On Certain McKay Numbers of Symmetric Groups

For primes $\ell$ and nonnegative integers $a$, we study the partition functions $$p_\ell(a;n):= \#\{\lambda \vdash n : \text{ord}_\ell(H(\lambda))=a\},$$ where $H(\lambda)$ denotes the product of hook lengths of a partition $\lambda$. These partition values arise as the McKay numbers $m_\ell(\text{ord}_\ell(n!) - a; S_n)$ in the representation theory of the symmetric group. We determine the generating functions for $p_\ell(a;n)$ in terms of $p_\ell(0;n)$ and specializations of specific D'Arcais polynomials. For $\ell = 2$ and $3$, we give an exact formula for the $p_\ell(a;n)$ and prove that these values are zero for almost all $n$. For larger primes $\ell$, the $p_\ell(a;n)$ are positive for sufficiently large $n$. Despite this positivity, we prove that $p_\ell(a;n)$ is almost always divisible by $m$ for any integer $m$. Furthermore, with these results we prove several Ramanujan-type congruences. These include the congruences $$p_\ell(a;\ell^k n - \delta(a,\ell)) \equiv 0 \pmod{\ell^{k+1}},$$ for $0<a< \ell$, where $\ell = 5, 7, 11$ and $\delta(a,\ell) := (\ell^2 - 1)/24 + a\ell$, which answer a question of Ono.Comment: 15 page

American Mastodon Mitochondrial Genomes Suggest Multiple Dispersal Events in Response to Pleistocene Climate Oscillations

Pleistocene glacial-interglacial cycles are correlated with dramatic temperature oscillations. Examining how species responded to these natural fluctuations can provide valuable insights into the impacts of present-day anthropogenic climate change. Here we present a phylogeographic study of the extinct American mastodon (Mammut americanum), based on 35 complete mitochondrial genomes. These data reveal the presence of multiple lineages within this species, including two distinct clades from eastern Beringia. Our molecular date estimates suggest that these clades arose at different times, supporting a pattern of repeated northern expansion and local extirpation in response to glacial cycling. Consistent with this hypothesis, we also note lower levels of genetic diversity among northern mastodons than in endemic clades south of the continental ice sheets. The results of our study highlight the complex relationships between population dispersals and climate change, and can provide testable hypotheses for extant species expected to experience substantial biogeographic impacts from rising temperatures

Electron Transfer from Cyt b559 and Tyrosine-D to the S2 and S3 states of the water oxidizing complex in Photosystem II at Cryogenic Temperatures

The Mn4CaO5 cluster of photosystem II (PSII) catalyzes the oxidation of water to molecular oxygen through the light-driven redox S-cycle. The water oxidizing complex (WOC) forms a triad with Tyrosine(Z) and P-680, which mediates electrons from water towards the acceptor side of PSII. Under certain conditions two other redox-active components, Tyrosine(D) (Y-D) and Cytochrome b (559) (Cyt b (559)) can also interact with the S-states. In the present work we investigate the electron transfer from Cyt b (559) and Y-D to the S-2 and S-3 states at 195 K. First, Y-D (aEuro cent) and Cyt b (559) were chemically reduced. The S-2 and S-3 states were then achieved by application of one or two laser flashes, respectively, on samples stabilized in the S-1 state. EPR signals of the WOC (the S-2-state multiline signal, ML-S-2), Y-D (aEuro cent) and oxidized Cyt b (559) were simultaneously detected during a prolonged dark incubation at 195 K. During 163 days of incubation a large fraction of the S-2 population decayed to S-1 in the S-2 samples by following a single exponential decay. Differently, S-3 samples showed an initial increase in the ML-S-2 intensity (due to S-3 to S-2 conversion) and a subsequent slow decay due to S-2 to S-1 conversion. In both cases, only a minor oxidation of Y-D was observed. In contrast, the signal intensity of the oxidized Cyt b (559) showed a two-fold increase in both the S-2 and S-3 samples. The electron donation from Cyt b (559) was much more efficient to the S-2 state than to the S-3 state

Predominant and novel de novo variants in 29 individuals with ALG13 deficiency: Clinical description, biomarker status, biochemical analysis, and treatment suggestions

