Circadian period is compensated for repressor protein turnover rates in single cells

Significance

The circadian clock is a cell-autonomous transcriptional–translational oscillator that allows the body to prepare for daily recurring tasks (e.g., rest-activity or eating patterns). Misalignment of the circadian clock with environmental cycles, such as in shift workers, has been linked to several common diseases. A hallmark of circadian clocks is that the speed of the clock is robust despite environmental fluctuations, such as changes in nutrient supply or temperature. Using live cell microscopy of thousands of fluorescent clock reporter cells, we show that large differences in protein turnover rates of circadian clock components do not unidirectionally change the length of the circadian period, contrary to previous assumptions. A mathematical model conceptualizes our results and suggests mechanisms for such metabolic compensation.

Abstract

Most mammalian cells have molecular circadian clocks that generate widespread rhythms in transcript and protein abundance. While circadian clocks are robust to fluctuations in the cellular environment, little is known about the mechanisms by which the circadian period compensates for fluctuating metabolic states. Here, we exploit the heterogeneity of single cells both in circadian period and a metabolic parameter—protein stability—to study their interdependence without the need for genetic manipulation. We generated cells expressing key circadian proteins (CRYPTOCHROME1/2 (CRY1/2) and PERIOD1/2 (PER1/2)) as endogenous fusions with fluorescent proteins and simultaneously monitored circadian rhythms and degradation in thousands of single cells. We found that the circadian period compensates for fluctuations in the turnover rates of circadian repressor proteins and uncovered possible mechanisms using a mathematical model. In addition, the stabilities of the repressor proteins are circadian phase dependent and correlate with the circadian period in a phase-dependent manner, in contrast to the prevailing model.

Circadian clocks have evolved in all kingdoms of life, enabling organisms to track, anticipate, and adapt to the ~24-h rhythm of day and night. They exist at all levels of hierarchy, from single cells to whole organisms—but the basis of all circadian rhythms is a cell-autonomous oscillator (1). Single-cell circadian rhythms have a high degree of noise and stochasticity, e.g., the circadian clock of genotypically identical cells can oscillate with periods ranging from about 18 to 30 h and beyond, (2–5). Intercellular communication allows noisy single-cell oscillations to give rise to a robust rhythmic signal at the population or organ level (6, 7). In mammals, the generation of molecular oscillations mainly relies on a transcriptional–translational feedback loop (TTFL): CLOCK:BMAL1 promotes the rhythmic expression of the repressors CRY1-2 and PER1-3, which form high molecular weight complexes that inhibit CLOCK:BMAL1 and thereby their own transcription (8–11). After the degradation of the complex, the monomeric CRY1 still independently represses CLOCK:BMAL1 until the inhibition is released and a new cycle begins (12, 13).

A hallmark of circadian rhythms is that they are robust against environmental fluctuations. Since misalignment of the internal clock with environmental rhythms—as occurring in shift workers—has been linked to diseases such as cancer and type 2 diabetes (14, 15), it would be detrimental if those fluctuations altered the length of the circadian period without compensatory mechanisms. While several mechanisms have been proposed for temperature compensation (16–18), less is known about how the clock is stabilized against changes in energy supply that affect the rates of macromolecule assembly and turnover (19–21). Rather, increasing the protein half-life of PERs and CRYs by mutation, inhibition, or ablation of ubiquitin ligases (e.g., FBXL3 and βTrCP) lengthens the circadian period (22–28), suggesting that lower protein turnover rates of repressor proteins would decrease the speed of the molecular clock if not otherwise compensated. However, when circadian oscillations are restored by introducing CRY1 mutants into arrhythmic Cry1/2-knockout cells (12), the rescued period does not always correlate with the mutant’s protein stability (29–31). Genetic manipulation by mutation almost always carries the risk of also altering protein function, and thus, a period phenotype may occur because of, in addition to, or despite the alteration in protein stability (29, 32).

Here, we exploit the natural heterogeneity of both the circadian period and protein degradation rates at the single-cell level, allowing us to study the interdependence of these traits without the need for genetic manipulation (2, 4, 33). Using tens of thousands of engineered single cells expressing CRYs and PERs as fluorescent fusion proteins, we found that the stability of these proteins varies with the time of day, which conditions rhythmic protein levels. The influence of repressor stability on the circadian period is also phase dependent: Early in the cycle, high stability correlates with a shorter period, late in the cycle with a longer period, suggesting compensation of the circadian period length against highly variable protein degradation rates.

Results

Visualization of Endogenous CRY2 and PER1 Proteins in Living Cells.

We have previously used CRISPR/Cas9-mediated knock-in approaches to generate U-2 OS cells expressing CRY1 and/or PER2 as fluorescent fusion proteins from the endogenous locus (4). Because the paralogs PER1 and CRY2 have overlapping but not redundant functions within the TTFL (34–37), and to study the protein dynamics of all circadian repressors side by side, we generated CRY2-mScarlet-I and PER1-mScarlet-I knock-in cells (referred to as CRY2-mSca and PER1-mSca). To this end, we inserted the sequence of the red fluorescent protein mScarlet-I (mSca) 5′ to the PER1 or CRY2 stop codon into the genome of U-2 OS cells (SI Appendix, Fig. S1A) and screened clones by fluorescence microscopy and genomic PCR. We selected two homozygous CRY2-mSca-I and two heterozygous PER1-mSca clones (SI Appendix, Fig. S1 B–E) and confirmed the specificity of the fluorescence using small hairpin RNA (shRNA) (Fig. 1 A and B).

Fig. 1.

CRY2 and PER1 protein oscillation in single cells. (A and B) Fluorescent knock-in and wild-type (wt) U-2 OS cells transduced with shRNA targeting either CRY2 or PER1 or with a nonsilencing control shRNA (shNS1). (Scale bar: 20 µm.) (C and D) Montage of a CRY2-mSca (C) or PER1-mSca (D) knock-in cell nucleus recorded at indicated hours after dexamethasone (dex) treatment and time course of mean fluorescence intensity. (Scale bar: 5 µm.) (E) Time series of mean nuclear fluorescence of indicated knock-in clones after dex treatment. Only time series with ≥60 h are shown. Y-axis ticks mark every 10th cell. (F) Median fluorescence intensities for individual cells from all time points after background subtraction. Horizontal lines: median of all cells, red line: median nuclear autofluorescence. (G) Percentage of rhythmic cells as a function of P-value cutoff. Vertical dashed lines represent P-values of 0.05 and the more stringent value used here, respectively. See SI Appendix, Supplementary Note 1. (H and I) Relative amplitudes (H) and periods (I) of rhythmic time series. (J) Montage of a CRY1-mClo/CRY2-mSca double knock-in (DKI) cell nucleus imaged in the two fluorescence channels at the indicated hours after dex treatment, and time course of mean fluorescence intensities. (Scale bar: 5 µm.) (K) Histogram of phase difference (30-min bins) in unsynchronized CRY1/CRY2 DKI cells. P-value: Wilcoxon signed-rank test. (L) Sequence of mean nuclear peak expression in U-2 OS cells. PER1 timing is estimated from SI Appendix, Fig. S3 B and C.

