Using AlphaFold and Experimental Structures for the Prediction of the Structure and Binding Affinities of GPCR Complexes via Induced Fit Docking and Free Energy Perturbation.

Free energy perturbation (FEP) remains an indispensable method for computationally assaying prospective compounds in advance of synthesis. However, before FEP can be deployed prospectively, it must demonstrate retrospective recapitulation of known experimental data where the subtle details of the atomic ligand-receptor model are consequential. An open question is whether AlphaFold models can serve as useful initial models for FEP in the regime where there exists a congeneric series of known chemical matter but where no experimental structures are available either of the target or of close homologues. As AlphaFold structures are provided without a bound ligand, we employ induced fit docking to refine the AlphaFold models in the presence of one or more congeneric ligands. In this work, we first validate the performance of our latest induced fit docking technology, IFD-MD, on a retrospective set of public experimental GPCR structures with 95% of cross-docks producing a pose with a ligand RMSD ≤ 2.5 Å in the top two predictions. We then apply IFD-MD and FEP on AlphaFold models of the somatostatin receptor family of GPCRs. We use AlphaFold models produced prior to the availability of any experimental structure from this family. We arrive at FEP-validated models for SSTR2, SSTR4, and SSTR5, with RMSE around 1 kcal/mol, and explore the challenges of model validation under scenarios of limited ligand data, ample ligand data, and categorical data.

Reliable and Accurate Prediction of Single-Residue pKa Values through Free Energy Perturbation Calculations.

Accurate prediction of the pKa's of protein residues is crucial to many applications in biological simulation and drug discovery. Here, we present the use of free energy perturbation (FEP) calculations for the prediction of single-protein residue pKa values. We begin with an initial set of 191 residues with experimentally determined pKa values. To isolate sampling limitations from force field inaccuracies, we develop an algorithm to classify residues whose environments are significantly affected by crystal packing effects. We then report an approach to identify buried histidines that require significant sampling beyond what is achieved in typical FEP calculations. We therefore define a clean data set not requiring algorithms capable of predicting major conformational changes on which other pKa prediction methods can be tested. On this data set, we report an RMSE of 0.76 pKa units for 35 ASP residues, 0.51 pKa units for 44 GLU residues, and 0.67 pKa units for 76 HIS residues.

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals.

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T0) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Predicting Ligand-Dissociation Energies of 3d Coordination Complexes with Auxiliary-Field Quantum Monte Carlo.

Transition-metal complexes are ubiquitous in biology and chemical catalysis, yet they remain difficult to accurately describe with ab initio methods because of the presence of a large degree of dynamic electron correlation, and, in some cases, strong static correlation which results from a manifold of low-lying states. Progress has been hindered by a scarcity of high-quality gas-phase experimental data, while exact ab initio predictions are usually computationally unaffordable because of the large size of the relevant complexes. In this work, we present a data set of 34 tetrahedral, square planar, and octahedral 3d metal-containing complexes with gas-phase ligand-dissociation energies that have reported uncertainties of ≤2 kcal/mol. We perform all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) calculations utilizing multideterminant trial wave functions selected by a black box procedure. We compare the results with those from the density functional theory (DFT) with the B3LYP, B97, M06, PBE0, ωB97X-V, and DSD-PBEP86/2013 functionals and a localized orbital variant of the coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)). We find mean averaged errors of 1.07 ± 0.27 kcal/mol for our most sophisticated ph-AFQMC approach versus 2.81 kcal/mol for DLPNO-CCSD(T) and 1.49-3.78 kcal/mol for DFT. We find maximum errors of 2.96 ± 1.71 kcal/mol for our best ph-AFQMC method versus 9.15 kcal/mol for DLPNO-CCSD(T) and 5.98-13.69 kcal/mol for DFT. The reasonable performance of a number of DFT functionals is in stark contrast to the much poorer accuracy previously demonstrated for diatomic species, suggesting a moderation in electron correlation because of ligand coordination in most cases. However, the unpredictably large errors for a small subset of cases with both DFT and DLPNO-CCSD(T) methods leave cause for concern, especially in light of the unreliability of common multireference indicators. In contrast, the robust and, in principle, systematically improvable results of ph-AFQMC for these realistic complexes establish the method as a useful tool for elucidating the electronic structure of transition-metal-containing complexes and predicting their gas-phase properties.

Accurate Quantum Chemical Calculation of Ionization Potentials: Validation of the DFT-LOC Approach via a Large Data Set Obtained from Experiments and Benchmark Quantum Chemical Calculations.

Density functional theory (DFT) is known to often fail when calculating thermodynamic values, such as ionization potentials (IPs), due to nondynamical error (i.e., the self-interaction term). Localized orbital corrections (LOCs), derived from assigning corresponding corrections for the atomic orbitals, bonds, and paired and unpaired electrons, are utilized to correct the IPs calculated from DFT. Some of the assigned parameters, which are physically due to the contraction of and change of the environment around a bond, depend on identifying the location in the molecule from which the electron is removed using differences in the charge density between neutral and oxidized species. In our training set, various small organic and inorganic molecules from the literature with the reported experimental IP were collected using the NIST database. For certain molecules with uncertain or no experimental measurements, we obtain the IP using coupled cluster theory and auxiliary field quantum Monte Carlo. After applying these corrections, as generated by least-squares regression, LOC reduces the mean absolute deviation (MAD) of the training set from 0.143 to 0.046 eV (R2 = 0.895), and LOC reduces the MAD of the test set from 0.192 to 0.097 eV (R2 = 0.833).

Evaluation of the Performance of the B3LYP, PBE0, and M06 DFT Functionals, and DBLOC-Corrected Versions, in the Calculation of Redox Potentials and Spin Splittings for Transition Metal Containing Systems.

We have evaluated the performance of the M06 and PBE0 functionals in their ability to calculate spin splittings and redox potentials for octahedral complexes containing a first transition metal series atom. The mean unsigned errors (MUEs) for these two functionals are similar to those obtained for B3LYP using the same data sets. We then apply our localized orbital correction approach for transition metals, DBLOC, in an effort to improve the results obtained with both functionals. The PBE0-DBLOC results are remarkably close in both MUE and parameter values to those obtained for the B3LYP-DBLOC method. The M06-DBLOC results are less accurate, but the parameter values and trends are still qualitatively very similar. These results demonstrate that DBLOC corrected methods are substantially more accurate for these systems than any of the uncorrected functionals we have tested and that the deviations between hybrid DFT methods and experiment for transition metal containing systems exhibit striking physically based regularities which are very similar for the three functionals that we have examined, despite significant differences in the details of each model.