220 research outputs found

    Maximal regularity for non-autonomous equations with measurable dependence on time

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    In this paper we study maximal LpL^p-regularity for evolution equations with time-dependent operators AA. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the LpL^p-boundedness of a class of vector-valued singular integrals which does not rely on H\"ormander conditions in the time variable. This is then used to develop an abstract operator-theoretic approach to maximal regularity. The results are applied to the case of mm-th order elliptic operators AA with time and space-dependent coefficients. Here the highest order coefficients are assumed to be measurable in time and continuous in the space variables. This results in an Lp(Lq)L^p(L^q)-theory for such equations for p,q∈(1,∞)p,q\in (1, \infty). In the final section we extend a well-posedness result for quasilinear equations to the time-dependent setting. Here we give an example of a nonlinear parabolic PDE to which the result can be applied.Comment: Application to a quasilinear equation added. Accepted for publication in Potential Analysi

    The â„“s\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

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    We prove the â„“s\ell^s-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the â„“s\ell^s-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of â„“s\ell^s-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

    Construction of Chimeric Dual-Chain Avidin by Tandem Fusion of the Related Avidins

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    BACKGROUND: Avidin is a chicken egg-white protein with high affinity to vitamin H, also known as D-biotin. Many applications in life science research are based on this strong interaction. Avidin is a homotetrameric protein, which promotes its modification to symmetrical entities. Dual-chain avidin, a genetically engineered avidin form, has two circularly permuted chicken avidin monomers that are tandem-fused into one polypeptide chain. This form of avidin enables independent modification of the two domains, including the two biotin-binding pockets; however, decreased yields in protein production, compared to wt avidin, and complicated genetic manipulation of two highly similar DNA sequences in the tandem gene have limited the use of dual-chain avidin in biotechnological applications. PRINCIPAL FINDINGS: To overcome challenges associated with the original dual-chain avidin, we developed chimeric dual-chain avidin, which is a tandem fusion of avidin and avidin-related protein 4 (AVR4), another member of the chicken avidin gene family. We observed an increase in protein production and better thermal stability, compared with the original dual-chain avidin. Additionally, PCR amplification of the hybrid gene was more efficient, thus enabling more convenient and straightforward modification of the dual-chain avidin. When studied closer, the generated chimeric dual-chain avidin showed biphasic biotin dissociation. SIGNIFICANCE: The improved dual-chain avidin introduced here increases its potential for future applications. This molecule offers a valuable base for developing bi-functional avidin tools for bioseparation, carrier proteins, and nanoscale adapters. Additionally, this strategy could be helpful when generating hetero-oligomers from other oligomeric proteins with high structural similarity

    Validation of a Chromosome 14 Risk Haplotype for Idiopathic Epilepsy in the Belgian Shepherd Dog Found to Be Associated with an Insertion in the RAPGEF5 Gene

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    An idiopathic epilepsy (IE) risk haplotype on canine chromosome (CFA) 14 has been reported to interact with the CFA37 common risk haplotype in the Belgian shepherd (BS). Additional IE cases and control dogs were genotyped for the risk haplotypes to validate these previous findings. In the new cohort, the interaction between the two regions significantly elevated IE risk. When the haplotypes were analyzed individually, particular haplotypes on both CFA14 (ACTG) and 37 (GG) were associated with elevated IE risk, though only the CFA37 AA was significantly associated (p < 0.003) with reduced risk in the new cohort. However, the CFA14 ACTG risk was statistically significant when the new and previous cohort data were combined. The frequency of the ACTG haplotype was four-fold higher in BS dogs than in other breeds. Whole genome sequence analysis revealed that a 3-base pair predicted disruptive insertion in the RAPGEF5 gene, which is adjacent to the CFA14 risk haplotype. RAPGEF5 is involved in the Wnt-β-catenin signaling pathway that is crucial for normal brain function. Although this risk variant does not fully predict the likelihood of a BS developing IE, the association with a variant in a candidate gene may provide insight into the genetic control of canine IE

    Novel Locus Associated with Symmetrical Lupoid Onychodystrophy in the Bearded Collie

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    Symmetrical lupoid onychodystrophy (SLO) is characterized by inflammation of the nail bed and nail sloughing that causes affected dogs considerable pain. Disease etiology remains unclear, although an autoimmune component is suspected. A genome-wide association study on Bearded Collies revealed regions of association on canine chromosomes (CFA) 12 and 17. The large region of association on CFA12 likely consists of two smaller linked regions, both of which are also linked to the dog leukocyte antigen (DLA) class II genes. Dogs homozygous for the alternate allele at the top CFA12 SNP also carried two DLA class II risk haplotypes for SLO, and this locus explained most of the increased risk for disease seen throughout the CFA12 region of association. A stronger peak was seen on CFA17 when analysis was done solely on dogs that carried DLA class II risk haplotypes for SLO. The majority of SLO dogs carried a homozygous alternate genotype on CFA12 and at least one CFA17 risk haplotype. Our findings offer progress toward uncovering the genetic basis of SLO. While the contribution of the CFA17 region remains unclear, both CFA12 and CFA17 regions are significantly associated with SLO disease expression in the Bearded Collie and contain potential candidate genes for this disease.Peer reviewe

    Correction to: Genetic characterization of Addison’s disease in Bearded Collies

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    An amendment to this paper has been published and can be accessed via the original article
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