Combinatorial proofs on the joint distribution of descents and inverse descents

Let $A_{n,i,j}$ be the number of permutations on $[n]$ with $i-1$ descents and $j-1$ inverse descents. Carlitz, Roselle and Scoville in 1966 first revealed some combinatorial and arithmetic properties of $A_{n,i,j}$, which contain a recurrence of $A_{n,i,j}$. Using the idea of balls in boxes, Petersen gave a combinatorial interpretation for the generating function of $A_{n,i,j}$, and obtained the same recurrence of $A_{n,i,j}$ from its generating function. Subsequently, Petersen asked whether there is a visual way to understand this recurrence. In this paper, after observing the internal structures of permutation grids, we present a combinatorial proof of the recurrence of $A_{n,i,j}$. Let $I_{n,k}$ and $J_{n,k}$ count the number of involutions and fixed-point free involutions on $[n]$ with $k$ descents, respectively. With the help of generating functions, Guo and Zeng derived two recurrences of $I_{n,k}$ and $J_{2n,k}$ that play an essential role in the proof of their unimodal properties. Unexpectedly, the constructive approach to the recurrence of $A_{n,i,j}$ is found to fuel the combinatorial interpretations of these two recurrences of $I_{n,k}$ and $J_{2n,k}$

Machine learning and structural analysis of Mycobacterium tuberculosis pan-genome identifies genetic signatures of antibiotic resistance.

Mycobacterium tuberculosis is a serious human pathogen threat exhibiting complex evolution of antimicrobial resistance (AMR). Accordingly, the many publicly available datasets describing its AMR characteristics demand disparate data-type analyses. Here, we develop a reference strain-agnostic computational platform that uses machine learning approaches, complemented by both genetic interaction analysis and 3D structural mutation-mapping, to identify signatures of AMR evolution to 13 antibiotics. This platform is applied to 1595 sequenced strains to yield four key results. First, a pan-genome analysis shows that M. tuberculosis is highly conserved with sequenced variation concentrated in PE/PPE/PGRS genes. Second, the platform corroborates 33 genes known to confer resistance and identifies 24 new genetic signatures of AMR. Third, 97 epistatic interactions across 10 resistance classes are revealed. Fourth, detailed structural analysis of these genes yields mechanistic bases for their selection. The platform can be used to study other human pathogens

Regional variation of microtubule flux reveals microtubule organization in the metaphase meiotic spindle

Continuous poleward movement of tubulin is a hallmark of metaphase spindle dynamics in higher eukaryotic cells and is essential for stable spindle architecture and reliable chromosome segregation. We use quantitative fluorescent speckle microscopy to map with high resolution the spatial organization of microtubule flux in Xenopus laevis egg extract meiotic spindles. We find that the flux velocity decreases near spindle poles by ∼20%. The regional variation is independent of functional kinetochores and centrosomes and is suppressed by inhibition of dynein/dynactin, kinesin-5, or both. Statistical analysis reveals that tubulin flows in two distinct velocity modes. We propose an association of these modes with two architecturally distinct yet spatially overlapping and dynamically cross-linked arrays of microtubules: focused polar microtubule arrays of a uniform polarity and slower flux velocities are interconnected by a dense barrel-like microtubule array of antiparallel polarities and faster flux velocities

Role of angiotensin II type 2 receptors and kinins in the cardioprotective effect of angiotensin II type 1 receptor antagonists in rats with heart failure

AbstractObjectivesWe studied the role of angiotensin II type 2 (AT2) receptors and kinins in the cardioprotective effect of angiotensin II type 1 antagonists (AT1-ant) in rats with heart failure (HF) after myocardial infarction.BackgroundThe AT1-ant is as effective as angiotensin-converting enzyme inhibitors in treating HF, but the mechanisms whereby AT1-ant exert their benefits on HF in vivo are more complex than previously understood.MethodsBrown Norway Katholiek rats (BNK), which are deficient in kinins because of a mutation in the kininogen gene, and their wild-type control (Brown Norway [BN]) underwent myocardial infarction. Two months later, they were treated for two months with: 1) vehicle; 2) AT1-ant (L158809, Merck, Rahway, New Jersey); 3) AT1-ant + AT2-ant (PD-123319, Parke Davis, Ann Arbor, Michigan); or 4) AT1-ant + kinin B2receptor antagonist (B2-ant) (icatibant) (only BN). We measured left ventricular weight (LVW) gravimetrically, myocyte cross-sectional area (MCSA) and interstitial collagen fraction (ICF) histologically, and ejection fraction by ventriculography.ResultsDevelopment of HF was comparable in BN and BNK rats. The AT1-ant reduced LVW and MCSA and the AT2-ant blocked these effects in BN rats, but the B2-ant did not. The AT1-ant reduced LVW and MCSA in BNK rats, and this effect was reversed by the AT2-ant. In BN rats, ICF was reduced and LVEF increased by AT1-ant, and both AT2-ant and B2-ant reversed these effects. In BNK rats, the AT1-ant failed to reduce ICF, and its therapeutic effect on LVEF was significantly blunted.ConclusionsIn HF, the AT2receptor plays an important role in the therapeutic effects of AT1-ant, and this effect may be mediated partly through kinins; however, kinins appear to play a lesser role in the antihypertrophic effect of AT1-ant

Dopamine Neuron-Specific Optogenetic Stimulation in Rhesus Macaques.

