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

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.