Asparagine-linked glycosylation 13 homolog (ALG13) encodes a nonredundant, highly conserved, X-linked uridine diphosphate (UDP)-N-acetylglucosaminyltransferase required for the synthesis of lipid linked oligosaccharide precursor and proper N-linked glycosylation. De novo variants in ALG13 underlie a form of early infantile epileptic encephalopathy known as EIEE36, but given its essential role in glycosylation, it is also considered a congenital disorder of glycosylation (CDG), ALG13-CDG. Twenty-four previously reported ALG13-CDG cases had de novo variants, but surprisingly, unlike most forms of CDG, ALG13-CDG did not show the anticipated glycosylation defects, typically detected by altered transferrin glycosylation. Structural homology modeling of two recurrent de novo variants, p.A81T and p.N107S, suggests both are likely to impact the function of ALG13. Using a corresponding ALG13-deficient yeast strain, we show that expressing yeast ALG13 with either of the highly conserved hotspot variants rescues the observed growth defect, but not its glycosylation abnormality. We present molecular and clinical data on 29 previously unreported individuals with de novo variants in ALG13. This more than doubles the number of known cases. A key finding is that a vast majority of the individuals presents with West syndrome, a feature shared with other CDG types. Among these, the initial epileptic spasms best responded to adrenocorticotropic hormone or prednisolone, while clobazam and felbamate showed promise for continued epilepsy treatment. A ketogenic diet seems to play an important role in the treatment of these individuals.Fil: Ng, Bobby G.. Sanford Burnham Prebys Medical Discovery Institute; Estados UnidosFil: Eklund, Erik A.. Sanford Burnham Prebys Medical Discovery Institute; Estados Unidos. Lund University; SueciaFil: Shiryaev, Sergey A.. Sanford Burnham Prebys Medical Discovery Institute; Estados UnidosFil: Dong, Yin Y.. University of Oxford; Reino UnidoFil: Abbott, Mary Alice. University of Massachusetts Medical School; Estados UnidosFil: Asteggiano, Carla Gabriela. Universidad Católica de Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Medicina. Centro de Estudios de las Metabolopatías Congénitas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: Bamshad, Michael J.. University of Washington; Estados UnidosFil: Barr, Eileen. University of Emory; Estados UnidosFil: Bernstein, Jonathan A.. University of Stanford; Estados UnidosFil: Chelakkadan, Shabeed. Monash Children's Hospital; AustraliaFil: Christodoulou, John. Sydney Medical School; Australia. University of Melbourne; AustraliaFil: Chung, Wendy K.. Columbia University; Estados UnidosFil: Ciliberto, Michael A.. University of Iowa; Estados UnidosFil: Cousin, Janice. National Human Genome Research Institute ; Estados UnidosFil: Gardiner, Fiona. University of Melbourne; AustraliaFil: Ghosh, Suman. University of Florida; Estados UnidosFil: Graf, William D.. University of Connecticut; Estados UnidosFil: Grunewald, Stephanie. University College London; Estados UnidosFil: Hammond, Katherine. University of Alabama at Birmingahm; Estados UnidosFil: Hauser, Natalie S.. Inova, Fairfax Hospital Falls Church; Estados UnidosFil: Hoganson, George E.. University Of Illinois At Chicago; Estados UnidosFil: Houck, Kimberly M.. Baylor College of Medicine; Estados UnidosFil: Kohler, Jennefer N.. University of Stanford; Estados UnidosFil: Morava, Eva. Mayo Clinic; Estados UnidosFil: Larson, Austin A.. University Of Colorado Anschutz Medical Campus.; Estados UnidosFil: Liu, Pengfei. Baylor Genetics; Estados Unidos. Baylor College Of Medicine; Estados UnidosFil: Madathil, Sujana. University of Iowa; Estados UnidosFil: McCormack, Colleen. University of Stanford; Estados UnidosFil: Meeks, Naomi J.L.. University Of Colorado Anschutz Medical Campus.; Estados UnidosFil: Papazoglu, Gabriela Magali. Universidad Nacional de Córdoba. Facultad de Medicina. Centro de Estudios de las Metabolopatías Congénitas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentin

Haploinsufficiency of PRR12 causes a spectrum of neurodevelopmental, eye, and multisystem abnormalities

