Refinement of protein crystal structures using energy restraints derived from linear-scaling quantum mechanics

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A novel method is proposed in which combined restraints derived from linear-scaling semiempirical quantum-mechanical (QM) calculations and X-ray diffraction data are combined to refine crystal structures of proteins. Its performance has been tested on a small protein molecule, bovine pancreatic trypsin inhibitor (BPTI). The refinement involves minimization of the sum of a geometric energy function and an X-ray target function based on either the least-squares residual or the maximum-likelihood formalism. For comparison, similar refinement runs have also been performed using energy restraints derived from the force field available in the Crystallography & NMR System (CNS) program. The QM refinements were carried out with weights that were varied by several orders of magnitude and the optimal weights were identified by observing the trend in the final free R values, QM heats of formation and coordinate root-mean-square deviations (r.m.s.d.s) from the crystal structure. It is found that the QM weights are typically smaller but generally on the same scale as the molecular-mechanics (MM) weights for the respective X-ray target functions. The crystallographic R, free R, real-space R values and correlation coefficients based on the structures refined with the energy restraints derived from our QM calculations and Engh and Huber parameters are comparable, suggesting that the QM restraints are capable of maintaining reasonable stereochemistry to a similar degree as the force-field parameters. A detailed inspection of the structures refined with the QM and MM energy restraints reveals that one of the common differences between them and the crystal structure is that the strained bond angles in the crystal structure are corrected after energetically restrained refinements. Systematic differences in certain bond lengths between the QM-refined structures and the statistical averages of experimental structures have also been observed and discussed.