An analysis of reduced Hessian methods for constrained optimization

We study the convergence properties of reduced Hessian successive quadratic programming for equality constrained optimization. The method uses a backtracking line search, and updates an approximation to the reduced Hessian of the Lagrangian by means of the BFGS formula. Two merit functions are considered for the line search: the ₁ function and the Fletcher exact penalty function. We give conditions under which local and superlinear convergence is obtained, and also prove a global convergence result. The analysis allows the initial reduced Hessian approximation to be any positive definite matrix, and does not assume that the iterates converge, or that the matrices are bounded. The effects of a second order correction step, a watchdog procedure and of the choice of null space basis are considered. This work can be seen as an extension to reduced Hessian methods of the well known results of Powell (1976) for unconstrained optimization.This author was supported, in part, by National Science Foundation grant CCR-8702403, Air Force Office of Scientific Research grant AFOSR-85-0251, and Army Research Office contract DAAL03-88-K-0086.This author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under contracts W-31-109-Eng-38 and DE FG02-87ER25047, and by National Science Foundation Grant No. DCR-86-02071.     

13C CPMAS spectroscopy of deuterated proteins: CP dynamics, line shapes, and T1 relaxation

(13)C CPMAS NMR has been investigated in application to protein samples with a variety of deuteration patterns. Samples were prepared with protons in either all hydrogen positions, only in the exchangeable sites, or in the exchangeable sites plus select methyl groups. CP dynamics, T(1) relaxation times, and (13)C line widths have been compared. Using ubiquitin as a model system, reasonable (1)H-(13)C CP transfer is observed for the extensively deuterated samples. In the absence of deuterium decoupling, the (13)C line widths observed for the deuterated samples are identical to those observed for the perprotio samples with a MAS rate of 20 kHz. Extensive deuteration has little effect on the T(1) of the exchangeable protons. On the basis of these observations, it is clear that there are no substantive compromises accompanying the use of extensive deuteration in the design of (1)H, (15)N, or (13)C solid-state NMR methods.     

A rapid LC-MS-MS method for the determination of nicotine and cotinine in serum and saliva samples from smokers: validation and comparison with a radioimmunoassay method

The development and validation of a rapid liquid chromatography (LC)-tandem mass spectrometry (MS-MS) method for determination of nicotine and cotinine in smokers' serum is described. The method is based on solid-phase extraction in a 96-well plate format and requires only 100 microL of serum. Using normal-phase chromatography, both analytes elute in less than 1 min, which permits high sample throughput applications. The calibrated range is 2-100 ng/mL nicotine and 20-1,000 ng/mL cotinine. For known samples, recovery is 95-116% for nicotine and 93-94% for cotinine. The method is extended to rat serum and human saliva (cotinine only) using partial validation techniques. When compared with an existing radioimmunoassay method in our laboratory, the LC-MS-MS method gives improved accuracy, precision, and sample throughput.     

Sensitive high resolution inverse detection NMR spectroscopy of proteins in the solid state

A new indirect detection scheme for obtaining (15)N/(1)H shift correlation spectra in crystalline proteins is described. Excellent water suppression is achieved without the need for pulsed field gradients, and using only a 2-step phase cycle. Careful attention to overall NMR instrument stability was found critical for obtaining the best resolution and sensitivity. Magnetic dilution by deuteration of the protein in combination with high-speed magic angle spinning produces (1)H resonances averaging only 0.22 ppm in width, and in some cases lines as narrow as 0.17 ppm are obtained. In application to two different polymorphs of ubiquitin, structure dependent differences in both (15)N and (1)H amide chemical shifts are observed. In one case, distinct shifts for different molecules in the asymmetric unit are seen, and all differ substantially from solution NMR shifts. A gain of 7 in sensitivity makes the method competitive with solution NMR as long as nanocrystalline samples are available.     

Completely automated, highly error-tolerant macromolecular structure determination from multidimensional nuclear overhauser enhancement spectra and chemical shift assignments

The major rate-limiting step in high-throughput NMR protein structure determination involves the calculation of a reliable initial fold, the elimination of incorrect nuclear Overhauser enhancement (NOE) assignments, and the resolution of NOE assignment ambiguities. We present a robust approach to automatically calculate structures with a backbone coordinate accuracy of 1.0-1.5 A from datasets in which as much as 80% of the long-range NOE information (i.e., between residues separated by more than five positions in the sequence) is incorrect. The current algorithm differs from previously published methods in that it has been expressly designed to ensure that the results from successive cycles are not biased by the global fold of structures generated in preceding cycles. Consequently, the method is highly error tolerant and is not easily funnelled down an incorrect path in either three-dimensional structure or NOE assignment space. The algorithm incorporates three main features: a linear energy function representation of the NOE restraints to allow maximization of the number of simultaneously satisfied restraints during the course of simulated annealing; a method for handling the presence of multiple possible assignments for each NOE cross-peak which avoids local minima by treating each possible assignment as if it were an independent restraint; and a probabilistic method to permit both inactivation and reactivation of all NOE restraints on the fly during the course of simulated annealing. NOE restraints are never removed permanently, thereby significantly reducing the likelihood of becoming trapped in a false minimum of NOE assignment space. The effectiveness of the algorithm is demonstrated using completely automatically peak-picked experimental NOE data from two proteins: interleukin-4 (136 residues) and cyanovirin-N (101 residues). The limits of the method are explored using simulated data on the 56-residue B1 domain of Streptococcal protein G.