Remarks on singular Cayley graphs and vanishing elements of simple groups

Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs Cay(G,H) when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs

On zeros of irreducible characters lying in a normal subgroup

[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we also study certain arithmetical properties of the G-conjugacy class sizes of the elements of N which are zeros of some irreducible character of G. In particular, if N=G, then new contributions are obtained.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). The research of the second author is partially funded by the Istituto Nazionale di Alta Matematica - INdAM. The third author acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The first and third authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovacion y Universidades (Spain).Felipe Román, MJ.; Grittini, N.; Ortiz-Sotomayor, VM. (2020). On zeros of irreducible characters lying in a normal subgroup. Annali di Matematica Pura ed Applicata (1923 -). 199:1777-1789. https://doi.org/10.1007/s10231-020-00942-1S17771789199Beltrán, A., Felipe, M.J.: Prime powers as conjugacy class lengths of $$\pi$$-elements. Bull. Aust. Math. Soc. 69, 317–325 (2004)Beltrán, A., Felipe, M.J., Malle, G., Moretó, A., Navarro, G., Sanus, L., Solomon, R., Tiep, P.H.: Nilpotent and abelian Hall subgroups in finite groups. Trans. Am. Math. Soc. 368, 2497–2513 (2016)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Bianchi, M., Chillag, D., Lewis, M.L., Pacifici, E.: Character degree graphs that are complete graphs. Proc. Am. Math. Soc. 135, 671–676 (2007)Brough, J., Kong, Q.: On vanishing criteria that control finite group structure II. Bull. Aust. Math. Soc. 98, 251–257 (2018)Brough, J.: Non-vanishing elements in finite groups. J. Algebra 460, 387–391 (2016)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Grüninger, M.: Two remarks about non-vanishing elements in finite groups. J. Algebra 460, 366–369 (2016)Isaacs, I.M.: Character Theory of Finite Groups. Academic Press Inc., London (1976)Isaacs, I.M., Navarro, G., Wolf, T.R.: Finite group elements where no irreducible character vanishes. J. Algebra 222, 413–423 (1999)Malle, G., Navarro, G.: Characterizing normal Sylow $$p$$-subgroups by character degrees. J. Algebra 370, 402–406 (2012)Malle, G., Navarro, G., Olsson, J.B.: Zeros of characters of finite groups. J. Group Theory 3, 353–368 (2000)The GAP Group: GAP—Groups, Algorithms, and Programming. Version 4.10.0 (2018). http://www.gap-system.or

Purkinje cell input to cerebellar nuclei in tottering: Ultrastructure and physiology

Homozygous tottering mice are spontaneous ataxic mutants, which carry a mutation in the gene encoding the ion pore of the P/Q-type voltage-gated calcium channels. P/Q-type calcium channels are prominently expressed in Purkinje cell terminals, but it is unknown to what extent these inhibitory terminals in tottering mice are affected at the morphological and electrophysiological level. Here, we investigated the distribution and ultrastructure of their Purkinje cell terminals in the cerebellar nuclei as well as the activities of their target neurons. The densities of Purkinje cell terminals and their synapses were not significantly affected in the mutants. However, the Purkinje cell terminals were enlarged and had an increased number of vacuoles, whorled bodies, and mitochondria. These differences started to occur between 3 and 5 weeks of age and persisted throughout adulthood. Stimulation of Purkinje cells in adult tottering mice resulted in inhibition at normal latencies, but the activities of their postsynaptic neurons in the cerebellar nuclei were abnormal in that the frequency and irregularity of their spiking patterns were enhanced. Thus, although the number of their terminals and their synaptic contacts appear quantitatively intact, Purkinje cells in tottering mice show several signs of axonal damage that may contribute to altered postsynaptic activities in the cerebellar nuclei

A principal component meta-analysis on multiple anthropometric traits identifies novel loci for body shape

