Blaschke's rolling theorem for manifolds¶with boundary

For a complete Riemannian manifold M with compact boundary ∂M denote by $\Cut$ the cut locus of $\f M$ in M. The rolling radius of M is roll(M)≔ dist(∂M, ?_{∂ M} ). Let Focal(∂M) be the focal distance of ∂M in M. Then conditions are given that imply the equality roll(M)= Focal(∂M). This generalizes Blaschke's rolling theorem from bounded convex domains in Euclidean space to more general Euclidean domains and to Riemannian manifolds with boundary. Received: 28 August 1998 / Revised version: 8 February 1999     

Fluctuation theorems and 1/f noise from a simple matrix

Here we present a model for a small system combined with an explicit entropy bath that iscomparably small. The dynamics of the model is defined by a simple matrix, M. Each row ofM corresponds to a macrostate of the system, e.g. net alignment, while the elements in therow represent microstates. The constant number of elements in each row ensures constantentropy, which allows reversible fluctuations, similar to information theory where aconstant number of bits allows reversible computations. Many elements in M come from themicrostates of the system, but many others come from the bath. Bypassing the bath statesyields fluctuations that exhibit standard white noise; whereas with bath states the powerspectral density varies as S(f) ∝ 1 /f overa wide range of frequencies, f. Thus, the explicit entropy bath is the mechanismof 1/f noisein this model. Both forms of the model match Crooks’ fluctuation theorem exactly,indicating that the theorem applies not only to infinite reservoirs, but also tofinite-sized baths. The model is used to analyze measurements of 1/f-like noise from asub-micron tunnel junction.     

Reactions of N-silylphosphoranimines with alcohols: synthesis and structure of cyclotriphosphazenes with nongeminal methyl and phenyl substituents

The reactions of Me(3)SiN=P(OR")RR'(R" = Ph, CH(2)CF(3); R, R' = Me, Ph) with alcohols were investigated. With nonequivalent amounts of CF(3)CH(2)OH, the reactions produced high yields of the cyclic phosphazene (Me(2)PN)(3) and both the cis and trans isomers of nongeminally substituted [(Ph)(Me)PN](3). The isomers of this new cyclic phosphazene were separated by column chromatography and characterized by NMR and IR spectroscopy, elemental analysis, and X-ray crystallography. Crystals of the cis isomer 6a have a monoclinic crystal system, while the trans isomer 6b has a triclinic crystal system with two different molecules in an asymmetric unit. The bond lengths and bond angles are very similar to those of the simpler cyclic trimers (Me(2)PN)(3) and (Ph(2)PN)(3.) A likely pathway for the formation of these compounds is discussed.     

4,10‐Dinitro‐2,6,8,12‐tetraoxa‐4,10‐diazaisowurtzitane (TEX): a nitramine with an exceptionally high density

The title compound (systematic name: 4,10‐di­nitro‐2,6,8,12‐tetraoxa‐4,10‐di­aza­tetra­cyclo­[5.5.0.0^3,11.0^5,9]­do­decane), C₆H₆N₄O₈, exhibits the highest density among known N‐nitramines, due to its close‐packed crystal structure. It may be regarded as consisting of a distorted hexagonal close‐packed lattice formed by the isowurtzitane cages, with the nitro groups occupying the free space between the cages.     

Protease sensors for bioimaging

Optical imaging of specific molecular targets and pathways in vivo has recently become possible through continued developments in imaging equipment, reconstruction algorithms, and more importantly the availability of imaging reporter molecules. These reporter molecules encompass photoproteins expressed in vivo and exogenously administered probes detectable by fluorescence and/or bioluminescence imaging. One particularly enticing aspect of optical imaging is the ability to design activatible probes with inherent amplification. This review summarizes our experience in developing novel near-infrared fluorescent (NIRF) imaging agents that report on protease activities. These agents are designed to be biocompatible, highly activatible, and able to produce bright NIRF following protease cleavage.     

