Proteases screening for the kinetic resolution of amines with N-acyl α-amino acid trifluoromethyl esters: automated docking approach of binding energies using Subtilisin Novo as a prototype for serine proteases

The screening of a panel of 17 proteases resulted in the selection of 4 serine proteases for the resolution of 3-amino-1-phenylbutane. The latter were used to determine the best acyl donor from a series of N-acyl α-amino acid trifluoroethyl esters selected as peptide mimetics (E factor up to 99). The results were correlated to an automated docking determination of their binding affinities for Subtilisin Novo.     

Photoionization of molecular oxygen in the X3Σg− and a1Δg states

Calculations are carried out, at similar levels of approximation, of the photoionization cross-sections for the ground X³Σ_g^? and metastable a¹Δ_g states of O₂ leading to the X²Π_g state of O₂⁺. Estimates, based upon measurements for the X³Σ_g^? state, are made of the photoionization cross-section of the a¹Δ_g state for transitions populating excited states of O₂⁺.     

A matrix generation approach for eigenvalue optimization

We study the extension of a column generation technique to nonpolyhedral models. In particular, we study the problem of minimizing the maximum eigenvalue of an affine combination of symmetric matrices. At each step of the algorithm a restricted master problem in the primal space, corresponding to the relaxed dual (original) problem, is formed. A query point is obtained as an approximate analytic center of a bounded set that contains the optimal solution of the dual problem. The original objective function is evaluated at the query point, and depending on its differentiability a column or a matrix is added to the restricted master problem. We discuss the issues of recovering feasibility after the restricted master problem is updated by a column or a matrix. The computational experience of implementing the algorithm on randomly generated problems are reported and the cpu time of the matrix generation algorithm is compared with that of the primal-dual interior point methods on dense and sparse problems using the software SDPT3. Our numerical results illustrate that the matrix generation algorithm outperforms primal-dual interior point methods on dense problems with no structure and also on a class of sparse problems. This work has been completed with the partial support of a summer grant from the College of Business Administration, California State University San Marcos, and the University Professional Development/Research and Creative Activity Grant     

The integration of an interior-point cutting plane method within a branch-and-price algorithm

This paper presents a novel integration of interior point cutting plane methods within branch-and-price algorithms. Unlike the classical method, columns are generated at a central dual solution by applying the analytic centre cutting plane method (ACCPM) on the dual of the full master problem. First, we introduce some modifications to ACCPM. We propose a new procedure to recover primal feasibility after adding cuts and use, for the first time, a dual Newtons method to calculate the new analytic centre after branching. Second, we discuss the integration of ACCPM within the branch-and-price algorithm. We detail the use of ACCPM as the search goes deep in the branch and bound tree, making full utilization of past information as a warm start. We exploit dual information from ACCPM to generate incumbent feasible solutions and to guide branching. Finally, the overall approach is implemented and tested for the bin-packing problem and the capacitated facility location problem with single sourcing. We compare against Cplex-MIP 7.5 as well as a classical branch-and-price algorithm.Mathematics Subject Classification (1991): 20E28, 20G40, 20C20     

An analytic center quadratic cut method for the convex quadratic feasibility problem

 We consider a quadratic cut method based on analytic centers for two cases of convex quadratic feasibility problems. In the first case, the convex set is defined by a finite yet large number, N, of convex quadratic inequalities. We extend quadratic cut algorithm of Luo and Sun [3] for solving such problems by placing or translating the quadratic cuts directly through the current approximate center. We show that, in terms of total number of addition and translation of cuts, our algorithm has the same polynomial worst case complexity as theirs [3]. However, the total number of steps, where steps consist of (damped) Newton steps, function evaluations and arithmetic operations, required to update from one approximate center to another is , where ε is the radius of the largest ball contained in the feasible set. In the second case, the convex set is defined by an infinite number of certain strongly convex quadratic inequalities. We adapt the same quadratic cut method for the first case to the second one. We show that in this case the quadratic cut algorithm is a fully polynomial approximation scheme. Furthermore, we show that, at each iteration, k, the total number steps (as described above) required to update from one approximate center to another is at most , with ε as defined above. Received: April 2000 / Accepted: June 2002 Published online: September 5, 2002 Key words. convex quadratic feasibility problem – interior-point methods – analytic center – quadratic cuts – potential function     