This is the final version of the article. Available from the publisher via the DOI in this record.Large consortia have revealed hundreds of genetic loci associated with anthropometric traits, one trait at a time. We examined whether genetic variants affect body shape as a composite phenotype that is represented by a combination of anthropometric traits. We developed an approach that calculates averaged PCs (AvPCs) representing body shape derived from six anthropometric traits (body mass index, height, weight, waist and hip circumference, waist-to-hip ratio). The first four AvPCs explain >99% of the variability, are heritable, and associate with cardiometabolic outcomes. We performed genome-wide association analyses for each body shape composite phenotype across 65 studies and meta-analysed summary statistics. We identify six novel loci: LEMD2 and CD47 for AvPC1, RPS6KA5/C14orf159 and GANAB for AvPC3, and ARL15 and ANP32 for AvPC4. Our findings highlight the value of using multiple traits to define complex phenotypes for discovery, which are not captured by single-trait analyses, and may shed light onto new pathways

Translational models for vascular cognitive impairment: a review including larger species.

BACKGROUND: Disease models are useful for prospective studies of pathology, identification of molecular and cellular mechanisms, pre-clinical testing of interventions, and validation of clinical biomarkers. Here, we review animal models relevant to vascular cognitive impairment (VCI). A synopsis of each model was initially presented by expert practitioners. Synopses were refined by the authors, and subsequently by the scientific committee of a recent conference (International Conference on Vascular Dementia 2015). Only peer-reviewed sources were cited. METHODS: We included models that mimic VCI-related brain lesions (white matter hypoperfusion injury, focal ischaemia, cerebral amyloid angiopathy) or reproduce VCI risk factors (old age, hypertension, hyperhomocysteinemia, high-salt/high-fat diet) or reproduce genetic causes of VCI (CADASIL-causing Notch3 mutations). CONCLUSIONS: We concluded that (1) translational models may reflect a VCI-relevant pathological process, while not fully replicating a human disease spectrum; (2) rodent models of VCI are limited by paucity of white matter; and (3) further translational models, and improved cognitive testing instruments, are required

Levodopa-Induced Dyskinesia Is Associated with Increased Thyrotropin Releasing Hormone in the Dorsal Striatum of Hemi-Parkinsonian Rats

Background Dyskinesias associated with involuntary movements and painful muscle contractions are a common and severe complication of standard levodopa (L-DOPA, L-3,4-dihydroxyphenylalanine) therapy for Parkinson's disease. Pathologic neuroplasticity leading to hyper-responsive dopamine receptor signaling in the sensorimotor striatum is thought to underlie this currently untreatable condition. Methodology/Principal Findings Quantitative real-time polymerase chain reaction (PCR) was employed to evaluate the molecular changes associated with L-DOPA-induced dyskinesias in Parkinson's disease. With this technique, we determined that thyrotropin releasing hormone (TRH) was greatly increased in the dopamine-depleted striatum of hemi-parkinsonian rats that developed abnormal movements in response to L-DOPA therapy, relative to the levels measured in the contralateral non-dopamine-depleted striatum, and in the striatum of non-dyskinetic control rats. ProTRH immunostaining suggested that TRH peptide levels were almost absent in the dopamine-depleted striatum of control rats that did not develop dyskinesias, but in the dyskinetic rats, proTRH immunostaining was dramatically up-regulated in the striatum, particularly in the sensorimotor striatum. This up-regulation of TRH peptide affected striatal medium spiny neurons of both the direct and indirect pathways, as well as neurons in striosomes. Conclusions/Significance TRH is not known to be a key striatal neuromodulator, but intrastriatal injection of TRH in experimental animals can induce abnormal movements, apparently through increasing dopamine release. Our finding of a dramatic and selective up-regulation of TRH expression in the sensorimotor striatum of dyskinetic rat models suggests a TRH-mediated regulatory mechanism that may underlie the pathologic neuroplasticity driving dopamine hyper-responsivity in Parkinson's disease.Morris K. Udall Center for Excellence in Parkinson’s Research at MGH/MITNational Institutes of Health (U.S.) (NIH NS38372)American Parkinson Disease Association, Inc.University of Alabama at BirminghamMassachusetts General HospitalNational Institute of Diabetes and Digestive and Kidney Diseases (U.S.) (NIDDK/NIH grant R01 DK58148)National Institute of Neurological Disorders and Stroke (U.S.) (R01 NINDS/NIH grant NS045231)Stanley H. and Sheila G. Sydney FundMichael J. Fox Foundation for Parkinson's Researc

