Magnetic resonance imaging of bone marrow metastasis with fluid-fluid levels from small cell neuroendocrine carcinoma of the urinary bladder

Fluid-fluid levels have been reported as an extremely infrequent and non-specific condition in many benign and malignant bone lesions. We present the first reported MRI findings of bone marrow metastasis with fluid-fluid levels from small cell neuroendocrine carcinoma of the urinary bladder to the lumbar spine. Radiologists should be aware of the MRI appearance of these extraordinary lesions in order to provide a complete differential diagnosis and to guide clinicians in adequate treatment.     

High-energy phosphate metabolism during incremental calf exercise in humans measured by 31 phosphorus magnetic resonance spectroscopy (31P MRS)

Several previous 31 phosphorus magnetic resonance spectroscopy ((31)P MRS) studies performing incremental or progressive muscle exercises have observed that a decrease in pH is accompanied with an acceleration in phosphocreatine (PCr) hydrolysis. The purpose of this study was to investigate the relationship between PCr breakdown and pH during isotonic, exhaustive, incremental plantar flexion exercises. We included eight healthy, male volunteers into this study. Using a 1.5 Tesla MR scanner and a self-built exercise bench, we performed serial free induction decay (FID) (31)P MRS measurements with a time resolution of 1 min at rest, isotonic calf muscle exercise, and recovery. The exercise protocol consisted of 5-min intervals with 4.5, 6, 7.5, and 9 W workload followed by 9-min recovery. Changes in PCr and inorganic phosphate (Pi) were determined as percent changes in comparison to the baseline. In addition, pH values were calculated. This study obtained significant decreases in PCr corresponding to the gradual increases in workload. In each workload level that was succeeded by all volunteers, PCr hydrolysis passed into a steady state. After an early biphasic response, we detected a significant decrease in pH from the first to the second minute of the 6-W workload level followed by a further continuous decrease in pH up to the second minute of the recovery phase. The decrease in pH was not accompanied by acceleration in PCr hydrolysis. In conclusion, this study shows that PCr hydrolysis during incremental plantar flexion exercises passes into a steady state at different workload levels. The observed decrease in pH does not result in acceleration of PCr hydrolysis.     

Combinatorics of Matrix Factorizations and Integrable Systems

We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a combinatorial–geometric way using a diagram of a cube. In this representation, vertices of the cube represent eigenvectors, edges are labeled by differences of locations of zeroes and poles of the determinant of our matrix function, and each face corresponds to a particular choice of a coordinate system on the space of such functions. Moreover, for each face this labeling encodes, in a neat and efficient way, a generating function for the expressions of the remaining four eigenvectors that label the opposing face of the cube in terms of the coordinates represented by the chosen face. The main motivation behind this work is that when our matrix is a Lax matrix of a discrete integrable system, such generating functions can be interpreted as Lagrangians of the system, and a choice of a particular face corresponds to a choice of the direction of the motion.     

A stochastic approach to a priori estimates and Liouville theorems for harmonic maps

Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type theorems is shown to follow as corollaries from such estimates by exhausting the domain through an increasing sequence of geodesic balls. This probabilistic method is well suited for proving sharp estimates under various curvature conditions. We discuss Liouville theorems for harmonic maps under the following conditions: small image, sublinear growth, non-positively curved targets, generalized bounded dilatation, Liouville manifolds as domains, certain asymptotic behaviour.     

Symbols of truncated Toeplitz operators

We consider three topics connected with coinvariant subspaces of the backward shift operator in Hardy spaces Hp:

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properties of truncated Toeplitz operators;

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Carleson-type embedding theorems for the coinvariant subspaces;

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factorizations of pseudocontinuable functions from H¹.

These problems turn out to be closely connected and even, in a sense, equivalent. The new approach based on the factorizations allows us to answer a number of challenging questions about truncated Toeplitz operators posed by D. Sarason.     

Postprocessing of docked protein-ligand complexes using implicit solvation models

Molecular docking plays an important role in drug discovery as a tool for the structure-based design of small organic ligands for macromolecules. Possible applications of docking are identification of the bioactive conformation of a protein-ligand complex and the ranking of different ligands with respect to their strength of binding to a particular target. We have investigated the effect of implicit water on the postprocessing of binding poses generated by molecular docking using MM-PB/GB-SA (molecular mechanics Poisson-Boltzmann and generalized Born surface area) methodology. The investigation was divided into three parts: geometry optimization, pose selection, and estimation of the relative binding energies of docked protein-ligand complexes. Appropriate geometry optimization afforded more accurate binding poses for 20% of the complexes investigated. The time required for this step was greatly reduced by minimizing the energy of the binding site using GB solvation models rather than minimizing the entire complex using the PB model. By optimizing the geometries of docking poses using the GB(HCT+SA) model then calculating their free energies of binding using the PB implicit solvent model, binding poses similar to those observed in crystal structures were obtained. Rescoring of these poses according to their calculated binding energies resulted in improved correlations with experimental binding data. These correlations could be further improved by applying the postprocessing to several of the most highly ranked poses rather than focusing exclusively on the top-scored pose. The postprocessing protocol was successfully applied to the analysis of a set of Factor Xa inhibitors and a set of glycopeptide ligands for the class II major histocompatibility complex (MHC) A(q) protein. These results indicate that the protocol for the postprocessing of docked protein-ligand complexes developed in this paper may be generally useful for structure-based design in drug discovery.     

Poly(vinyl alcohol) physical hydrogels: new vista on a long serving biomaterial

Poly(vinyl alcohol), PVA, and physical hydrogels derived thereof have an excellent safety profile and a successful history of biomedical applications. However, these materials are hardly in the focus of biomedical research, largely due to poor opportunities in nano- and micro-scale design associated with PVA hydrogels in their current form. In this review we aim to demonstrate that with PVA, a (sub)molecular control over polymer chemistry translates into fine-tuned supramolecular association of chains and this, in turn, defines macroscopic properties of the material. This nano- to micro- to macro- translation of control is unique for PVA and can now be accomplished using modern tools of macromolecular design. We believe that this strategy affords functionalized PVA physical hydrogels which meet the demands of modern nanobiotechnology and have a potential to become an indispensable tool in the design of biomaterials.     

Electrical conductivity of PUR/MWCNT nanocomposites in the molten state, during crystallization and in the solid state

The electrical conductivity of a nanocomposite constituted of multiwalled carbon nanotubes (MWCNT) dispersed in a semicrystalline polyurethane matrix, is investigated during cooling from the melt to the solid state. The same percolation threshold, ?_c = 0.85 wt.%, is obtained in the molten and in the solid state, although the exponent t of the percolation equation is significantly higher in the solid state. A remarkable increase of the conductivity during crystallization is observed for nanocomposites of MWCNT content above ?_c, but for contents below ?_c the conductivity decreases. Combined conductivity and PVT results, lead us to discard the hypothesis of an increase of the density of the conductive network (associated with volume shrinkage) as being the cause of the conductivity enhancement during crystallization. Instead, the analysis of the parameters of the percolation equation for the molten and the solid state, suggests a transition from a less effective conductive network to a more performing three dimensional network.