Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms

Ultra-low density polymers, metals, and ceramic nanofoams are valued for their high strength-to-weight ratio, high surface area and insulating properties ascribed to their structural geometry. We obtain the labrynthine internal structure of a tantalum oxide nanofoam by X-ray diffractive imaging. Finite element analysis from the structure reveals mechanical properties consistent with bulk samples and with a diffusion limited cluster aggregation model, while excess mass on the nodes discounts the dangling fragments hypothesis of percolation theory.Comment: 8 pages, 5 figures, 30 reference

Confident and sensitive phosphoproteomics using combinations of collision induced dissociation and electron transfer dissociation

We present a workflow using an ETD-optimised version of Mascot Percolator and a modified version of SLoMo (turbo-SLoMo) for analysis of phosphoproteomic data. We have benchmarked this against several database searching algorithms and phosphorylation site localisation tools and show that it offers highly sensitive and confident phosphopeptide identification and site assignment with PSM-level statistics, enabling rigorous comparison of data acquisition methods. We analysed the Plasmodium falciparum schizont phosphoproteome using for the first time, a data-dependent neutral loss-triggered-ETD (DDNL) strategy and a conventional decision-tree method. At a posterior error probability threshold of 0.01, similar numbers of PSMs were identified using both methods with a 73% overlap in phosphopeptide identifications. The false discovery rate associated with spectral pairs where DDNL CID/ETD identified the same phosphopeptide was < 1%. 72% of phosphorylation site assignments using turbo-SLoMo without any score filtering, were identical and 99.8% of these cases are associated with a false localisation rate of < 5%. We show that DDNL acquisition is a useful approach for phosphoproteomics and results in an increased confidence in phosphopeptide identification without compromising sensitivity or duty cycle. Furthermore, the combination of Mascot Percolator and turbo-SLoMo represents a robust workflow for phosphoproteomic data analysis using CID and ETD fragmentation. Biological significance Protein phosphorylation is a ubiquitous post-translational modification that regulates protein function. Mass spectrometry-based approaches have revolutionised its analysis on a large-scale but phosphorylation sites are often identified by single phosphopeptides and therefore require more rigorous data analysis to unsure that sites are identified with high confidence for follow-up experiments to investigate their biological significance. The coverage and confidence of phosphoproteomic experiments can be enhanced by the use of multiple complementary fragmentation methods. Here we have benchmarked a data analysis pipeline for analysis of phosphoproteomic data generated using CID and ETD fragmentation and used it to demonstrate the utility of a data-dependent neutral loss triggered ETD fragmentation strategy for high confidence phosphopeptide identification and phosphorylation site localisation

Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets

It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of {\fR}^2. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted proof of existence of a "universal" area-preserving map $F_*$ -- a map with orbits of all binary periods 2^k, k \in \fN. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics. We first demonstrate that the map $F_*$ admits a "bi-infinite heteroclinic tangle": a sequence of periodic points $\{z_k\}$, k \in \fZ, |z_k| \converge{{k \to \infty}} 0, \quad |z_k| \converge{{k \to -\infty}} \infty, whose stable and unstable manifolds intersect transversally; and, for any N \in \fN, a compact invariant set on which $F_*$ is homeomorphic to a topological Markov chain on the space of all two-sided sequences composed of $N$ symbols. A corollary of these results is the existence of {\it unbounded} and {\it oscillating} orbits. We also show that the third iterate for all maps close to $F_*$ admits a horseshoe. We use distortion tools to provide rigorous bounds on the Hausdorff dimension of the associated locally maximal invariant hyperbolic set: $$ 0.7673 \ge {\rm dim}_H(\cC_F) \ge \varepsilon \approx 0.00044 e^{-1797}.$

Occurrence and Treatment of Bone Atrophic Non-Unions Investigated by an Integrative Approach

Recently developed atrophic non-union models are a good representation of the clinical situation in which many nonunions develop. Based on previous experimental studies with these atrophic non-union models, it was hypothesized that in order to obtain successful fracture healing, blood vessels, growth factors, and (proliferative) precursor cells all need to be present in the callus at the same time. This study uses a combined in vivo-in silico approach to investigate these different aspects (vasculature, growth factors, cell proliferation). The mathematical model, initially developed for the study of normal fracture healing, is able to capture essential aspects of the in vivo atrophic non-union model despite a number of deviations that are mainly due to simplifications in the in silico model. The mathematical model is subsequently used to test possible treatment strategies for atrophic non-unions (i.e. cell transplant at post-osteotomy, week 3). Preliminary in vivo experiments corroborate the numerical predictions. Finally, the mathematical model is applied to explain experimental observations and identify potentially crucial steps in the treatments and can thereby be used to optimize experimental and clinical studies in this area. This study demonstrates the potential of the combined in silico-in vivo approach and its clinical implications for the early treatment of patients with problematic fractures

Novel echocardiographic techniques to assess left atrial size, anatomy and function

Three-dimensional echocardiography (3DE) and speckle tracking echocardiography (STE) have recently applied as imaging techniques to accurately evaluate left atrial (LA) size, anatomy and function. 3DE and off-line quantification softwares, have allowed, in comparison to magnetic resonance imaging, the most time-efficient and accurate method of LA volume quantification. STE provides a non-Doppler, angle-independent and objective quantification of LA myocardial deformation. Data regarding feasibility, accuracy and clinical applications of LA analysis by 3DE and STE are rapidly gathering. This review describes the fundamental concepts of LA 3DE and STE, illustrates how to obtain respective measurements and discuss their recognized and emerging clinical applications

Unveiling novel genes upregulated by both rhBMP2 and rhBMP7 during early osteoblastic transdifferentiation of C2C12 cells