Circadian rhythms were intact in all clones (SI Appendix, Fig. S1 F–J). CRY2-mSca fluorescence was seen exclusively in the nucleus of the knock-in cells (Fig. 1A), similar to what we have observed for CRY1. In contrast, cytoplasmatic fluorescence above background was observed in PER1 knock-in cells (Fig. 1B). Thus, these clones express fluorescent CRY2-mSca or PER1-mSca from the endogenous loci while the circadian oscillator remains intact.

CRY2 and PER1 Protein Abundance Oscillates in Single Cells.

The protein abundance of both PER1 and CRY2 oscillates at the population level (38, 39), but little is known about their expression dynamics in single cells. To address this, we recorded fluorescence of single cells from knock-in clones for 3 d after dexamethasone synchronization. The nuclear abundance of both PER1-mSca and CRY2-mSca oscillated in single cells, but with different characteristics: CRY2-mSca was detected in the nucleus of expressing cells throughout the circadian cycle and did not exceed background levels in the cytoplasm at any time point (Fig. 1C). In contrast, nuclear PER1-mSca levels of many cells dropped to near background fluorescence levels in the trough of the circadian oscillation (Fig. 1D).

To quantify circadian dynamics, we developed an automated approach to track and extract signals from thousands of cells in a single experiment. Cells were stably transduced to express a nuclear infrared protein (histone-2B-monomeric infrared fluorescent protein (miRFP) 720), nuclei were segmented and tracked based on miRFP720 fluorescence using CellProfiler software, and the background-subtracted mean nuclear fluorescence was extracted. Mistracked nuclei were identified by an apparent abrupt size change in the absence of cell division and filtered out using a Python script (Materials and Methods). Using this approach, we extracted nuclear fluorescence signals from hundreds of synchronized PER1-mSca, CRY2-mSca, and CRY1-mSca and CRY1-mClover3 reporter cells over the course of 68 h (Fig. 1E, SI Appendix, Fig. S2, and Movie S1). In contrast to the much lower expressed PER2-fusion protein (4), the average intensity levels of PER1-mSca, CRY1-mSca, and CRY2-mSca were similar (Fig. 1F).

Next, we analyzed circadian parameters and the rhythmicity of these time series using Metacycle 2D (40–42) (SI Appendix, Fig. S2). We defined a dataset-specific stringent P-value cutoff based on the autofluorescence recording (P < 10⁻⁵, see SI Appendix, Supplementary Note 1 for details) and excluded time series whose calculated period exactly matched the allowed limits (18 to 32 h). Using these criteria, 59 to 66% of the time series from CRY2-mSca and PER1-mSca cells were classified as “highly rhythmic”, compared to ~33% of those from CRY1 reporter cells. These differences between repressor oscillations were present regardless of the P-value cutoffs (Fig. 1G). Among the highly rhythmic time series, PER1 protein oscillations had the highest relative amplitude, while CRY1 oscillations had the lowest (Fig. 1H). The average periods of the rhythmic signals were similar for all six clones analyzed (Fig. 1I). Notably, the periods of individual cells—even within clonal populations—were highly variable.

Phase Relationship between CRY and PER Proteins.

Previously, we observed that the expression phase of CRY1 protein was delayed by ~5 h relative to PER2 (4), consistent with delayed messenger RNA (mRNA) expression and repressive activity of CRY1 compared to the other repressors (13, 39). To obtain a more complete profile of circadian repressor expression, we estimated the difference in the expression phase of CRY2 and PER1 in relation to CRY1 from the mean of all normalized time series (SI Appendix, Fig. S3 A and B). This revealed that the nuclear accumulation of PER1 peaked first, followed by CRY2 and CRY1 last, with the limitation that the clonal difference was larger than the differences between the different reporters.

To overcome this limitation, we generated double knock-in (DKI) cells expressing CRY1-mClover together with either PER1-mSca or CRY2-mSca to visualize and study the dynamics of two proteins within the same cell. Unexpectedly, PER1-mSca/CRY1-mClo DKI cells showed an exclusively cytoplasmic mSca fluorescence signal, suggesting a deleterious interplay of the two fusion proteins. However, both mClo and mSca fluorescence signals were localized to the nucleus in CRY1-mClo/CRY2-mSca DKI cells, as seen in cells expressing either fusion protein alone (Fig. 1J and SI Appendix, Fig. S4A). Knock-in was verified by genomic PCR (SI Appendix, Fig. S4 B and C) and the specificity of the fluorescence signal by knockdown (SI Appendix, Fig. S4A) for four clones, which showed similar circadian rhythmicity compared to their respective parental clone (SI Appendix, Fig. S4 D–H), allowing us to simultaneously monitor both CRY proteins in single cells with intact circadian clocks (Fig. 1J).

We recorded the nuclear fluorescence of unsynchronized CRY1/CRY2 DKI cells for 2 d. In cells in which both signals were rhythmic, CRY2 nuclear accumulation peaked on average 1.9 ± 4.3 h (mean ± SD) before that of CRY1 (Fig. 1K). Thus, we propose the following sequence of events in the nucleus of U-2 OS cells: 1) peak of PER2 protein, 2) peak of PER1 protein ~1.5 to 3 h later, 3) peak of CRY2 protein 3 h after the peak of PER2 and finally peak of CRY1 protein another 2 h later (Fig. 1L). While this sequence aligns well with lower-resolution data from proteomic studies, it is slightly different from that of transcript abundance, where PER1 mRNA usually peaks first. This supports earlier findings that rhythms of RNA and corresponding protein abundance can differ substantially (13, 39, 43–46).

Stability of Repressor Proteins.

Next, we sought to address the fundamental unresolved question of how the period of the molecular circadian clock is tuned to ~24 h. Evidence that altering the stability of circadian repressor proteins, i.e., CRYs and PERs, can affect the circadian period (22, 27), has mostly been derived from genetic perturbation studies, and it remains unclear whether the altered period is due to altered stability or to the perturbation itself. Given the high variability of circadian oscillations in single cells, we hypothesized that we could exploit their heterogeneity to analyze the interdependence of repressor stability and circadian period without the need for genetic manipulation. To simultaneously obtain circadian parameters and repressor protein stability in the same cells, we recorded nuclear protein abundance of unsynchronized single and DKI cells (SI Appendix, Table S1) for 3 d, capturing rhythms in the first 2 d and recording degradation dynamics on the third day after stopping protein synthesis with cycloheximide (CHX, 20 µg/mL, Movie S2). Circadian parameters and the circadian phase at which CHX was added—and at which protein half-life is assessed—were calculated from time points prior to CHX, and protein half-lives were obtained from time series after CHX addition (Fig. 2A).

Fig. 2.

