Progressive alignment of crystals: reproducible and efficient assessment of crystal structure similarity

Abstract

During in silico crystal structure prediction of organic molecules, millions of candidate structures are often generated. These candidates must be compared to remove duplicates prior to further analysis (e.g. optimization with electronic structure methods) and ultimately compared with structures determined experimentally. The agreement of predicted and experimental structures forms the basis of evaluating the results from the Cambridge Crystallographic Data Centre (CCDC) blind assessment of crystal structure prediction, which further motivates the pursuit of rigorous alignments. Evaluating crystal structure packings using coordinate root-mean-square deviation (RMSD) for N molecules (or N asymmetric units) in a reproducible manner requires metrics to describe the shape of the compared molecular clusters to account for alternative approaches used to prioritize selection of molecules. Described here is a flexible algorithm called Progressive Alignment of Crystals (PAC) to evaluate crystal packing similarity using coordinate RMSD and introducing the radius of gyration (R g) as a metric to quantify the shape of the superimposed clusters. It is shown that the absence of metrics to describe cluster shape adds ambiguity to the results of the CCDC blind assessments because it is not possible to determine whether the superposition algorithm has prioritized tightly packed molecular clusters (i.e. to minimize R g) or prioritized reduced RMSD (i.e. via possibly elongated clusters with relatively larger R g). For example, it is shown that when the PAC algorithm described here uses single linkage to prioritize molecules for inclusion in the superimposed clusters, the results are nearly identical to those calculated by the widely used program COMPACK. However, the lower R g values obtained by the use of average linkage are favored for molecule prioritization because the resulting RMSDs more equally reflect the importance of packing along each dimension. It is shown that the PAC algorithm is faster than COMPACK when using a single process and its utility for biomolecular crystals is demonstrated. Finally, parallel scaling up to 64 processes in the open-source code Force Field X is presented.

Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field

“… a The RMSDs were calculated using the progressive alignment of crystals (PAC) method, 61 with a single peptide molecule used for the comparison. Coformers were ignored in the RMSD comparison.…”

“…The asymmetric unit could not be appropriately simulated for CURLOQ due to the presence of atoms with fractional occupancy. The RMSDs were calculated using the progressive alignment of crystals (PAC) method, 61 with a single peptide molecule used for the comparison. Coformers were ignored in the RMSD comparison.…”

Crystal Polymorph Search in the NPT Ensemble via a Deposition/Sublimation Alchemical Path

“…The PAC algorithm, which compares crystal structures using an efficient algorithm that prioritizes low radius of gyration molecular clusters, was used to compare all snapshots for a given space group . PAC (via the FFX command SuperposeCrystals ) calculates the root-mean-square deviation (rmsd) between the heavy atoms of two crystals by optimally superimposing a cluster of N molecules (where N = 20 is denoted by rmsd 20 ).…”

“…The PAC algorithm, which compares crystal structures using an efficient algorithm that prioritizes low radius of gyration molecular clusters, was used to compare all snapshots for a given space group. 52 PAC (via the FFX command SuperposeCrystals ) calculates the root-mean-square deviation (rmsd) between the heavy atoms of two crystals by optimally superimposing a cluster of N molecules (where N = 20 is denoted by rmsd 20 ). PAC was used to compute a similarity matrix for all snapshots of each space group against themselves (e.g., all P snapshots vs all P snapshots), which then served as input to the clustering algorithm described below.…”

“…Once candidate polymorphs have been collected, the goal of CSP pipelines is generally to eliminate duplicates using crystal packing comparisons 52 and/or clustering, followed by rescoring a subset of the most favorable polymorphs (e.g., using DFT). 53 As the discrepancies between the potential energy function used during the search phase (e.g., the AMOEBA force field) and the electronic structure method are reduced, fewer polymorphs need to be rescored.…”