Azides of N-substituted aziridine-2-carboxylic acids. Reaction with methyl esters of amino acids

The corresponding azide was obtained by nitrosation of 1-benzylaziridine-2-carboxylic acid hydrazide. Reaction of the azide with methyl esters of amino acids gave N-(1-benzyl-2-aziridinylcarbonyl)-substituted methyl esters of amino acids.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1350–1352, October, 1980.     

Primal-Dual Nonlinear Rescaling Method for Convex Optimization

In this paper, we consider a general primal-dual nonlinear rescaling (PDNR) method for convex optimization with inequality constraints. We prove the global convergence of the PDNR method and estimate the error bounds for the primal and dual sequences. In particular, we prove that, under the standard second-order optimality conditions, the error bounds for the primal and dual sequences converge to zero with linear rate. Moreover, for any given ratio 0 > > 1, there is a fixed scaling parameter k > 0 such that each PDNR step shrinks the primal-dual error bound by at least a factor 0 > > 1, for any k k. The PDNR solver was tested on a variety of NLP problems including the constrained optimization problems (COPS) set. The results obtained show that the PDNR solver is numerically stable and produces results with high accuracy. Moreover, for most of the problems solved, the number of Newton steps is practically independent of the problem size.     

Computer modeling of binding of diverse weak toxins to nicotinic acetylcholine receptors

Weak toxins are the "three-fingered" snake venoms toxins grouped together by having an additional disulfide in the N-terminal loop I. In general, weak toxins have low toxicity, and biological targets have been identified for some of them only, recently by detecting the effects on the nicotinic acetylcholine receptors (nAChR). Here the methods of docking and molecular dynamics simulations are used for comparative modeling of the complexes between four weak toxins of known spatial structure (WTX, candoxin, bucandin, gamma-bungarotoxin) and nAChRs. WTX and candoxin are those toxins whose blocking of the neuronal alpha7- and muscle-type nAChR has been earlier shown in binding assays and electrophysiological experiments, while for the other two toxins no such activity has been reported. Only candoxin and WTX are found here to give stable solutions for the toxin-nAChR complexes. These toxins appear to approach the binding site similarly to short alpha-neurotoxins, but their final position resembles that of alpha-cobratoxin, a long alpha-neurotoxin, in the complex with the acetylcholine-binding protein. The final spatial structures of candoxin and WTX complexes with the alpha7 neuronal or muscle-type nAChR are very similar and do not provide immediate answer why candoxin has a much higher affinity than WTX, but both of them share a virtually irreversible mode of binding to one or both these nAChR subtypes. Possible explanation comes from docking and MD simulations which predict fast kinetics of candoxin association with nAChR, no gross changes in the toxin conformation (with smaller toxin flexibility on alpha7 nAChR), while slow WTX binding to nAChR is associated with slow irreversible rearrangement both of the tip of the toxin loop II and of the binding pocket residues locking finally the toxin molecule. Computer modeling showed that the additional disulfide in the loop I is not directly involved in receptor binding of WTX and candoxin, but it stabilizes the structure of loop I which plays an important role in toxin delivery to the binding site. In summary, computer modeling visualized possible modes of binding for those weak toxins which interact with the nAChR, provided no solutions for those weak toxins whose targets are not the nAChRs, and demonstrated that the additional disulfide in loop I cannot be a sound criteria for joining all weak toxins into one group; the conclusion about the diversity of weak toxins made from computer modeling is in accord with the earlier phylogenetic analysis.     

Novel Oxidovanadium Complexes with Redox-Active R-Mian and R-Bian Ligands: Synthesis,Structure, Redox and Catalytic Properties

A new monoiminoacenaphthenone 3,5-(CF₃)₂C₆H₃-mian (complex 2) was synthesized and further exploited, along with the already known monoiminoacenaphthenone dpp-mian, to obtain oxidovanadium(IV) complexes [VOCl₂(dpp-mian)(CH₃CN)] (3) and [VOCl(3,5-(CF₃)₂C₆H₃-bian)(H₂O)][VOCl₃(3,5-(CF₃)₂C₆H₃-bian)]·2.85DME (4) from [VOCl₂(CH₃CN)₂(H₂O)] (1) or [VCl₃(THF)₃]. The structure of all compounds was determined using X-ray structural analysis. The vanadium atom in these structures has an octahedral coordination environment. Complex 4 has an unexpected structure. Firstly, it contains 3,5-(CF₃)₂C₆H₃-bian instead of 3,5-(CF₃)₂C₆H₃-mian. Secondly, it has a binuclear structure, in contrast to 3, in which two oxovanadium parts are linked to each other through V=O···V interaction. This interaction is non-covalent in origin, according to DFT calculations. In structures 2 and 3, non-covalent π-π staking interactions between acenaphthene moieties of the neighboring molecules (distances are 3.36–3.40 Å) with an estimated energy of 3 kcal/mol were also found. The redox properties of the obtained compounds were studied using cyclic voltammetry in solution. In all cases, the reduction processes initiated by the redox-active nature of the mian or bian ligand were identified. The paramagnetic nature of complexes 3 and 4 has been proven by EPR spectroscopy. Complexes 3 and 4 exhibited high catalytic activity in the oxidation of alkanes and alcohols with peroxides. The yields of products of cyclohexane oxidation were 43% (complex 3) and 27% (complex 4). Based on the data regarding the study of regio- and bond-selectivity, it was concluded that hydroxyl radicals play the most crucial role in the reaction. The initial products in the reactions with alkanes are alkyl hydroperoxides, which are easily reduced to their corresponding alcohols by the action of triphenylphosphine (PPh₃). According to the DFT calculations, the difference in the catalytic activity of 3 and 4 is most likely associated with a different mechanism for the generation of ^●OH radicals. For complex 4 with electron-withdrawing CF₃ substituents at the diimine ligand, an alternative mechanism, different from Fenton’s and involving a redox-active ligand, is assumed.     

A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization

We present and analyze an interior-exterior augmented Lagrangian method for solving constrained optimization problems with both inequality and equality constraints. This method, the modified barrier—augmented Lagrangian (MBAL) method, is a combination of the modified barrier and the augmented Lagrangian methods. It is based on the MBAL function, which treats inequality constraints with a modified barrier term and equalities with an augmented Lagrangian term. The MBAL method alternatively minimizes the MBAL function in the primal space and updates the Lagrange multipliers. For a large enough fixed barrier-penalty parameter the MBAL method is shown to converge Q-linearly under the standard second-order optimality conditions. Q-superlinear convergence can be achieved by increasing the barrier-penalty parameter after each Lagrange multiplier update. We consider a dual problem that is based on the MBAL function. We prove a basic duality theorem for it and show that it has several important properties that fail to hold for the dual based on the classical Lagrangian.     

Peak effects in stable linear difference equations

We consider asymptotically stable scalar difference equations with unit-norm initial conditions. First, it is shown that the solution may happen to deviate far away from the equilibrium point at finite time instants prior to converging to zero. Second, for a number of root distributions and initial conditions, exact values of deviations or lower bounds are provided. Several specific difference equations known from the literature are also analysed and estimates of deviations are proposed. Third, we consider difference equations with non-random noise (ie bounded-noise autoregression) and provide upper bounds on the solutions. Possible generalizations, eg to the vector case are discussed and directions for future research are outlined.