Biomolecular Resolution as a Quantification of Structural Information Content

Abstract

Resolution is a poorly defined, ad hoc concept in structural biology, and multiple, seemingly conflicting definitions exist. In part, this ambiguity is because the structural information describing a biomolecule manifests in different ways depending upon the length scale being considered, while typical approaches to resolution just consider a single length scale. To address this shortcoming, here we develop a definition of resolution as a measure of how effectively those different manifestations of biomolecular structural information are embedded in experimental data across different length scales. We show how biomolecular structures can be decomposed into a hierarchy of structural elements, and combinations of those structural elements yield representations of the biomolecule with different degrees of spatial detail. A probabilistic measure, which we call "hierarchical resolution," can then be calculated to determine the statistically optimal representation of a biomolecule in an experiment. Hierarchical resolution is a local, detection-sensitive resolution measure capable of quantifying the biomolecular structural content of an experiment. Altogether, these advances comprise a technique-independent definition of resolution, and clarify the term "atomic resolution" for high-resolution techniques.