Non-Linear Canonical Transformations in Classical and Quantum Mechanics

$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations affect $p$-mechanical observables and states. Using this we show how canonical transformations change a quantum mechanical system. We seek an operator on the set of $p$-mechanical observables which corresponds to the classical canonical transformation. In order to do this we derive a set of integral equations which when solved will give us the coherent state expansion of this operator. The motivation for these integral equations comes from the work of Moshinsky and a variety of collaborators. We consider a number of examples and discuss the use of these equations for non-bijective transformations.Comment: The paper has been improved in light of a referee's report. The paper will appear in the Journal of Mathematical Physics. 24 pages, no figure

Small oscillations and the Heisenberg Lie algebra

The Adler Kostant Symes [A-K-S] scheme is used to describe mechanical systems for quadratic Hamiltonians of $\mathbb R^{2n}$ on coadjoint orbits of the Heisenberg Lie group. The coadjoint orbits are realized in a solvable Lie algebra $\mathfrak g$ that admits an ad-invariant metric. Its quadratic induces the Hamiltonian on the orbits, whose Hamiltonian system is equivalent to that one on $\mathbb R^{2n}$. This system is a Lax pair equation whose solution can be computed with help of the Adjoint representation. For a certain class of functions, the Poisson commutativity on the coadjoint orbits in $\mathfrak g$ is related to the commutativity of a family of derivations of the 2n+1-dimensional Heisenberg Lie algebra $\mathfrak h_n$. Therefore the complete integrability is related to the existence of an n-dimensional abelian subalgebra of certain derivations in $\mathfrak h_n$. For instance, the motion of n-uncoupled harmonic oscillators near an equilibrium position can be described with this setting.Comment: 17 pages, it contains a theory about small oscillations in terms of the AKS schem

A Quantum-Classical Brackets from p-Mechanics

We provide an answer to the long standing problem of mixing quantum and classical dynamics within a single formalism. The construction is based on p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and classical dynamics from the representation theory of the Heisenberg group. To achieve a quantum-classical mixing we take the product of two copies of the Heisenberg group which represent two different Planck's constants. In comparison with earlier guesses our answer contains an extra term of analytical nature, which was not obtained before in purely algebraic setup. Keywords: Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, representation theory, Planck's constant, quantum-classical mixingComment: LaTeX, 7 pages (EPL style), no figures; v2: example of dynamics with two different Planck's constants is added, minor corrections; v3: major revion, a complete example of quantum-classic dynamics is given; v4: few grammatic correction

Elevated Paracellular Glucose Flux across Cystic Fibrosis Airway Epithelial Monolayers Is an Important Factor for Pseudomonas aeruginosa Growth.

People with cystic fibrosis (CF) who develop related diabetes (CFRD) have accelerated pulmonary decline, increased infection with antibiotic-resistant Pseudomonas aeruginosa and increased pulmonary exacerbations. We have previously shown that glucose concentrations are elevated in airway surface liquid (ASL) of people with CF, particularly in those with CFRD. We therefore explored the hypotheses that glucose homeostasis is altered in CF airway epithelia and that elevation of glucose flux into ASL drives increased bacterial growth, with an effect over and above other cystic fibrosis transmembrane conductance regulator (CFTR)-related ASL abnormalities. The aim of this study was to compare the mechanisms governing airway glucose homeostasis in CF and non-CF primary human bronchial epithelial (HBE) monolayers, under normal conditions and in the presence of Ps. aeruginosa filtrate. HBE-bacterial co-cultures were performed in the presence of 5 mM or 15 mM basolateral glucose to investigate how changes in blood glucose, such as those seen in CFRD, affects luminal Ps. aeruginosa growth. Calu-3 cell monolayers were used to evaluate the potential importance of glucose on Ps. aeruginosa growth, in comparison to other hallmarks of the CF ASL, namely mucus hyperviscosity and impaired CFTR-dependent fluid secretions. We show that elevation of basolateral glucose promotes the apical growth of Ps. aeruginosa on CF airway epithelial monolayers more than non-CF monolayers. Ps. aeruginosa secretions elicited more glucose flux across CF airway epithelial monolayers compared to non-CF monolayers which we propose increases glucose availability in ASL for bacterial growth. In addition, elevating basolateral glucose increased Ps. aeruginosa growth over and above any CFTR-dependent effects and the presence or absence of mucus in Calu-3 airway epithelia-bacteria co-cultures. Together these studies highlight the importance of glucose as an additional factor in promoting Ps. aeruginosa growth and respiratory infection in CF disease

CK2 is a key regulator of SLC4A2-mediated Cl-/HCO3 (-) exchange in human airway epithelia

Transepithelial bicarbonate secretion by human airway submucosal glands and surface epithelial cells is crucial to maintain the pH-sensitive innate defence mechanisms of the lung. cAMP agonists stimulate HCO3 (-) secretion via coordinated increases in basolateral HCO3 (-) influx and accumulation, as well as CFTR-dependent HCO3 (-) efflux at the luminal membrane of airway epithelial cells. Here, we investigated the regulation of a basolateral located, DIDS-sensitive, Cl-/HCO3 (-) exchanger, anion exchanger 2 (AE2; SLC4A2) which is postulated to act as an acid loader, and therefore potential regulator of HCO3 (-) secretion, in human airway epithelial cells. Using intracellular pH measurements performed on Calu-3 cells, we demonstrate that the activity of the basolateral Cl-/HCO3 (-) exchanger was significantly downregulated by cAMP agonists, via a PKA-independent mechanism and also required Ca2+ and calmodulin under resting conditions. AE2 contains potential phosphorylation sites by a calmodulin substrate, protein kinase CK2, and we demonstrated that AE2 activity was reduced in the presence of CK2 inhibition. Moreover, CK2 inhibition abolished the activity of AE2 in primary human nasal epithelia. Studies performed on mouse AE2 transfected into HEK-293T cells confirmed almost identical Ca2+/calmodulin and CK2 regulation to that observed in Calu-3 and primary human nasal cells. Furthermore, mouse AE2 activity was reduced by genetic knockout of CK2, an effect which was rescued by exogenous CK2 expression. Together, these findings are the first to demonstrate that CK2 is a key regulator of Cl--dependent HCO3 (-) export at the serosal membrane of human airway epithelial cells

Modality and uncertainty in data visualizations : A corpus approach to the use of connecting lines

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Recombinant Acid Ceramidase Reduces Inflammation and Infection in Cystic Fibrosis.

