Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with $3/p+2/q\leq 2$, $1\leq q\leq \infty$, or the $L^{p,q}_{x,t}$-norm of the vorticity with $3/p+2/q\leq 3$, $1 \leq q < \infty$, or the $L^{p,q}_{x,t}$-norm of the gradient of the vorticity with $3/p+2/q\leq 4$, $1 \leq q$, $1 \leq p$, is sufficiently small near $z$

Water and ion permeation of aquaporin-1 in planar lipid bilayers. Major differences in structural determinants and stoichiometry.

The aquaporin-1 (AQP1) water channel protein is known to facilitate the rapid movement of water across cell membranes, but a proposed secondary role as an ion channel is still unsettled. Here we describe a method to simultaneously measure water permeability and ion conductance of purified human AQP1 after reconstitution into planar lipid bilayers. Water permeability was determined by measuring Na(+) concentrations adjacent to the membrane. Comparisons with the known single channel water permeability of AQP1 indicate that the planar lipid bilayers contain from 10(6) to 10(7) water channels. Addition of cGMP induced ion conductance in planar bilayers containing AQP1, whereas cAMP was without effect. The number of water channels exceeded the number of active ion channels by approximately 1 million-fold, yet p-chloromethylbenzenesulfonate inhibited the water permeability but not ion conductance. Identical ion channel parameters were achieved with AQP1 purified from human red blood cells or AQP1 heterologously expressed in Saccharomyces cerevisae and affinity purified with either N- or C-terminal poly-histidine tags. Rp-8-Br-cGMP inhibited all of the observed conductance levels of the cation selective channel (2, 6, and 10 pS in 100 mm Na(+) or K(+)). Deletion of the putative cGMP binding motif at the C terminus by introduction of a stop codon at position 237 yielded a truncated AQP1 protein that was still permeated by water but not by ions. Our studies demonstrate a method for simultaneously measuring water permeability and ion conductance of AQP1 reconstituted into planar lipid bilayers. The ion conductance occurs (i) through a pathway distinct from the aqueous pathway, (ii) when stimulated directly by cGMP, and (iii) in only an exceedingly small fraction of AQP1 molecules

Generalised Gagliardo–Nirenberg inequalities using weak Lebesgue spaces and BMO

Using elementary arguments based on the Fourier transform we prove that for $1 \leq q n(1/2-1/p)$, if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^s(\R^n)$ then $f \in L^p(\R^n)$ and there exists a constant $c_{p,q,s}$ such that $$\|f\|_{L^p} \leq c_{p,q,s} \|f\|_{L^{q,\infty}}^\theta \|f\|_{\dot H^s}^{1-\theta},$$ where $1/p = \theta/q + (1-\theta)(1/2-s/n)$. In particular, in $\R^2$ we obtain the generalised Ladyzhenskaya inequality $\|f\|_{L^4}\le c\|f\|_{L^{2,\infty}}^{1/2}\|f\|_{\dot H^1}^{1/2}$. We also show that for $s=n/2$ the norm in $\|f\|_{\dot H^{n/2}}$ can be replaced by the norm in BMO. As well as giving relatively simple proofs of these inequalities, this paper provides a brief primer of some basic concepts in harmonic analysis, including weak spaces, the Fourier transform, the Lebesgue Differentiation Theorem, and Calderon-Zygmund decompositions

Genome-wide shRNA screen revealed integrated mitogenic signaling between dopamine receptor D2 (DRD2) and epidermal growth factor receptor (EGFR) in glioblastoma

Glioblastoma remains one of the deadliest of human cancers, with most patients succumbing to the disease within two years of diagnosis. The available data suggest that simultaneous inactivation of critical nodes within the glioblastoma molecular circuitry will be required for meaningful clinical efficacy. We conducted parallel genome-wide shRNA screens to identify such nodes and uncovered a number of G-Protein Coupled Receptor (GPCR) neurotransmitter pathways, including the Dopamine Receptor D2 (DRD2) signaling pathway. Supporting the importance of DRD2 in glioblastoma, DRD2 mRNA and protein expression were elevated in clinical glioblastoma specimens relative to matched non-neoplastic cerebrum. Treatment with independent si-/shRNAs against DRD2 or with DRD2 antagonists suppressed the growth of patient-derived glioblastoma lines both in vitro and in vivo. Importantly, glioblastoma lines derived from independent genetically engineered mouse models (GEMMs) were more sensitive to haloperidol, an FDA approved DRD2 antagonist, than the premalignant astrocyte lines by approximately an order of magnitude. The pro-proliferative effect of DRD2 was, in part, mediated through a GNAI2/Rap1/Ras/ERK signaling axis. Combined inhibition of DRD2 and Epidermal Growth Factor Receptor (EGFR) led to synergistic tumoricidal activity as well as ERK suppression in independent in vivo and in vitro glioblastoma models. Our results suggest combined EGFR and DRD2 inhibition as a promising strategy for glioblastoma treatment

Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

This paper establishes the local-in-time existence and uniqueness of strong solutions in Hs for s > n/2 to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rn, n = 2, 3, as well as for a related model where the advection terms are removed from the velocity equation. The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato & Ponce (Comm. Pure Appl. Math. 41(7), 891–907, 1988)

An IRAK1-PIN1 signalling axis drives intrinsic tumour resistance to radiation therapy

Drug-based strategies to overcome tumour resistance to radiotherapy (R-RT) remain limited by the single-agent toxicity of traditional radiosensitizers (for example, platinums) and a lack of targeted alternatives. In a screen for compounds that restore radiosensitivity in p53 mutant zebrafish while tolerated in non-irradiated wild-type animals, we identified the benzimidazole anthelmintic oxfendazole. Surprisingly, oxfendazole acts via the inhibition of IRAK1, a kinase thus far implicated in interleukin-1 receptor (IL-1R) and Toll-like receptor (TLR) immune responses. IRAK1 drives R-RT in a pathway involving IRAK4 and TRAF6 but not the IL-1R/TLR-IRAK adaptor MyD88. Rather than stimulating nuclear factor-κB, radiation-activated IRAK1 prevented apoptosis mediated by the PIDDosome complex (comprising PIDD, RAIDD and caspase-2). Countering this pathway with IRAK1 inhibitors suppressed R-RT in tumour models derived from cancers in which TP53 mutations predict R-RT. Moreover, IRAK1 inhibitors synergized with inhibitors of PIN1, a prolyl isomerase essential for IRAK1 activation in response to pathogens and, as shown here, in response to ionizing radiation. These data identify an IRAK1 radiation-response pathway as a rational chemoradiation therapy target

Circulating miR-29a and miR-150 correlate with delivered dose during thoracic radiation therapy for non-small cell lung cancer

Background: Risk of normal tissue toxicity limits the amount of thoracic radiation therapy (RT) that can be routinely prescribed to treat non-small cell lung cancer (NSCLC). An early biomarker of response to thoracic RT may provide a way to predict eventual toxicities—such as radiation pneumonitis—during treatment, thereby enabling dose adjustment before the symptomatic onset of late effects. MicroRNAs (miRNAs) were studied as potential serological biomarkers for thoracic RT. As a first step, we sought to identify miRNAs that correlate with delivered dose and standard dosimetric factors. Methods: We performed miRNA profiling of plasma samples obtained from five patients with Stage IIIA NSCLC at five dose-points each during radical thoracic RT. Candidate miRNAs were then assessed in samples from a separate cohort of 21 NSCLC patients receiving radical thoracic RT. To identify a cellular source of circulating miRNAs, we quantified in vitro miRNA expression intracellularly and within secreted exosomes in five NSCLC and stromal cell lines. Results: miRNA profiling of the discovery cohort identified ten circulating miRNAs that correlated with delivered RT dose as well as other dosimetric parameters such as lung V20. In the validation cohort, miR-29a-3p and miR-150-5p were reproducibly shown to decrease with increasing radiation dose. Expression of miR-29a-3p and miR-150-5p in secreted exosomes decreased with radiation. This was concomitant with an increase in intracellular levels, suggesting that exosomal export of these miRNAs may be downregulated in both NSCLC and stromal cells in response to radiation. Conclusions: miR-29a-3p and miR-150-5p were identified as circulating biomarkers that correlated with delivered RT dose. miR-150 has been reported to decrease in the circulation of mammals exposed to radiation while miR-29a has been associated with fibrosis in the human heart, lungs, and kidneys. One may therefore hypothesize that outlier levels of circulating miR-29a-3p and miR-150-5p may eventually help predict unexpected responses to radiation therapy, such as toxicity. Electronic supplementary material The online version of this article (doi:10.1186/s13014-016-0636-4) contains supplementary material, which is available to authorized users