Addressing the metabolic activation potential of new leads in drug discovery: a case study using ion trap mass spectrometry and tritium labeling techniques

Metabolic activation of drug candidates to electrophilic reactive metabolites that can covalently modify cellular macromolecules may result in acute and/or idiosyncratic immune system-mediated toxicities in humans. This presents a significant potential liability for the future development of these compounds as safe therapeutic agents. We present here an example of an approach where sites of metabolic activation within a new drug candidate series were rapidly identified using online liquid chromatography/multi-stage mass spectrometry on an ion trap mass spectrometer. This was accomplished by trapping the reactive intermediates formed upon incubation of compounds with rat and human liver microsomes as their corresponding glutathione conjugates and mass spectral characterization of these thiol adducts. Based on the structures of the GSH adducts identified, potential sites and mechanisms of bioactivation within the chemical structure were proposed. These metabolism studies were interfaced with iterative structural modifications of the chemical series in order to block these bioactivation sites within the molecule. This strategy led to a significant reduction in the propensity of the compounds to undergo metabolic activation as evidenced by reductions in the irreversible binding of radioactivity to liver microsomal material upon incubation of tritium-labeled compounds with this in vitro system. With the efficiency and throughput achievable with such an approach, it appears feasible to identify and address the metabolic activation potential of new drug leads during routine metabolite identification studies in an early drug discovery setting.     

Formation and structure of self-assembled monolayers of alkanethiolates on palladium

The adsorption of n-alkanethiols onto polycrystalline thin films of palladium containing a strong (111) texture produces well-organized, self-assembled monolayers. The organization of the alkane chains in the monolayer and the nature of the bonding between the palladium and the thiol were studied by contact angle measurements, optical ellipsometry, reflection absorption infrared spectroscopy (RAIRS), and X-ray photoelectron spectroscopy (XPS). The XPS data reveals that a compound palladium-sulfide interphase is present at the surface of the palladium film. The RAIR spectra, ellipsometry data, and wetting properties show that the palladium-sulfide phase is terminated with an organized, methyl-terminated monolayer of alkanethiolates. The local molecular environment of the alkane chains transitions from a conformationally disordered, liquidlike state to a mostly all-trans, crystalline-like structure with increasing chain length (n = 8-26). The intensities and dichroism of the methylene and methyl stretching modes support a model for the average orientation of an ensemble of all-trans-conformer chains with a tilt angle of approximately 14-18 degrees with respect to the surface normal and a twist angle of the CCC plane relative to the tilt plane of approximately 45 degrees. The SAMs are stable in air, although the sulfur present at the surface oxidizes in air over a period of 2-5 days at room temperature. The differences in chain organization between SAMs formed by microcontact printing and by solution deposition are also examined by RAIRS and XPS.     

The Binomial Distribution of Hydrogen and Deuterium in Arsanes, Diarsanes, and Triarsanes Generated from As(Iii)/[BH n D4-n ]? and the Effect of Trace Amounts of Rh(Iii) Ions

Recent studies of the formation of arsane in the borohydride/arsenate reaction demonstrate the occurrence of condensation cascades whereby small quantities of di- and triarsanes are formed. In this study, the isotopic composition of these di- and triarsanes was examined using deuterium labelled borohydrides. A statistical model was employed to construct the mass spectra of all diarsane and triarsane isotopologues (As₂H _n D_4-n and As₃H _n D_5-n ) from the mass spectra of isotopically pure compounds (As₂H₄, As₂D₄, As₃H₅, and As₃D₅). Subsequent deconvolution of the experimental mixed spectra shows that incorporation of hydrogen closely follows the binomial distribution, in accord with arsane formation. The H/D distribution in arsane, diarsane, and triarsane isotopologues is binomial in the absence of any interference. However, this is significantly altered by the presence of some transition metals; presented here, for the first time, are the effects of Rh(iii). The presence of Rh(iii) in the As(iii)/[BD₄]^? system entails the incorporation of hydrogen into the arsanes arising from the solvent, altering the expected binomial H/D distribution.