Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Lack of myostatin results in excessive muscle growth but impaired force generation

The lack of myostatin promotes growth of skeletal muscle, and blockade of its activity has been proposed as a treatment for various muscle-wasting disorders. Here, we have examined two independent mouse lines that harbor mutations in the myostatin gene, constitutive null (Mstn(-/-)) and compact (Berlin High Line, BEH(c/c)). We report that, despite a larger muscle mass relative to age-matched wild types, there was no increase in maximum tetanic force generation, but that when expressed as a function of muscle size (specific force), muscles of myostatin-deficient mice were weaker than wild-type muscles. In addition, Mstn(-/-) muscle contracted and relaxed faster during a single twitch and had a marked increase in the number of type IIb fibers relative to wild-type controls. This change was also accompanied by a significant increase in type IIB fibers containing tubular aggregates. Moreover, the ratio of mitochondrial DNA to nuclear DNA and mitochondria number were decreased in myostatin-deficient muscle, suggesting a mitochondrial depletion. Overall, our results suggest that lack of myostatin compromises force production in association with loss of oxidative characteristics of skeletal muscle.

Development of the mammalian urethra is controlled by Fgfr2-IIIb

Development of external genitalia in mammalian embryos requires tight coordination of a complex series of morphogenetic events involving outgrowth, proximodistal and dorsoventral patterning, and epithelial tubulogenesis. Hypospadias is a congenital defect of the external genitalia that results from failure of urethral tube closure. Although this is the second most common birth defect in humans, affecting one in every 250 children, the molecular mechanisms that regulate morphogenesis of the mammalian urethra are poorly understood. We report that mice lacking the IIIb isoform of fibroblast growth factor receptor 2 (Fgfr2) exhibit severe hypospadias. Urethral signaling regions, as indicated by Shh and Fgf8 expression, are established in Fgfr2-IIIb null mice; however, cell proliferation arrests prematurely and maturation of the urethral epithelium is disrupted. Fgfr2-IIIb(-/-) mutants fail to maintain the progenitor cell population required for uroepithelial renewal during tubular morphogenesis. In addition, we show that antagonism of the androgen receptor (AR) leads to loss of Fgfr2-IIIb and Fgf10 expression in the urethra, and an associated hypospadias phenotype, suggesting that these genes are downstream targets of AR during external genital development. Genitourinary defects resulting from disruption of AR activity, by either genetic or environmental factors, may therefore involve negative regulation of the Fgfr2 pathway. This represents the first example of how the developing genitourinary system integrates cues from systemically circulating steroid hormones with a locally expressed growth factor pathway.

Growth of copper nanoparticles within VOx nanotubes

The synthesis of new Cu-VOx nanotubes has been achieved by exchanging a Cu(II) salt against the protonated template in the parent dodecylamine-VOx nanotubes. The intercalation of Cu(II) species induces some significant morphological and structural changes within the material, but the tubular shape is still well preserved. Controlled thermolysis under nitrogen of the Cu(II) species initially dispersed within the multiwalls induces the growth and sintering of copper nanoparticles, which are formed without destroying the tubular morphology of the host carrier. (C) 2002 Elsevier Science B.V. All rights reserved.

Microfabrication of high-performance aromatic polymers as nanotubes or fibrils by in situ ring-opening polymerisation of macrocyclic precursors

Melt-phase nucleophilic ring-opening polymerisation of macrocyclic aromatic ethers and thioethers at high temperatures within the cylindrical pores of an anodic-alumina membrane, followed by dissolution of the template, enables replication of the membrane's internal pore structure and so affords high-performance aromatic polymers with well-defined fibrillar or tubular morphologies.

