Conformation of receptor-associated PGI2: An investigation by molecular modeling

Summary To elucidate the conformation of receptor-associated prostacyclin (PGI₂), we first performed structure-activity correlation analysis of over 200 PGI₂ analogues and derived from this analysis several crucial features pertaining to structural requirements for PGI₂ activity [Ah-lim Tsai and Kenneth K. Wu, Eicosanoids, 2 (1989) 131–143]. These structural features proved to be useful guidelines for selecting model molecules for further investigations by molecular mechanics. By properly selecting four analogues with either rigid or uniquely oriented -side chain structure for geometric fitting, we succeeded in maximally minimizing the degree of freedom of the carboxylate terminus of PGI₂. We were able to define the spatial relationship among the four critical functional groups, i.e., C1-COOH, C6a-O, C11-OH and C15-OH. More information is needed, however, to define the geometry of the -side chain, particularly for the moiety beyond C15. Nevertheless, results from structure-activity correlation analysis and molecular modeling provide useful information regarding the conformation of receptor-associated PGI₂, which assumes an elongated conformation instead of the traditional hairpin structure.     

Partially and totally asynchronous algorithms for linear complementarity problems

A unified treatment is given for partially and totally asynchronous parallel successive overrelaxation (SOR) algorithms for the linear complementarity problem. Convergence conditions are established and compared to previous results. Convergence of the partially asynchronous method for the symmetric linear complementarity problem can be guaranteed if the relaxation factor is sufficiently small. Unlike previous results, this relaxation factor interval does not depend explicitly on problem size.This material is based on research supported by the Air Force Office of Scientific Research Grant No. AFOSR-89-0410.The author wishes to thank the referee for pointing out how to improve the bound (12). The same technique can be used to reduce the factorn in Ref. 5, p. 553, to .     

Potential surfaces for time-like geodesics in the Curzon metric

In this paper we deduce the general pattern of the potential surfaces for time-like geodesics in the Curzon metric. We find that for fairly small energies and orbital angular momenta, the time-like geodesics group into two sets; the geodesics of one set tend to thez-axis asR=(r²+z²)^1/2 0,R=0 being a directional singularity, the others tend to ther-axis. At low energies these two sets are detached but they merge together as the energy increases. Stable circular motion is confined to thez = 0-plane and an energy threshold for stationary motion exists and is equal (per unit of rest-mass energy) to 0.945, a value almost indistinguishable from that in the Schwarzschild space-time.     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.