Filament sets and homogeneous continua

New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament, non-filament, and ample, with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.     

Temperature dependence of the configurational free energy of a branched polymer

We consider a lattice model of branched polymers in dilute solution in which the polymer is modelled as an animal, weakly embeddable in the (simple cubic) lattice. In order to model the effect on the thermodynamic properties of changing the temperature or the quality of the solvent, we include an energy associated with the number of nearneighbour contacts between pairs of vertices of the animals. We show that the configurational free energy of the animal is a continuous function of the temperature and derive rigorous upper and lower bounds on the temperature dependence of the free energy. Finally, we comment on similarities between these results and corresponding ones for a model in which the energy is associated with the cyclomatic index of the animal.     

The “Facilitated Transition” hypothesis as an explanation for the gemdialkyl effect

A new technique of searching the conformational space of transition states was used to explore the cause of the rate acceleration in the gem-dialkyl effect in intramolecular cyclization reactions. Several previous hypotheses were discarded and a new hypothesis was advanced based on this new data. This hypothesis, the “Facilitated Transition” hypothesis, states that increased steric hindrance reduces the overall activation energy by facilitating rotation through the transition state. The older “Reactive Rotamer” hypothesis was eliminated by generating all conformations of the starting materials using the and computer programs and demonstrating that no relationship is found between rate increase and a change in the concentration of “reactive rotamers”.     

S1P1-selective in vivo-active agonists from high-throughput screening: off-the-shelf chemical probes of receptor interactions, signaling, and fate

The essential role of the sphingosine 1-phosphate (S1P) receptor S1P(1) in regulating lymphocyte trafficking was demonstrated with the S1P(1)-selective nanomolar agonist, SEW2871. Despite its lack of charged headgroup, the tetraaromatic compound SEW2871 binds and activates S1P(1) through a combination of hydrophobic and ion-dipole interactions. Both S1P and SEW2871 activated ERK, Akt, and Rac signaling pathways and induced S1P(1) internalization and recycling, unlike FTY720-phosphate, which induces receptor degradation. Agonism with receptor recycling is sufficient for alteration of lymphocyte trafficking by S1P and SEW2871. S1P(1) modeling and mutagenesis studies revealed that residues binding the S1P headgroup are required for kinase activation by both S1P and SEW2871. Therefore, SEW2871 recapitulates the action of S1P in all the signaling pathways examined and overlaps in interactions with key headgroup binding receptor residues, presumably replacing salt-bridge interactions with ion-dipole interactions.     

Entangled polymers in condensed phases

We present Monte Carlo results on a model of polymers in a condensed phase, over a range of monomer densities. We imagine cutting a cube out of the system. This cube will typically have several polymer molecules running through its interior, and starting and ending on the boundary. These subchains will be mutually entangled and we present a way to assess the extent of entanglement complexity as a function of the monomer density and the number of subchains in the cube. The model is a set of k self-avoiding and mutually avoiding walks, properly embedded in the cube.     

Ruthenium cluster compounds containing 1,1′-bis(diphenylphosphino)ferrocene (dppf): an electrochemical analysis and the crystal structure of [Ru3(CO)11]2(μ-dppf)

The electrochemistry of 1,1′-bis(diphenylphosphino)ferrocene (dppf) derivatives of Ru₃(CO)₁₂ was investigated. Two known compounds [Ru₃(CO)₈(μ-dppf)₂ (1) and Ru₃(CO)₁₀dppf (2)] and a new compound [Ru₃(CO)₁₁(μ-dppf)Ru₃(CO)₁₁ (3)] were prepared. Compound 3 was characterized spectroscopically and an X-ray crystal structure was obtained. The reductive electrochemistry of 1 and 2 showed an irreversible reduction and a follow-up oxidation, similar to Ru₃(CO)₁₂. The electrochemistry of compound 3 showed two irreversible waves and a follow-up oxidation. A trend in the reduction potential vs. the number of coordinated phosphorus atoms was noted. The oxidative electrochemistry of 1-3 showed a dppf-based chemically reversible wave, and an irreversible wave similar to that of Ru₃(CO)₁₂. Trends were also noted between the oxidation potential and the number of coordinated phosphorus atoms.     

