Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Optimisation of exposure parameters for spinal curvature measurements in paediatric radiography

This review aims to identify strategies to optimise radiography practice using digital technologies, for full spine studies on paediatrics focusing particularly on methods used to diagnose and measure severity of spinal curvatures. The literature search was performed on different databases (PubMed, Google Scholar and ScienceDirect) and relevant websites (e.g., American College of Radiology and International Commission on Radiological Protection) to identify guidelines and recent studies focused on dose optimisation in paediatrics using digital technologies. Plain radiography was identified as the most accurate method. The American College of Radiology (ACR) and European Commission (EC) provided two guidelines that were identified as the most relevant to the subject. The ACR guidelines were updated in 2014; however these guidelines do not provide detailed guidance on technical exposure parameters. The EC guidelines are more complete but are dedicated to screen film systems. Other studies provided reviews on the several exposure parameters that should be included for optimisation, such as tube current, tube voltage and source-to-image distance; however, only explored few of these parameters and not all of them together. One publication explored all parameters together but this was for adults only. Due to lack of literature on exposure parameters for paediatrics, more research is required to guide and harmonise practice.

Optimisation of paediatrics computed radiography for full spine curvature measurements using a phantom: a pilot study

Aim: Optimise a set of exposure factors, with the lowest effective dose, to delineate spinal curvature with the modified Cobb method in a full spine using computed radiography (CR) for a 5-year-old paediatric anthropomorphic phantom. Methods: Images were acquired by varying a set of parameters: positions (antero-posterior (AP), posteroanterior (PA) and lateral), kilo-voltage peak (kVp) (66-90), source-to-image distance (SID) (150 to 200cm), broad focus and the use of a grid (grid in/out) to analyse the impact on E and image quality (IQ). IQ was analysed applying two approaches: objective [contrast-to-noise-ratio/(CNR] and perceptual, using 5 observers. Monte-Carlo modelling was used for dose estimation. Cohen’s Kappa coefficient was used to calculate inter-observer-variability. The angle was measured using Cobb’s method on lateral projections under different imaging conditions. Results: PA promoted the lowest effective dose (0.013 mSv) compared to AP (0.048 mSv) and lateral (0.025 mSv). The exposure parameters that allowed lower dose were 200cm SID, 90 kVp, broad focus and grid out for paediatrics using an Agfa CR system. Thirty-seven images were assessed for IQ and thirty-two were classified adequate. Cobb angle measurements varied between 16°±2.9 and 19.9°±0.9. Conclusion: Cobb angle measurements can be performed using the lowest dose with a low contrast-tonoise ratio. The variation on measurements for this was ±2.9° and this is within the range of acceptable clinical error without impact on clinical diagnosis. Further work is recommended on improvement to the sample size and a more robust perceptual IQ assessment protocol for observers.

Fatigue life assessment of endodontic instruments subjected to multi planar curvature

This present study aimed to investigate the fatigue life of unused (new) endodontic instruments made of NiTi with control memory by Coltene™ and subjected to the multi curvature of a mandibular first molar root canal. Additionally, the instrument‟s structural behaviour was analysed through non-linear finite element analysis (FEA). The fatigue life of twelve Hyflex™ CM files was assessed while were forced to adopt a stance with multiple radius of curvature, similar to the ones usually found in a mandibular first molar root canal; nine of them were subjected to Pecking motion, a relative movement of axial type. To achieve this, it was designed an experimental setup with the aim of timing the instruments until fracture while worked inside a stainless steel mandibular first molar model with relative axial motion to simulate the pecking motion. Additionally, the model‟s root canal multi-curvature was confirmed by radiography. The non-linear finite element analysis was conducted using the computer aided design software package SolidWorks™ Simulation, in order to define the imposed displacement required by the FEA, it was necessary to model an endodontic instrument with simplified geometry using SolidWorks™ and subsequently analyse the geometry of the root canal CAD model. The experimental results shown that the instruments subjected to pecking motion displayed higher fatigue life values and higher lengths of fractured tips than those with only rotational relative movement. The finite element non-linear analyses shown, for identical conditions, maximum values for the first principal stress lower than the yield strength of the material and those were located in similar positions to the instrument‟s fracture location determined by the experimental testing results.

Rol de motores moleculares y tráfico vesicular en el establecimiento de la polaridad neuronal. Molecular motors and vesicle trafficking role in neuronal polarity establishment.

