11 research outputs found
Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
We completely classify the locally finite, infinite graphs with pure mapping
class groups admitting a coarsely bounded generating set. We also study
algebraic properties of the pure mapping class group: We establish a semidirect
product decomposition, compute first integral cohomology, and classify when
they satisfy residual finiteness and the Tits alternative. These results
provide a framework and some initial steps towards quasi-isometric and
algebraic rigidity of these groups.Comment: 36 pages, 10 figure
The Automorphism Group of the Infinite-Rank Free Group is Coarsely Bounded
We prove that the full automorphism group and the outer automorphism group of
the free group of countably infinite rank are coarsely bounded. That is, these
groups admit no continuous actions on a metric space with unbounded orbits, and
have the quasi-isometry type of a point.Comment: 4 pages. v2: Incorporated referee's comment. To appear in New York
Journal of Mathematic
Finding and Combining Indicable Subgroups of Big Mapping Class Groups
We explicitly construct new subgroups of the mapping class groups of an
uncountable collection of infinite-type surfaces, including, but not limited
to, right-angled Artin groups, free groups, Baumslag-Solitar groups, mapping
class groups of other surfaces, and a large collection of wreath products. For
each such subgroup and surface , we show that there are countably many
non-conjugate embeddings of into ; in certain cases, there
are uncountably many such embeddings. The images of each of these embeddings
cannot lie in the isometry group of for any hyperbolic metric and are not
contained in the closure of the compactly supported subgroup of
. In this sense, our construction is new and does not rely on
previously known techniques for constructing subgroups of mapping class groups.
Notably, our embeddings of into are not
induced by embeddings of into . Our main tool for all of these
constructions is the utilization of special homeomorphisms of called shift
maps, and more generally, multipush maps.Comment: 31 pages, 19 figures. Results have been improved to show countably
many non-conjugate embeddings of each subgroup we construc
Genotype-phenotype correlation at codon 1740 ofSETD2
The SET domain containing 2, histone lysine methyltransferase encoded by SETD2 is a dual-function methyltransferase for histones and microtubules and plays an important role for transcriptional regulation, genomic stability, and cytoskeletal functions. Specifically, SETD2 is associated with trimethylation of histone H3 at lysine 36 (H3K36me3) and methylation of α-tubulin at lysine 40. Heterozygous loss of function and missense variants have previously been described with Luscan-Lumish syndrome (LLS), which is characterized by overgrowth, neurodevelopmental features, and absence of overt congenital anomalies. We have identified 15 individuals with de novo variants in codon 1740 of SETD2 whose features differ from those with LLS. Group 1 consists of 12 individuals with heterozygous variant c.5218C>T p.(Arg1740Trp) and Group 2 consists of 3 individuals with heterozygous variant c.5219G>A p.(Arg1740Gln). The phenotype of Group 1 includes microcephaly, profound intellectual disability, congenital anomalies affecting several organ systems, and similar facial features. Individuals in Group 2 had moderate to severe intellectual disability, low normal head circumference, and absence of additional major congenital anomalies. While LLS is likely due to loss of function of SETD2, the clinical features seen in individuals with variants affecting codon 1740 are more severe suggesting an alternative mechanism, such as gain of function, effects on epigenetic regulation, or posttranslational modification of the cytoskeleton. Our report is a prime example of different mutations in the same gene causing diverging phenotypes and the features observed in Group 1 suggest a new clinically recognizable syndrome uniquely associated with the heterozygous variant c.5218C>T p.(Arg1740Trp) in SETD2
Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
We discuss the large-scale geometry of pure mapping class groups of locally
finite, infinite graphs, motivated by recent work of Algom-Kfir--Bestvina and
the work of Mann--Rafi on the large-scale geometry of mapping class groups of
infinite-type surfaces. Using the framework of Rosendal for coarse geometry of
non-locally compact groups, we classify when the pure mapping class group of a
locally finite, infinite graph is globally coarsely bounded (an analog of
compact) and when it is locally coarsely bounded (an analog of locally
compact). Our techniques also give lower bounds on the first integral
cohomology of the pure mapping class group for some graphs and allow us to
compute the asymptotic dimension of all of the locally coarsely bounded pure
mapping class groups of infinite rank graphs. This dimension is always either
zero or infinite.Comment: 50 pages, 14 figures. Added a new section 9 computing asymptotic
dimension for locally CB pure mapping class groups. Also made several edits
throughout the document and included new figure
From the Dance Floor to the Rifle Range: The Evolution of Manliness in the National Guards, 1870-1917
Dihydrodipicolinate synthase from Thermotoga maritima
DHDPS (dihydrodipicolinate synthase) catalyses the branch point in lysine biosynthesis in bacteria and plants and is feedback inhibited by lysine. DHDPS from the thermophilic bacterium Thermotoga maritima shows a high level of heat and chemical stability. When incubated at 90 °C or in 8 M urea, the enzyme showed little or no loss of activity, unlike the Escherichia coli enzyme. The active site is very similar to that of the E. coli enzyme, and at mesophilic temperatures the two enzymes have similar kinetic constants. Like other forms of the enzyme, T. maritima DHDPS is a tetramer in solution, with a sedimentation coefficient of 7.2 S and molar mass of 133 kDa. However, the residues involved in the interface between different subunits in the tetramer differ from those of E. coli and include two cysteine residues poised to form a disulfide bond. Thus the increased heat and chemical stability of the T. maritima DHDPS enzyme is, at least in part, explained by an increased number of inter-subunit contacts. Unlike the plant or E. coli enzyme, the thermophilic DHDPS enzyme is not inhibited by (S)-lysine, suggesting that feedback control of the lysine biosynthetic pathway evolved later in the bacterial lineage
Genotype–phenotype correlation at codon 1740 of SETD2
The SET domain containing 2, histone lysine methyltransferase encoded by SETD2 is a dual-function methyltransferase for histones and microtubules and plays an important role for transcriptional regulation, genomic stability, and cytoskeletal functions. Specifically, SETD2 is associated with trimethylation of histone H3 at lysine 36 (H3K36me3) and methylation of α-tubulin at lysine 40. Heterozygous loss of function and missense variants have previously been described with Luscan-Lumish syndrome (LLS), which is characterized by overgrowth, neurodevelopmental features, and absence of overt congenital anomalies. We have identified 15 individuals with de novo variants in codon 1740 of SETD2 whose features differ from those with LLS. Group 1 consists of 12 individuals with heterozygous variant c.5218C>T p.(Arg1740Trp) and Group 2 consists of 3 individuals with heterozygous variant c.5219G>A p.(Arg1740Gln). The phenotype of Group 1 includes microcephaly, profound intellectual disability, congenital anomalies affecting several organ systems, and similar facial features. Individuals in Group 2 had moderate to severe intellectual disability, low normal head circumference, and absence of additional major congenital anomalies. While LLS is likely due to loss of function of SETD2, the clinical features seen in individuals with variants affecting codon 1740 are more severe suggesting an alternative mechanism, such as gain of function, effects on epigenetic regulation, or posttranslational modification of the cytoskeleton. Our report is a prime example of different mutations in the same gene causing diverging phenotypes and the features observed in Group 1 suggest a new clinically recognizable syndrome uniquely associated with the heterozygous variant c.5218C>T p.(Arg1740Trp) in SETD2