Optogenetic studies in mice have revealed new relationships between well-defined neurons and brain functions. However, there are currently no means to achieve the same cell-type specificity in monkeys, which possess an expanded behavioral repertoire and closer anatomical homology to humans. Here, we present a resource for cell-type-specific channelrhodopsin expression in Rhesus monkeys and apply this technique to modulate dopamine activity and monkey choice behavior. These data show that two viral vectors label dopamine neurons with greater than 95% specificity. Infected neurons were activated by light pulses, indicating functional expression. The addition of optical stimulation to reward outcomes promoted the learning of reward-predicting stimuli at the neuronal and behavioral level. Together, these results demonstrate the feasibility of effective and selective stimulation of dopamine neurons in non-human primates and a resource that could be applied to other cell types in the monkey brain.This work was supported by the Wellcome Trust (Principal Research Fellowship and Programme Grant 095495), European Research Council (ERC Advanced Grant 293549), and NIH Caltech Conte Center (P50MH094258)

Cloning, Analysis and Functional Annotation of Expressed Sequence Tags from the Earthworm \u3ci\u3eEisenia fetida\u3c/i\u3e

Background Eisenia fetida, commonly known as red wiggler or compost worm, belongs to the Lumbricidae family of the Annelida phylum. Little is known about its genome sequence although it has been extensively used as a test organism in terrestrial ecotoxicology. In order to understand its gene expression response to environmental contaminants, we cloned 4032 cDNAs or expressed sequence tags (ESTs) from two E. fetida libraries enriched with genes responsive to ten ordnance related compounds using suppressive subtractive hybridization-PCR. Results A total of 3144 good quality ESTs (GenBank dbEST accession number EH669363–EH672369 and EL515444–EL515580) were obtained from the raw clone sequences after cleaning. Clustering analysis yielded 2231 unique sequences including 448 contigs (from 1361 ESTs) and 1783 singletons. Comparative genomic analysis showed that 743 or 33% of the unique sequences shared high similarity with existing genes in the GenBank nr database. Provisional function annotation assigned 830 Gene Ontology terms to 517 unique sequences based on their homology with the annotated genomes of four model organisms Drosophila melanogaster, Mus musculus, Saccharomyces cerevisiae, and Caenorhabditis elegans. Seven percent of the unique sequences were further mapped to 99 Kyoto Encyclopedia of Genes and Genomes pathways based on their matching Enzyme Commission numbers. All the information is stored and retrievable at a highly performed, web-based and user-friendly relational database called EST model database or ESTMD version 2. Conclusion The ESTMD containing the sequence and annotation information of 4032 E. fetida ESTs is publicly accessible at http://mcbc.usm.edu/estmd

Cloning, analysis and functional annotation of expressed sequence tags from the Earthworm Eisenia fetida

<p>Abstract</p> <p>Background</p> <p><it>Eisenia fetida</it>, commonly known as red wiggler or compost worm, belongs to the Lumbricidae family of the Annelida phylum. Little is known about its genome sequence although it has been extensively used as a test organism in terrestrial ecotoxicology. In order to understand its gene expression response to environmental contaminants, we cloned 4032 cDNAs or expressed sequence tags (ESTs) from two <it>E. fetida </it>libraries enriched with genes responsive to ten ordnance related compounds using suppressive subtractive hybridization-PCR.</p> <p>Results</p> <p>A total of 3144 good quality ESTs (GenBank dbEST accession number <ext-link ext-link-type="gen" ext-link-id="EH669363">EH669363</ext-link>–<ext-link ext-link-type="gen" ext-link-id="EH672369">EH672369</ext-link> and <ext-link ext-link-type="gen" ext-link-id="EL515444">EL515444</ext-link>–<ext-link ext-link-type="gen" ext-link-id="EL515580">EL515580</ext-link>) were obtained from the raw clone sequences after cleaning. Clustering analysis yielded 2231 unique sequences including 448 contigs (from 1361 ESTs) and 1783 singletons. Comparative genomic analysis showed that 743 or 33% of the unique sequences shared high similarity with existing genes in the GenBank nr database. Provisional function annotation assigned 830 Gene Ontology terms to 517 unique sequences based on their homology with the annotated genomes of four model organisms <it>Drosophila melanogaster</it>, <it>Mus musculus</it>, <it>Saccharomyces cerevisiae</it>, and <it>Caenorhabditis elegans</it>. Seven percent of the unique sequences were further mapped to 99 Kyoto Encyclopedia of Genes and Genomes pathways based on their matching Enzyme Commission numbers. All the information is stored and retrievable at a highly performed, web-based and user-friendly relational database called EST model database or ESTMD version 2.</p> <p>Conclusion</p> <p>The ESTMD containing the sequence and annotation information of 4032 <it>E. fetida </it>ESTs is publicly accessible at <url>http://mcbc.usm.edu/estmd/</url>.</p

Single-Cell Transcriptomic Profiling of Pluripotent Stem Cell-Derived SCGB3A2+ Airway Epithelium.

Lung epithelial lineages have been difficult to maintain in pure form in&nbsp;vitro, and lineage-specific reporters have proven invaluable for monitoring their emergence from cultured pluripotent stem cells (PSCs). However, reporter constructs for tracking proximal airway lineages generated from PSCs have not been previously available, limiting the characterization of these cells. Here, we engineer mouse and human PSC lines carrying airway secretory lineage reporters that facilitate the tracking, purification, and profiling of this lung subtype. Through bulk and single-cell-based global transcriptomic profiling, we find PSC-derived airway secretory cells are susceptible to phenotypic plasticity exemplified by the tendency to co-express both a proximal airway secretory program as well as an alveolar type 2 cell program, which can be minimized by inhibiting endogenous Wnt signaling. Our results provide global profiles of engineered lung cell fates, a guide for improving their directed differentiation, and a human model of the developing airway