En los últimos años se ha establecido que un gran número de enfermedades neurodegenerativas están asociadas a defectos en el transporte vesicular, particularmente aquel mediado por motores moleculares y proteínas quinasas, estando directamente relacionado al establecimiento y mantenimiento de la polaridad neuronal.El estudio de los mecanismos moleculares que regulan la formación y diferenciación de dendritas, especialmente a nivel del tráfico de organelas túbulo-vesiculares, nos permitirá entender el papel de los motores moleculares retrógrados y de las proteínas quinasas en el establecimiento de la polaridad neuronal, evento crucial para el mantenimiento y función del sistema nervioso.Para ello contamos con las herramientas necesarias para el estudio del transporte de proteínas a nivel molecular y celular, como cDNAs para expresar varias proteínas de estudio, siRNAs para bloquear la expresión de proteínas específicas, dominantes negativos y constitutivamente activos de algunos de los componentes a analizar, así como anticuerpos que nos permitan monitorear su localización celular, para lo cual contamos con equipos de microscopía de última generación.Es de esperar que se obtengan resultados que confirmen el papel específico de motores retrógrados, como dineína, y quinasas de las familias C y D, en el transporte de proteínas de membrana al compartimiento somato-dendrítico, demostrando su importancia en el establecimiento de la polaridad neuronal. Entender el desarrollo y el mantenimiento de esta polaridad axón-dendrita es de vital importancia, tanto para incrementar el conocimiento del funcionamiento y la biología del sistema nervioso, como para comprender aquellos mecanismos que se desarrollan en ciertas enfermedades neurodegenerativas y neuropsiquiátricas.

Assessing the role of Piccolo and Bassoon zinc finger domains on synapse vesicle recycling and maintenance

Magdeburg, Univ., Fak. für Naturwiss., Diss., 2013

Smoothing singularities of Riemannian metrics while preserving lower curvature bounds

Magdeburg, Univ., Fak. für Mathematik, Diss., 2014

Synaptobrevin N-terminally bound to syntaxin-SNAP-25 defines the primed vesicle state in regulated exocytosis.

Rapid neurotransmitter release depends on the ability to arrest the SNAP receptor (SNARE)-dependent exocytosis pathway at an intermediate "cocked" state, from which fusion can be triggered by Ca(2+). It is not clear whether this state includes assembly of synaptobrevin (the vesicle membrane SNARE) to the syntaxin-SNAP-25 (target membrane SNAREs) acceptor complex or whether the reaction is arrested upstream of that step. In this study, by a combination of in vitro biophysical measurements and time-resolved exocytosis measurements in adrenal chromaffin cells, we find that mutations of the N-terminal interaction layers of the SNARE bundle inhibit assembly in vitro and vesicle priming in vivo without detectable changes in triggering speed or fusion pore properties. In contrast, mutations in the last C-terminal layer decrease triggering speed and fusion pore duration. Between the two domains, we identify a region exquisitely sensitive to mutation, possibly constituting a switch. Our data are consistent with a model in which the N terminus of the SNARE complex assembles during vesicle priming, followed by Ca(2+)-triggered C-terminal assembly and membrane fusion.

Rest/nrsf governs the expression of dense-core vesicle gliosecretion in astrocytes

Astrocytes are the brain nonnerve cells that are competent for gliosecretion, i.e., for expression and regulated exocytosis of clear and dense-core vesicles (DCVs). We investigated whether expression of astrocyte DCVs is governed by RE-1-silencing transcription factor (REST)/neuron-restrictive silencer factor, the transcription repressor that orchestrates nerve cell differentiation. Rat astrocyte cultures exhibited high levels of REST and expressed neither DCVs nor their markers (granins, peptides, and membrane proteins). Transfection of dominant-negative construct of REST induced the appearance of DCVs filled with secretogranin 2 and neuropeptide Y (NPY) and distinct from other organelles. Total internal reflection fluorescence analysis revealed NPY-monomeric red fluorescent protein-labeled DCVs to undergo Ca21 -dependent exocytosis, which was largely prevented by botulinum toxin B. In the I-II layers of the human temporal brain cortex, all neurons and microglia exhibited the expected inappreciable and high levels of REST, respectively. In contrast, astrocyte RESTwas variable, going from inappreciable to high, and accompanied by a variable expression of DCVs. In conclusion, astrocyte DCV expression and gliosecretion are governed by REST. The variable in situ REST levels may contribute to the wellknown structural/ functional heterogeneity of astrocytes.

Phosphatidylinositol 4,5-bisphosphate clusters act as molecular beacons for vesicle recruitment.

