Genomic profiling of PML bodies reveals transcriptional regulation by PML bodies through the DNMT3A exclusion

The promyelocytic leukaemia (PML) body is a phase-separated nuclear structure involved in various biological processes, including senescence, and tumour suppression1. PML bodies consist of various proteins, including PML proteins and several chromatin regulators2,3and physically associate with chromatin4,5, implying their crucial roles in particular genome functions. However, their roles in transcriptional regulation are largely unknown. Here, we developed APEX-mediated chromatin labelling and purification (ALaP), to identify the genomic regions associated with PML bodies. We find that PML bodies associate with active regulatory regions across the genome and prominently with a ∼300 kb of the short arm of the Y chromosome (YS300) in mouse embryonic stem cells (mESCs). The association with YS300 is essential for the transcriptional activities of neighbouring Y-linked cluster genes. Mechanistically, we show that PML bodies play a novel role in 3D nuclear organization by providing specific nuclear spaces that the de novo DNA methyltransferase DNMT3A cannot access, which results in the robust maintenance of the hypo-methylated states at the Y-linked gene promoters. Our study underscores a new mechanism for gene regulation in the 3D-nuclear space and provides insights into the functional properties of nuclear structures for genome functions.

Infinite degrees of freedom Weyl representation: Characterization and application

By means of infinite-dimensional nuclear spaces, we generalize important results on the representation of the Weyl commutation relations. For this purpose, we construct a new nuclear Lie group generalizing the groups introduced by Parthasarathy [An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992)] and Gelfand–Vilenkin [Generalized Functions (Academic Press, 1964)] (see Ref. 15). Then we give an explicit construction of Weyl representations generated from a non-Fock representation. Moreover, we characterize all these Weyl representations in quantum white noise setting.

NEW TOPOLOGICAL ℂ-ALGEBRAS WITH APPLICATIONS IN LINEAR SYSTEMS THEORY

Motivated by the Schwartz space of tempered distributions [Formula: see text] and the Kondratiev space of stochastic distributions [Formula: see text] we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces [Formula: see text], with decreasing norms ‖⋅‖p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form ‖f * g‖p ≤ A(p - q)‖f‖q‖g‖p for all p ≥ q + d, where * denotes the convolution in the monoid, A(p - q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological ℂ-algebras). Such an inequality holds in [Formula: see text], but not in [Formula: see text]. We give an example of such a ring which contains [Formula: see text]. We characterize invertible elements in these rings and present applications to linear system theory.