Deriving interatomic distance bounds from chemical structure
Michael W. Trosset, George N. Phillips · Lecture notes-monograph series · 1999
this report, we assume the importance of such knowledge and focus on one class of mathematical problems that are sometimes solved to obtain it. The problem that motivates this report is that of calculating 3-dimensional Cartesian coordinates of atoms from information about interatomic distances. Such information usually assumes the form of lower and upper bounds on the distances. This report is concerned with the derivation of such bounds from a molecule's chemical structure, which we assume to be known. It is addressed to computational scientists who are interested in problems that involve determining 3-dimensional molecular structures that are consistent with specified bounds on interatomic distances. These researchers require sample problems on which to test new algorithms. The methods described herein provide an alternative to (1) inventing structures with no chemical plausiblity and (2) mastering specialized techniques that require considerable expertise in structural molecular biology. In Section 2 we introduce some technical notation and provide some relevant background material. In Section 3 we provide detailed descriptions of several useful calculations for inferring lower and upper bounds on interatomic distances from chemical structure. In Section 4 we apply the techniques of Section 3 to an analogue of the antibiotic trichogin A IV. This is a small (n = 38 atoms) molecule on which we have been testing prototype algorithms. In Section 5 we conclude by identifying broader contexts in which having bounds on interatomic distances may be useful. INTERATOMC DISTANCE BOUNDS 3