Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Measurement of elastin hydrolysis by reverse-phase HPLC with on-line post-colum derivatization

Summary Excessive breakdown of elastin, a structural protein, may be related to aortic disease and emphysema. Since L-valyl-L-proline occurs in high concentrations in elastin, a rapid and sensitive method using HPLC with post-column on-line derivatization was used to measure the dipeptide from swine aortic tissue, and the amount of elastin present was determined. Elastin was extracted by alkaline hydrolysis. After neutralization and filtration, the sample was injected onto a ODS-2 gel column, and the dipeptide was eluted by a linear gradient of 0 to 10% of 1-propanol in 50 mM heptafluorobutyrate, pH 3, at a flow rate of 1 ml/min. The eluent was reacted with fluorescamine at pH 8.6, and fluorescence was detected at an excitation wavelength of 395 nm and a 455 nm cutoff emission filter.Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

Book Review: The Emerging Consensus in Social Systems Theory. By Kenneth C. Bausch. Kluwer Academic/Plenum Publishers, 2001. ISBN 0-306-46539-6, $69.50

Nonlinear Dynamics, Psychology, and Life Sciences -     

On Constraint Qualifications in Nonsmooth Optimization

We introduce extensions of the Mangasarian-Fromovitz and Abadie constraint qualifications to nonsmooth optimization problems with feasibility given by means of lower-level sets. We do not assume directional differentiability, but only upper semicontinuity of the defining functions. By deriving and reviewing primal first-order optimality conditions for nonsmooth problems, we motivate the formulations of the constraint qualifications. Then, we study their interrelation, and we show how they are related to the Slater condition for nonsmooth convex problems, to nonsmooth reverse-convex problems, to the stability of parametric feasible set mappings, and to alternative theorems for the derivation of dual first-order optimality conditions.In the literature on general semi-infinite programming problems, a number of formally different extensions of the Mangasarian-Fromovitz constraint qualification have been introduced recently under different structural assumptions. We show that all these extensions are unified by the constraint qualification presented here.     

Justification of the Shallow-Water Limit for a Rigid-Lid Flow with Bottom Topography

The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H ^m for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude of the initial data in H ^m , the gradient of the bottom topography in H ^m+1 , and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small. Received 10 October 1996 and accepted 15 May 1997     

Consecutive reactions of diethoxydimethylsilane and triethoxymethylsilane with methoxide ions in methanol solution

The consecutive reactions of (CH₃)₂Si(OC₂H₅)₂ and CH₃Si(OC₂H₅)₃ with methoxide ions were investigated in methanol solutions. The reverse transesterification reactions with ethoxide ions could be neglected in both cases since the concentration of ethoxide in methanol solution was assumed to be low due to the fast equilibrium reaction C₂H₅O^? + CH₃OH ? C₂H₅OH + CH₃O^?. The progress of the reactions was followed by monitoring the formation of ethanol with a Fourier-transform infrared spectrometer. All rate constants were determined at 295 K. The reactions between the dialkoxydimethylsilanes and methoxide ions were assumed to consist of two consecutive steps that can be represented by the net reaction; (CH₃)₂Si(OC₂H₅)₂ + 2CH₃O^? → (CH₃)₂Si(OCH₃)₂ + 2C₂H₅O^?. The two consecutive rate constants were established as 1.93 ± 0.12M^?1s^?1 and 1.00 ± 0.12M^?1s^?1, respectively. The consecutive rate constants for the reactions between the trialkoxymethylsilanes and methoxide ions can be written according to the total reaction; CH₃Si(OC₂H₅)₃ + 3CH₃O^? → CH₃Si(OCH₃)₃ + 3C₂H₅O^?. The three rate constants corresponding to each consecutive step were established as 1.12 ± 0.09 M^?1s^?1, 0.82 ± 0.10 M^?1s^?1, and 0.51 ± 0.06 M^?1s^?1, respectively. © 1995 John Wiley & Sons, Inc.