An atlas for tridiagonal isospectral manifolds

Let ${\cal T}_\Lambda$ be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix $\Lambda$ with simple spectrum. We introduce {\it bidiagonal coordinates}, charts defined on open dense domains forming an explicit atlas for ${\cal T}_\Lambda$. In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, every matrix in ${\cal T}_\Lambda$ now lies in the interior of some chart domain. We provide examples of the convenience of these new coordinates for the study of asymptotics of isospectral dynamics, both for continuous and discrete time.Comment: Fixed typos; 16 pages, 3 figure

Le risque de vivre

Myocardial constitutive No production depends on the activity of both endothelial and neuronal NOS (eNOS and nNOS, respectively). Stimulation of myocardial β(3)-adrenergic receptor (β(3)-AR) produces a negative inotropic effect that is dependent on eNOS. We evaluated whether nNOS also plays a role in β(3)-AR signaling and found that the β(3)-AR-mediated reduction in cell shortening and [Ca(2+)](i) transient amplitude was abolished both in eNOS(−/−) and nNOS(−/−) left ventricular (LV) myocytes and in wild type LV myocytes after nNOS inhibition with S-methyl-l-thiocitrulline. LV superoxide (O(2)(˙̄)) production was increased in nNOS(−/−) mice and reduced by l-N(ω)-nitroarginine methyl ester (l-NAME), indicating uncoupling of eNOS activity. eNOS S-glutathionylation and Ser-1177 phosphorylation were significantly increased in nNOS(−/−) myocytes, whereas myocardial tetrahydrobiopterin, eNOS Thr-495 phosphorylation, and arginase activity did not differ between genotypes. Although inhibitors of xanthine oxidoreductase (XOR) or NOX2 NADPH oxidase caused a similar reduction in myocardial O(2)(˙̄), only XOR inhibition reduced eNOS S-glutathionylation and Ser-1177 phosphorylation and restored both eNOS coupled activity and the negative inotropic and [Ca(2+)](i) transient response to β(3)-AR stimulation in nNOS(−/−) mice. In summary, our data show that increased O(2)(˙̄) production by XOR selectively uncouples eNOS activity and abolishes the negative inotropic effect of β(3)-AR stimulation in nNOS(−/−) myocytes. These findings provide unequivocal evidence of a functional interaction between the myocardial constitutive NOS isoforms and indicate that aspects of the myocardial phenotype of nNOS(−/−) mice result from disruption of eNOS signaling

Endothelial cell-specific roles for tetrahydrobiopterin in myocardial function, cardiac hypertrophy, and response to myocardial ischemia-reperfusion injury

The cofactor tetrahydrobiopterin (BH4) is a critical regulator of nitric oxide synthase (NOS) function and redox signaling, with reduced BH4 implicated in multiple cardiovascular disease states. In the myocardium, augmentation of BH4 levels can impact on cardiomyocyte function, preventing hypertrophy and heart failure. However, the specific role of endothelial cell BH4 biosynthesis in the coronary circulation and its role in cardiac function and the response to ischemia has yet to be elucidated. Endothelial cell-specific Gch1 knockout mice were generated by crossing Gch1fl/fl with Tie2cre mice, generating Gch1fl/flTie2cre mice and littermate controls. GTP cyclohydrolase protein and BH4 levels were reduced in heart tissues from Gch1fl/flTie2cre mice, localized to endothelial cells, with normal cardiomyocyte BH4. Deficiency in coronary endothelial cell BH4 led to NOS uncoupling, decreased NO bioactivity, and increased superoxide and hydrogen peroxide productions in the hearts of Gch1fl/flTie2cre mice. Under physiological conditions, loss of endothelial cell-specific BH4 led to mild cardiac hypertrophy in Gch1fl/flTie2cre hearts. Endothelial cell BH4 loss was also associated with increased neuronal NOS protein, loss of endothelial NOS protein, and increased phospholamban phosphorylation at serine-17 in cardiomyocytes. Loss of cardiac endothelial cell BH4 led to coronary vascular dysfunction, reduced functional recovery, and increased myocardial infarct size following ischemia-reperfusion injury. Taken together, these studies reveal a specific role for endothelial cell Gch1/BH4 biosynthesis in cardiac function and the response to cardiac ischemia-reperfusion injury. Targeting endothelial cell Gch1 and BH4 biosynthesis may provide a novel therapeutic target for the prevention and treatment of cardiac dysfunction and ischemia-reperfusion injury. NEW & NOTEWORTHY We demonstrate a critical role for endothelial cell Gch1/BH4 biosynthesis in coronary vascular function and cardiac function. Loss of cardiac endothelial cell BH4 leads to coronary vascular dysfunction, reduced functional recovery, and increased myocardial infarct size following ischemia/reperfusion injury. Targeting endothelial cell Gch1 and BH4 biosynthesis may provide a novel therapeutic target for the prevention and treatment of cardiac dysfunction, ischemia injury, and heart failure