Stability of repressor proteins and correlation with circadian dynamics. (A) Experimental setup: Unsynchronized single knock-in reporter cells transduced with shRNA were imaged 2 d prior and 1 d after CHX addition. Circadian parameters were extracted from days 1 and 2, and protein half-life from day 3. (B) Median periods of reporter cells transduced with the indicated shRNAs, each calculated from ≥10 rhythmic cells. The same colors (green: mClo clones, purple: mSca clones) represent the same clonal population from different experiments. P-value: Wilcoxon signed-rank test. (C and D) Median protein half-life of clonal populations transduced with control shRNA (C) or the indicated shRNAs (D), each calculated from ≥10 decay fits. Black lines (C) indicate the median. P-values: Mann–Whitney U test (C) and Wilcoxon signed-rank test (D). (E) Half-life of individual PER2-mSca cells. Shown are means ±95% CI (CI). P-value: Wilcoxon signed-rank test. (F) Correlation of CRY1 and CRY2 half-life in DKI cells (Spearman). (G) Highly rhythmic time series (SI Appendix, Supplementary Note 1) were filtered for reliable decay fits. (H–J) Correlation of measured half-lives with signal intensity (abundance, H), relative circadian amplitude (I), and circadian period length (J). Correlation coefficient (r) and P-value from Spearman correlation, line: linear regression.

To test our ability to accurately determine periods and protein half-lives in single cells, we sought to reproduce the observation that knockdown of FBXL3 results in a long circadian period and increased CRY half-lives (27). To this end, we transduced all cells with either a nonsilencing shRNA or an shRNA targeting FBXL3. Median knockdown efficiency was 70.6% (Supplementary Fig. S5 A and B). In total, we obtained more than 20,000 time series of nuclear fluorescence from three independent experiments (SI Appendix, Table S2). Using the same threshold criterion as described above, approximately 30% of all time series were classified as highly rhythmic (24.4% for FBXL3 knockdown and 36.9% for control cells, SI Appendix, Table S2). Most cell populations oscillated with average periods between 23 and 25 h and had various phases when CHX was added (SI Appendix, Fig. S5C). Knockdown of FBXL3 increased the average period of almost all clonal populations by 1.5 ± 1.1 h (mean ± SD, Fig. 2B), similar to what has been described previously (27), demonstrating that the differences in period distribution can be faithfully detected in single-cell data. Next, we calculated the half-life of the mean nuclear fluorescence signal after addition of CHX, which we will refer to as the half-life of the respective protein for ease of reading. After correction for photobleaching (Materials and Methods), we fitted monoexponential decay curves to the second part of the time series, starting 2 h after addition of CHX. We required i) that the initial intensity be significantly above background levels (~54% of all traces), and ii) a r² value of at least 0.7 for a successful fit (9,211 traces, ~82%).

Overall, the protein half-lives obtained were highly variable, with 95% of the values falling between 2.3 and 19.0 h (SI Appendix, Fig. S5 D and E). On average, CRY1 proteins had a significantly longer half-life (5.9 ± 0.7 h, median ± SD) than CRY2 (5.1 ± 0.6 h, P = 9.3*10⁻⁵, Mann–Whitney U test) and, although not statistically significant, PER1 (5.2 ± 1.2 h, P = 0.14, Fig. 2C). For PER2, we could only reliably determine the half-life in 25 cells (5.8 ± 4.6 h, Fig. 2E) because the signal’s intensity was too low in most cells, and therefore focused all further analysis on the other three repressors. Consistent with previous reports, FBXL3 knockdown significantly increased the average half-life of CRY1 and CRY2 (by 3.2 h and 1.4 h, P = 6.1*10⁻⁵ and 1.2*10⁻⁴, respectively, Wilcoxon signed-rank test), but not of PER proteins (Fig. 2 D and E). Thus, we were able to detect known changes in protein half-lives using noisy single-cell data, despite the wide distribution of half-lives within clonal populations (SI Appendix, Fig. S5E). Furthermore, the half-lives of the fusion proteins represent those of the repressors and not those of the fluorescent reporter because only CRY, but not PER fusion protein half-lives increased after FBXL3 knockdown, and fluorescent protein half-lives are typically much longer (47). Interestingly, we observed a strong correlation between CRY1 and CRY2 half-lives in cells expressing both reporters (Fig. 2F) indicating coregulation.

To investigate the effect of repressor stability on circadian dynamics, we focused on those ~3,100 highly rhythmic time series with reliable decay fits (Fig. 2G). We observed the expected positive correlation of half-life with expression level (magnitude, Fig. 2H) and the negative correlation of half-life with relative amplitude (Fig. 2I) (46). Surprisingly and in contrast to the prevailing model, we did not detect a significant correlation between repressor half-life and circadian period (Fig. 2J and SI Appendix, Fig. S5F). In cells with similar circadian periods, the half-life of, e.g., CRY1 can differ by a factor of up to 10 (Fig. 2J).

Protein Stability of Repressor Proteins Changes with Circadian Phase.

We speculated that the half-life of CRY1, CRY2, and PER1 may not be a static value but may itself be subject to circadian changes, as reported for PER2 (48). If this were the case, the measured decay rates at a certain phase may be insufficient to explain the period of a cell. Strikingly, the half-life of all three proteins showed significant rhythmicity, with a peak of stability during the rising phase (Fig. 3A).

Fig. 3.

Stability of repressor proteins is circadian phase dependent. (A) Harmonic regression analysis of protein half-life and circadian phase in which the half-life was measured. P-values: F-test. (B) Relative expression at time of CHX addition (mean ± SEM) for each 3-h phase window. (C) Protein half-life (median and 95% CI) and cell number for each 3-h phase window. Dashed lines represent the median, and * indicates a statistically significant (P < 0.05) difference from the median (one-sample Wilcoxon signed-rank test, corrected for multiple testing (Sidak–Holmes). (D) Harmonic regression analysis of protein half-life and circadian phase after knockdown of FBXL3. P-values: F-test. (E) Protein half-lives as in C after knockdown of FBXL3. (F) Increase in median protein half-life in FBXL3 knockdown cells compared to controls, number of cells as in C and E. *P < 0.05, Mann–Whitney U test, corrected for multiple testing (Sidak–Holmes).

To get a clearer picture of how the repressor half-life changes with circadian phase, we binned the half-life and relative expression data into 24 overlapping phase windows of 0.78 rad, corresponding to 3 h of a 24-h cycle (SI Appendix, Fig. S6), with each cell represented in three consecutive bins. Plotting relative expression against circadian phase at the time of CHX addition showed the expected rhythmic patterns (Fig. 3B). The stability of all three proteins was lowest in cells assayed at or after the peak phase (Fig. 3 B and C), when protein abundance declines, and highest during and after the trough phase, when proteins reaccumulate. Notably, the number of time series that could be analyzed was lower in the trough phase (Fig. 3 C, Lower) because the lower initial signal levels more often precluded a faithful determination of the decay dynamic, especially for time series from PER1 reporter cells, whose nuclear trough expression levels are close to background (Fig. 1D).