Variable metric relaxation methods,part II: The ellipsoid method

The deepest, or least shallow, cut ellipsoid method is a polynomial (time and space) method which finds an ellipsoid, representable by polynomial space integers, such that the maximal ellipsoidal distance relaxation method using this fixed ellipsoid is polynomial: this is equivalent to finding a linear transforming such that the maximal distance relaxation method of Agmon, Motzkin and Schoenberg in this transformed space is polynomial. If perfect arithmetic is used, then the sequence of ellipsoids generated by the method converges to a set of ellipsoids, which share some of the properties of the classical Hessian at an optimum point of a function; and thus the ellipsoid method is quite analogous to a variable metric quasi-Newton method. This research was supported in part by the F.C.A.C. of Quebec, and the N.S.E.R.C. of Canada under Grant A 4152.     

New insights into self-organization of a model lipid mixture and quantification of its adsorption on spherical polymer particles

The adsorption of lipids onto spherical polymer colloids led to original assemblies presenting structural characteristics adjustable with the lipid formulation. The model system selected for this work involved sulfate-charged poly(styrene) submicrometer particles and zwitterionic/cationic lipid mixtures composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dipalmitoyl-3-trimethylammonium-propane (DPTAP). According to the theoretical packing parameter calculations and whatever the DPPC/DPTAP ratio, the two lipids self-assembled in aqueous media to spontaneously form vesicles. A phase transition investigation of these DPPC/DPTAP vesicles using differential scanning calorimetry revealed particular thermotropic behaviors, especially for the equimolar formulation where very strong interactions occurred between DPPC and DPTAP. Furthermore, the coating of the lipids around particles was monitored versus DPPC/DPTAP ratio by means of numerous appropriate techniques. First, a thermogravimetric analysis, providing decomposition profiles of lipid/polymer particle assemblies with temperature, was atypically carried out for such nanostructures. Then, 1H NMR spectroscopy enabled the exact DPPC/DPTAP molar ratios adsorbed on particles to be determined by differentiating both lipids. Subsequently, it also pointed out the major role of electrostatic interactions as driving forces in the assembly elaboration process. In addition to these findings, quantitative information has been collected and correlated with chemical lipid assays and permitted the statement of a lipid bilayer coverage for the assemblies prepared in water, in agreement with quasi-elastic light scattering data.     

PtCl2-Catalyzed transannular cycloisomerization of 1,5-enynes: a new efficient regio- and stereocontrolled access to tricyclic derivatives

[reaction: see text] Transannular PtCl(2)-catalyzed cycloisomerizations open a new route to cyclopropanic tricyclic systems. Ketones A or C were efficiently prepared from the same cycloundec-5-en-1-yne precursor B, depending on the substituent at the propargylic position (either benzoate or methoxy).     

Fe(II)-induced reduction of labelled endoperoxides. NMR degradation studies on G3 factor and its methyl ether

The behavior of G3 factor and of its methylated or fluorinated analogues G3Me and G3F, was studied under Fe(II) conditions. Degradation products were isolated and characterized in each case. The use of labelled compounds allowed us to propose mechanisms in which a tertiary radical is involved. This radical rearranges by 5-exo-trig cyclization, or disproportionates in the case of G3Me. A correlation between antiplasmodial activity and stability of this radical is proposed.     

On convergence rates of subgradient optimization methods

Rates of convergence of subgradient optimization are studied. If the step size is chosen to be a geometric progression with ratio the convergence, if it occurs, is geometric with rate. For convergence to occur, it is necessary that the initial step size be large enough, and that the ratio be greater than a sustainable ratez(), which depends upon a condition number, defined for both differentiable and nondifferentiable functions. The sustainable ratez() is closely related to the rate of convergence of the steepest ascent method for differentiable functions: in fact it is identical if the function is not too well conditioned.This research was supported in part by the D.G.E.S. (Quebec) and the N.R.C. of Canada under grants A8970 and A4152.