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Enabled by long-read sequencing technologies, particularly Single Molecule, Real-Time sequencing, N6-methyladenine (6mA) footprinting is a transformative methodology for revealing the heterogenous and dynamic distribution of nucleosomes and other DNA-binding proteins. Here, we present ipdTrimming, a novel 6mA-calling pipeline that outperforms existing tools in both computational efficiency and accuracy. Utilizing this optimized experimental and computational framework, we are able to map nucleosome positioning and transcription factor occupancy in nuclear DNA and establish high-resolution, long-range binding events in mitochondrial DNA. Our study highlights the potential of 6mA footprinting to capture coordinated nucleoprotein binding and to unravel epigenetic heterogeneity. 

Given a simple graph $$G$$, the irregularity strength of $$G$$, denoted $s(G)$, is the least positive integer $$k$$ such that there is a weight assignment on edges $$f: E(G) \to \{1,2,\dots, k\}$$ for which each vertex weight $$f^V(v):= \sum_{u: \{u,v\}\in E(G)} f(\{u,v\})$$ is unique amongst all $$v\in V(G)$$. In 1987, Faudree and Lehel conjectured that there is a constant $$c$$ such that $$s(G) \leq n/d + c$$ for all $$d$$-regular graphs $$G$$ on $$n$$ vertices with $d>1$, whereas it is trivial that $$s(G) \geq n/d$$. In this short note we prove that the Faudree-Lehel Conjecture holds when $$d \geq n^{0.8+\epsilon}$$ for any fixed $$\epsilon >0$$, with a small additive constant $c=28$ for $$n$$ large enough. Furthermore, we confirm the conjecture asymptotically by proving that for any fixed $$\beta\in(0,1/4)$$ there is a constant $$C$$ such that for all $$d$$-regular graphs $$G$$, $$s(G) \leq \frac{n}{d}(1+\frac{C}{d^{\beta}})+28$$, extending and improving a recent result of Przybyło that $$s(G) \leq \frac{n}{d}(1+ \frac{1}{\ln^{\epsilon/19}n})$$ whenever $$d\in [\ln^{1+\epsilon} n, n/\ln^{\epsilon}n]$$ and $$n$$ is large enough. 

Stable inheritance of DNA N⁶-methyladenine (6mA) is crucial for its biological functions in eukaryotes. Here, we identify two distinct methyltransferase (MTase) complexes, both sharing the catalytic subunit AMT1, but featuring AMT6 and AMT7 as their unique components, respectively. While the two complexes are jointly responsible for 6mA maintenance methylation, they exhibit distinct enzymology, DNA/chromatin affinity, genomic distribution, and knockout phenotypes. AMT7 complex, featuring high MTase activity and processivity, is connected to transcription-associated epigenetic marks, including H2A.Z and H3K4me3, and is required for the bulk of maintenance methylation. In contrast, AMT6 complex, with reduced activity and processivity, is recruited by PCNA to initiate maintenance methylation immediately after DNA replication. These two complexes coordinate in maintenance methylation. By integrating signals from both replication and transcription, this mechanism ensures the faithful and efficient transmission of 6mA as an epigenetic mark in eukaryotes. 

Abstract We suggest two related conjectures dealing with the existence of spanning irregular subgraphs of graphs. The first asserts that any $$d$$ -regular graph on $$n$$ vertices contains a spanning subgraph in which the number of vertices of each degree between $$0$$ and $$d$$ deviates from $$\frac{n}{d+1}$$ by at most $$2$$ . The second is that every graph on $$n$$ vertices with minimum degree $$\delta$$ contains a spanning subgraph in which the number of vertices of each degree does not exceed $$\frac{n}{\delta +1}+2$$ . Both conjectures remain open, but we prove several asymptotic relaxations for graphs with a large number of vertices $$n$$ . In particular we show that if $$d^3 \log n \leq o(n)$$ then every $$d$$ -regular graph with $$n$$ vertices contains a spanning subgraph in which the number of vertices of each degree between $$0$$ and $$d$$ is $$(1+o(1))\frac{n}{d+1}$$ . We also prove that any graph with $$n$$ vertices and minimum degree $$\delta$$ contains a spanning subgraph in which no degree is repeated more than $$(1+o(1))\frac{n}{\delta +1}+2$$ times.