A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Detection of peptide-based nanoparticles in blood plasma by ELISA

Aims: The aim of the current study was to develop a method to detect peptide-linked nanoparticles in blood plasma. Materials & Methods: A convenient enzyme linked immunosorbent assay (ELISA) was developed for the detection of peptides functionalized with biotin and fluorescein groups. As a proof of principle, polymerized pentafluorophenyl methacrylate nanoparticles linked to biotin-carboxyfluorescein labeled peptides were intravenously injected in Wistar rats. Serial blood plasma samples were analyzed by ELISA and by liquid chromatography mass spectrometry (LC/MS) technology. Results: The ELISA based method for the detection of FITC labeled peptides had a detection limit of 1 ng/mL. We were able to accurately measure peptides bound to pentafluorophenyl meth-acrylate nanoparticles in blood plasma of rats, and similar results were obtained by LC/MS. Conclusions: We detected FITC-labeled peptides on pentafluorophenyl methacrylate nanoparticles after injection in vivo. This method can be extended to detect nanoparticles with different chemical compositions

Self-assembly of polysaccharides gives rise to distinct mechanical signatures in marine gels

Marine-gel biopolymers were recently visualized at the molecular level using atomic force microscopy (AFM) to reveal fine fibril-forming networks with low to high degrees of cross-linking. In this work, we use force spectroscopy to quantify the intra- and intermolecular forces within the marine-gel network. Combining force measurements, AFM imaging, and the known chemical composition of marine gels allows us to identify the microscopic origins of distinct mechanical responses. At the single-fibril level, we uncover force-extension curves that resemble those of individual polysaccharide fibrils. They exhibit entropic elasticity followed by extensions associated with chair-to-boat transitions specific to the type of polysaccharide at high forces. Surprisingly, a low degree of cross-linking leads to sawtooth patterns that we attribute to the unraveling of polysaccharide entanglements. At a high degree of cross-linking, we observe force plateaus that arise from unzipping, as well as unwinding, of helical bundles. Finally, the complex 3D network structure gives rise to force staircases of increasing height that correspond to the hierarchical peeling of fibrils away from the junction zones. In addition, we show that these diverse mechanical responses also arise in reconstituted polysaccharide gels, which highlights their dominant role in the mechanical architecture of marine gels

Generation and characterization of standardized forms of trehalose dihydrate and their associated solid-state behavior

Trehalose dihydrate is a nonreducing disaccharide which has generated great interest in the food and pharmaceutical industries. However, it is well recognized that considerable batch to batch variation exists for supposedly identical samples, particularly in terms of the thermal response. In this investigation, two standardized forms of trehalose dihydrate were generated using two distinct crystallization pathways. The two batches were characterized using scanning electron microscopy, X-ray powder diffraction, and FTIR. The thermal responses of the two forms were then studied using modulated temperature differential scanning calorimetry (MTDSC) and thermogravimetric analysis (TGA). In particular, we describe the technique of quasi-isothermal MTDSC as a means of studying the change in equilibrium heat capacity as a function of temperature. Finally, variable temperature FTIR was utilized to assess the change in bonding configuration as a function of temperature. SEM revealed significant differences in the continuity and grain structure of the two batches. The TGA, MTDSC, and quasi-isothermal MTDSC studies all indicated significant differences in the thermal response and water loss profile. This was confirmed using variable temperature FTIR which indicated differences in bond reconfiguration as a function of temperature. We ascribe these differences to variations in the route by which water may leave the structure, possibly associated with grain size. The study has therefore demonstrated that chemically identical dihydrate forms may show significant differences in thermal response. We believe that this may assist in interpreting and hence controlling interbatch variation for this material