Homologous recombination maintains genomic integrity by repairing broken chromosomes. The broken chromosome is partially resected to produce single-stranded DNA (ssDNA) that is used to search for ...homologous double-stranded DNA (dsDNA). This homology driven ‘search and rescue’ is catalyzed by a class of DNA strand exchange proteins that are defined in relation to Escherichia coli RecA, which forms a filament on ssDNA. Here, we review the regulation of RecA filament assembly and the mechanism by which RecA quickly and efficiently searches for and identifies a unique homologous sequence among a vast excess of heterologous DNA. Given that RecA is the prototypic DNA strand exchange protein, its behavior affords insight into the actions of eukaryotic RAD51 orthologs and their regulators, BRCA2 and other tumor suppressors.
Single molecule methods have yielded new insight into how RecA filaments form and find homologous DNA.
RecA nucleation and growth on SSB-coated ssDNA is kinetically regulated by the RecFOR and RecOR complexes, which both microscopically and macroscopically alter the SSB–ssDNA nucleoprotein fiber.
RecA finds homology through many random, weak, and transient interactions made in parallel and ignores very short regions of microhomology resulting in a reduction of both dimensionality and complexity.
Let
F
be an algebraically closed field of positive characteristic and let
R
be a finitely generated
F
-algebra with a filtration with the property that the associated graded ring of
R
is a finitely ...generated integral domain of Krull dimension two. We show that under these conditions
R
satisfies a polynomial identity, answering a question of Etingof in the affirmative in a special case.
The repair of DNA by homologous recombination is an essential, efficient, and high-fidelity process that mends DNA lesions formed during cellular metabolism; these lesions include double-stranded DNA ...breaks, daughter-strand gaps, and DNA cross-links. Genetic defects in the homologous recombination pathway undermine genomic integrity and cause the accumulation of gross chromosomal abnormalities-including rearrangements, deletions, and aneuploidy-that contribute to cancer formation. Recombination proceeds through the formation of joint DNA molecules-homologously paired but metastable DNA intermediates that are processed by several alternative subpathways-making recombination a versatile and robust mechanism to repair damaged chromosomes. Modern biophysical methods make it possible to visualize, probe, and manipulate the individual molecules participating in the intermediate steps of recombination, revealing new details about the mechanics of genetic recombination. We review and discuss the individual stages of homologous recombination, focusing on common pathways in bacteria, yeast, and humans, and place particular emphasis on the molecular mechanisms illuminated by single-molecule methods.
Understanding complex tissues requires single-cell deconstruction of gene regulation with precision and scale. Here, we assess the performance of a massively parallel droplet-based method for mapping ...transposase-accessible chromatin in single cells using sequencing (scATAC-seq). We apply scATAC-seq to obtain chromatin profiles of more than 200,000 single cells in human blood and basal cell carcinoma. In blood, application of scATAC-seq enables marker-free identification of cell type-specific cis- and trans-regulatory elements, mapping of disease-associated enhancer activity and reconstruction of trajectories of cellular differentiation. In basal cell carcinoma, application of scATAC-seq reveals regulatory networks in malignant, stromal and immune cells in the tumor microenvironment. Analysis of scATAC-seq profiles from serial tumor biopsies before and after programmed cell death protein 1 blockade identifies chromatin regulators of therapy-responsive T cell subsets and reveals a shared regulatory program that governs intratumoral CD8
T cell exhaustion and CD4
T follicular helper cell development. We anticipate that scATAC-seq will enable the unbiased discovery of gene regulatory factors across diverse biological systems.
Abstract
We give a combinatorial characterization of amenability of monomial algebras and prove the existence of monomial Følner sequences, answering a question due to Ceccherini–Silberstein and ...Samet–Vaillant. We then use our characterization to prove that over projectively simple monomial algebras, every module is exhaustively amenable; we conclude that convolution algebras of minimal subshifts admit the same property. We deduce that any minimal subshift of positive entropy gives rise to a graded algebra, which does not satisfy an extension of Vershik’s conjecture on amenable groups, proposed by Bartholdi. Finally, we show that non-amenable monomial algebras must contain noncommutative free subalgebras. Examples are given to emphasize the sharpness and necessity of the assumptions in our results.