Ustekinumab as Induction and Maintenance Therapy for Crohn’s Disease

BACKGROUND Ustekinumab, a monoclonal antibody to the p40 subunit of interleukin-12 and inter-leukin-23, was evaluated as an intravenous induction therapy in two populations with moderately to severely active Crohn’s disease. Ustekinumab was also evaluated as subcutaneous maintenance therapy. METHODS We randomly assigned patients to receive a single intravenous dose of ustekinumab (either 130 mg or approximately 6 mg per kilogram of body weight) or placebo in two induction trials. The UNITI-1 trial included 741 patients who met the criteria for primary or secondary nonresponse to tumor necrosis factor (TNF) antagonists or had unacceptable side effects. The UNITI-2 trial included 628 patients in whom conventional therapy failed or unacceptable side effects occurred. Patients who completed these induction trials then participated in IM-UNITI, in which the 397 patients who had a response to ustekinumab were randomly assigned to receive subcutaneous maintenance injections of 90 mg of ustekinumab (either every 8 weeks or every 12 weeks) or placebo. The primary end point for the induction trials was a clinical response at week 6 (defined as a decrease from baseline in the Crohn’s Disease Activity Index [CDAI] score of ≥100 points or a CDAI score <150). The primary end point for the maintenance trial was remission at week 44 (CDAI score <150). RESULTS The rates of response at week 6 among patients receiving intravenous ustekinumab at a dose of either 130 mg or approximately 6 mg per kilogram were significantly higher than the rates among patients receiving placebo (in UNITI-1, 34.3%, 33.7%, and 21.5%, respectively, with P≤0.003 for both comparisons with placebo; in UNITI-2, 51.7%, 55.5%, and 28.7%, respectively, with P<0.001 for both doses). In the groups receiving maintenance doses of ustekinumab every 8 weeks or every 12 weeks, 53.1% and 48.8%, respectively, were in remission at week 44, as compared with 35.9% of those receiving placebo (P = 0.005 and P = 0.04, respectively). Within each trial, adverse-event rates were similar among treatment groups. CONCLUSIONS Among patients with moderately to severely active Crohn’s disease, those receiving intravenous ustekinumab had a significantly higher rate of response than did those receiving placebo. Subcutaneous ustekinumab maintained remission in patients who had a clinical response to induction therapy. (Funded by Janssen Research and Development; ClinicalTrials.gov numbers, NCT01369329, NCT01369342, and NCT01369355.

Synthetic biology to access and expand nature's chemical diversity

Bacterial genomes encode the biosynthetic potential to produce hundreds of thousands of complex molecules with diverse applications, from medicine to agriculture and materials. Accessing these natural products promises to reinvigorate drug discovery pipelines and provide novel routes to synthesize complex chemicals. The pathways leading to the production of these molecules often comprise dozens of genes spanning large areas of the genome and are controlled by complex regulatory networks with some of the most interesting molecules being produced by non-model organisms. In this Review, we discuss how advances in synthetic biology — including novel DNA construction technologies, the use of genetic parts for the precise control of expression and for synthetic regulatory circuits — and multiplexed genome engineering can be used to optimize the design and synthesis of pathways that produce natural products

Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk.

Blood pressure is a heritable trait influenced by several biological pathways and responsive to environmental stimuli. Over one billion people worldwide have hypertension (≥140 mm Hg systolic blood pressure or  ≥90 mm Hg diastolic blood pressure). Even small increments in blood pressure are associated with an increased risk of cardiovascular events. This genome-wide association study of systolic and diastolic blood pressure, which used a multi-stage design in 200,000 individuals of European descent, identified sixteen novel loci: six of these loci contain genes previously known or suspected to regulate blood pressure (GUCY1A3-GUCY1B3, NPR3-C5orf23, ADM, FURIN-FES, GOSR2, GNAS-EDN3); the other ten provide new clues to blood pressure physiology. A genetic risk score based on 29 genome-wide significant variants was associated with hypertension, left ventricular wall thickness, stroke and coronary artery disease, but not kidney disease or kidney function. We also observed associations with blood pressure in East Asian, South Asian and African ancestry individuals. Our findings provide new insights into the genetics and biology of blood pressure, and suggest potential novel therapeutic pathways for cardiovascular disease prevention