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

Abstract

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.

QM methods in structure based design: Utility in probing protein–ligand interactions

“…While this work is not representative due to the focus on small numbers of structures from a single target class, from a more general consideration of the literature [21,20,[24][25][26][27]51] it does appear that the atomic coordinates derived from X-ray analyses, while capable of demonstrating the overall ligand binding modes, should not necessarily be taken as a "perfect" reference given the intrinsic errors that arise from protein mobility and choices made during structural refinement [21]. This is particularly important for the validation of ligand docking methods since the X-ray coordinates are often used in quantitative way to assess the performance of software [51].…”

“…This is because repulsive interactions, either real or due to sub-optimal refinement, can be unrealistically dissipated into the wider protein by very small changes in the overall protein conformation following MM optimization. This could arise due to the limitations of MM forcefields [8,9,[24][25][26] or the coupling between QM and MM regions in QM/MM calculations [46].…”

“…This might also be pertinent in light of research that show the ligand density associated with relatively weak binding inhibitors can be less distinct, even for protein structures of good overall resolution [20], which can complicate their application to SBD [21]. Indeed classical molecular mechanical (MM) [22,23] and QM based methods [24,25] have been specifically developed to help improve the active site placement of ligands and co-factors. MM techniques are widely used in the pharmaceutical industry as they are both fast and the results are easily interpretable due to the relatively simple terms used in the derivation of their forcefields.…”

Comment onStereochemical restraints revisited: how accurate are refinement targets and how much should protein structures be allowed to deviate from them?by Jaskolski, Gilski, Dauter & Wlodawer (2007)

“…This particular problem calls for special methods that couple restraints with nonlinear optimization. For example, methods that combine ab initio quantum-mechanical optimization with crystallographic refinement are being developed, and such methods need to be mentioned (Yu et al, 2005;Zarychta et al, 2007;Volkov et al, 2007).…”

Improved ligand geometries in crystallographic refinement usingAFITTinPHENIX

“…We have chosen to only compare refinement using AFITT-derived CIF restraint dictionaries versus obtaining the ligand geometry gradients in refinement directly from AFITT (PHENIX-AFITT). Thus, our comparison is not complicated by differences in potential functions and target values for the methods used by various other ligand restraint-file generation and modeling methods (Borbulevych, Moriarty et al, 2014;Borbulevych, Plumley, et al, 2014;Davis et al, 2003;Fu et al, 2011;Lebedev et al, 2012;Moriarty et al, 2009;Schü ttelkopf & van Aalten, 2004;Smart et al, 2010Smart et al, , 2012Yu et al, 2005). Instead, differences hinge only on the improvement gained by representing the ligand with the full molecular-mechanics force field during the course of refinement.…”