<p>Abstract</p> <p>Findings</p> <p>We set out to analyse the gene expression profile of pre-osteoblastic C2C12 cells during osteodifferentiation induced by both rhBMP2 and rhBMP7 using DNA microarrays. Induced and repressed genes were intercepted, resulting in 1,318 induced genes and 704 repressed genes by both rhBMP2 and rhBMP7. We selected and validated, by RT-qPCR, 24 genes which were upregulated by rhBMP2 and rhBMP7; of these, 13 are related to transcription (<it>Runx2, Dlx1, Dlx2, Dlx5, Id1, Id2, Id3, Fkhr1, Osx, Hoxc8, Glis1, Glis3 </it>and <it>Cfdp1</it>), four are associated with cell signalling pathways (<it>Lrp6, Dvl1, Ecsit </it>and <it>PKCδ</it>) and seven are associated with the extracellular matrix (<it>Ltbp2, Grn, Postn, Plod1, BMP1, Htra1 </it>and <it>IGFBP-rP10</it>). The novel identified genes include: <it>Hoxc8, Glis1, Glis3, Ecsit, PKCδ, LrP6, Dvl1, Grn, BMP1, Ltbp2, Plod1, Htra1 </it>and <it>IGFBP-rP10</it>.</p> <p>Background</p> <p>BMPs (bone morphogenetic proteins) are members of the TGFβ (transforming growth factor-β) super-family of proteins, which regulate growth and differentiation of different cell types in various tissues, and play a critical role in the differentiation of mesenchymal cells into osteoblasts. In particular, rhBMP2 and rhBMP7 promote osteoinduction <it>in vitro </it>and <it>in vivo</it>, and both proteins are therapeutically applied in orthopaedics and dentistry.</p> <p>Conclusion</p> <p>Using DNA microarrays and RT-qPCR, we identified both previously known and novel genes which are upregulated by rhBMP2 and rhBMP7 during the onset of osteoblastic transdifferentiation of pre-myoblastic C2C12 cells. Subsequent studies of these genes in C2C12 and mesenchymal or pre-osteoblastic cells should reveal more details about their role during this type of cellular differentiation induced by BMP2 or BMP7. These studies are relevant to better understanding the molecular mechanisms underlying osteoblastic differentiation and bone repair.</p

Serotonin Antagonism Improves Platelet Inhibition in Clopidogrel Low-Responders after Coronary Stent Placement: An In Vitro Pilot Study

Increased residual platelet reactivity remains a burden for coronary artery disease (CAD) patients who received a coronary stent and do not respond sufficiently to treatment with acetylsalicylic acid and clopidogrel. We hypothesized that serotonin antagonism reduces high on-treatment platelet reactivity. Whole blood impedance aggregometry was performed with arachidonic acid (AA, 0.5 mM) and adenosine diphosphate (ADP, 6.5 µM) in addition to different concentrations of serotonin (1–100 µM) in whole blood from 42 CAD patients after coronary stent placement and 10 healthy subjects. Serotonin increased aggregation dose-dependently in CAD patients who responded to clopidogrel treatment: After activation with ADP, aggregation increased from 33.7±1.3% to 40.9±2.0% in the presence of 50 µM serotonin (p<0.05) and to 48.2±2.0% with 100 µM serotonin (p<0.001). The platelet serotonin receptor antagonist ketanserin decreased ADP-induced aggregation significantly in clopidogrel low-responders (from 59.9±3.1% to 37.4±3.5, p<0.01), but not in clopidogrel responders. These results were confirmed with light transmission aggregometry in platelet-rich plasma in a subset of patients. Serotonin hence increased residual platelet reactivity in patients who respond to clopidogrel after coronary stent placement. In clopidogrel low-responders, serotonin receptor antagonism improved platelet inhibition, almost reaching responder levels. This may justify further investigation of triple antiplatelet therapy with anti-serotonergic agents

Heterologous mesenchymal stem cells successfully treat femoral pseudarthrosis in rats

<p>Abstract</p> <p>Background</p> <p>This study evaluated the effectiveness of treating pseudarthrosis in rats by using bone marrow cell suspensions or cultures of bone marrow mesenchymal stromal cells</p> <p>Methods</p> <p>Thirty-eight specific pathogen-free (SPF) animals were randomly assigned to four groups: Group 1, Control, without surgical intervention; Group 2 (Placebo), experimental model of femoral pseudarthrosis treated only with saline solution; Group 3, experimental model of femoral pseudarthrosis treated with heterologous bone marrow cells suspension; Group 4, experimental model of femoral pseudarthrosis treated with cultures of heterologous mesenchymal stromal cells from bone marrow. When pseudarthrosis was confirmed by simple radiological studies, digital radiography and histopathology after a 120-day postoperative period, Groups 2, 3 and 4 were treated as above. At 30, 60 and 90 days after the treatment, all animals were evaluated by simple radiological studies, and at the end of the experiment, the animals were assessed by computed axial tomography and anatomopathological and histomorphometric examinations.</p> <p>Results</p> <p>Injected cells were detected in the areas affected by pseudarthrosis using scintigraphy within the first 24 hours after their administration. After 60 days, the animals of Group 3 showed callus formation while the animals of Group 4 presented periosteal reaction and had some consolidated areas. In contrast, Group 2 showed a predominance of fibro-osteoid tissue. After 90 days, bone consolidation and remodeling was observed in all animals from Group 3 whereas animals from Group 4 exhibited partial consolidation and those ones from Group 2 persisted with pseudarthrosis.</p> <p>Conclusion</p> <p>The treatment with heterologous bone marrow cells suspension proved to be effective in the treatment of pseudarthrosis whereas cultures of heterologous bone marrow mesenchymal stromal cells did not show the same potential to aid bone healing.</p