Synaptic-vesicle exocytosis is mediated by the vesicular Ca(2+) sensor synaptotagmin-1. Synaptotagmin-1 interacts with the SNARE protein syntaxin-1A and acidic phospholipids such as phosphatidylinositol 4,5-bisphosphate (PIP2). However, it is unclear how these interactions contribute to triggering membrane fusion. Using PC12 cells from Rattus norvegicus and artificial supported bilayers, we show that synaptotagmin-1 interacts with the polybasic linker region of syntaxin-1A independent of Ca(2+) through PIP2. This interaction allows both Ca(2+)-binding sites of synaptotagmin-1 to bind to phosphatidylserine in the vesicle membrane upon Ca(2+) triggering. We determined the crystal structure of the C2B domain of synaptotagmin-1 bound to phosphoserine, allowing development of a high-resolution model of synaptotagmin bridging two different membranes. Our results suggest that PIP2 clusters organized by syntaxin-1 act as molecular beacons for vesicle docking, with the subsequent Ca(2+) influx bringing the vesicle membrane close enough for membrane fusion.

Astrocyte dense-core vesicle gliosecretion is governed by rest/nrsf

Astrocytes are the brain non-nerve cells competent for the expression of clear and dense-core vesicles (DCVs) and for their regulated exocytosis. This process, called gliosecretion, nearly resembles the neurosecretion occurring in neurons and neurosecretory cells. REST/NRSF is a transcription repressor known to orchestrate nerve-cell differentiation, governing the expression of hundreds of neuron-specific genes through their repression in the non-nerve and their fine modulation in the nerve cells. Our previous studies in neurosecretory rat PC12 cells identified REST as the critical factor for the expression not only of individual genes, but also of the whole neurosecretory process via multiple, direct and indirect mechanisms (D'Alessandro et al., J. Neurochem., 2008; Klajn et al., J. Neurosci., 2009). Therefore we wondered whether gliosecretion was governed by REST. We investigated rat astrocyte primary cultures: they exhibited high REST, which directly represses the transcription of at least one target gene, and expressed neither DCVs nor their markers (granins, peptides, membrane proteins). Transfection of a dominant-negative construct of REST (REST/ DBD-GFP) induced the appearance of DCVs filled with secretogranin2 and NPY that are distinct from other intracellular organelles. TIRF analysis of astrocytes co-transfected with REST/DBD-GFP and NPY-mRFP constructs revealed NPY-mRFP-positive DCVs undergoing Ca2þ-dependent exocytosis, largely prevented by BoNT/B. Immunohistochemistry of the I-II layers of the human temporal brain cortex showed all neurons and microglia exhibiting the expected inappreciable and high levels of REST, respectively. In contrast astrocyte RESTwas variable, going from inappreciable to high, accompanied by variable expression of DCVs. In this work it has been demonstrated that astrocyte DCV expression and gliosecretion are governed by REST (Prada et al., 2011 in press). The variable in situ REST levels may contribute to the well known structural/functional heterogeneity of astrocytes and this new observation might be of great interest for the understanding of both astrocyte physiology and pathology.

Glucose and lactate are equally effective in energizing activity-dependent synaptic vesicle turnover in purified cortical neurons.

This study examines the role of glucose and lactate as energy substrates to sustain synaptic vesicle cycling. Synaptic vesicle turnover was assessed in a quantitative manner by fluorescence microscopy in primary cultures of mouse cortical neurons. An electrode-equipped perfusion chamber was used to stimulate cells both by electrical field and potassium depolarization during image acquisition. An image analysis procedure was elaborated to select in an unbiased manner synaptic boutons loaded with the fluorescent dye N-(3-triethylammoniumpropyl)-4-(4-(dibutylamino)styryl)pyridinium dibromide (FM1-43). Whereas a minority of the sites fully released their dye content following electrical stimulation, others needed subsequent K(+) depolarization to achieve full release. This functional heterogeneity was not significantly altered by the nature of metabolic substrates. Repetitive stimulation sequences of FM1-43 uptake and release were then performed in the absence of any metabolic substrate and showed that the number of active sites dramatically decreased after the first cycle of loading/unloading. The presence of 1 mM glucose or lactate was sufficient to sustain synaptic vesicle cycling under these conditions. Moreover, both substrates were equivalent for recovery of function after a phase of decreased metabolic substrate availability. Thus, lactate appears to be equivalent to glucose for sustaining synaptic vesicle turnover in cultured cortical neurons during activity.