Multi-state Ensemble Refinement for Occupancy Statistics (MEROS) in Time-Resolved X-ray Crystallography

Abstract

Accurate determination of state occupancies is essential for interpreting the structural heterogeneity inherent in time-resolved crystallography. However, in cases of high spatial overlap between states, as commonly observed in time-resolved crystallography data, the strong correlation between occupancy and atomic displacement parameters (ADPs) can render single point estimates from standard refinement protocols unreliable. We introduce MEROS (Multi-state Ensemble Refinement for Occupancy Statistics), a pipeline that implements an ensemble refinement approach to assess the post-refinement occupancy-ADP statistics of multiple overlapping states. MEROS utilizes a Monte Carlo sampling of the parameter space, performing independent refinements from randomized starting occupancies and ADP values to empirically characterize the convergence and uncertainty of the solution. The method is implemented as a modular Python pipeline that wraps established refinement programs, ensuring compatibility with existing workflows. We demonstrate its applicability in two case studies: a two-state ligand binding model in T4 lysozyme L99A and a four-state covalent catalysis mechanism in {beta}-lactamase CTX-M-14. MEROS provides occupancy and ADP mean values with standard deviations that directly quantify the informational content of the experimental diffraction data.