The mammalian liver is a central hub for systemic metabolic homeostasis. Liver tissue is spatially structured, with hepatocytes operating in repeating lobules, and sub-lobule zones performing distinct functions. The liver is also subject to extensive temporal regulation, orchestrated by the interplay of the circadian clock, systemic signals and feeding rhythms. However, liver zonation was previously analyzed as a static phenomenon, and liver chronobiology at tissue level resolution. Here, we use single-cell RNA-seq to investigate the interplay between gene regulation in space and time. Using mixed-effect models of mRNA expression and smFISH validations, we find that many genes in the liver are both zonated and rhythmic, most of them showing multiplicative space-time effects. Such dually regulated genes cover key hepatic functions such as lipid, carbohydrate and amino acid metabolism, but also previously unassociated genes, such as protein chaperones. Our data also suggest that rhythmic and localized expression of Wnt targets could be explained by rhythmically expressed Wnt ligands from non-parenchymal cells near the central vein. Core circadian clock genes are expressed in a non-zonated manner, indicating that the liver clock is robust to zonation. Together, our scRNA-seq analysis reveals how liver function is compartmentalized spatio-temporally at the sub-lobular scale.

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The circadian clock and the cell cycle are two biological oscillatory processes that coexist within individual cells. These two oscillators were found to interact, which can lead to their synchronization. Here, we develop a method to identify a low-dimensional stochastic model of the coupled system directly from time-lapse imaging in single cells. In particular, we infer the coupling and non-linear dynamics of the two oscillators from thousands of mouse and human single-cell fluorescence microscopy traces. This coupling predicts multiple phase-locked states showing different degrees of robustness against molecular fluctuations inherent to cellular-scale biological oscillators. For the 1:1 state, the predicted phase-shifts upon period perturbations were validated experimentally. Moreover, the phase-locked states are temperature-independent and evolutionarily conserved from mouse to human, hinting at a common underlying dynamical mechanism. Finally, we detect a signature of the coupled dynamics in a physiological context, explaining why tissues with different proliferation states exhibited shifted circadian clock phases.