Characterizing and monitoring respiratory aerosols by light scattering

The elastic-scattering intensity pattern from a single particle as a function of spherical coordinate angles theta and phi provides detailed information on the pattern's morphology. By use of an ellipsoidal reflector and a CCD camera, a single-laser-shot intensity pattern from a large angular range (theta from 90 degrees to 168 degrees and phi from 0 degrees to 360 degrees) was detected from a single aerosol (e.g., a Bacillus subtilisspore, a 1-microm-diameter polystyrene latex sphere, or a cluster of either of these) flowing through the reflectors focal volume at 5 m/s. Noticeable difference in the large-angle-range two-dimensional angular optical scattering (LATAOS) suggest that the LATAOS pattern could be useful in differentiating and classifying life-threatening aerosols from normal background aerosols.     

Trapping specific quaternary states of the allosteric enzyme aspartate transcarbamoylase in silica matrix sol-gels

The extreme T and R quaternary structures of the allosteric enzyme aspartate transcarbamoylase have been trapped by encapsulation in a silica sol-gel matrix. Detection of the specific quaternary structure present in the sol-gel was accomplished using a pyrene-labeled version of the enzyme that exhibited monomer fluorescence in the T quaternary structure and excimer fluorescence in the R quaternary structure. Using thin films of the encapsulated enzyme, kinetics of the T and R states could be determined without interconversion of the states. Using a monolith form of the encapsulated enzyme, the transition from the T or the R structure was monitored. Within the sol-gel matrix, the rate of the transition was slowed approximately 105 over that observed in solution.     

A three-curves theorem for viscosity subsolutions of parabolic equations

We prove a three-curves theorem for viscosity subsolutions of fully nonlinear uniformly parabolic equations .

     

A Note on Q-order of Convergence

To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q [1,+] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.This revised version was published online in October 2005 with corrections to the Cover Date.     

Thin points for Brownian motion

Let Θ(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {W_t}_0≤t≤1 in . We prove that for any analytic set E in [0,1], we have

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, where dim_P(E) is the packing dimension of E. We deduce that for any a≥1, the Hausdorff dimension of the set of “thin points” x for which

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, is almost surely 2−2/a; this is the correct scaling to obtain a nondegenerate “multifractal spectrum” for the “thin” part of Brownian occupation measure. The methods of this paper differ considerably from those of our work on Brownian thick points, due to the high degree of correlation in the present case. To prove our results, we establish general criteria for determining which deterministic sets are hit by random fractals of ‘limsup type' in the presence of long-range correlations. The hitting criteria then yield lower bounds on Hausdorff dimension. This refines previous work of Khoshnevisan, Xiao and the second author, that required decay of correlations.     

Catalytic alcoholysis of tetramethylsilane via Pt-mediated C-H bond activation

Tetramethylsilane reacts with 2,2,2-trifluoroethanol (TFE) in the presence of a cationic platinum(II) catalyst [(NN)PtMe(TFE)]+ (NN = 1,2-bis(3,5-dimethylphenylimino)butane). Catalytic Si-C bond heterolysis results in the formation of the trimethylsilyl ether, Me3SiOCH2CF3, accompanied by liberation of one equivalent of methane. Preliminary experiments suggest that a rate-determining C-H bond activation precedes rapid attack by solvent at silicon to yield the silyl ether product and regenerate the active platinum methyl cation.     

Kinetic control of histidine-tagged protein surface density on supported lipid bilayers

Nickel-chelating lipids are general tools for anchoring polyhistidine-tagged proteins to supported lipid bilayers (SLBs), but controversy exists over the stability of the protein-lipid attachment. Here, we show that chelator lipids are suitable anchors for building stable, biologically active surfaces but that a simple Langmuirian model is insufficient to describe their behavior. Desorption kinetics from chelator lipids are governed by the valency of surface binding: monovalently bound proteins desorb within minutes (t1/2 approximately 6 min), whereas polyvalently bound species remain bound for hours (t1/2 approximately 12 h). Evolution between surface states is slow, so equilibrium is unlikely to be reached on experimental timescales. However, by tuning incubation conditions, the populations of each species can be kinetically controlled, providing a wide range of protein densities on SLBs with a single concentration of chelator lipid. We propose guidelines for the assembly of SLB surfaces functionalized with specific protein densities and demonstrate their utility in the formation of hybrid immunological synapses.