Rhythmic CRY1 Stability Is Dependent on FBXL3.

Next, we asked how the observed rhythmic stabilities might be generated. We observed that the phase dependence of CRY1 stability is lost upon FBXL3 knockdown, (Fig. 3D) and CRY1 half-lives are high in all phases (Fig. 3E). Thus, the presence of FBXL3 seems to be necessary for the rhythmic stability of CRY1. For CRY2, phase-dependent differences in protein half-life are still present but reduced in the absence of FBXL3. In contrast, FBXL3 does not alter the pattern of rhythmic PER1 stability. The increase in stability of CRY proteins upon knockdown of FBXL3 was less prominent during the rising phase when CRY stability was already highest in control cells (Fig. 3F). This suggests that FBXL3 targets CRY proteins for degradation mainly during the falling phase, resulting in phase-dependent differences in protein stability.

Impact of CRY Half-Life on Circadian Period Is Phase Dependent.

Since PER and CRY stabilities change in a phase-dependent manner, the decay rate obtained from a cell represents only a snapshot of a dynamic measure. Therefore, we investigated whether the observed independence of the period from repressor stability (Fig. 2J) could be an artifact of analyzing pooled data. To this end, we grouped time series into overlapping phase windows of 3 h (as before, SI Appendix, Fig. S6B) and correlated repressor half-life and period separately for cells within these phase windows (Fig. 4 A–E).

Fig. 4.

Circadian period depends on repressor protein stability in a phase-dependent manner. (A–E) Three-dimensional plots of circadian period, CRY1 half-life, and circadian phase at half-life measurement. Data from indicated phase windows (A–D) or from all phases (E) are shown (see text for details). Colored lines represent linear regression (m: slope, r: Spearman correlation coefficient). (F–H) Spearman correlation coefficient and slope (m) of linear regression (median and 95% CI) for each 3-h phase window, and number of cells for each correlation. Red dashed line: n = 30 cells (minimum for correlation analysis).

Indeed, we found correlations between repressor stability and circadian period, but to an unexpected extent: Depending on the circadian phase, we observed a significantly positive (Fig. 4B), negative (Fig. 4D), or no correlation (Fig. 4 A and C). When the Spearman correlation coefficient and the slope of the linear regression were plotted for all phase windows, a general pattern emerged (Fig. 4 E–H): In cells assayed during the rising phase, CRY1 stability and circadian period were negatively correlated, i.e., a relatively longer CRY1 half-life in this phase was correlated with shorter periods and vice versa (Fig. 4 B and F). In contrast, CRY1 half-life and period were positively correlated in cells analyzed during the late falling phase (Fig. 4 D and F). This was very similar for the phase-dependent correlation of period and CRY2 half-life (Fig. 4G). For PER1, the correlation analysis suffered from lower cell numbers and did not show clear trends (Fig. 4H).

Interestingly, even if only the stabilities assessed during the same phase are compared, cells with very different repressor half-lives can have a similar period length (Fig. 4 A–D).

Circadian Period Is Compensated for Protein Turnover Rates.

One implication of the phase-dependent correlation between CRY half-life and period is that the stability of circadian repressor proteins may affect the length of the circadian cycle differentially. Intuitively, overall low protein stability could i) prolong the time to reach a threshold of repression during the rising phase, but ii) also shorten the time to release repression due to the accelerated disappearance of repressor proteins (Fig. 5A) (49).

Fig. 5.

Period is compensated for protein turnover rates: a mathematical model. (A) Simple schematic of how CRY1 stability differentially affects period length. (B) Architecture of the mathematical model (see text for details). x: CRY1 mRNA, y: “early”, nonrepressive CRY1, z1: CRY1 in high molecular weight complexes, z2: “late” monomeric, repressive CRY1. (C) Oscillation in the absolute abundance of the state variables for the default parameters. (D) Regression analysis of the period and total “pool half-life” (i.e., all CRY1 species y, z1, and z2) of a simulated population of single cells with stochastically varying turnover rates of early and late CRY1 for two indicated phases (n = 155). (E) Pool half-lives of the simulated population described in D. For each cell, decay is simulated at five random time points. (F and G) Effect of changes in early CRY1 (y) stability on period length (F) and expression level of early CRY1 protein (y) and CRY1 mRNA (x) (G). Stability = 1/dy, dz1 and dz2 are constant. (H) Effect of changes in late CRY1 (z2) stability on length of rising phase, falling phase, and total period (rising + falling). Stability = 1/dz2, dy is constant. (I) Heatmap of period changes for different combinations of y and z2 stabilities (1/y and 1/dz2, normalized to default values). The gray area shows a period length of ±0.5 h from that for default parameters. The white line shows where the degradation rate of y is equal to that of z2.

Thereby, the resulting period length may be less effected—i.e., compensated—by cellular fluctuations affecting protein turnover. However, intuition can easily be misled by the complexity present in the TTFL. Therefore, we developed an adapted mathematical model of the TTFL based on a single prototypical CRY1 repressor (Fig. 5B). Using linear kinetics for production terms, Michaelis–Menten kinetics for degradation terms, and Hill functions for transcriptional repression, our model has four variables describing different types of the CRY1 repressor (SI Appendix, Table S4 and Materials and Methods).

Repressor transcription leads to accumulation of mRNA (x) and translation into an early nonrepressive CRY1 protein (y), which is degraded at a basal rate (dy). Posttranslational modifications (e.g., phosphorylation) allow the repressor to inhibit its own transcription, but also render it more susceptible to degradation. This mature CRY1 (z1 and z2) can either inhibit E-Box-mediated transcription in a complex (e.g., with PERs, z1), shielded from FBXL3-mediated ubiquitination/degradation, or as monomeric CRY1 (z2), in which case it is degraded at a higher rate (degradation rate dz2 > dy, dz1). To evaluate the total half-life of all species, analogous to the experimentally measured half-life (see Figs. 2 and 3, hereafter referred to as pool half-life), translation is set to 0 and the decay curve is analyzed for 15 h.

In this model, the mRNA and all three repressor types, as well as the total amount of protein, oscillate in a self-sustained manner (Fig. 5C), with the contribution of each CRY1 species to the total amount of CRY1 changing over the course of the day. While the early, nonrepressive CRY1 (y) is the most abundant species during the accumulation phase, the late, monomeric repressive CRY1 (z2) dominates during the falling phase. A simulated population of single cells with stochastically varying turnover rates of early and late CRY1 (SI Appendix, Fig. S7A) shows the experimentally observed negative and positive correlation between total CRY1 half-life and period during the rising and falling phases, respectively (Fig. 5D). Moreover, the average of pool half-life was time of day dependent, as observed in our experiments (Fig. 5E). Thus, the model reproduced key features of our experimental data, which motivated us to take a closer look at the underlying principles.

