The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide chains: A study of 1830 independently computed conformations

Abstract

In this paper we study the statistical geometry of ensembles of poly(L-alanine) conformations computed by several different distance geometry algorithms. Since basic theory only permits us to predict the statistical properties of such ensembles a priori when the distance constraints have a very simple form, the only constraints used for these calculations are those necessary to obtain reasonable bond lengths and angles, together with a lack of short- and long-range atomic overlaps. The geometric properties studied include the squared end-to-end distance and radius of gyration of the computed conformations, in addition to the usual rms coordinate and ϕ / ψ angle deviations among these conformations. The distance geometry algorithms evaluated include several variations of the well-known embed algorithm, together with optimizations of the torsion angles using the ellipsoid and variable target function algorithms. The conclusions may be summarized as follows: First, the distribution with which the trail distances are chosen in most implementations of the embed algorithm is not appropriate when no long-range upper bounds on the distances are present, because it leads to unjustifiable expanded conformations. Second, chosing the trail distances independently of one another leads to a lack of variation in the degree of expansion, which in turn produces a relatively low rms square coordinate difference among the members of the ensemble. Third, when short-range steric constraints are present, torsion angle optimizations that start from conformations obtained by choosing their ϕ / ψ angles randomly with a uniform distribution between − 180° and + 180° do not converge to conformations whose angles are uniformly distributed over the sterically allowed regions of the ϕ / ψ plane. Finally, in an appendix we show how the sampling obtained with the embed algorithm can be substantially improved upon by the proper application of existing methodology.