The circadian oscillator analysed at the single‐transcript level

Abstract

The circadian clock is an endogenous and self-sustained oscillator that anticipates daily environmental cycles. 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 hybridisation (smFISH) at multiple time points to measure pairs of core clock transcripts, Rev-erbα (Nr1d1), Cry1 and Bmal1, in mouse fibroblasts. The mean mRNA level oscillates over 24 h for all three genes, but mRNA numbers show considerable spread between cells. We develop a probabilistic model for multivariate mRNA counts using mixtures of negative binomials, which accounts for transcriptional bursting, circadian time and cell-to-cell heterogeneity, notably in cell size. Decomposing the mRNA variability into distinct noise sources shows that clock time contributes 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.

Approximating Solutions of the Chemical Master Equation using Neural Networks

“…Indeed, it is known that single-time marginal distributions predicted by the CME for many different reaction networks can be modeled as a mixture of negative binomials in the presence of timescale separation [25,[38][39][40][41]. Experimental measurements of mRNA and protein distributions in bacterial, yeast and mammalian cells show that these are often fit well by such mixtures, even when timescale separation is not applicable [42][43][44][45]. We remark that a mixture of negative binomials always has a Fano factor (variance over mean) greater than 1, and systems whose Fano factor is significantly less than 1 (see e.g.…”

Inference and Uncertainty Quantification of Stochastic Gene Expression via Synthetic Models

“…1c. When timescale separation is not applicable, such an approximation cannot be derived analytically, yet measurements of the distribution of mRNA and protein numbers in bacterial, yeast and mammalian cells show that these are still well fit by such mixtures in many cases [36][37][38][39].…”

“…In this paper we propose a new method for inference in a wide class of biochemical reaction networks, specifically those modelling gene expression, which is rooted in the specific characteristics exhibited by models of gene regulatory networks. Gene expression systems can often be thought of systems switching between discrete states of expression, broadly speaking corresponding to patterns of activation states of the genes' promoters [36][37][38][39]. It is therefore natural to abstract the dynamics of gene systems as an indirectly observed dynamical system over a discrete (finite) set of states.…”

Circadian Proteins Cry and Rev-erb Converge to Deepen Cellular Quiescence by Downregulating Cyclin D and Cdk4,6

“…S2) were converted to molecule numbers. We considered the cell reenters the cell cycle with the E2f-ON state, when the E2f molecule number at the Quiescent (2-day serum-starved) cells were circadian-synchronized with dexamethasone (Dex, 100 nM) treatment for 2 hours followed by 12 hours of stabilization time (as in [67]). Cells were subsequently, and every 3 hours afterward, stimulated with serum (1% and 1.5%, respectively) for 30 hours, followed by the measurement of EdU+%.…”