Geographic differences between functional groups in patterns of bird species richness in North America

Geographic divergences in patterns of species richness were studied for the terrestrial birds of North America using Breeding Bird Survey (BBS) census data subdivided for guild and migratory groups. Our aim was to study if species richness patterns for North American birds were best viewed as the convergent response of different groups to a common mechanism or as the result of several different processes. We observed opposite geographical patterns of species richness and differences in the variables associated with species richness depending on the guild or migratory status considered. Several ecological variables seem to regulate large-scale patterns of terrestrial bird species richness in North America, mainly temperature-, productivity- and landscape habitat structure-related variables. These variables are diverse and group-specific. For instance, the results supported the productivity hypothesis in migratory and frugivore groups and the winter tolerance hypothesis in residents. Habitat structure was also identified as an important factor driving species richness, total abundance and community body mass variation. Overall, our results indicate that the large-scale patterns of bird species richness are the result of several divergent, group-specific processes, and that understanding diversity gradients requires the identification of the functional ecological groups included. © 2008 Elsevier Masson SAS. All rights reserved.Peer Reviewe

Correction: Fast, quantitative, murine cardiac 19F MRI/MRS of PFCE-labeled progenitor stem cells and macrophages at 9.4T.

[This corrects the article DOI: 10.1371/journal.pone.0190558.]

Evaluation of the role of miR-31-dependent reduction in dystrophin and nNOS on atrial-fibrillation-induced electrical remodelling in man

The management of atrial fibrillation remains a challenge. This condition remodels atrial electrical properties, which promote resistance to treatment. Although remodelling has long been a therapeutic target in atrial fibrillation, its causes remain incompletely understood. We aimed to evaluate the role of miR-31-dependent reduction in dystrophin and neuronal nitric oxide synthase (nNOS, also known as NOS1) on atrial electrical properties and atrial fibrillation inducibility.We recruited 258 patients (209 patients in sinus rhythm and 49 with permanent atrial fibrillation) from the John Radcliffe Hospital, Oxford, UK; written informed consent was obtained from each participant. We also used a goat model of pacing-induced atrial fibrillation (24 with atrial fibrillation vs 20 controls in normal sinus rythm) and nNos-knock-out mice (n=28 compared with 27 wild-type littermates). Gene expression of miR-31, dystrophin, and nNOS was assessed by quantitative RT-PCR; protein content was measured by immunoblotting; NOS activity was evaluated with high-performance liquid chromatography; action potential duration (APD) and rate dependent adaptation were assessed by single-cell patch-clamping, and atrial fibrillation inducibility was evaluated by transoesophageal atrial burst stimulation.We found that atrial-specific upregulation of miR-31 in human atrial fibrillation caused dystrophin (DYS) translational repression and accelerated mRNA degradation of nNOS leading to a profound reduction in atrial DYS and nNOS protein content and in nitric oxide availability. In human atrial myocytes obtained from patients in sinus rhythm, nNOS inhibition was sufficient to recapitulate hallmark features of remodelling induced by atrial fibrillation, such as shortening of APD and loss of APD rate-dependency, but had no effect in patients with atrial fibrillation. In mice, nNos gene deletion or inhibition shortened atrial APD and increased atrial fibrillation inducibility in vivo. Inhibition of miR-31 in human atrial fibrillation recovered DYS and nNOS, and normalised APD and APD rate-dependency. Prevention of miR-31 binding to nNOS 3'UTR recovered both nNOS protein and gene expression but had no effect on the DYS protein or mRNA level (consistent with the mRNA degradation of nNOS by miR-31). Prevention of miR-31 binding to DYS 3'UTR increased DYS protein but not mRNA is consistent with translation repression of DYS by miR-31; recovery of DYS protein increased nNOS protein but not mRNA in keeping with a stabilising effect of DYS on nNOS protein. In goats, a reduction in dystrophin and nNOS protein content was associated with upregulation of miR-31 in the atria but not in the ventricles.The findings suggest that atrial-specific upregulation of miR-31 in human atrial fibrillation is a key mechanism causing atrial loss of dystrophin and nNOS; this loss leads to the electrical phenotype induced by atrial fibrillation.British Heart Foundation (BHF) Programme grant (for BC and XL), BHF Centre of Excellence in Oxford (SR), Leducq Foundation (in part for BC and SR), the European Union's seventh Framework Programme Grant Agree

