Protamine neutralisation of low molecular weight heparins and their oligosaccharide components

Protamine sulphate is an effective inhibitor of heparin and is used clinically to neutralise both low molecular weight heparins (LMWH) and unfractionated heparin (UFH). However, protamine sulphate does not fully counter the anti-Xa effect of LMWH, even in excess (>40 μg to 1 IU/ml). To investigate the molecular basis for this observation, the residual potencies in the presence and absence of plasma as well as the molecular weight profiles of commercial LMWH neutralised with increasing amounts of protamine were measured. Materials over 5000 Da are preferentially neutralised by protamine. To further investigate this molecular weight dependence, monodisperse oligosaccharides were prepared from three commercial LMWHs. The specific anti-Xa activity for the fractions increased with molecular weight, and was found to vary between the three preparations for oligosaccharides of the same molecular weight. Our results indicate that protamine sulphate neutralisation is largely dependent on molecular weight, leading to the implication that LMWHs containing a larger proportion of small oligosaccharides will not be as effectively neutralised. Protamine sulphate neutralisation of any given LMWH is also affected by the specific anticoagulant activities of its low molecular weight components, which varies between LMWH products, presumably with the method of manufacture.     

Cell receptor and surface ligand density effects on dynamic states of adhering circulating tumor cells

Dynamic states of cancer cells moving under shear flow in an antibody-functionalized microchannel are investigated experimentally and theoretically. The cell motion is analyzed with the aid of a simplified physical model featuring a receptor-coated rigid sphere moving above a solid surface with immobilized ligands. The motion of the sphere is described by the Langevin equation accounting for the hydrodynamic loadings, gravitational force, receptor-ligand bindings, and thermal fluctuations; the receptor-ligand bonds are modeled as linear springs. Depending on the applied shear flow rate, three dynamic states of cell motion have been identified: (i) free motion, (ii) rolling adhesion, and (iii) firm adhesion. Of particular interest is the fraction of captured circulating tumor cells, defined as the capture ratio, via specific receptor-ligand bonds. The cell capture ratio decreases with increasing shear flow rate with a characteristic rate. Based on both experimental and theoretical results, the characteristic flow rate increases monotonically with increasing either cell-receptor or surface-ligand density within certain ranges. Utilizing it as a scaling parameter, flow-rate dependent capture ratios for various cell-surface combinations collapse onto a single curve described by an exponential formula.     

Invariant subsets of rank 1 manifolds

It is proved that for a Riemannian manifold M with nonpositive sectional curvature and finite volume the space of directions at each point in which geodesic rays avoid a sufficiently small neighborhood of a fixed rank 1 vector v∈UM looks very much like a generalized Sierpinski carpet. We also show for nonpositively curved manifolds M with dim M≥ 3 the existence of proper closed flow invariant subsets of the unit tangent bundle UM whose footpoint projection is the whole of M. Received: 6 July 2000 / Revised version: 11 October 2001     

Hyperbolic rank and subexponential corank of metric spaces

We introduce a new quasi-isometry invariant corank X of a metric space X called subexponential corank. A metric space X has subexponential corank k if roughly speaking there exists a continuous map , T is a topological space, such that for each the set g ^-1(t) has subexponential growth rate in X and the topological dimension dimT = k is minimal among all such maps. Our main result is the inequality for a large class of metric spaces X including all locally compact Hadamard spaces, where rank _h X is the maximal topological dimension of among all CAT(—1) spaces Y quasi-isometrically embedded into X (the notion introduced by M. Gromov in a slightly stronger form). This proves several properties of rank _h conjectured by Gromov, in particular, that any Riemannian symmetric space X of noncompact type possesses no quasi-isometric embedding of the standard hyperbolic space H ⁿ with . Submitted: February 2001, Revised: October 2001.     

