Thermally activated escape rate for a Brownian particle in a double-well potential for all values of the dissipation

The translational Brownian motion in a (2-4) double-well potential is considered. The escape rate, the position correlation function and correlation time, and the generalized susceptibility are evaluated from the solution of the underlying Langevin equation by using the matrix-continued fraction method. The escape rate and the correlation time are compared with the Kramers theory of the escape rate of a Brownian particle from a potential well as extended by Mel'nikov and Meshkov [J. Chem. Phys. 85, 1018 (1986)]. It is shown that in the low-temperature limit, the universal Mel'nikov and Meshkov expression for the escape rate provides a good estimate of both escape rate and inverse position correlation time for all values of the dissipation including the very low damping (VLD), very high damping (VHD), and turnover regimes. Moreover, for low barriers, where the Mel'nikov and Meshkov method is not applicable, analytic equations for the correlation time in the VLD and VHD limits are derived.     

Comparing the efficiencies of hydrazide labels in the study of protein carbonylation in human serum albumin

In this work, we establish a methodology for comparing the efficiencies of different hydrazide labels for detecting protein carbonyls. We have chosen acrolein-modified human serum albumin as a model. This system provides a convenient means of reproducibly generating carbonylated protein. Five hydrazide-based labels were tested. Three carry a biotin affinity tag, and the others are simple fatty acid hydrazides. For the biotin-based labels, the yield of the labeling reaction varies considerably, and the most commonly used label, biotin hydrazide, gives the lowest yield. The total tandem mass spectrometry (MS/MS) spectrum counts of modified peptides are similar for all of the biotin-based tags, indicating that factors beyond the labeling efficiency are important in determining the effectiveness of the label. In addition, there is a large variation in the number of spectra obtained for specific, modified peptides depending on the nature of the labeling group. This variation implies that the relative detectability of a particular modification site is highly dependent on the tagging reagent, and more importantly, titration schemes aimed at identifying the most reactive site based on its threshold concentration will be biased by the choice of tagging reagent. The fatty acid hydrazides are somewhat more effective than the biotin-based hydrazides in generating identifiable MS/MS spectra but offer no opportunity for enrichment. For the biotin-based tags, avidin affinity chromatography was used with the tryptic digests, and each tag led to similar enrichment levels.     

Rebuttal of Kowalenko’s Paper As Concerns the Irrationality of Euler’s Constant γ

We rebut Kowalenko??s claims in this journal that he proved the irrationality of Euler??s constant ??, and that his rational series for ?? is new.     

Investigating the spectrum of biological activity of substituted quinoline-2-carboxamides and their isosteres

In this study, a series of thirty-five substituted quinoline-2-carboxamides and thirty-three substituted naphthalene-2-carboxamides were prepared and characterized. They were tested for their activity related to the inhibition of photosynthetic electron transport (PET) in spinach (Spinacia oleracea L.) chloroplasts. Primary in vitro screening of the synthesized compounds was also performed against four mycobacterial species. N-Cycloheptylquinoline-2-carboxamide, N-cyclohexylquinoline-2-carboxamide and N-(2-phenylethyl)quinoline-2-carboxamide showed higher activity against M. tuberculosis than the standards isoniazid or pyrazinamide and 2-(pyrrolidin-1-ylcarbonyl)quinoline and 1-(2-naphthoyl)pyrrolidine expressed higher activity against M. kansasii and M. avium paratuberculosis than the standards isoniazid or pyrazinamide. The most effective antimycobacterial compounds demonstrated insignificant toxicity against the human monocytic leukemia THP-1 cell line. The PET-inhibiting activity expressed by IC(50) value of the most active compound N-benzyl-2-naphthamide was 7.5 μmol/L. For all compounds, the structure-activity relationships are discussed.     

Exact solution for rotational relaxation times for problems governed by axially symmetric Fokker-Planck equations

Exact integral expressions valid for any potential barrier height for mean first passage times (and so the exit time and the reaction rate) for relaxation processes governed by the rotational Fokker-Planck equation with an axially symmetric potential are derived in a manner exactly analogous to that used to derive an integral expression for the correlation time by Coffey and Crothers (W.T. Coffey and D.S.F. Crothers, Phys. Rev. E. 54 (1996) 4768). This is accomplished by constructing the adjoint Fokker-Planck operator (Kolmogorov backward operator) and so forming the partial differential equation for the mean first passage time, which for axial symmetry may be directly integrated by quadratures. The results constitute a generalization of the work of Klein, (G. Klein, Proc. R. Soc. London, Ser. A 211 (1952) 431) originally given for the free rotational Brownian movement, to the rotational Brownian movement in an axially symmetric potential.     

DERIVATION OF THE LEHNERT FIELD EQUATIONS FROM GAUGE THEORY IN VACUUM: SPACE CHARGE AND CURRENT

It is shown that the Lehnert field equations in vacuum, with concomitant space charge and current, can be derived straightforwardly from standard gauge theory applied in vacuum, using the concept of covariant derivative and Feynman's universal influence. The Lehnert and Proca field equations are shown to be inter-related through the well-known de Broglie theorem, in which the photon mass can be interpreted as finite. These ideas go some way towards addressing the inconsistency inherent in Maxwell's famous displacement current, which has no concomitant vacuum space charge.