We first investigated why the overall half-life of the CRY1 pool is time dependent. Our model suggests two possible mechanisms. First, the high amount of stable early CRY1 during the rising phase makes the pool more stable, whereas during the falling phase an unstable monomeric CRY1 dominates the pool composition and half-life (SI Appendix, Fig. S7B). Second, due to rate limitation of degradation processes, half-lives are longer when CRY1 abundance is high and shorter when abundance is low, resulting in a minimum pool half-life near the trough of expression (SI Appendix, Fig. S7C).

Next, we examined how the stability of the two monomeric CRY1 species affects period. We observed different effects on period depending on whether the stability of early y or late z2 was changed. Increasing the stability of early CRY1 (y) shortens the period (Fig. 5F), but only to a small extent, likely due to a compensatory mechanism by reducing its production. In short, even when y stability is increased, y levels remain relatively stable because increased feedback repression leads to less mRNA (x) and thus less production of y (Fig. 5G), partially decoupling the dynamics of CRY1 accumulation from its stability (SI Appendix, Fig. S7D). In contrast, increasing the stability of late monomeric, repressive CRY1 (z2) lengthens the period with a saturation of the effect at very high stabilities (Fig. 5H). This can be explained by the effect of late CRY1 stabilization on both the onset and duration of repression: While z2 stabilization prolongs the repression, leading to a longer falling phase, it also shortens the rising phase, probably by accelerating its own accumulation, so that the threshold for repression is reached more quickly (Fig. 5H). These two processes have opposite effects on the period, and for stable z2, the shortening of the rising phase offsets the lengthening of the falling phase.

Thus, the model suggests three different mechanisms by which period may be compensated for variations in repressor stability: First, adjusted production may compensate for changes in turnover rates (e.g., of y). Second, changes in the stability of a particular CRY1 species (e.g., z2) may affect the length of the rising and falling phases differentially. Third, changes in the stability of different subspecies (y and z2) may have opposite effects on period length. As a consequence, different combinations of (basal and FBXL3-dependent) turnover rates may result in similar period lengths (Fig. 5I), and cells with the same period may have different half-lives of the CRY1 pool even when assayed at the same circadian phase (Fig. 5D). Thus, our model conceptualizes how a broad distribution of repressor stabilities can lead to similar circadian periods.

FBXL3 Prolongs the Falling Phase of CRY Protein Levels.

One prediction of our model is that the period lengthening caused by FBXL3 knockdown, i.e., the stabilization of late CRY1, would be due to an increase in the length of the falling phase (Fig. 5H). Indeed, we found evidence of altered CRY1 expression dynamic during the falling phase—but not during the rising phase—when comparing the average peak shapes in the presence or absence of FBXL3 (Fig. 6A).

Fig. 6.

The effects of FBXL3 on circadian period is CRY1 dependent. (A) Average peak shape of CRY1 expression after normalization (Materials and Methods). (B) Histogram of trough-to-peak durations in CRY1 time series. Lines represent kernel density estimation. P-value: Mann–Whitney U test, n as in A. (C and D) Detrended bioluminescence time series of wt, Cry1^−/−, and Cry2^−/− Bmal1:Luc reporter cells after dexamethasone synchronization either transduced with nonsilencing or FBXL3-targeting shRNA (C) and treated with dimethyl sulfoxide (DMSO) [solvent control, (C) and (D)] or 1 µM KL001 (D). Mean ± SD of 5 to 8 replicates representative of three (C) and two (D) experiments. (E) Periods from the recordings shown exemplarily in C and D, n = 2 (KL001+shNS1) and 3 (DMSO+shNS1, DMSO+shFBXL3) independent experiments, respectively.

Furthermore, while the distance between peak and trough at the single-cell level (SI Appendix, Fig. S8A) was of similar length for rising and falling phases in wild-type cells (mean: 11.7 h vs. 12.3 h, Fig. 6B), FBXL3 knockdown significantly prolonged the falling phase, resulting in an asymmetric peak shape (11.9 h vs. 13.2 h, Fig. 6B). This was similar for CRY2 (SI Appendix, Fig. S8 B and E), indicating that FBXL3 depletion indeed lengthens the period by prolonging the repressive phase, consistent with FBXL3 knockdown increasing CRY half-life mainly at times when CRY levels are decreasing (Fig. 3F). For PER1 and PER2, FBXL3 knockdown primarily prolonged the rising phase (SI Appendix, Fig. S8 C, D, F, and G). Since FBXL3 is not known to directly affect PER stability, this effect is likely caused indirectly by altered transcriptional dynamics within the TTFL.

FBXL3 Effect on Period Is Dependent on CRY1.

While depletion of FBXL3 increases the half-life of both CRY1 and CRY2, it had a greater effect on CRY1, as indicated by a greater increase in CRY1 protein half-life upon knockdown and greater loss of rhythmicity of CRY1 stability. We therefore asked whether the associated long period phenotype depends on both CRY proteins. To test this, we depleted FBXL3 in CRY1 or CRY2 knockout reporter cells (50) and found that the period of CRY2 knockout cells and wild-type cells was lengthened by several hours after FBXL3 knockdown, but to our surprise, the period of CRY1 knockout cells was not affected (Fig. 6 C and E and SI Appendix, Fig. S8H). Similar results were obtained when FBXL3 binding to CRY proteins was pharmacologically inhibited by KL001 (Fig. 6 D and E and SI Appendix, Fig. S8I) suggesting that FBXL3 destabilizes CRY1 and CRY2, but its effect on circadian period is modulated primarily by its action on CRY1.

Discussion

The circadian clock allows internal processes to adapt to a periodically changing environment, and disrupted circadian rhythms or misalignment of internal rhythms with the environment have been associated with various diseases (14, 15). To serve this purpose, circadian clocks need to be both robust (e.g., the period is temperature-compensated), and plastic (i.e., they respond to zeitgebers). Several mechanisms have been proposed that allow cells to maintain a normal period at different temperatures, even though response rates change with temperature (16, 17). In contrast, less is known about how changes in energy supply are compensated, which similarly affect global reaction rates (19–21).

In this study, we exploit the natural heterogeneity of single-cell clocks to identify fundamental principles for metabolic compensation of the circadian period without genetic manipulation. By generating fluorescent knock-in cells targeting all major circadian repressors and simultaneously monitoring thousands of individual cells for circadian dynamics and decay characteristics, we have uncovered three key insights: i) the length of the circadian period correlates with the stability of repressor proteins, but, contrasting the prevailing model, in a complex, phase-dependent manner; ii) the circadian period is compensated for fluctuations in the turnover rates of circadian repressor proteins; iii) the repressor protein stabilities are not constant, but circadian phase dependent, and for CRY proteins this is mediated by FBXL3.

At first, we were surprised that in the naturally variable cell population, there appeared to be no dependence of circadian period on repressor protein stability, in contrast to what has often been observed (22, 27, 29). However, when analyzed separately for different phases, a complex picture emerged. First, both period length and repressor stability covered a surprisingly wide range in individual cells. Second, repressor stability and circadian period were correlated in a phase-dependent manner. Our mathematical model suggests that this is because the turnover rates of CRY subspecies are not only different but also correlate in opposite ways with circadian period length. Depending on which species is dominant, the resulting pool half-life changes, providing an explanation for the inverse correlations: When—and only when—the stability of one species dominates the pool half-life, its true influence on period is revealed.

