Towards chemical accuracy in QM/MM modelling of enzyme catalytic mechanisms and protein-ligand binding

Part of the BioExcel Virtual Workshop on Best Practices in QM/MM Simulation of Biomolecular Systems Video recording available at https://www.youtube.com/watch?v=8PGHcNKOLqY Abstract This presentation will cover practical aspects of combined quantum mechanics/molecular mechanics (QM/MM) calculations and their application to biomolecular systems [1,2,42,49,50]. QM/MM methods are now well established in computational biochemistry and enzymology [1,2]. Early applications included reactions in enzymes [3-10] and DNA [11]. QM/MM barriers were found to correlate with experimental rate constants for alternative substrates in para-hydroxybenzoate hydroxylase [6] and phenol hydroxylase [7], showing the QM/MM approach to be predictive for modelling enzyme catalysed reactions. QM/MM methods have demonstrated their value in revealing mechanisms of enzyme catalysis [1-10, 12-14], predicting reactivity of covalent inhibitors [15-17]; analysing effects of conformation [13, 13, 18-21], dynamics [22] and quantum tunnelling [23,24] in catalysis ; identifying novel catalytic interactions [6,7,25] analysing determinants of specificity in drug metabolism [26-29] and causes of drug resistance [30]. QM/MM simulations can be used as computational ‘assays’ of enzyme activity [31], e.g. distinguishing between beta-lactamases that can effectively hydrolyse carbapenem antibiotics from those that cannot [32]. QM/MM simulations also reproduce their susceptibility to inhibitors such as clavulanate [33]. QM/MM of Class D beta-lactamases reveal the molecular basis of differences in activity against cephalosporin antibiotics, showing that subtle changes in the active site account for experimentally observed differences in activity between OXA-48 and OXA-163 enzymes [34]. Recent QM/MM applications include modelling mechanisms of covalent inhibition of the SARS-CoV-2 main protease and suggesting modifications to tune reversibility [35]. High level ab initio quantum chemical methods can be applied in QM/MM calculations and can give barriers to enzyme-catalysed reactions with ‘chemical accuracy’ (~1kcal/mol, 4 kJ/mol) [36-39]. At this level of accuracy, reliable predictions can be made about the mechanisms of enzyme-catalysed reactions [40]. The excellent agreement with experiment shows the applicability of transition state theory for enzyme-catalysed reactions [40]. Projector-based embedding provides a practical approach to high level ab initio QM/MM calculations, rigorously embedding an ab initio region within a larger region treated by density functional theory (DFT) [41]. This removes uncertainty in reaction barriers and energies by removing dependence on the DFT functional [42], including for metalloenzymes [43]. Different types of application require different levels of treatment, which can be effectively combined in multiscale models to tackle a range of time- and length-scales, e.g. to study drug metabolism by cytochrome P450 enzymes [44], combining coarse-grained and atomistic molecular dynamics simulations, and QM/MM methods. Multiscale simulation schemes also now allow QM/MM methods to be applied to free energy simulations to study e.g. protein-ligand binding [45]. This approach allows the difference between a QM and a MM description of a ligand to be quantified, e.g. to calculate the contribution of changes in electronic polarization to binding affinity [46] and also to test the consistency of different QM and MM methods [47]. Such QM/MM free energy calculations, combined with metadynamics simulations, reveal changes in electronic polarization of a ligand (ibrutinib) as it binds to/dissociates from its protein target, showing limitations of MM forcefields for predicting binding kinetics [48]. References [1] Ryde U (2016) QM/MM Calculations on Proteins. Methods Enzymol 577:119–158. https://doi.org/10.1016/bs.mie.2016.05.014 [2] Cao L, Ryde U (2018) On the difference between additive and subtractive QM/MM calculations. Front Chem 6:89. https://doi.org/10.3389/fchem.2018.00089 [3] Ryde U, Olsen L, Nilsson K (2002) Quantum chemical geometry optimizations in proteins using crystallographic raw data. J Comput Chem 23:1058–1070. https://doi.org/10.1002/jcc.10093 [4] Hsiao Y, Drakenberg T, Ryde U (2005) NMR structure determination of proteins supplemented by quantum chemical calculations: Detailed structure of the Ca2+ sites in the EGF34 fragment of protein S. J Biomol NMR 31:97–114. https://doi.org/10.1007/s10858-004-6729-7 [5] Hsiao Y, Tao Y, Shokes JE, et al (2006) EXAFS structure refinement supplemented by computational chemistry. Phys Rev B 74:214101. https://doi.org/10.10.1103/PhysRevB.74.214101 [6] Caldararu O, Manzoni F, Oksanen E, et al (2019) Refinement of protein structures using a combination of quantum-mechanical calculations with neutron and X-ray crystallographic data. Acta Crystallogr Sect D Biol Crystallogr 75:368–380 [7] Ryde U, Nilsson K (2003) Quantum Chemistry Can Locally Improve Protein Crystal Structures. J Am Chem Soc 125:14232–14233. https://doi.org/10.1021/ja0365328 [8] Nilsson K, Ryde U (2004) Protonation status of metal-bound ligands can be determined by quantum refinement. J Inorg Biochem 98:1539–1546. https://doi.org/10.1016/j.jinorgbio.2004.06.006 [9] Söderhjelm P, Ryde U (2006) Combined computational and crystallographic study of the oxidised states of [NiFe] hydrogenase. J Mol Struct THEOCHEM 770:199–219. https://doi.org/10.1016/j.theochem.2006.06.008 [10] Cao L, Caldararu O, Rosenzweig AC, Ryde U (2018) Quantum Refinement Does Not Support Dinuclear Copper Sites in Crystal Structures of Particulate Methane Monooxygenase. Angew Chemie – Int Ed 57:162–166. https://doi.org/10.1002/anie.201708977 [11] Hu L, Söderhjelm P, Ryde U (2013) Accurate reaction energies in proteins obtained by combining QM/MM and large QM calculations. J Chem Theory Comput 9:640–649. https://doi.org/10.1021/ct3005003 [12] Sumner S, Söderhjelm P, Ryde U (2013) Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins. J Chem Theory Comput 9:4205–4214. https://doi.org/10.1021/ct400339c [13] Rod TH, Ryde U (2005) Accurate QM/MM free energy calculations of enzyme reactions: Methylation by catechol O-methyltransferase. J Chem Theory Comput 1:1240–1251. https://doi.org/10.1021/ct0501102 [14] Olsson MA, Ryde U (2017) Comparison of QM/MM Methods To Obtain Ligand-Binding Free Energies. J Chem Theory Comput 13:2245–2253. https://doi.org/10.1021/acs.jctc.6b0121