Formation of the three primary germ layers during gastrulation is an essential step in the establishment of the vertebrate body plan and is associated with major transcriptional changes [1][2][3][4][5] . Global epigenetic reprogramming accompanies these changes [6][7][8] , but the role of the epigenome in regulating early cell fate choice remains unresolved, and the coordination between different molecular layers is unclear. Here we describe the first single cell triple-omics map of chromatin accessibility, DNA methylation and RNA expression during the onset of gastrulation in mouse embryos. The initial exit from pluripotency coincides with the establishment of a global repressive epigenetic landscape, followed by the emergence of lineage-specific epigenetic patterns during gastrulation. Notably, cells committed to mesoderm and endoderm undergo widespread coordinated epigenetic rearrangements at enhancer marks, driven by TET-mediated demethylation, and a concomitant increase of accessibility. In striking contrast, the methylation and accessibility landscape of ectodermal cells is already established in the early epiblast. Hence, regulatory elements associated with each germ layer are either epigenetically primed or remodelled prior to cell fate decisions, providing the molecular logic for a hierarchical emergence of the primary germ layers.Recent technological advances have enabled the profiling of multiple molecular layers at single cell resolution 9-13 , providing novel opportunities to study the relationship between the transcriptome and epigenome during cell fate decisions. We applied scNMT-seq (singlecell Nucleosome, Methylome and Transcriptome sequencing 12 ) to profile 1,105 single cells isolated from mouse embryos at four developmental stages (Embryonic Day (E) 4.5, E5.5, E6.5 and E7.5) which comprise the exit from pluripotency and primary germ layer specification (Figure 1a-d, Extended Data Fig. 1). Cells were assigned to a specific lineage by mapping their RNA expression profiles to a comprehensive single-cell atlas 4 from the same stages, when available, or using marker genes (Extended Data Fig. 2). By performing Argelaguet et al.

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

Parallel single-cell sequencing protocols represent powerful methods for investigating regulatory relationships, including epigenome-transcriptome interactions. Here, we report a single-cell method for parallel chromatin accessibility, DNA methylation and transcriptome profiling. scNMT-seq (single-cell nucleosome, methylation and transcription sequencing) uses a GpC methyltransferase to label open chromatin followed by bisulfite and RNA sequencing. We validate scNMT-seq by applying it to differentiating mouse embryonic stem cells, finding links between all three molecular layers and revealing dynamic coupling between epigenomic layers during differentiation.

The vast majority of cancer next-generation sequencing data consist of bulk samples composed of mixtures of cancer and normal cells. To study tumor evolution, subclonal reconstruction approaches based on machine learning are used to separate subpopulation of cancer cells and reconstruct their ancestral relationships. However, current approaches are entirely data-driven and agnostic to evolutionary theory. We demonstrate that systematic errors occur in subclonal reconstruction if tumor evolution is not accounted for, and that those errors increase when multiple samples are taken from the same tumor. To address this issue, we present a novel approach for model-based subclonal reconstruction that combines data-driven machine learning with evolutionary theory. Using public, synthetic and newly generated data, we show the method is more robust and accurate than current techniques in both single-sample and multi-region sequencing data. With careful data curation and interpretation, we show how the method allows minimizing the confounding factors that affect non-evolutionary methods, leading to a more accurate recovery of the evolutionary history of human tumors..