Thus, these opposite correlations are likely caused by the differential stabilities of the CRY subspecies and the phase-dependent differential composition of the CRY pool, providing one explanation for the compensation of the period against fluctuating degradation rates. Our model suggests two additional, not mutually exclusive, mechanisms: Adapted production may counteract changes in turnover, thereby stabilizing protein levels and net flux. For example, greater CRY stability leads to greater transcriptional repression and thus less CRY production. Indeed, despite increased stability, average CRY1 protein levels remain constant after FBXL3 ablation, whereas mRNA levels decrease (23, 24, 51). Finally, even changing the stability of a single CRY species can have both lengthening and shortening effects on the period, as seen for late CRY1. Thus, we propose that the circadian period is to some extent insensitive to changes in cellular protein turnover rates due to several counteracting effects.

However, mutations that affect only the turnover rate of late CRY and not the basal degradation may well affect the average period. Upon deletion of FBXL3, late CRY1 is likely to be degraded only at the basal rate (white diagonal line in Fig. 5I), resulting in a long period. The model predicts that even under this condition, the period is compensated for the different basal degradation rates, consistent with the lack of correlation between period and half-life observed for FBXL3 knockdown (SI Appendix, Fig. S5F). Therefore, we hypothesize that CRY mutations that prolong both CRY half-life and circadian period mainly reduce FBXL3-dependent but not basal CRY degradation.

Interestingly, we also observed that the protein half-lives of CRY1, CRY2, and PER1 are not constant but decrease during the repression phase, paralleling previous findings on the rhythmic stability of PER2 (48). Circadian rhythms in protein stability have long been postulated to contribute to rhythmic protein abundance. In addition to differences in translation efficiency (52–55), rhythmic degradation can explain rhythmic protein despite constant mRNA levels, as well as large delays between transcript and protein expression (39, 44, 46, 56, 57). Direct experimental evidence for rhythmic degradation of individual proteins is limited (17, 48, 58), but our findings suggest widespread degradation rhythms (45), consistent with circadian rhythms in autophagy and protein ubiquitination (43, 59). For CRY1—and to a lesser extent for CRY2—the oscillation in protein stability depends on FBXL3, but the molecular basis is unclear. FBXL3 expression rhythms peak at times of lowest CRY1 abundance (26) and thus cannot explain the high CRY1 stability we observed at this phase (Fig. 3C). Whether FBXL3 activity is regulated in a circadian manner is unknown. In addition, CRY might be targeted rhythmically for ubiquitination, e.g., by phosphorylation. Indeed, all circadian repressors show rhythmic phosphorylation patterns suggesting that the pool of cellular repressors is not homogeneous, but consists of differentially modified subspecies (60, 61). Thus, circadian changes in average degradation rates may result from changes in the composition of a pool of species with different stabilities. Target accessibility may also affect degradation rates: Both CRY1 and CRY2 can bind to PER2 with high affinity, and the CRY–PER2 interface overlaps with the FBXL3 binding site (8, 10, 62). Thus, binding of PERs protects CRYs from degradation (63). A lower stability of CRYs during the falling phase could therefore be due to the absence of PERs, since CRYs are expressed later than PERs and PER concentrations at the trough are very low (Fig. 1D).

In CRY1-deficient U-2 OS cells, we see no effect of FBXL3 knockdown or inhibition on the circadian period, in contrast to period lengthening in fibroblasts from Cry1 knockout mice (27, 64). This suggests that in mice the long period phenotype in the absence of FBXL3 is not entirely dependent on CRY1. Possibly, this discrepancy is due to differences between the mouse and human: While in mice, the E3 ligase FBXL21 plays an additional competing role (65, 66), the human FBXL21 locus is a pseudogene containing a premature stop codon (NR_152421.1) (67).

Limitations

The human osteosarcoma U-2 OS cell line is a widely used model for cells with an intact circadian clock (discussed in ref. 4); however, generalization of the results to primary cells should be made with caution. CHX has been demonstrated to inhibit the translation of all proteins, which may result in alterations to the proteome composition and degradation dynamics when compared to those observed under normal conditions. In this study, repressor half-life of each cell was assessed once. Thus, we cannot measure whether this half-life changes within a single cell over the circadian cycle but had to infer this from a population of cells from different circadian phases. In contrast, our mathematical model allows for the direct half-life calculation over the entire circadian cycle. However, it describes the PER and CRY proteins and the protein complexes containing them as a single species and relies on assumptions without rigorous experimental verification, such as the use of Hill functions to represent the two inhibition mechanisms of CRY1 or the application of Michaelis-Menten kinetics for its degradation.

Materials and Methods

Cells Lines.

U-2 OS (RRID:CVCL_0042, human, female, American Type Culture Collection HTB-96) cells were cultured in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% fetal bovine serum (FBS) (Life, lot 2453915), 25 mM 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES), and penicillin/streptomycin at 37 °C and 5% CO₂. CRISPR KI cell lines expressing CRY1-mScarlet, CRY1-mClover, and PER2-mScarlet have been described previously (4). Cells were tested for the absence of Mycoplasma using Lonza’s MycoAlert kit. For long-term imaging, cells were cultured in FluroBrite medium (Thermo Fisher) supplemented with 2% FBS, 1× GlutaMax, 25 mM HEPES, and penicillin/streptomycin from 9 d prior to imaging.

To allow automated detection of nuclei, all clones were transduced with a histone-2B-miRFP720 fusion protein, which results in nuclear expression of the infrared protein miRFP720, and cells were sorted for high expression by fluorescence-activated cell sorting (FACS).

Plasmids.

The generation of the original donor vectors (pDB) has been described in detail (4). The original donor vector was modified as follows: The His/Flag tag was replaced by a 3×FLAG tag, and glycine-serine-glycine linker sequences were introduced between protein and fluorophore and between fluorophore and 3×FLAG tag (designated pDB2). Sequences homologous to regions surrounding the stop codon of PER1 and CRY2 were synthesized by Twist bioscience and were inserted into pDB2 by restriction enzyme cloning. The pCAG-i53bp expression plasmid was a gift from Ralf Kuhn and was modified from Addgene (RRID:Addgene_74939). The SV40-NLS-CRE recombinase was a gift from Christoph Harms and was subcloned into the pLenti6 backbone. The pLenti-H2B-miRFP720 was obtained from Addgene (RRID:Addgene_128961).

