Applications of random sampling to virtual screening of combinatorial libraries

We describe statistical techniques for effective evaluation of large virtual combinatorial libraries (> 10(10) potential compounds). The methods described are used for computationally evaluating templates (prioritization of candidate libraries for synthesis and screening) and for the design of individual combinatorial libraries (e.g., for a given diversity site, reagents can be selected based on the estimated frequency with which they appear in products that pass a computational filter). These statistical methods are powerful because they provide a simple way to estimate the properties of the overall library without explicitly enumerating all of the possible products. In addition, they are fast and simple, and the amount of sampling required to achieve a desired precision is calculable. In this article, we discuss the computational methods that allow random product selection from a combinatorial library and the statistics involved in estimating errors from quantities obtained from such samples. We then describe three examples: (1) an estimate of average molecular weight for the several billion possible products in a four-component Ugi reaction, a quantity that can be calculated exactly for comparison; (2) the prioritization of four templates for combinatorial synthesis using a computational filter based on four-point pharmacophores; and (3) selection of reagents for the four-component Ugi reaction based on their frequency of occurrence in products that pass a pharmacophore filter.