PURPOSE: Proline Rich 12 (PRR12) is a gene of unknown function with suspected DNA-binding activity, expressed in developing mice and human brains. Predicted loss-of-function variants in this gene are extremely rare, indicating high intolerance of haploinsufficiency. METHODS: Three individuals with intellectual disability and iris anomalies and truncating de novo PRR12 variants were described previously. We add 21 individuals with similar PRR12 variants identified via matchmaking platforms, bringing the total number to 24. RESULTS: We observed 12 frameshift, 6 nonsense, 1 splice-site, and 2 missense variants and one patient with a gross deletion involving PRR12. Three individuals had additional genetic findings, possibly confounding the phenotype. All patients had developmental impairment. Variable structural eye defects were observed in 12/24 individuals (50%) including anophthalmia, microphthalmia, colobomas, optic nerve and iris abnormalities. Additional common features included hypotonia (61%), heart defects (52%), growth failure (54%), and kidney anomalies (35%). PrediXcan analysis showed that phecodes most strongly associated with reduced predicted PRR12 expression were enriched for eye- (7/30) and kidney- (4/30) phenotypes, such as wet macular degeneration and chronic kidney disease. CONCLUSION: These findings support PRR12 haploinsufficiency as a cause for a novel disorder with a wide clinical spectrum marked chiefly by neurodevelopmental and eye abnormalities

Spectroscopic Studies of the Iron and Manganese Reconstituted Tyrosyl Radical in Bacillus Cereus Ribonucleotide Reductase R2 Protein

Ribonucleotide reductase (RNR) catalyzes the rate limiting step in DNA synthesis where ribonucleotides are reduced to the corresponding deoxyribonucleotides. Class Ib RNRs consist of two homodimeric subunits: R1E, which houses the active site; and R2F, which contains a metallo cofactor and a tyrosyl radical that initiates the ribonucleotide reduction reaction. We studied the R2F subunit of B. cereus reconstituted with iron or alternatively with manganese ions, then subsequently reacted with molecular oxygen to generate two tyrosyl-radicals. The two similar X-band EPR spectra did not change significantly over 4 to 50 K. From the 285 GHz EPR spectrum of the iron form, a g1-value of 2.0090 for the tyrosyl radical was extracted. This g1-value is similar to that observed in class Ia E. coli R2 and class Ib R2Fs with iron-oxygen cluster, suggesting the absence of hydrogen bond to the phenoxyl group. This was confirmed by resonance Raman spectroscopy, where the stretching vibration associated to the radical (C-O, ν7a = 1500 cm−1) was found to be insensitive to deuterium-oxide exchange. Additionally, the 18O-sensitive Fe-O-Fe symmetric stretching (483 cm−1) of the metallo-cofactor was also insensitive to deuterium-oxide exchange indicating no hydrogen bonding to the di-iron-oxygen cluster, and thus, different from mouse R2 with a hydrogen bonded cluster. The HF-EPR spectrum of the manganese reconstituted RNR R2F gave a g1-value of ∼2.0094. The tyrosyl radical microwave power saturation behavior of the iron-oxygen cluster form was as observed in class Ia R2, with diamagnetic di-ferric cluster ground state, while the properties of the manganese reconstituted form indicated a magnetic ground state of the manganese-cluster. The recent activity measurements (Crona et al., (2011) J Biol Chem 286: 33053–33060) indicates that both the manganese and iron reconstituted RNR R2F could be functional. The manganese form might be very important, as it has 8 times higher activity

Mn 2+ reduces Y z + in manganese-depleted Photosystem II preparations

Manganese in the oxygen-evolving complex is a physiological electron donor to Photosystem II. PS II depleted of manganese may oxidize exogenous reductants including benzidine and Mn 2+ . Using flash photolysis with electron spin resonance detection, we examined the room-temperature reaction kinetics of these reductants with Y z + , the tyrosine radical formed in PS II membranes under illumination. Kinetics were measured with membranes that did or did not contain the 33 kDa extrinsic polypeptide of PS II, whose presence had no effect on the reaction kinetics with either reductant. The rate of Y z + reduction by benzidine was a linear function of benzidine concentration. The rate of Y z + reduction by Mn 2+ at pH 6 increased linearly at low Mn 2+ concentrations and reached a maximum at the Mn 2+ concentrations equal to several times the reaction center concentration. The rate was inhibited by K + , Ca 2+ and Mg 2+ . These data are described by a model in which negative charge on the membrane causes a local increase in the cation concentration. The rate of Y z + reduction at pH 7.5 was biphasic with a fast 400 μs phase that suggests binding of Mn 2+ near Y z + at a site that may be one of the native manganese binding sites.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43534/1/11120_2004_Article_BF00048306.pd

