Efficiency of Stratification for Ensemble Docking Using Reduced Ensembles

Molecular docking can account for receptor flexibility by combining the docking score over multiple rigid receptor conformations, such as snapshots from a molecular dynamics simulation. Here, we evaluate a number of common snapshot selection strategies using a quality metric from stratified sampling, the efficiency of stratification, which compares the variance of a selection strategy to simple random sampling. We also extend the metric to estimators of exponential averages (which involve an exponential transformation, averaging, and inverse transformation) and minima. For docking sets of over 500 ligands to four different proteins of varying flexibility, we observe that, for estimating ensemble averages and exponential averages, many clustering algorithms have similar performance trends: for a few snapshots (less than 25), medoids are the most efficient, while, for a larger number, optimal (the allocation that minimizes the variance) and proportional (to the size of each cluster) allocation become more efficient. Proportional allocation appears to be the most consistently efficient for estimating minima.