Single-cell bioluminescence recordings show that higher stochastic noise results in faster damping at the population-level.

<p>Data on the bioluminescence of single-cell fibroblasts was taken from Leise <i>et al</i>., 2012 [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004451#pcbi.1004451.ref022" target="_blank">22</a>]. (<b>A</b>) Cells were sorted into two groups depending on their degree of stochastic noise. An example trace from each of the two groups is shown, demonstrating different levels of noise present in the dataset. (<b>B</b>) After artificially synchronizing each cell, we calculate averaged bioluminescence rhythms of each group (solid lines). A damped sinusoid fit to both groups reveals a difference in damping rate, demonstrated by fitted envelope functions (±<i>A</i>exp−<i>dt</i>, dashed lines). (<b>C</b>) The observed absolute difference in damping rate was shown to be significant (<i>p</i> = 0.0264) using 10,000 bootstrap trials.</p

Mathematical model accurately predicts dose-dependent changes in damping rate.

<p>(<b>A</b>) Example single-cell trajectories (top) and population-averaged trajectories (bottom, mean of 1,000 cells) of cells under various treatments. Cells with the nominal parameter set (left, black) closely match the experimental damping rate for unperturbed cells. Cells with simulated KL001 action (red, center) are noisier at the single-cell level, and show faster damping at the population-level. Cells with simulated longdaysin action show slightly more accurate single-cell rhythms, with a corresponding reduction in the population-level damping rate. (<b>B</b>) The model accurately predicts the general trend of period vs. damping rate for both KL001 and longdaysin perturbations. Experimental data points represent the mean of two replications at each concentration. Computational data points represent the mean of ten independent population simulations.</p

Effects of siRNA knockdowns on amplitude and damping rate.

<p>Clock robustness is a function of both amplitude and damping rate. Distributions in amplitude and damping rate for control wells (<b>A</b>) or perturbed wells (<b>B</b>) indicate that perturbations tend to shift the clock towards regions of higher damping rate or lower amplitude. Green dots in each figure indicates the mean of the control population. (<b>C</b>) Averaged effect of siRNA knockdown after grouping the perturbed population by Gene ID. Only those genes that were significantly different from the control distribution are shown (Hotelling’s <i>T</i>² test, <i>α</i> = 0.01). (<b>D</b>) Radial histogram of the significant gene perturbations shown in (C). The area of each slice is proportional to the frequency of perturbations away from the mean in that direction. Very few gene knockdowns result in both higher amplitude and lower damping rate (red slices, lower right quadrant).</p

Distributions in fitted parameters for the genome-wide siRNA screen.

<p>For each well in the high-throughput screen, the period, amplitude and damping rate are calculated. After normalization, distributions in robust z-scores closely resemble normal distributions. For all parameters, the region of highest density is consistent between the control and perturbed populations, indicating many perturbations do not appreciably change clock dynamics.</p

Fit quality vs. damping rate for the genome-wide siRNA screen.

<p>(<b>A</b>) A plot of the 111,743 individual fits shows that the majority of fits have a high <i>R</i>² value and positive damping rate. Only fits with <i>R</i>² > 0.8 were kept for further analysis. (<b>B</b>) Examples chosen randomly from each of the four quadrant regions in (A). Sinusoidal parameters for fits 1–2 can be more confidently inferred than those for fits 3–4.</p

Correlation among normalized parameters of the high-throughput siRNA screen.

<p>Pearson correlation coefficients are relatively low between fitted parameters, indicating that changes to damping rate (and thereby stochastic noise) are not explained by changes to period, amplitude, or phase.</p

Small molecule modulator KL001 increases damping rate in a dose-dependent fashion.

<p>Experimental data on the dose-dependent effects of small molecules KL001 and longdaysin on cultured circadian reporter cells was taken from Hirota <i>et al</i>., 2012 [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004451#pcbi.1004451.ref028" target="_blank">28</a>]. (<b>A</b>) Detrended bioluminescence signals from the two reporter systems and two small molecules are shown normalized by the fitted amplitude, period, and phase. The normalized bioluminescence highlights the dose-dependent change in damping rate seen with the KL001 application (top), but not with longdaysin (bottom). (<b>B</b>) Quantification of the dose-dependent change in damping rate caused by small molecule modulators. While both molecules lead to a dose-dependent increase in period, only KL001 shows a reliable change in damping rate.</p

Moments of the fitted parameter distributions (Fig 5) after normalization and outlier removal.

<p>Parameters were normalized by subtracting the median and dividing by the median absolute deviation on a plate-by-plate basis. Control distributions had less variance, were less skewed, and were more peaked then their perturbed counterparts.</p

Local relative sensitivity analysis for the estimated parameters.

<p>The bars show in blue the sensitivity due to the effect of the parameters on HSF13S and in red the corresponding to HHp. As expected, there are several parameters having very little influence on the measured states, therefore, the parameter values obtained from the global optimization have to be taken with caution. Most of the parameters that appear insensitive in this analysis are sensitive to other species, thus experimental data of these intermediate states would help to better estimate these values. The numbers on the abscissa corresponds to the kinetic constants given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042958#pone-0042958-t001" target="_blank">Table 1</a>.</p

Fitted and experimental time series of the phosphorylated HH complex.

<p>Simulated mono-phosphorylated (shown in continuous line) for value of 0.9557, and the experimental data (shown in red circles) is taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042958#pone.0042958-Kline1" target="_blank">[25]</a>. The percent conversion of the time series is calculated as , for all the dynamical variables, and Y is the simulated time series.</p