Rationale: In cystic fibrosis the major cause of morbidity and mortality is lung disease characterized by inflammation and infection. The influence of sphingolipid metabolism is poorly understood with a lack of studies using human airway model systems. Objectives: To investigate sphingolipid metabolism in cystic fibrosis and the effects of treatment with recombinant human acid ceramidase on inflammation and infection. Methods: Sphingolipids were measured using mass spectrometry in fully-differentiated cultures of primary human airway epithelial cells and co-cultures with Pseudomonas aeruginosa. In situ activity assays, Western blotting and quantitative polymerase chain reaction were used to investigate function and expression of ceramidase and sphingomyelinase. Effects of treatment with recombinant human acid ceramidase on sphingolipid profile and inflammatory mediator production were assessed in cell cultures and murine models. Measurements and Main Results: Ceramide is increased in cystic fibrosis airway epithelium due to differential function of enzymes regulating sphingolipid metabolism. Sphingosine, a metabolite of ceramide with antimicrobial properties, is not upregulated in response to Pseudomonas aeruginosa by cystic fibrosis airway epithelia. Tumor necrosis factor receptor 1 is increased in the apical membrane of cystic fibrosis epithelia and activates NF-κB signaling, generating inflammation. Treatment with recombinant human acid ceramidase, to decrease ceramide, reduced both inflammatory mediator production and susceptibility to infection. Conclusions: Sphingolipid metabolism is altered in airway epithelial cells cultured from people with cystic fibrosis. Treatment with recombinant acid ceramidase ameliorates the two pivotal features of cystic fibrosis lung disease, inflammation and infection, and thus represents a therapeutic approach worthy of further exploration. This article is open access and distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives License 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Hyperglycaemia and Pseudomonas aeruginosa acidify cystic fibrosis airway surface liquid by elevating epithelial monocarboxylate transporter 2 dependent lactate-H⁺ secretion

The cystic fibrosis (CF) airway surface liquid (ASL) provides a nutrient rich environment for bacterial growth including elevated glucose, which together with defective bacterial killing due to aberrant HCO3− transport and acidic ASL, make the CF airways susceptible to colonisation by respiratory pathogens such as Pseudomonas aeruginosa. Approximately half of adults with CF have CF related diabetes (CFRD) and this is associated with increased respiratory decline. CF ASL contains elevated lactate concentrations and hyperglycaemia can also increase ASL lactate. We show that primary human bronchial epithelial (HBE) cells secrete lactate into ASL, which is elevated in hyperglycaemia. This leads to ASL acidification in CFHBE, which could only be mimicked in non-CF HBE following HCO3− removal. Hyperglycaemia-induced changes in ASL lactate and pH were exacerbated by the presence of P. aeruginosa and were attenuated by inhibition of monocarboxylate lactate-H+ co-transporters (MCTs) with AR-C155858. We conclude that hyperglycaemia and P. aeruginosa induce a metabolic shift which increases lactate generation and efflux into ASL via epithelial MCT2 transporters. Normal airways compensate for MCT-driven H+ secretion by secreting HCO3−, a process which is dysfunctional in CF airway epithelium leading to ASL acidification and that these processes may contribute to worsening respiratory disease in CFRD

Unsupervised home spirometry is not equivalent to supervised clinic spirometry in children and young people with cystic fibrosis: results from the CLIMB-CF study

BACKGROUND: Handheld spirometry allows monitoring of lung function at home, of particular importance during the COVID-19 pandemic. Pediatric studies are unclear on whether values are interchangeable with traditional, clinic-based spirometry. We aimed to assess differences between contemporaneous, home (unsupervised) and clinic (supervised) spirometry and the variability of the former. The accuracy of the commercially available spirometer used in the study was also tested. METHODS: Data from participants in the Clinical Monitoring and Biomarkers to stratify severity and predict outcomes in children with cystic fibrosisc (CLIMB-CF) Study aged ≥ 6 years who had paired (±1 day) clinic and home forced expiratory volume in 1 s (FEV1 ) readings were analyzed. Variability during clinical stability over 6-months was assessed. Four devices from Vitalograph were tested using 1 and 3 L calibration syringes. RESULTS: Sixty-seven participants (median [interquartile range] age 10.7 [7.6-13.9] years) provided home and clinic FEV1 data pairs. The mean (SD) FEV1 % bias was 6.5% [±8.2%]) with wide limits of agreement (-9.6% to +22.7%); 76.2% of participants recorded lower results at home. Coefficient of variation of home FEV1 % during stable periods was 9.9%. Data from the testing of the handheld device used in CLIMB-CF showed a potential underread. CONCLUSION: In children and adolescents, home spirometry using hand-held equipment cannot be used interchangeably with clinic spirometry. Home spirometry is moderately variable during clinical stability. New handheld devices underread, particularly at lower volumes of potential clinical significance for smaller patients; this suggests that supervision does not account fully for the discrepancy. Opportunities should be taken to obtain dual device measurements in clinic, so that trend data from home can be utilized more accurately