Single-guide RNAs (SI Appendix, Table S3) were designed to cut just after the STOP codon using CRISPOR (68), and corresponding DNA oligos were ligated into pCRISPR-Lenti-v2 (RRID:Addgene_52961). To test the efficiency of the guides, cells were transduced with lentiviruses harboring the Cas9/single guide RNA (sgRNA) expression plasmid, gDNA from puromycin-resistant cells was isolated, and the corresponding region was amplified by PCR and sequenced. Efficiency was assessed using the TIDE (Tracking of Indels by DEcomposition) (69) assay.

pGIPZ clones expressing shRNA targeting FBXL3 (V2LHS_254986), CRY1 (V2LHS_172866), CRY2 (V2LHS_67009), PER1 (V2LHS_7714), or a nonsilencing control (NS1), (SI Appendix, Table S3) were purchased from Open Biosystems (GE Healthcare), and the green fluorescent protein was mutated to abolish fluorescence. The 0.9-kb Bmal1 promoter-driven luciferase reporter construct has been described (49). The sgRNA-Cas9 plasmids and donor vectors generated for this manuscript are available at Addgene (#189979-189989) along with their sequences.

Transfection.

For knock-in experiments, 10⁶ cells were harvested by trypsinization and transfected with 2 μg each of i53 bp, donor vector, and pCRSIPR-Lenti-V2 by electroporation using the NEON system (Thermo Fisher, buffer N, 4 pulses, 10 ms, 1,230 V). After electroporation, cells were seeded in antibiotic-free DMEM and cultured for 24 h before selection. Transient transfections of CRE recombinase to remove positive selection cassette were performed using 1 μL Lipofectamine 2000 and 200 ng CRE expression plasmid in a 48-well plate format. Subsequently, single-cell clones were isolated from a FACS-sorted CD4/CFP negative population (see Supporting Information for details) and screened as described.

Nucleic Acid Isolation and PCR.

Genomic DNA was extracted using Direct PCR Lysis Reagent Cell (VWR). RNA was extracted using the AMBION PureLink RNA Mini Kit (Thermo Fisher) according to the manufacturer’s instructions, including an on-column DNase digest. RNA was reverse transcribed using a primer that anneals to the 3×FLAG sequence in a two-step protocol. PCR amplification was performed with Phusion polymerase (New England Biolabs), and products were analyzed by agarose gel electrophoresis and detected using RedSafe/ultraviolet light. For quantitation of knockdown, RNA was extracted from pooled cells [CRY1-single knock-in (SKI) cells, CRY2-SKI cells, CRY1/CRY2 DKI cells, PER2 SKIs+PER2/CRY1 DKI cells, and PER1 SKI cells] after imaging and reversely transcribed using random hexamers. FBXL3 was quantified in knockdown and control cells in relation to GAPDH by real-time PCR, and knockdown efficiency was calculated using the ΔΔ^ct method. Primer sequences are listed in SI Appendix, Table S3.

Fluorescence Microscopy.

For microscopy, cells were seeded on glass bottom #1.5H-N 96-well plates (Cellvis, USA) coated with 50 µg/mL human serum fibronectin (Merck, Germany). Imaging was performed on a Nikon Widefield Ti2 equipped with a scientific complementary metal-oxide semiconductor sensor (sCMOS), PCO.edge camera, and a live cell incubator. Images were acquired in Flurobrite medium (Thermo Fisher) supplemented with 2% FBS, 1:100 PenStrep, and 1× GlutaMax at 37 °C and 5% CO2. The following light sources (LEDs) and emission filters were used for the different channels: yellow fluorescent protein (YFP) (mClover3): excitation 511/16 nm, 12.3 mW, 30% intensity, emission 540/30 nm; RFP (mScarlet-I): excitation 555/28 nm, 145 mW, 12% intensity, emission 642/80 nm; infrared fluorescent protein (iRFP): excitation 635/22 nm, 38.9 mW, 75% intensity, emission 697/60 nm. Objectives: 40× ApoFluor, NA 0.95, WD 250 μm. Illumination time for iRFP was 700 ms and 2 s for all other channels. Images were acquired in a regular imaging interval of 1 h.

Cell Tracking and Quality Control.

Cell tracking was performed automatically using CellProfiler. Multidimensional .nd2 files were decomposed into individual tiff files using Fiji. Per channel, 100 images from buffer-only wells were loaded into CellProfiler (pipeline 1, available on GitHub) and used to generate relative illumination patterns for each channel. Images from each time series were loaded into CellProfiler (pipeline 2, modified from Manella et al. (70), available on GitHub). Within this pipeline, images were corrected for nonuniform illumination by dividing pixel by pixel by the previously generated patterns. The iRFP channel was used for segmentation of nuclei in each image and subsequent tracking of nuclei throughout the time series. The background of the illumination-corrected RFP and YFP images was determined by the median fluorescence intensity of all unsegmented pixels (i.e., not identified as nuclei). Finally, the mean fluorescence intensity for each tracked nucleus for each time point was extracted from the RFP and YFP channels. After cell division, tracking continued with one daughter cell, while the other daughter cell was considered a newly emerging object. Only objects tracked for at least 24 subsequent images were retained at this stage (primary objects).

For quality control, we developed a Python script (available on GitHub) that detects abrupt changes in the nuclear size of >20% and cell division events, defined as a peak in average H2B-iRFP720 fluorescence due to chromatin condensation, followed by a decrease (>20%) in nuclear size. Subsequently, all size changes not related to cell divisions were flagged as potential tracking/segmentation errors. Time series were cropped to exclude errors and accepted if they contained ≥60 error-free consecutive images. Overall, 9 to 31% of primary objects passed these quality control criteria. We visually inspected a subset of accepted time series and estimated that ~90% were correctly tracked. Fluorescence intensities at cell division and subsequent time points were linearly extrapolated from neighboring time points because detachment of dividing cells produced fluorescence artifacts.

Circadian Parameter Extraction and Rhythmicity Threshold.

Circadian parameters were determined using metacycle2D (40) with Lomb-Scargle and Jonckheere-Terpstra-Kendall (JTK) cycle analysis, a period range of 18 to 32 h and Fisher-corrected P-values. Where appropriate, input data were truncated to begin 24 h after synchronization or to end at the time of CHX addition. Phase at CHX addition was calculated from phase and period using Eq. E1:

$$\begin{array}{c}phase\left(CHX addition\right)\hfill \\ =2\pi \ast \frac{\left(time point CHX addition-phase\right)mod period}{\mathit{period}}.\hfill \end{array}$$ [E1]

To calculate a high-confidence threshold for rhythmicity for each channel, time series of nonfluorescent cells recorded during the same experiment were analyzed in parallel, and the threshold was set to the 5th percentile of the p-value from these time series. For a time series to be considered rhythmic, its P-value had to exceed this threshold. See SI Appendix, Supplementary Note 1 for details.

Determination of Photobleaching.

Prior to each experiment, photobleaching was measured by imaging cells from different clones 20 times within 1 h using the same microscope settings, a time frame in which signal decay is expected to be dominated by photobleaching. Cells were tracked, and monoexponential decay curves were fitted to time points 3 to 16 of the individual cell time series using the Python package scipy.optimze.curve_fit and Eq. E2:

$$y(t)=y_0\ast e^{-t*\frac{1}{\tau }},$$ [E2]

where t is the time point, y(t) is the signal at time point t, and τ is the time constant, and filtered for fits with a correlation coefficient r²>0.7. The median time constant τ was then calculated for each fluorophore.