The role of terminal tyrosine residues in the formation of tripeptide nanotubes: a crystallographic insight

Terminally protected acyclic tripeptides containing tyrosine residues at both termini self-assemble into nanotubes in crystals through various non-covalent interactions including intermolecular hydrogen bonds. The nanotube has an average internal diameter of 5 angstrom (0.5 nm) and the tubular ensemble is developed through the hydrogen-bonded phenolic-OH side chains of tyrosine (Tyr) residues [Org. Lett. 2004, 6, 4463]. We have synthesized and studied several tripeptides 3-6 to probe the role of tyrosine residues in nanotube structure formation. These peptides either have only one Tyr residue at N- or C-termini or they have one or two terminally located phenylalanine (Phe) residues. These tripeptides failed to form any kind of nanotubular structure in the solid state. Single crystal X-ray diffraction studies of these peptides 3-6 clearly demonstrate that substitution of any one of the terminal Tyr residues in the Boc-Tyr-X-Tyr-OMe (X=VaI or Ile) sequence disrupts the formation of the nanotubular structure indicating that the presence of two terminally located Tyr residues is vital for nanotube formation. (c) 2006 Elsevier Ltd. All rights reserved.

A new motif in the formation of peptide nanotubes: the crystallographic signature

Terminally protected acyclic tripeptides Boc-Tyr(1)-Val(2)-Tyr(3)-OMe 1 and Boc-Tyr(1)-lle(2)-Tyr(3)-OMe 2 self-assemble into nanotubes in crystals through various noncovalent interactions with an average internal diameter of 5 Angstrom (0.5 nm), and the tubular ensemble is developed through the hydrogen-bonded side chains of tyrosine residues. The inside of the hollow nanotubular structures is hydrophilic; however, no solvent molecules have been crystallographically detected.

Critical flux in ultrafiltration of skimmed milk

he best operating conditions, using the critical flux concept during ultrafiltration of skimmed milk, were evaluated for tubular membranes. It was found that irreversible fouling was greatly reduced by operating at or below the critical flux, but was not totally eliminated. The critical flux of skimmed milk was found to be the weak form. The critical flux at cross flow velocity 3.4 in s(-1) for MWCO 200 kDa membrane was 56.9 kg m(-2) h(-1) while for MWCO 25 kDa membranes it was 45 kg m(2) h(-1) suggesting that membrane pore size influenced the flux. The critical flux increased with increasing wall shear stress and decreased with increasing protein concentration. Empirical equations, for predicting the critical flux (J(crit)) for skimmed milk with a protein concentration (c(b)) in the range 3-7% w/w and wall shear stress (tau(w)) in the range 7-60 Pa for MWCO 200 kDa and 25 kDa membranes were J(crit) = 5.1 (tau(w)/c(b)) and J(crit) = 4.0 (tau(w)/c(b)) respectively. In general, the rejections of protein and lactose at the critical flux were not affected by protein concentration, wall shear stress and membrane used, and they were similar to those found when operating at the limiting flux.

An engineering model of the human colon

The development and performance of a three-stage tubular model of the large human intestine is outlined. Each stage comprises a membrane fermenter where flow of an aqueous polyethylene glycol solution on the outside of the tubular membrane is used to control the removal of water and metabolites (principally short chain fatty acids) from, and thus the pH of, the flowing contents on the fermenter side. The three stage system gave a fair representation of conditions in the human gut. Numbers of the main bacterial groups were consistently higher than in an existing three-chemostat gut model system, suggesting the advantages of the new design in providing an environment for bacterial growth to represent the actual colonic microflora. Concentrations of short chain fatty acids and Ph levels throughout the system were similar to those associated with corresponding sections of the human colon. The model was able to achieve considerable water transfer across the membrane, although the values were not as high as those in the colon. The model thus goes some way towards a realistic simulation of the colon, although it makes no pretence to simulate the pulsating nature of the real flow. The flow conditions in each section are characterized by low Reynolds numbers: mixing due to Taylor dispersion is significant, and the implications of Taylor mixing and biofilm development for the stability, that is the ability to operate without washout, of the system are briefly analysed and discussed. It is concluded that both phenomena are important for stabilizing the model and the human colon.