the two-peak rhythm in psbAI expression is generated by an incoherent feedforward loop between the clock, sigC and psbAI Modelling and experiments suggest that this could be a general network motif to allow frequency doubling of outputs.

Keywords: circadian clock; cyanobacteria; mathematical modelling; network motifs; single‐cell time‐lapse microscopy.

Figure 1. psbAI expression shows two peaks per circadian cycle

1. Time traces of P_psbAI‐YFP reporter grown under constant low light (ca. 15 μE m⁻² s⁻¹ cool white light). Individual lineages (black and green lines) show the existence of a second peak following the first (dusk timed) peak of expression. Owing to cell‐to‐cell desynchronisation, this second peak is often hidden when expression is measured at the population level (dashed red line, with pink shades representing one standard deviation from the mean). The white and grey shades represent subjective day and subjective night, respectively. 1,319 cells from 10 movies (with up to 419 cells per time point) were collected.

2. Measure of the distance between the first peak in each circadian cycle and the following peak. The majority of peak pairs occur in the same circadian cycle, with a mean peak‐to‐peak distance of ca. 9 h within this subpopulation.

3. Distribution of the difference in peak amplitudes between the first and second peaks in a circadian cycle (for cycles where a double peak is present). The second peak is, on average, smaller in amplitude than the first peak.

4. Neither single‐cell traces nor a population average of psbAI expression shows a double peak in a sigC deletion strain (lines and shades as in A). 1,088 cells from eight movies (with up to 419 cells per time point) were collected.

5. Measure of the distance between the first peak in each circadian cycle and the following peak shows that the vast majority of lineages have one peak of expression per day.

6. Distribution of peak amplitudes in wild‐type and sigC deletion strains shows that sigC negatively regulates psbAI expression.

Source data are available online for this figure.

Figure EV1. Single‐cell lineages from two movies of psbAI expression show two‐peak oscillations

1. Time traces of P_psbAI‐YFP reporter strains grown under low light (ca. 15 μE m⁻² s⁻¹ cool white light). Individual lineages show the existence of a secondary peak following the main (dusk timed) peak of expression. Cells remain synchronised, allowing double peak to be observed in the mean trace (black line).

2. In a different movie, due to desynchronisation, the double peak is less apparent in the mean trace (black line).

Data information: In (A) and (B), each line under the black mean trace represents one single‐cell lineage.

Figure 2. Two‐peak circadian oscillations in growth can be observed in wild‐type cells

1. A

   Mean auto‐correlation function of the elongation rate from nine movies (we removed one movie from the analysis as it ended after just 80 h) of the strain carrying the P_psbAI‐YFP reporter in a wild‐type background shows daily double peaks.

2. B

   Mean cross‐correlation function between expression rate of P_psbAI‐YFP and elongation rate shows daily double peaks and a ca. 1‐h delay of the elongation rate relative to the expression rate (inset with zoom‐in of the mean trace between lags of −3 h and 3 h).

3. C, D

   Both the mean auto‐correlation function of the elongation rate (C) and the cross‐correlation function between expression rate and elongation rate (D) from eight movies in a sigC deletion background show a single peak per circadian cycle. However, the elongation rate has a similar delay of ca. 1 h relative to the expression rate (D, inset).

Data information: Pink and light blue shades represent one standard error of the mean across all movies.

Figure 3. sigC single‐cell traces do not show a double peak, but show that sigC is negatively auto‐regulated

1. Neither single‐cell traces nor a population average of a reporter for sigC, P_sigC‐YFP, shows a double peak of expression. 664 cells from nine movies (with up to 213 cells per time point) were collected.

2. Measure of the distance between the first peak in each circadian cycle and the following peak confirms that there is only one peak per circadian cycle.

3. The amplitude in sigC expression is raised by 3.5‐fold in a sigC knock‐out strain, consistent with a sigC‐negative auto‐regulation. 1,084 cells from six movies (with up to 352 cells per time point) were collected.

4. Measurement of the distance between the first peak in each circadian cycle and the next peak confirms that there is only one peak per circadian cycle.

Data information: Pink and light blue shades represent one standard deviation from the mean. Black and green lines represent two single‐cell traces.Source data are available online for this figure.

Figure EV2. P_sigC‐YFP levels are upregulated in high light, suggesting a reduced functionality of SigC in higher light conditions

1. Histogram of P_sigC‐YFP expression in wild‐type (red) and sigC deletion mutant (blue) under ca. 15 μE m⁻² s⁻¹ cool white light. For the wild type, 664 cells from nine movies were collected, whereas for the sigC deletion strain, 1,084 cells from six movies were collected.

2. Histogram of P_sigC‐YFP expression in wild‐type (red) and sigC deletion mutant (blue) under ca. 35 μE m⁻² s⁻¹ cool white light. P_sigC‐YFP in wild type is upregulated by twofold between light conditions. A smaller fold change of 1.2 is seen in the sigC deletion mutant. In the higher light condition, 1,003 cells from two movies were collected for the wild‐type strain, whereas 920 cells from two movies were collected for the sigC deletion strain.