Calculation of Protein Half-Life.

Protein half-life was calculated from time points 2 to 8 h after CHX addition. For each channel, background was determined as the mean intensity of nonfluorescent nuclei. We excluded data from cells whose intensity at time point 2 h did not clearly exceed background (median + 2*SD). Median background was subtracted from all time series, and time series were corrected for additive photobleaching using Eq. E3:

$${\mathit{int}}_{fb\_corr}=(int-{\mathit{int}}_{\mathit{BG}})\ast e^{t*\frac{1}{\tau }},$$ [E3]

where int_{fb_corr} is the photobleaching-corrected intensity, ${\mathit{int}}_{\mathit{BG}}$ is the median background intensity, t is the time point, equals number of illuminations, and τ is the time constant.

Decay parameters were calculated by fitting monoexponential decay curves (no plateau) to the photobleach-corrected time series after CHX addition as described above and filtering for fits with a correlation coefficient r² of >0.7. Finally, the half-life was calculated using Eq. E4:

$$protein half-life=\tau \ast \text{ln} 2.$$ [E4]

Analysis of Phase Length and Average Peak Shapes.

Rhythmic fluorescence time series were smoothed by calculating the running average of three consecutive time points. Peak time was determined as the maximum intensity within 5 h of the first calculated peak phase time (Metacylce2D), and trough time was determined as the minimum within 20 h either before or after the peak time. The length of the rising and falling phases was determined as the time difference between peak and trough times.

For extraction of average peak shapes, signal intensities of rising and falling phases were further normalized independently between 0 and 1. The time axes of the time series were stretched to the median period of each genotype, and the average peak shape was calculated as mean ± SEM.

Mathematical Modeling.

We have developed an adapted mathematical model of the transcription–translation feedback loop (TTFL) based on a single CRY1 repressor, which is based on the classical model described by Goodwin more than 50 y ago (71). Our model was developed to capture the dual inhibition mechanism of CRY1: In the earlier phase of repression, CRY1 interacts with other PER and CRY proteins to form a high molecular weight complex that binds and inhibits the activator complex containing CLOCK and BMAL1 (8–11). In the later circadian repression phase, CRY1 independently represses E-box-induced transcription (12, 13, 72, 73).

We used linear terms to model production and import/export terms, Michaelis–Menten kinetics for degradation processes, and Hill functions with an “AND” funnel (74) for both modes of transcriptional repression. The model equations are given below as (Eqs. E5–E8):

$$\frac{\mathit{dx}}{\mathit{dt}}=V\frac{K_1^h}{K_1^h+z{1}^h}\frac{K_2^h}{K_2^h+z{2}^h}-d_x\frac{x}{K_x+x},$$ [E5]

$$\frac{\mathit{dy}}{\mathit{dt}}=b_{0}x-\left(t_1+t_2\right)y-d_y\frac{y}{K_y+y},$$ [E6]

$$\frac{dz1}{\mathit{dt}}=t_{1}y-q_{1}z1+q_{2}z2-d_{z1}\frac{z1}{K_{z1}+z1},$$ [E7]

$$\frac{dz2}{\mathit{dt}}=q_{1}z1+t_{2}y-q_{2}z2-d_{z2}\frac{z2}{K_{z2}+z2}.$$ [E8]

With the above assumptions (dual inhibition mechanism of CRY1, and linear, Michaelis–Menten and Hill kinetics to describe the biological processes), we systematically explored the parameter space to find sets of parameters that reproduce our experimental findings, namely i) the phase-dependent stability of total CRY1 protein (y + z1 + z2) (Fig. 3); ii) a later peak phase of z2 than that of z1 (Fig. 1L); iii) a positive correlation of the oscillator period with the overall stability of total CRY1 protein during the falling phase (Fig. 4B); and iv) a negative correlation of the circadian period with the overall stability of total CRY1 protein (y + z1 + z2) during the rising phase (Fig. 4D). Stability of total CRY1 (y + z1 + z2) was calculated by setting the translation rate (b0) to 0 (mimicking CHX addition) and fitting a monoexponential decay function to the decay curve of total CRY1 protein (y + z1 + z2). The pool half-life was calculated from the fitted parameters.

The default values of the wild-type parameters are listed in SI Appendix, Table S4. These values were chosen to demonstrate the plausibility of our conceptual model and should not be considered as exact representations of the true biochemical rate constants. To simulate cell-to-cell heterogeneity, we randomly varied the turnover rates of early and late CRY1 (SI Appendix, Fig. S6A). The turnover rates of y were drawn from a uniform distribution, allowing dy to vary between 20% and 300% of its default parameter value. In the case of z2, we limited the range of variation to 80 to 120% of its default parameter value, as large changes in dz2 resulted in the loss of oscillations. We also ensured that dz2 was at least as large as the basal degradation rate dy. Numerical simulations were performed in Python using the odeint function from the scipy library to solve the ordinary differential equations.

Blinding, Statistical Analysis, and Data Exclusion.

For two of the three experimental runs, virus (shRNA) was blinded to the experimenter. Before seeding, clonal identity was blinded to the experimenter, which also meant cells were randomized. Deblinding occurred during automated quality control of cell tracking, and no data were subsequently excluded manually, with the exception of one clone in experiment 2 that did not show the expected fluorescence. During data analysis, nonrhythmic time series were excluded from all analyses requiring determination of circadian periods, phases, or amplitudes. Protein half-lives derived from poor fits (r² < 0.70) or low initial intensities were ignored, and corresponding time series were excluded from all analyses requiring determination of protein half-life. Statistical analyses were performed in Python using the scipy library. Statistical tests used are indicated in the main text and/or figure legends. Unless otherwise stated, all statistical tests were two sided.

Further methods are provided in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (XLSX)

Movie S1.

Fluorescence image sequences of 25 nuclei per cell clone, acquired indicated hours after synchronization by dexamethasone.

Movie S2.

Fluorescence image sequences of 25 nuclei per cell clone either treated with solvent (top) or 20 µg/ml cycloheximide (CHX, bottom), acquired indicated hours before or after treatment.

Data, Materials, and Software Availability

Imaging raw and metadata are provided via the EMBL-EBI BioImage Archive (https://www.ebi.ac.uk/bioimage-archive) with accession number S-BIAD1038 (10.6019/S-BIAD1038) (75). The CellProfiler pipelines used for analysis are deposited on GitHub. All own Python scripts can be found on GitHub (https://github.com/Kramer-Lab/Gabriel-et-al-2024) (76). A data table of all successfully tracked cells including raw data and derived values is included in supplement (Dataset S1). All relevant plasmids are deposited at Addgene (#179441, 179453, and 189979 to 189989). All cell lines generated in this study are available from the corresponding author with a completed Material Transfer Agreement.