Persistent Cell-Autonomous Circadian Oscillations in Fibroblasts Revealed by Six-Week Single-Cell Imaging of PER2::LUC Bioluminescence

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude

Persistent cell-autonomous circadian oscillations in fibroblasts revealed by six-week single-cell imaging of PER2::LUC bioluminescence.

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude

Correlations among fibroblast parameters, as defined in Table 1.

<p>Pearson correlation coefficients were calculated; Spearman correlation coefficients gave very similar results.</p

Comparison of cell parameters.

<p>Parameters are defined in the caption to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033334#pone-0033334-t001" target="_blank">Table 1</a>, with correlation coefficients given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033334#pone-0033334-t002" target="_blank">Table 2</a>. Greater amplitude tends to be associated with reduced variability, and variability in period tends to be much less than that in amplitude.</p

Analysis of cell periods.

<p>(A) Histogram of cell periods (mean peak-to-peak times). (B) Raster plot showing two cells with clearly different periods. In the raster plot, time of day is plotted left to right and successive days down the page, such that vertically adjacent points are 24 h apart. Each row is extended to 48 h, duplicating data in the next row, so that patterns crossing midnight can be appreciated. Thick bars designate times when the luminescence for a cell was above the mean for each row. Cell #66 with period 25.5 h is plotted in red; cell #68 with period 22.5 h is plotted in blue. Due to different circadian periods, the two cells' phase relationship changes over time. (C) Standard deviation in period over the population of cells as a function of the number of cycles used for period determination. Here period for each cell is calculated as the mean of peak-to-peak times over the indicated number of cycles. This curve is expected to decrease to the true value in proportion to one over the square root of the number of cycles used. The dashed line shows the ANOVA prediction of the true value of the standard deviation in period among the fibroblasts. Note that if all cells had the same intrinsic period, and variability of observed period was only due to stochastic fluctuations, then we would expect this graph to approach zero, rather than having a positive horizontal asymptote.</p

Assessment of cell rhythmicity.

<p>(A) Percent of cells with rhythmic 3-day windows is greater for later start times. (B) Percent of rhythmic windows increases with length of window, combining over all cells with start times spaced every 12 h. (C) Strength of rhythmicity (new metric described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033334#s2" target="_blank">Results</a>) of 3-day windows increases over time. (D) CVs of period and amplitude decrease over time, measured using 6 consecutive peak-to-peak times and peak-to-trough amplitudes starting at the indicated day.</p

Examples of fibroblast PER2::LUC recordings.

<p>The time series for each example is shown above the corresponding analytic wavelet transform (AWT) to illustrate the variability over time in period and amplitude. Period as a function of time is indicated by the black ridge curve, while amplitude is indicated by the color scale (in photons/min). A line at period 25 h is included for reference. (A) Typical cell #11, cell area 1.12×10⁴ µm², period 24.3 h with CV 0.067, amplitude 2.94 photons/min with CV 0.35. Note that red in the AWT corresponds to cycles with high amplitude, yellow those with moderate amplitude, and blue those with low amplitude. Period variability is indicated by the black ridge curve moving up and down over time. (B) Large cell #25, cell area 1.74×10⁴ µm², period 25.3 h with CV 0.030, amplitude 12.2 photons/min with CV 0.23, exhibiting steady rhythms, with both amplitude and period varying less than in (A). (C) Cell #36 with strong oscillations except for a pause on days 13–14 (reflected by the blue region of the AWT), cell area 8.36×10³ µm², period 24.8 h with CV 0.055, amplitude 2.93 photons/min with CV 0.27.</p

Stochastic modeling.

<p>(A) Results from fitting the fibroblast data to the stochastic model, as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0033334#s4" target="_blank">Methods</a>. Fit values with the parameter <i>s</i><1 indicate that the oscillations are noise-induced (the deterministic system would be steady state), while fit values with <i>s</i>≥1 indicate that the oscillations are self-sustained. (B) Results of simulations of the stochastic model for different values of the parameter s, fixing the amplitude of <i>z</i> to be 500 molecules (by adjusting the value of Ω with respect to <i>s</i>). The mean value of the period CV over 500 simulations is shown for each value of <i>s</i>. The period CV is minimized for <i>s</i> in the range 1.1–1.2. (C) Example of a stochastic simulation with <i>s</i> = 1.03, where Ω is chosen so that the amplitude of <i>z</i> is 500 molecules. The period CV for this simulation is 0.073.</p

Period and amplitude are remarkably stable over time.

<p>Error bars indicate mean±SD across the 80 cells on each day. The mean period changes very gradually, with a slight upward slope of 0.02 hours/day (F = 15,p<0.001), an average change of 0.1% per day. The mean amplitude decreases with a slope of −0.04 photons/min/day (F = 60,p<0.001), an average change of about 1% per day.</p