Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution

Abstract

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wavefunction method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.well with the CI-NEB path and indicates that the reaction coordinate used here performs well for this reaction.Structures were taken from the corresponding solution or enzyme SCCDFTB/CHARMM22 MD stochastic boundary simulations (120 ps) of the model systems for use in adiabatic mapping calculations. For this, Jaguar 68 and Tinker 69 , linked by the interface program QoMMMa 70 , were used for QM and MM calculations, with electronic coupling between the two regions treated by including MM charges in the QM Hamiltonian.CHARMM27 Lennard-Jones parameters (for standard CHARMM27 atom types, see Table S1) were used to describe QM/MM van der Waals interactions. The QM region was treated at the hybrid density functional B3LYP/6-31G(d) level of theory, which gives a reasonably good description of the reaction. 12 The enzyme model consisted of 7077 atoms and the solution model contained 7218 atoms. The MM region comprised an approximate 25 Å radius sphere of protein and/or solvent, treated with the CHARMM27 forcefield. 71 The outer 5 Å in each case was fixed (3324 atoms fixed in the enzyme model and 3535 fixed in the solution model),with all other atoms free to move. As there is no evidence for large-scale conformational changes during the reaction, this approach should give a representative sample of reactive conformations in the enzyme. 49,51, 53,54 Each initial structure was fully optimized at the B3LYP/6-31G(d)/CHARMM27 QM/MM level, while restraining the reaction coordinate (r) to -0.5 Å with a harmonic force constant of 500 kcal/mol/Å 2 , to generate starting structures.Reaction pathways were generated by restrained optimizations in both directions along the reaction coordinate, towards the reactant and the product, in steps of 0.2 Å (0.1 Å around the TS), with both the MM and QM systems fully and consistently optimized at each step. Energy profiles were calculated from r = −2.2 Å to 2.2 Å, to identify the reactant and product mini...

Electronic structure benchmark calculations of CO2 fixing elementary chemical steps in RuBisCO using the projector‐based embedding approach

“…Figure 2 shows the activation (blue) and reaction (orange) energies obtained for each chemical step within the sequence of reactions catalyzed by RuBisCO enzyme (carboxylation, hydration, bond dissociation and protonation). In biological systems that have an electronic state that is well described by a single electronic configuration the performance of SCS‐MP2 is often comparable to other high‐level electronic structure methods like CCSD(T), [ 27–29,44 ] therefore, SCS‐MP2 was selected as the reference in this particular selection of methods and its results are shown as dotted line in Figure 2.…”

“…Among the electronic structure methods, SCS‐MP2 is the highest level method considering the 77 atoms and 316 electrons of the whole system and provides the reference, which in general gives better results than MP2 and is very close to CCSD(T) in some cases. [ 27–29,44 ]…”

“…The embedding approach has been shown to remove the dependence of enzyme reaction barriers on density functional. [ 29 ] To our knowledge, the calculations here are the first application of this approach to a metalloenzyme.…”

“…This shows that the embedding method provides accurate results for this metalloenzyme, as has been found previously for reactions catalyzed by enzymes that do not use metal ions in catalysis. [ 27–30 ] Considering that this method enables high‐level post‐HF calculations on electronic systems of several hundreds of electrons, its direct application along the reaction path obtained from QM/MM calculations becomes possible. From the potential energy profiles, high‐level post‐HF activation barriers will be derived, which will consider the electrostatic effect of the surrounding enzyme, contributing to the understanding of enzymatic reaction mechanisms.…”

“…Here, a computational study of the carboxylase activity of RuBisCO enzyme assesses different ab initio and DFT electronic structure methods for the reaction path proposed by Gready et al [ 5 ] The projector‐based embedding approach is used: this can eliminate the variability often found when different DFT exchange‐correlation functionals (DFT xc‐functional) are selected. [ 27–30 ] This embedding approach has not previously been applied to a metalloenzyme, to our knowledge. This methodology allows us to obtain accurate activation and reaction energies, by describing the most important part of the reactions with a high‐level ab initio post‐HF electronic structure method, within a DFT treatment of the active‐site model.…”