OVID and SUPER: Two overlap programs for drug design

Summary Two programs, OVID and SUPER, for exploring the similarity of molecules with respect to their action at a receptor are described. OVID accepts two molecules as input and optimizes the three-dimensional overlap of specified atoms in one molecule with specified atoms in the second molecule. The result is expressed as a percent of the theoretical maximum. OVID gives a quantitative measure of the extent of a guessed correspondence between two molecules based on volume overlap of selected atoms. The Achilles' heel of OVID is that the correspondence between the two molecules has to be guessed. We realized that it would be better to systematically examine all possible correspondences of two structures to minimize the chance of overlooking a superior correspondence. We created SUPER to satisfy this need. SUPER accepts two molecules as input and finds the top twenty correspondences of their surfaces and charge distributions, giving a quantitative measure of the extent of each correspondence. An instructive example of the application of OVID and SUPER to the design of leukotriene D₄ receptor antagonists is described. SUPER appears to be a practical brainstorming tool for the medicinal chemist trying to understand how molecules whose structures may not resemble one another in an obvious way can bind to the same site.     

Orbital Polarization and Magnetization for Independent Particles in Disordered Media

Formulas for the contribution of the conduction electrons to the polarization and magnetization are derived for disordered systems and within a one-particle framework. These results generalize known formulas for Bloch electrons and the presented proofs considerably simplify and strengthen prior justifications. The new formulas show that orbital polarization and magnetization are of geometric nature. This leads to quantization for a periodically driven Piezo effect as well as the derivative of the magnetization w.r.t. the chemical potential. It is also shown how the latter is connected to boundary currents in Chern insulators. The main technical tools in the proofs are an adaption of Nenciu’s super-adiabatic theory to C*-dynamical systems and Bellissard’s Ito derivatives w.r.t. the magnetic field.     

The maximal ideal space of with respect to the Hadamard product

It is shown that the space of all regular maximal ideals in the Banach algebra with respect to the Hadamard product is isomorphic to The multiplicative functionals are exactly the evaluations at the -th Taylor coefficient. It is a consequence that for a given function in and for a function holomorphic in a neighborhood of with and for all the function is in

     

Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows

This paper describes the parallelization of a two-phase metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The underlying objective function combines the minimization of the number of vehicles in the first search phase of the metaheuristic with the minimization of the total travel distance in the second search phase. The parallelization of the metaheuristic follows a type 3 parallelization strategy (cf. Crainic and Toulouse (2001). In F. Glover and G. Kochenberger (eds.). State-of-the-Art Handbook in Metaheuristics. Norwell, MA: Kluwer Academic Publishers), i.e. several concurrent searches of the solution space are carried out with a differently configured metaheuristic. The concurrently executed processes cooperate through the exchange of solutions. The parallelized two-phase metaheuristic was subjected to a comparative test on the basis of 358 problems from the literature with sizes varying from 100 to 1000 customers. The derived results seem to justify the proposed parallelization concept.