Source data are available online for this figure.

Figure 4. A minimal mathematical model, containing an incoherent feedforward loop modulated by an oscillatory signal, reproduces the experimental observations

1. Schematics of the proposed regulatory network. The circadian clock regulates both PsbAI and SigC, and SigC represses both PsbAI and itself. Since the circadian clock regulates PsbAI through two separate branches of opposite signs, one of which is mediated by an intermediate gene, this network contains an incoherent feedforward loop motif.

2. Numerical simulations of the wild‐type network show double peaks of expression (red line), and numerical simulations of a SigC knock‐out model (in which the terms representing the regulation of PsbAI by SigC are set to zero) show only single‐peaked oscillations (blue line).

3. The trajectory of the normalised production rate of PsbAI in the wild‐type (red line) simulation shows the dependence of the double peak on the states of the clock and SigC. The surface represents the two‐input production rate function. When the levels of both the clock and SigC are low, the production rate is also low (time point 1, brown circle). As the state of the clock rises, the production rate follows and reaches a plateau (time point 2, which corresponds to the main peak of PsbAI in panel B). However, SigC also rises, crossing a threshold and overcoming the clock, thus imposing a trough in the production rate (time point 3). Later, SigC drops low enough to relieve its negative regulatory activity, and the production rate reaches a second peak (time point 4).

4. In the SigC deletion simulation (the terms representing the regulation of PsbAI by SigC are set to zero, but SigC expression is tracked for reference), the production rate of PsbAI only responds to the clock, which is a single‐peak oscillation, and so the trajectory of the production rate (blue line) only has a single peak itself (the plateau where time points 2, 3 and 4 lie).

Figure 5. The double peak in expression of psbAI is largely lost at higher light conditions

1. Time traces of P_psbAI‐YFP reporter grown under ca. 35 μE m⁻² s⁻¹ cool white light. Most individual lineages (black and green lines) show one circadian peak of gene expression. 2,601 cells from eight movies (with up to 776 cells per time point) were collected.

2. Measure of the distance between the first peak in each circadian cycle and the following peak shows a single peak per day is the dominant mode.

3. Time traces of P_psbAI‐YFP reporter in a sigC deletion background look similar to the wild type. 2,306 cells from five movies (with up to 623 cells per time point) were collected.

4. Measure of peak‐to‐peak distance shows a single circadian peak.

Data information: Pink and light blue shades represent one standard deviation from the mean. Source data are available online for this figure.

Figure EV3. Simulations of reduced SigC activity at high light qualitatively match experimental data

1. Increasing the deactivation rate of SigC by two orders of magnitude produces only a minor double peak in PsbAI expression. This is comparable to that observed experimentally in higher light conditions (Fig 5A).

2. The reduction in SigC activity in simulations results in an increase in SigC expression, which qualitatively matches experimental results (Fig EV2). The traces represent the sum of the concentration of the two forms of SigC we considered in the model (see Section II in Appendix).

Figure 6. The clock‐sigC circuit represents a general mechanism to generate multi‐peak oscillations in oscillatory networks

1. Time traces of P_rpoD6‐YFP reporter grown under low light conditions (ca. 15 μE m⁻² s⁻¹ cool white light). Individual lineages (black and green lines) show the existence of a shoulder or a secondary peak of reduced prominence when compared to P_psbAI‐YFP. 947 cells from 12 movies (with up to 272 cells per time point) were collected. Pink shades represent one standard deviation from the mean.

2. Time traces of P_rpoD6‐YFP reporter in a sigC deletion background show only a smooth single‐peaked oscillation. 1,352 cells from seven movies (with up to 502 cells per time point) were collected. Light blue shades represent one standard deviation from the mean.

3. Numerical simulations of the RpoD6 wild‐type network show a shoulder of expression trailing the main peak (red line). All the parameters describing the clock and SigC are as in Fig 4B, and only the threshold of activation of the rpoD6 promoter by the clock was modified. Numerical simulations of a SigC knock‐out model (in which the terms representing the regulation of RpoD6 by SigC are set to zero) show only single‐peaked oscillations (blue line).

4. The incoherent feedforward loop circuit that regulates rpoD6 and psbAI is capable of generating diverse oscillatory dynamics in vivo and in silico. Networks where a target gene (Y) is co‐regulated by an oscillator and another regulator (X, which itself is regulated by the oscillator) may represent a general mechanism for generating multi‐peak oscillations.

Figure EV4. Double peaks in P_rpoD6‐YFP expression are dependent on sigC

1. Measure of the distance between the first peak in each circadian cycle and the following peak shows only a subfraction of cells display a double peak. 947 cells from 12 movies (with up to 272 cells per time point) were collected.

2. Single‐cell lineages of a representative movie show that all lineages show either a second peak, or a shoulderlike feature, in P_rpoD6‐YFP levels.

3. In the sigC deletion mutant, the two‐peak oscillations are abolished. 1,352 cells from seven movies (with up to 502 cells per time point) were collected.

4. Single‐cell lineages of a representative movie show a single peak of P_rpoD6‐YFP.

Source data are available online for this figure.