Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Improving virtual screening of G protein-coupled receptors via ligand-directed modeling

G protein-coupled receptors (GPCRs) play crucial roles in cell physiology and pathophysiology. There is increasing interest in using structural information for virtual screening (VS) of libraries and for structure-based drug design to identify novel agonist or antagonist leads. However, the sparse availability of experimentally determined GPCR/ligand complex structures with diverse ligands impedes the application of structure-based drug design (SBDD) programs directed to identifying new molecules with a select pharmacology. In this study, we apply ligand-directed modeling (LDM) to available GPCR X-ray structures to improve VS performance and selectivity towards molecules of specific pharmacological profile. The described method refines a GPCR binding pocket conformation using a single known ligand for that GPCR. The LDM method is a computationally efficient, iterative workflow consisting of protein sampling and ligand docking. We developed an extensive benchmark comparing LDM-refined binding pockets to GPCR X-ray crystal structures across seven different GPCRs bound to a range of ligands of different chemotypes and pharmacological profiles. LDM-refined models showed improvement in VS performance over origin X-ray crystal structures in 21 out of 24 cases. In all cases, the LDM-refined models had superior performance in enriching for the chemotype of the refinement ligand. This likely contributes to the LDM success in all cases of inhibitor-bound to agonist-bound binding pocket refinement, a key task for GPCR SBDD programs. Indeed, agonist ligands are required for a plethora of GPCRs for therapeutic intervention, however GPCR X-ray structures are mostly restricted to their inactive inhibitor-bound state

The program for biodiversity research in Brazil: The role of regional networks for biodiversity knowledge, dissemination, and conservation

The Program for Biodiversity Research (PPBio) is an innovative program designed to integrate all biodiversity research stakeholders. Operating since 2004, it has installed long-term ecological research sites throughout Brazil and its logic has been applied in some other southern-hemisphere countries. The program supports all aspects of research necessary to understand biodiversity and the processes that affect it. There are presently 161 sampling sites (see some of them at Supplementary Appendix), most of which use a standardized methodology that allows comparisons across biomes and through time. To date, there are about 1200 publications associated with PPBio that cover topics ranging from natural history to genetics and species distributions. Most of the field data and metadata are available through PPBio web sites or DataONE. Metadata is available for researchers that intend to explore the different faces of Brazilian biodiversity spatio-temporal variation, as well as for managers intending to improve conservation strategies. The Program also fostered, directly and indirectly, local technical capacity building, and supported the training of hundreds of undergraduate and graduate students. The main challenge is maintaining the long-term funding necessary to understand biodiversity patterns and processes under pressure from global environmental changes

The impact of viral mutations on recognition by SARS-CoV-2 specific T cells.

We identify amino acid variants within dominant SARS-CoV-2 T cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T cell responsiveness was seen due to Q213K in the A∗01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215; due to P13L, P13S, and P13T in the B∗27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17; and due to T362I and P365S in the A∗03:01/A∗11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T cell lines unable to recognize variant epitopes have diverse T cell receptor repertoires. These data demonstrate the potential for T cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T cell as well as humoral immunity.This work is supported by the UK Medical Research Council (MRC); Chinese Academy of Medical Sciences(CAMS) Innovation Fund for Medical Sciences (CIFMS), China; National Institute for Health Research (NIHR)Oxford Biomedical Research Centre, and UK Researchand Innovation (UKRI)/NIHR through the UK Coro-navirus Immunology Consortium (UK-CIC). Sequencing of SARS-CoV-2 samples and collation of data wasundertaken by the COG-UK CONSORTIUM. COG-UK is supported by funding from the Medical ResearchCouncil (MRC) part of UK Research & Innovation (UKRI),the National Institute of Health Research (NIHR),and Genome Research Limited, operating as the Wellcome Sanger Institute. T.I.d.S. is supported by a Well-come Trust Intermediate Clinical Fellowship (110058/Z/15/Z). L.T. is supported by the Wellcome Trust(grant number 205228/Z/16/Z) and by theUniversity of Liverpool Centre for Excellence in Infectious DiseaseResearch (CEIDR). S.D. is funded by an NIHR GlobalResearch Professorship (NIHR300791). L.T. and S.C.M.are also supported by the U.S. Food and Drug Administration Medical Countermeasures Initiative contract75F40120C00085 and the National Institute for Health Research Health Protection Research Unit (HPRU) inEmerging and Zoonotic Infections (NIHR200907) at University of Liverpool inpartnership with Public HealthEngland (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford.L.T. is based at the University of Liverpool. M.D.P. is funded by the NIHR Sheffield Biomedical ResearchCentre (BRC – IS-BRC-1215-20017). ISARIC4C is supported by the MRC (grant no MC_PC_19059). J.C.K.is a Wellcome Investigator (WT204969/Z/16/Z) and supported by NIHR Oxford Biomedical Research Centreand CIFMS. The views expressed are those of the authors and not necessarily those of the NIHR or MRC