Comparisons of NMR spectral quality and success in crystallization demonstrate that NMR and X-ray crystallography are complementary methods for small protein structure determination

X-ray crystallography and NMR spectroscopy provide the only sources of experimental data from which protein structures can be analyzed at high or even atomic resolution. The degree to which these methods complement each other as sources of structural knowledge is a matter of debate; it is often proposed that small proteins yielding high quality, readily analyzed NMR spectra are a subset of those that readily yield strongly diffracting crystals. We have examined the correlation between NMR spectral quality and success in structure determination by X-ray crystallography for 159 prokaryotic and eukaryotic proteins, prescreened to avoid proteins providing polydisperse and/or aggregated samples. This study demonstrates that, across this protein sample set, the quality of a protein's [15N-1H]-heteronuclear correlation (HSQC) spectrum recorded under conditions generally suitable for 3D structure determination by NMR, a key predictor of the ability to determine a structure by NMR, is not correlated with successful crystallization and structure determination by X-ray crystallography. These results, together with similar results of an independent study presented in the accompanying paper (Yee, et al., J. Am. Chem. Soc., accompanying paper), demonstrate that X-ray crystallography and NMR often provide complementary sources of structural data and that both methods are required in order to optimize success for as many targets as possible in large-scale structural proteomics efforts.     

Dynamic forces between bubbles and surfaces and hydrodynamic boundary conditions

A bubble attached to the end of an atomic force microscope cantilever and driven toward or away from a flat mica surface across an aqueous film is used to characterize the dynamic force that arises from hydrodynamic drainage and electrical double layer interactions across the nanometer thick intervening aqueous film. The hydrodynamic response of the air/water interface can range from a classical fully immobile, no-slip surface in the presence of added surfactants to a partially mobile interface in an electrolyte solution without added surfactants. A model that includes the convection and diffusion of trace surface contaminants can account for the observed behavior presented. This model predicts quantitatively different interfacial dynamics to the Navier slip model that can also be used to fit dynamic force data with a post hoc choice of a slip length.     

Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.     

Nonvacuum taub-type cosmological model

The Einstein universe is a simple model describing a static cosmological spacetime, having a constant radius and a constant curvature, and, as is well known, it does not describe our universe. We propose a model which is an extension of Einstein's. Our metric, havingR × S ³ topology, describes a nonisotropic homogeneous closed (finite) universe of Bianchi type IX. This metric is similar to that of Taub, but is simpler. Unlike the Taub solution (which is a cosmological extension of the NUT solution), however, the universe described by our metric contains matter. Like the Taub metric, our metric has two positive constants (, T). The gravitational red shift calculated from our metric is given. Similarly to the Schwarzschild metric, which has a singularity atr = 2m, this metric has the same kind of singularity att = 2. The maximal extension of the coordinates in our metric is fairly analogous to that of the Schwarzschild metric.     

Polymeric stabilized emulsions: steric effects and deformation in soft systems

Polymeric stabilizers are used in a broad range of processes and products, from pharmaceuticals and engine lubricants to formulated foods and shampoos. In rigid particulate systems, the stabilization mechanism is attributed to the repulsive force that arises from the compression of the polymer coating or "steric brush" on the interacting particles. This mechanism has dictated polymer design and selection for more than thirty years. Here we show, through direct measurement of the repulsive interactions between immobilized drops with adsorbed polymers layers in aqueous electrolyte solutions, that the interaction is a result of both steric stabilization and drop deformation. Drops driven together at slow collision speeds, where hydrodynamic drainage effects are negligible, show a strong dependence on drop deformation instead of brush compression. When drops are driven together at higher collision speeds where hydrodynamic drainage affects the interaction force, simple continuum modeling suggests that the film drainage is sensitive to flow through the polymer brush. These data suggest, for drop sizes where drop deformation is appreciable, that the stability of emulsion drops is less sensitive to the molecular weight or size of the adsorbed polymer layer than for rigid particulate systems.     

Some applications of Ball's extension theorem

We present two applications of Ball's extension theorem. First we observe that Ball's extension theorem, together with the recent solution of Ball's Markov type problem due to Naor, Peres, Schramm and Sheffield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Second, we prove that the distortion required to embed the integer lattice , equipped with the metric, in any -uniformly convex Banach space is of order .

     

Metallophilic and Inter-Ligand Interactions in Diargentous Compounds Bound by a Geometrically Flexible Macrocycle

A series of mono- and di-nuclear Ag^I complexes supported by a flexible macrocyclic ligand are reported. The geometric flexibility of the ligand was found to allow for a range of Ag−Ag interactions in the disilver complexes, depending on the identities of both the ancillary ligand and the counterion. Studies of the solution-phase dynamic exchange processes for these latter complexes found rapid interconversion through a mechanism that retained the multi-nuclearity. Quantum Theory of Atoms in Molecules (QTAIM) and Independent Gradient Model based on Hirshfeld partition (IGMH) analyses are used to evaluate the d¹⁰-d¹⁰ interactions between silver centers in the various geometries observed for the solid-state structures of these complexes, revealing nearly identical Ag−Ag interactions, regardless of the relative geometries of the Ag centers. Instead, a weak, but non-negligible, inter-ligand interaction between two isocyanide units may contribute to the folded-ligand geometry observed in the solid state.     

Particle Network Self-Assembly of Similar Size Sub-Micron Calcium Alginate and Polystyrene Particles Atop Glass

Particle-mediated self-assembly, such as nanocomposites, microstructure formation in materials, and core-shell coating of biological particles, offers precise control over the properties of biological materials for applications in drug delivery, tissue engineering, and biosensing. The assembly of similar-sized calcium alginate (CAG) and polystyrene sub-micron particles is studied in an aqueous sodium nitrate solution as a model for particle-mediated self-assembly of biological and synthetic mixed particle species. The objective is to reinforce biological matrices by incorporating synthetic particles to form hybrid particulate networks with tailored properties. By varying the ionic strength of the suspension, the authors alter the energy barriers for particle attachment to each other and to a glass substrate that result from colloidal surface forces. The particles do not show monotonic adsorption trend to glass with ionic strength. Hence, apart from DLVO theory—van der Waals and electrostatic interactions—the authors further consider solvation and bridging interactions in the analysis of the particulate adsorption-coagulation system. CAG particles, which support lower energy barriers to attachment relative to their counterpart polystyrene particles, accumulate as dense aggregates on the glass substrate. Polystyrene particles adsorb simultaneously as detached particles. At high electrolyte concentrations, where electrostatic repulsion is largely screened, the mixture of particles covers most of the glass substrate; the CAG particles form a continuous network throughout the glass substrate with pockets of polystyrene particles. The particulate structure is correlated with the adjustable energy barriers for particle attachment in the suspension.     

Effect of non-homogeneous surface viscosity on the Marangoni migration of a droplet in viscous fluid

Marangoni migration of a single droplet in an unbounded viscous fluid under the additional effect of variable surface viscosity is studied. The surface tension and the surface viscosity depend on concentration of dissolved species. Cases of the motion induced by the presence of a point source and by a given constant concentration gradient are considered. The dependence of the migration velocity on the governing parameters is computed under quasi-stationary approximation. The effect of weak advective transport is studied making use of singular perturbations in the Peclet number, Pe. It is shown that, when the source is time dependent a Basset-type history term appears in the expansion of the concentration and, as a result, the leading order correction to the flow and to the migration velocity is of O(Pe(1/2)). If the source of active substance driving the flow is steady, the effect of convective transport on the migration is weaker.