A statistical framework for hierarchical methods in molecular simulation and design

A statistical framework for performance analysis in hierarchical methods is described, with a focus on applications in molecular design. A theory is derived from statistical principles, describing the relationships between the results of each hierarchical level by a functional correlation and an error model for how values are distributed around the correlation curve. Two key measures are then defined for evaluating a hierarchical approach - completeness and excess cost - conceptually similar to the sensitivity and specificity of dichotomous prediction methods. We demonstrate the use of this method using a simple model problem in conformational search, refining the results of an in vacuo search of glucose conformations with a continuum solvent model. Second, we show the usefulness of this approach when structural hierarchies are used to efficiently make use of large rotamer libraries with the Dead-end Elimination and A* algorithms for protein design. The framework described is applicable not only to the specific examples given but to any problem in molecular simulation or design that involves a hierarchical approach.