Formal Reduction Potential of 3,5-Difluorotyrosine in a Structured Protein: Insight into Multistep Radical Transfer

The reversible Y–O•/Y–OH redox properties of the α[subscript 3]Y model protein allow access to the electrochemical and thermodynamic properties of 3,5-difluorotyrosine. The unnatural amino acid has been incorporated at position 32, the dedicated radical site in α[subscript 3]Y, by in vivo nonsense codon suppression. Incorporation of 3,5-difluorotyrosine gives rise to very minor structural changes in the protein scaffold at pH values below the apparent pK (8.0 ± 0.1) of the unnatural residue. Square-wave voltammetry on α[subscript 3](3,5)F[subscript 2]Y provides an E°′(Y–O•/Y–OH) of 1026 ± 4 mV versus the normal hydrogen electrode (pH 5.70 ± 0.02) and shows that the fluoro substitutions lower the E°′ by −30 ± 3 mV. These results illustrate the utility of combining the optimized α[subscript 3]Y tyrosine radical system with in vivo nonsense codon suppression to obtain the formal reduction potential of an unnatural aromatic residue residing within a well-structured protein. It is further observed that the protein E°′ values differ significantly from peak potentials derived from irreversible voltammograms of the corresponding aqueous species. This is notable because solution potentials have been the main thermodynamic data available for amino acid radicals. The findings in this paper are discussed relative to recent mechanistic studies of the multistep radical-transfer process in Escherichia coli ribonucleotide reductase site-specifically labeled with unnatural tyrosine residues.National Institutes of Health (U.S.) (Grant GM29595

SLC35A2â CDG: Functional characterization, expanded molecular, clinical, and biochemical phenotypes of 30 unreported Individuals

Pathogenic de novo variants in the Xâ linked gene SLC35A2 encoding the major Golgiâ localized UDPâ galactose transporter required for proper protein and lipid glycosylation cause a rare type of congenital disorder of glycosylation known as SLC35A2â congenital disorders of glycosylation (CDG; formerly CDGâ IIm). To date, 29 unique de novo variants from 32 unrelated individuals have been described in the literature. The majority of affected individuals are primarily characterized by varying degrees of neurological impairments with or without skeletal abnormalities. Surprisingly, most affected individuals do not show abnormalities in serum transferrin Nâ glycosylation, a common biomarker for most types of CDG. Here we present data characterizing 30 individuals and add 26 new variants, the single largest study involving SLC35A2â CDG. The great majority of these individuals had normal transferrin glycosylation. In addition, expanding the molecular and clinical spectrum of this rare disorder, we developed a robust and reliable biochemical assay to assess SLC35A2â dependent UDPâ galactose transport activity in primary fibroblasts. Finally, we show that transport activity is directly correlated to the ratio of wildâ type to mutant alleles in fibroblasts from affected individuals.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/150498/1/humu23731_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150498/2/humu23731-sup-0001-Supp_Mat__2019.2.10_.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/150498/3/humu23731.pd

Crystal structure of oxygen-evolving photosystem II at a resolution of 1.9 Å

Photosystem II is the site of photosynthetic water oxidation and contains 20 subunits with a total molecular mass of 350 kDa. The structure of photosystem II has been reported at resolutions from 3.8 to 2.9 angstrom. These resolutions have provided much information on the arrangement of protein subunits and cofactors but are insufficient to reveal the detailed structure of the catalytic centre of water splitting. Here we report the crystal structure of photosystem II at a resolution of 1.9 angstrom. From our electron density map, we located all of the metal atoms of the Mn(4)CaO(5) cluster, together with all of their ligands. We found that five oxygen atoms served as oxo bridges linking the five metal atoms, and that four water molecules were bound to the Mn(4)CaO(5) cluster; some of them may therefore serve as substrates for dioxygen formation. We identified more than 1,300 water molecules in each photosystem II monomer. Some of them formed extensive hydrogen-bonding networks that may serve as channels for protons, water or oxygen molecules. The determination of the high-resolution structure of photosystem II will allow us to analyse and understand its functions in great detail