Abstract
Proteins naturally adopt multiple conformations in mediating cellular processes, and ensemble models are used to fit X-ray crystallography data that captures this heterogeneity. In practice, ensemble refinement produces only minor improvements in agreement with experimental data (
R
free
) over single-conformation models. It has recently been shown that ensemble models are universally trapped, or “tangled”; refinement algorithms strain each individual conformation in the model to fit the electron density in its immediate vicinity, missing more harmonious ways to arrange the collection of protein conformations to fit the electron density. Here, we demonstrate that this type of trap may be escaped by formulating the construction of low-energy conformations from individual conformer coordinates as an integer linear programming problem. The method successfully recovered the two original protein conformations from a previously published synthetic dataset that traps current refinement methods. Inclusion of the method in an automated refinement procedure with real data is shown to improve
R
free
and reduce geometric strain in a four-conformation model by comparison with controls. Applying this method in combination with human input and fitting low-occupancy waters to density features in the bulk solvent, we produce models for deposited datasets of three separate 14–19 kDa proteins with greatly improved geometry and
R
-factors. This includes a 0.77 Å six-conformation model of the SARS-CoV-2 macrodomain Mac1 (PDB ID: 44PS) with an
R
work
of 4.7% and an
R
free
of 6.4%.