Protein inhibitor of NOS1 plays a central role in the regulation of NOS1 activity in human dilated hearts

An essential factor for the production of nitric oxide by nitric oxide synthase 1 (NOS1), major modulator of cardiac function, is the cofactor tetrahydrobiopterin (BH4). BH4 is regulated by GTP cyclohydrolase 1, the rate-limiting enzyme in BH4 biosynthesis which catalyses the formation of dihydroneopterin 3′triphosfate from GTP, producing BH4 after two further steps catalyzed by 6-pyruvoyltetrahydropterin synthase and sepiapterin reductase. However, there are other essential factors involved in the regulation of NOS1 activity, such as protein inhibitor of NOS1 (PIN), calmodulin, heat shock protein 90, and NOS interacting protein. All these molecules have never been analysed in human non-ischemic dilated hearts (DCM). In this study we demonstrated that the upregulation of cardiac NOS1 is not accompanied by increased NOS1 activity in DCM, partly due to the elevated PIN levels and not because of alterations in biopterin biosynthesis. Notably, the PIN concentration was significantly associated with impaired ventricular function, highlighting the importance of this NOS1 activity inhibitor in Ca2+ homeostasis. These results take a central role in the current list of targets for future studies focused on the complex cardiac dysfunction processes through more efficient harnessing of NOS1 signalling

Protein inhibitor of NOS1 plays a central role in the regulation of NOS1 activity in human dilated hearts

An essential factor for the production of nitric oxide by nitric oxide synthase 1 (NOS1), major modulator of cardiac function, is the cofactor tetrahydrobiopterin (BH4). BH4 is regulated by GTP cyclohydrolase 1, the rate-limiting enzyme in BH4 biosynthesis which catalyses the formation of dihydroneopterin 3′triphosfate from GTP, producing BH4 after two further steps catalyzed by 6-pyruvoyltetrahydropterin synthase and sepiapterin reductase. However, there are other essential factors involved in the regulation of NOS1 activity, such as protein inhibitor of NOS1 (PIN), calmodulin, heat shock protein 90, and NOS interacting protein. All these molecules have never been analysed in human non-ischemic dilated hearts (DCM). In this study we demonstrated that the upregulation of cardiac NOS1 is not accompanied by increased NOS1 activity in DCM, partly due to the elevated PIN levels and not because of alterations in biopterin biosynthesis. Notably, the PIN concentration was significantly associated with impaired ventricular function, highlighting the importance of this NOS1 activity inhibitor in Ca2+ homeostasis. These results take a central role in the current list of targets for future studies focused on the complex cardiac dysfunction processes through more efficient harnessing of NOS1 signalling