Amphiphilic maleic acid-containing alternating copolymers—2. Dilute solution characterization by light scattering,intrinsic viscosity,and PGSE NMR spectroscopy

The dilute solution behavior of several alternating copolymers of maleic acid has been characterized by static and dynamic light scattering, intrinsic viscosity, and pulsed-gradient spin-echo NMR spectroscopy. The copolymer of maleic acid–sodium salt and isobutylene (IBMA-Na, M_w ∼350 kg/mol) dissolves readily in concentrated aqueous salt solutions. Changes in chain dimensions with ionic strength and pH are similar to those of the lesser salt solution-soluble poly(acrylic acid-sodium salt). The hydrophobically modified (with n-butyl, n-hexyl, n-octyl, and phenethyl amines) copolymers of maleic acid–sodium salts and isobutylene (IBMA-NHR-Na) show no sign of large intermolecular aggregation in 0.1 N sodium acetate (NaAc). However, the sizes of the copolymers are relatively small compared to that of the ionized parent copolymer (IBMA-Na, M_w ∼350 kg/mol), suggesting intramolecular aggregation of the alkyl side-chain groups along the polymer backbone. The copolymer modified with the longer chain n-decyl, on the other hand, forms stable large intermolecular aggregates containing 33 chains/aggregate. The copolymers of maleic acid–sodium salt and styrene (SMA-Na) appear to have no signs of aggregation, despite being a hydrophobic polyelectrolyte. The copolymer of maleic acid–sodium salt and di-isobutylene (DIBMA-Na) has a similar salting-out concentration as SMA-Na. The radius of gyration measurements by static light scattering suggest that at least some fraction of the DIBMA-Na chains form large intermolecular aggregates. The copolymers of maleic acid–sodium salt with n-alkenes (n-C_mMA-Na) in 0.1 N NaAc form small intermolecular aggregates (three to five chains/aggregate). In contrast to these static light scattering results, PGSE NMR diffusion measurements for the above aggregated systems indicate only one diffusion coefficient consistent with the motion of single isolated chains. A plausible explanation for this discrepancy is that the population of the aggregates is too small to be sufficiently detected in the PGSE NMR experiment. Furthermore, it is likely that the aggregate has a larger relaxation rate than the nonaggregate, and therefore has a comparatively reduced signal in the PGSE NMR experiment. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3584–3597, 2004     

Homological methods in algebraic map theory

The primary intent of the present paper is to adapt familiar notions of algebraic topology, such as the fundamental group, homology, and cohomology to the context of algebraic maps and their (ramified) covering projections. The notion of a principal derived map is already fairly well understood in terms of the defining voltages; however, once it is recognized that voltages are essentially cohomological in nature, the functorial interplay among homology provides a very tractible methodology for studying such properties as connectivity or regularity of the covering, or for obtaining explicit constructions of the voltages affording the given covering map.     

Die näherungsweise Berücksichtigung der mittragenden Breite bei Spannungs-, Stabilitäts- und Schwingungsproblemen

Übersicht Um die Schubverformungen in den Deckplatten von Plattenbalken und Hohlkästen zu berücksichtigen, wird mit Hilfe eines Variationsprinzips vom Minimum der potentiellen Energie ein Näherungsverfahren entwickelt. Bei der Annahme über den Formänderungszustand wird die Bernoullische Annahme vom Ebenbleiben der Querschnitte verlassen. Die Euler-Gleichungen des Variationsproblems ergeben einfache gewöhnliche Differentialgleichungen, die eine Behandlung von Spannungs-, Stabilitäts- und Schwingungsproblemen ermöglichen. Es zeigt sich, daß die Spannungen, Knicklasten und Eigenfrequenzen ganz erheblich von den bekannten Werten der elementaren Stabtheorie abweichen können. Die Genauigkeit der Lösung wurde durch Vergleich mit der exakten Scheibentheorie überprüft, wobei sich eine gute Übereinstimmung ergab.

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Summary A method of determining the shear deformations of the cover plates of T- and box-beams is developed, employing a variational principle of minimum potential energy. In assuming a convenient shape of deformation Bernoulli's hypothesis is rendered invalid. The Euler equations yield ordinary differential equations for the solution of stress, stability, and vibration problems. It is shown that the stresses, the buckling loads and the characteristic frequencies may differ significantly from the values obtained with the elemantary theory of elasticity. The accuracy of the solution is investigated and shown to be of a high degree by comparing the results with those obtained with the exact theory of disks.