On Dynamical Cancellation Bell, Jason P; Matsuzawa, Yohsuke; Satriano, Matthew
International mathematics research notices,
04/2023, Letnik:
2023, Številka:
8
Journal Article
Recenzirano
Abstract
Let $X$ be a projective variety and let $f$ be a dominant endomorphism of $X$, both of which are defined over a number field $K$. We consider a question of the 2nd author, Meng, Shibata, and ...Zhang, who asks whether the tower of $K$-points $Y(K)\subseteq (f^{-1}(Y))(K)\subseteq (f^{-2}(Y))(K)\subseteq \cdots $ eventually stabilizes, where $Y\subset X$ is a subvariety invariant under $f$. We show this question has an affirmative answer when the map $f$ is étale. We also look at a related problem of showing that there is some integer $s_0$, depending only on $X$ and $K$, such that whenever $x, y \in X(K)$ have the property that $f^{s}(x) = f^{s}(y)$ for some $s \geqslant 0$, we necessarily have $f^{s_{0}}(x) = f^{s_{0}}(y)$. We prove this holds for étale morphisms of projective varieties, as well as self-morphisms of smooth projective curves. We also prove a more general cancellation theorem for polynomial maps on ${\mathbb {P}}^1$ where we allow for composition by multiple different maps $f_1,\dots ,f_r$.
Escherichia coli RecA is the defining member of a ubiquitous class of DNA strand-exchange proteins that are essential for homologous recombination, a pathway that maintains genomic integrity by ...repairing broken DNA. To function, filaments of RecA must nucleate and grow on single-stranded DNA (ssDNA) in direct competition with ssDNA-binding protein (SSB), which rapidly binds and continuously sequesters ssDNA, kinetically blocking RecA assembly. This dynamic self-assembly on a DNA lattice, in competition with another protein, is unique for the RecA family compared to other filament-forming proteins such as actin and tubulin. The complexity of this process has hindered our understanding of RecA filament assembly because ensemble measurements cannot reliably distinguish between the nucleation and growth phases, despite extensive and diverse attempts. Previous single-molecule assays have measured the nucleation and growth of RecA--and its eukaryotic homologue RAD51--on naked double-stranded DNA and ssDNA; however, the template for RecA self-assembly in vivo is SSB-coated ssDNA. Using single-molecule microscopy, here we directly visualize RecA filament assembly on single molecules of SSB-coated ssDNA, simultaneously measuring nucleation and growth. We establish that a dimer of RecA is required for nucleation, followed by growth of the filament through monomer addition, consistent with the finding that nucleation, but not growth, is modulated by nucleotide and magnesium ion cofactors. Filament growth is bidirectional, albeit faster in the 5'→3' direction. Both nucleation and growth are repressed at physiological conditions, highlighting the essential role of recombination mediators in potentiating assembly in vivo. We define a two-step kinetic mechanism in which RecA nucleates on transiently exposed ssDNA during SSB sliding and/or partial dissociation (DNA unwrapping) and then the RecA filament grows. We further demonstrate that the recombination mediator protein pair, RecOR (RecO and RecR), accelerates both RecA nucleation and filament growth, and that the introduction of RecF further stimulates RecA nucleation.
A famous result of Christol gives that a power series
F
(
t
)
=
∑
n
≥
0
f
(
n
)
t
n
with coefficients in a finite field
F
q
of characteristic
p
is algebraic over the field of rational functions in
t
...if and only if there is a finite-state automaton accepting the base-
p
digits of
n
as input and giving
f
(
n
) as output for every
n
≥
0
. An extension of Christol’s theorem, giving a complete description of the algebraic closure of
F
q
(
t
)
, was later given by Kedlaya. When one looks at the support of an algebraic power series, that is the set of
n
for which
f
(
n
)
≠
0
, a well-known dichotomy for sets generated by finite-state automata shows that the support set is either sparse—with the number of
n
≤
x
for which
f
(
n
)
≠
0
bounded by a polynomial in
log
(
x
)
—or it is reasonably large in the sense that the number of
n
≤
x
with
f
(
n
)
≠
0
grows faster than
x
α
for some positive
α
. The collection of algebraic power series with sparse supports forms a ring and we give a purely algebraic characterization of this ring in terms of Artin–Schreier extensions and we extend this to the context of Kedlaya’s work on generalized power series.
RNA is a critical component of chromatin in eukaryotes, both as a product of transcription, and as an essential constituent of ribonucleoprotein complexes that regulate both local and global ...chromatin states. Here, we present a proximity ligation and sequencing method called
romatin-
ssociated
NA
uencing (ChAR-seq) that maps all RNA-to-DNA contacts across the genome. Using
cells, we show that ChAR-seq provides unbiased, de novo identification of targets of chromatin-bound RNAs including nascent transcripts, chromosome-specific dosage compensation ncRNAs, and genome-wide trans-associated RNAs involved in co-transcriptional RNA processing.
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