Scoring functions: A view from the bench

Computational approaches to drug design are presently hindered by the complexity of the physical chemistry which underlies weak, non- covalent interactions between protein targets and small molecule ligands. Although a number of programs are now available for the design of novel potential ligands, it remains a key problem to rank these rapidly and reliably by estimated binding affinity. Such a step is necessary to select only the most promising candidates for synthesis and experimental characterisation. To calculate ligand affinity quickly and reliably is an extremely difficult problem, but it may well prove possible to estimate sufficiently accurately given an appropriate set of parameters to score individual protein–ligand interactions. Improvements in the situation will require a wider set of thermodynamically characterised systems than is currently available.     

Gem-dinitro compounds in organic synthesis. 4. Use of the condensation product of glyoxal and dinitromethane in the synthesis of nitro-1,2,3-triazoles

The condensation of dinitromethane with glyoxal has been investigated and it has been demonstrated that 1,1,4,4-tetranitro-2,3-butandiol, -hydroxy-,-dinitropropionic acid or their mixture may be formed. Interaction of 1,1,4,4-tetranitro-2,3-butandiol or 1,4-dibromo-1,1,4,4-tetranitro-2,3-butanediol diacetates with sodium azide leads to bis(5-nitro-1,2,3-triazol-4-yl) via intermediate 1,1,4,4-tetranitro-1,3-butadiene.For communication 3, see [1].N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 9, pp. 2123–2131, September, 1992.     

Exploring bioanalytical applications of assisted protein reassembly

Reassembly of protein from its peptide fragments is a technique that can have many applications in the bioanalytical field. Typically, a reporter protein fragmented into its two peptides is employed as a label in this study. This fragments of peptide can reassemble yielding an active functional reporter. This reassembly of the protein can be assisted by non-covalently interacting peptides or proteins, which are attached to the fragmented reporter. This technique has been employed in several applications including study of protein–protein interactions, antibody screening, immunoassays, and high-throughput screening. This review focuses on different reporters employed in the study of reassembly of proteins and applications of this strategy in bioanalysis.     

Packing directed circuits fractionally

LetG be a digraph, and letk1, such that no fractional packing of directed circuits ofG has value >k, when every vertex is given capacity 1. We prove there is a set ofO (k logk logk) vertices meeting all directed circuits ofG.     

Orientations of chain groups

We prove generalizations to chain groups, of Minty's Arc Colouring Lemma and its extension, the well-known Farkas Lemma. In these the orientation of the edges is replaced by an arbitrary chain.A function on a chain groupN isrepresentable if there exists a chainR such that (X)=R·X for allXN. Anorientation is a chain with values ±1. We prove that for a regular chain group a linear function that is representable by an orientation for each chainXN locally, is representable by an orientation globally.     

The influence of cyclodextrin complexation on proton transfer in piperidinomethyl-2-naphthol

Summary Piperidinomethyl-2-naphthol forms inclusion complexes with -cyclodextrin with an equilibrium constant of 265M ^–1 in aqueous solution. The proton transfer equilibrium between the neutral and the zwitterionic form is strongly influenced by the association.

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Der Einfluß der Komplexierung mit -Cyclodextrin auf das Protontransfer-Gleichgewicht in Piperidino-2-naphthol (Kurze Mitt.)

Zusammenfassung Piperidinomethyl-2-naphthol bildet Einschlußkomplexe mit -Cyclodextrin mit einer Gleichgewichtskonstante von 265M ^–1. Das Protontransfer-Gleichgewicht zwischen neutraler Form und zwitterionischer Struktur wird durch diese Assoziation stark beeinflußt.

     

On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

Stable σ-adducts of 4,6-dinitrotetrazolo[1,5-a]pyridine with alkoxide anions

The reaction of 2-chloro-3,5-dinitropyridine with two equivalents of KN₃ in the presence of ROH results in stable Meisenheimer-type -adducts of 4,6-dinitrotetra-zolo[1,5-a]pyridine with RO^– anions (R = H, Alk, Ph). The mechanism of -complex formation was suggested. The structure of the -adduct with R = Me was established by IR and NMR spectroscopy and by X-ray diffraction analysis.For the preliminary communication, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1278–1283, July, 1994.This work was supported by the Russian Foundation for Basic Research (project code 93-03-5329).     

Monotone path systems in simple regions

A monotone path system (MPS) is a finite set of pairwise disjoint paths (polygonal areas) in thexy-plane such that every horizontal line intersects each of the paths in at most one point. A MPS naturally determines a pairing of its top points with its bottom points. We consider a simple polygon in thexy-plane wich bounds the simple polygonal (closed) regionD. LetT andB be two finite, disjoint, equicardinal sets of points ofD. We give a good characterization for the existence of a MPS inD which pairsT withB, and a good algorithm for finding such a MPS, and we solve the problem of finding all MPSs inD which pairT withB. We also give sufficient conditions for any such pairing to be the same.The first author's research is supported by the Natural Sciences and Engineering Research Council of Canada     

The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.