Sampling efficiency

Sampling efficiency (SE) for a given simulation trajectory is defined as the probability of finding a simulation decoy with RMSD from the target (R) smaller than RMSD of the initial structure from the target (R₁). It can be computed as follows

Any simulation trajectory with the known target structure can thus be assigned a specific value of the actual SE. In addition to the actual SE, we also introduce the hypothetical SE, which is based on the assumption of even sampling of objects with spherical symmetry. In a simple geometrical model, the sampling range R₂ can be represented by the length of a line segment (1D), the radius of a circle (2D) or the radius of a sphere (3D) that encloses 95% of all simulation decoys. R₁, on the other hand, is given in this simple picture by the distance between the points (in 1D, 2D or 3D) representing the initial and target structures. The hypothetical SE is then given by the ratio of the overlapped length (1D), area (2D) or volume (3D), as illustrated in Fig 3, to the overall sampling length (1D), area (2D) or volume (3D). The hypothetical SE is thus given by the following formulas

The hypothetical SE is a continuous function of the ratio R₂/R₁. It takes the values between 0 and 0.5, which reflects the assumption about even sampling. The actual SE, on the other hand, takes the values between 0 and 1. Thus, if the actual SE is significantly higher or lower than the hypothetical SE, it indicates uneven or biased sampling.