Entanglement complexity of lattice ribbons

We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as n, and similar results hold for the twist and writhe.     

Optical properties of human prostate at 732 nm measured in mediated photodynamic therapy

Characterization of the tissue light penetration in prostate photodynamic therapy (PDT) is important to plan the arrangement and weighting of light sources so that sufficient light fluence is delivered to the treatment volume. The optical properties (absorption [mu(a)], transport scattering [mu(s)'] and effective attenuation [mu(eff)] coefficients) of 13 patients with locally recurrent prostate cancer were measured in situ using interstitial isotropic detectors. Measurements were made at 732 nm before and after motexafin lutetium (MLu)-mediated PDT in four quadrants. Optical properties were derived by applying the diffusion theory to the fluence rates measured at several distances (0.5-5 cm) from a point source. mu(a) and mu(s)' varied between 0.07 and 1.62 cm(-1) (mean 0.37 +/- 0.24 cm(-1)) and 1.1 and 44 cm(-1) (mean 14 +/- 11 cm(-1)), respectively. mu(a) was proportional to the concentration of MLu measured by an ex vivo fluorescence assay. We have observed, on average, a reduction of the MLu concentration after PDT, presumably due to the PDT consumption of MLu. mu(eff) varied between 0.91 and 6.7 cm(-1) (mean 2.9 +/- 0.7 cm(-1)), corresponding to an optical penetration depth (delta = 1/micro(eff)) of 0.1-1.1 cm (mean 0.4 +/- 0.1 cm). The mean penetration depth at 732 nm in human prostate is at least two times smaller than that found in normal canine prostates, which can be explained by a four times increase of the mean value of mu(s)' in human prostates. The mean light fluence rate per unit source strength at 0.5 cm from a point source was 1.5 +/- 1.1 cm(-2), excluding situations when bleeding occurs. The total number of measurements was N = 121 for all mean quantities listed above. This study showed significant inter- and intraprostatic differences in the optical properties, suggesting that a real-time dosimetry measurement and feedback system for monitoring light fluences during treatment should be considered for future PDT studies.     

Component B binding to the soluble methane monooxygenase hydroxylase by saturation-recovery EPR spectroscopy of spin-labeled MMOB

Spin-labeled Cys89 of the soluble methane monooxygenase regulatory protein (MMOB) from Methylococcus capsulatus (Bath) binds within 15 +/- 4 A of the hydroxylase (MMOH) diiron center, placing the MMOB docking site in the MMOH "canyon" region on iron-coordinating helices E and F of the alpha-subunit.     

Estimation of binding constants between ristocetin and teicoplanin and peptides using on-column ligand derivatization coupled to affinity capillary electrophoresis

This work utilizes on-column ligand synthesis and affinity capillary electrophoresis (ACE) to determine binding constants (K_b) of 9-flourenylmethyloxy carbonyl (Fmoc)-amino acid derivatives to the glycopeptide antibiotics ristocetin (Rist) and teicoplanin (Teic). In this technique, two separate plugs of sample are injected on to the capillary column and electrophoresed. The initial sample plug contains a d-Ala-d-Ala terminus peptide and either one or two non-interacting standard(s). The second plug contains a Fmoc-amino acid-N-hydroxysuccinimide (NHS) ester. The electrophoresis is then carried out with an increasing concentration of Rist or Teic in the running buffer. Upon electrophoresis the initial d-Ala-d-Ala peptide reacts with the Fmoc-amino acid yielding a new Fmoc-amino acid-d-Ala-d-Ala peptide derivative. Continued electrophoresis results in the binding of Rist or Teic to the Fmoc-amino acid-d-Ala-d-Ala peptide derivatives. Analysis of the change in the relative migration time ratio (RMTR) or electrophoretic mobility () of the Fmoc-amino acid-d-Ala-d-Ala peptide derivatives relative to the non-interacting standards, as a function of the concentration of Rist and Teic, yields a value for K_b. These findings demonstrate the advantage of coupling on-column ligand synthesis to ACE for estimating binding parameters between antibiotics and ligands.Abbreviations Rist Ristocetin - Teic Teicoplanin - ACE Affinity capillary electrophoresis - RMTR Relative migration time ratio