The circadian oscillator analysed at the single-transcript level

The circadian clock is an endogenous and self-sustained oscillator that anticipates daily environmental cycles and coordinates physiology accordingly. While rhythmic gene expression of circadian genes is well-described in populations of cells, the single-cell mRNA dynamics of multiple core-clock genes remain largely unknown. Here we use single molecule fluorescence in-situ hybridization (smFISH) at multiple time points to measure pairs of core-clock transcripts, Rev-erbα (Nr1d1), Cry1 and Bmal1, in mouse fibroblasts at single-molecule resolution. The mean mRNA level oscillates over 24 hours for all three genes, but mRNA numbers show considerable spread between cells. While transcript number scales with cell size for all genes, gene-to-gene correlations of mRNA number depends on the gene pair. To account for these features of the data, we develop a probabilistic model for multivariate smFISH mRNA counts that quantifies changes in transcriptional bursting across genes and over circadian time. We identify a mixture model of negative binomials as the preferred model of the mRNA count distributions, which accounts for cell-to-cell heterogeneity, notably in cell size. The paired count data and modelling allows the decomposition of mRNA variability into distinct noise sources, showing that circadian clock time contributes only a small fraction of the total variability in mRNA number between cells. Thus, our results highlight the intrinsic biological challenges in estimating circadian phase from single-cell mRNA counts and suggest that circadian phase in single cells is encoded post-transcriptionally.


37
In animals, the circadian clock is a 24-hour period oscillator that dynamically regulates central   [5][6][7] 42 have revealed that circadian oscillations are cell-autonomous and self-sustained, with a period 43 that fluctuates from cycle to cycle by typically 10%. Molecularly, it is thought that the 44 oscillations involve interactions between core circadian clock proteins including BMAL1, CRY1 45 and REV-ERBα (encoded by Arntl, Cry1, and Nr1d1 genes, respectively), establishing 46 negative feedback loops [8]. Live-cell studies of circadian oscillators in individual cells have thus far remained limited to one gene product at a time, and hence the properties of circadian 48 oscillators in single cells across multiple genes remain largely uncharacterized [4,5]. explore the joint relationship between transcript numbers of different clock genes. Our dual-142 channel imaging allows either Bmal1/Cry1 or Nr1d1/Cry1 to be measured in the same cells 143 (Fig. 2B). The bivariate relationships between the gene pairs show that Bmal1/Cry1 are 144 positively correlated at each time point (R from 0.12 to 0.53), whereas Nr1d1/Cry1 show 145 negative correlations (R from 0.0 to -0.19) (Fig. 2C). Since all genes are positively correlated 146 with area ( Fig. 2A), the negative correlation between Cry1 and Nr1d1 could be caused by a 147 spread in the phases between cells [36], or regulatory interactions (e.g. NR1D1 protein 148 represses Cry1 transcription), which can cause different steady-state correlations depending 149 on whether feedback is negative or positive [11]. Below, we formulate these hypotheses as    Fig. 3A).
Since we measured cellular area instead of volume, we set the dependence between burst 188 size and cell area using an additional, gene-specific exponent ", which is also supported by 189 the linear relationship between log area and the log mean mRNA observed in Fig. 2A.

191
To compare models M1 and M2, we first inferred parameters using the data for both   Having selected a preferred model to describe the data, we next analysed the model to

258
For all three genes we found that the variance was dominated by intrinsic noise (Fig 4A)

274
Somewhat surprisingly, the contribution of the 24-h cycle to mRNA variance was low across

312
While we have developed an analysis approach for the circadian clock i.e. a temporal system 313 with a periodic structure, we anticipate that the modelling of smFISH developed in this paper,

314
in particular the ability to include and distinguish intrinsic and extrinsic noise sources, will be

328
The considered models for the circadian smFISH data (Table 1)  contributed only a small fraction to the total variability in mRNA counts, which is also reflected 349 in the relatively low oscillatory amplitudes we found (Fig. 1B). Though cells that were subjected 350 to temperature entrainment did not yield significantly larger amplitudes (Supp figure 1), one outcome was that partial synchrony was not a likely explanation of the low amplitudes, though 353 it could be that we have not found the true minimum of M3 due to too many local minima.

465
For all models, the probability of observing an smFISH count < for gene g and for cell i follows

500
We assume that the noise term & !,# is multivariate log-normally distributed between two genes 501 and is parameterised as follows: where ' # $ and ( # $ represent the mean and standard deviation for gene 1 and ) represents 504 the correlation in burst size between genes (in log space). We used an LKJ prior with shape 505 parameter 4 to regularise ). The correlation coefficient ) is inferred between Bmal1-Cry1 and 506 Nr1d1-Cry1, but it is not directly inferred between Nr1d1 and Bmal1. As such, for the 3-507 dimensional simulations we assume the & !,# parameters are conditionally independent 508 between these two genes (i.e. the entry in the precision matrix for Nr1d1-Bmal1 is zero).

532
where ! is the dispersion parameter of the negative binomial. Under our model, the

573
The conditional mean given the area E[m|A] is then the mean mRNA count of each bin. The

574
area is normalised such that the average area is equal to one.