Computational experience with an algorithm for tetrangle inequality bound smoothing

An important component of computer programs for determining the solution conformation of proteins and other flexible molecules from nuclear magnetic resonance data are the so-called “bound smoothing algorithms”, which compute lower and upper limits on the values of all the interatomic distances from the relatively sparse set which can usually be measured experimentally. To date, the only methods efficient enough for use in large problems take account of only the triangle inequality, but an appreciable improvement in the precision of the limits is possible if the algebraic relations between the distances among each quadruple of atoms are also considered. The goal of this paper is to use a recently improved algorithm for computing these “tetrangle inequality limits” to determine just how much improvement really is possible, given the types of experimental data that are usually available.