Robust prediction of relative binding energies for protein-protein complex mutations using free energy perturbation calculations

Computational free energy-based methods have the potential to significantly improve throughput and decrease costs of protein design efforts. Such methods must reach a high level of reliability, accuracy, and automation to be effectively deployed in practical industrial settings in a way that impacts protein design projects. Here, we present a benchmark study for the calculation of relative changes in protein-protein binding affinity for single point mutations across a variety of systems from the literature, using free energy perturbation (FEP+) calculations. We describe a method for robust treatment of alternate protonation states for titratable amino acids, which yields improved correlation with and reduced error compared to experimental binding free energies. Following careful analysis of the largest outlier cases in our dataset, we assess limitations of the default FEP+ protocols and introduce an automated script which identifies probable outlier cases that may require additional scrutiny and calculates an empirical correction for a subset of charge-related outliers. Through a series of three additional case study systems, we discuss how protein FEP+ can be applied to real-world protein design projects, and suggest areas of further study.

Predicted and Experimental NMR Chemical Shifts at Variable Temperatures: The Effect of Protein Conformational Dynamics

NMR chemical shifts provide a sensitive probe of protein structure and dynamics but remain challenging to predict and interpret. We examine the effect of protein conformational distributions on 15N chemical shifts for dihydrofolate reductase (DHFR), comparing QM/MM predicted shifts with experimental shifts in solution as well as frozen distributions. Representative snapshots from MD trajectories exhibit variation in predicted 15N chemical shifts of up to 25 ppm. The average over the fluctuations is in significantly better agreement with room temperature solution experimental values than the prediction for any single optimal conformations. Meanwhile, solid-state NMR (SSNMR) measurements of frozen solutions at 105 K exhibit broad lines whose widths agree well with the widths of distributions of predicted shifts for samples from the trajectory. The backbone torsion angle ψi-1 varies over 60° on the picosecond time scale, compensated by φi. These fluctuations can explain much of the shift variation.

Highly efficient implementation of analytic nonadiabatic derivative couplings within the pseudospectral method

A pseudospectral implementation of nonadiabatic derivative couplings in the Tamm-Dancoff approximation is reported, and the accuracy and efficiency of the pseudospectral nonadiabatic derivative couplings are studied. Our results demonstrate that the pseudospectral method provides mean absolute errors of 0.2%-1.9%, while providing a significant speedup. Benchmark calculations on fullerenes (Cn, n up to 100) using B3LYP achieved 10- to 15-fold, 8- to 17-fold, and 43- to 75-fold speedups for 6-31G**, 6-31++G**, and cc-pVTZ basis sets, respectively, when compared to the conventional spectral method.

Electron and Spin Delocalization in [Co6 Se8 (PEt3 )6 ]0/+1 Superatoms

Molecular clusters can function as nanoscale atoms/superatoms, assembling into superatomic solids, a new class of solid-state materials with designable properties through modifications on superatoms. To explore possibilities on diversifying building blocks, here we thoroughly studied one representative superatom, Co6 Se8 (PEt3 )6 . We probed its structural, electronic, and magnetic properties and revealed its detailed electronic structure as valence electrons delocalize over inorganic [Co6 Se8 ] core while ligands function as an insulated shell. 59 Co SSNMR measurements on the core and 31 P, 13 C on the ligands show that the neutral Co6 Se8 (PEt3 )6 is diamagnetic and symmetric, with all ligands magnetically equivalent. Quantum computations cross-validate NMR results and reveal degenerate delocalized HOMO orbitals, indicating aromaticity. Ligand substitution keeps the inorganic core nearly intact. After losing one electron, the unpaired electron in [Co6 Se8 (PEt3 )6 ]+1 is delocalized, causing paramagnetism and a delocalized electron spin. Notably, this feature of electron/spin delocalization over a large cluster is attractive for special single-electron devices.

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.

Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo

We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.

Accurate Quantum Chemical Reaction Energies for Lithium-Mediated Electrolyte Decomposition and Evaluation of Density Functional Approximations

An important concern related to the performance of Li-ion batteries is the formation of a solid electrolyte interphase on the surface of the anode. This film is formed from the decomposition of electrolytes and can have important effects on the stability and performance. Here, we evaluate the decomposition pathway of ethylene carbonate and related organic electrolyte molecules using a series of density functional approximations and correlated wave function (WF) methods, including the coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)] and auxiliary-field quantum Monte Carlo (AFQMC). We find that the transition state barrier associated with ring opening varies widely across different functionals, ranging from 3.01 to 17.15 kcal/mol, which can be compared to the value of 12.84 kcal/mol predicted by CCSD(T). This large variation underscores the importance of benchmarking against accurate WF methods. A performance comparison of all of the density functionals used in this study reveals that the M06-2X-D3 (a meta-hybrid GGA), CAM-B3LYP-D3 (a range-separated hybrid), and B2GP-PLYP-D3 (a double hybrid) perform the best, with average errors of about 1.50-1.60 kcal/mol compared to CCSD(T). We also compared the performance of the WF methods that are more scalable than CCSD(T), finding that DLPNO-CCSD(T) and phaseless AFQMC with a DFT trial wave function exhibit average errors of 1.38 and 1.74 kcal/mol, respectively.

Toward Benchmark-Quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts: A Comparison of CCSD(T) and ph-AFQMC

Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy─roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) in the def2-SVP basis set. A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics and find that spin-symmetry breaking of the CCSD wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of density functional theory (DFT) functionals on the 3dTMV set.

Free Energy Perturbation Calculations of Mutation Effects on SARS-CoV-2 RBD::ACE2 Binding Affinity

The strength of binding between human angiotensin converting enzyme 2 (ACE2) and the receptor binding domain (RBD) of viral spike protein plays a role in the transmissibility of the SARS-CoV-2 virus. In this study we focus on a subset of RBD mutations that have been frequently observed in infected individuals and probe binding affinity changes to ACE2 using surface plasmon resonance (SPR) measurements and free energy perturbation (FEP) calculations. Our SPR results are largely in accord with previous studies but discrepancies do arise due to differences in experimental methods and to protocol differences even when a single method is used. Overall, we find that FEP performance is superior to that of other computational approaches examined as determined by agreement with experiment and, in particular, by its ability to identify stabilizing mutations. Moreover, the calculations successfully predict the observed cooperative stabilization of binding by the Q498R N501Y double mutant present in Omicron variants and offer a physical explanation for the underlying mechanism. Overall, our results suggest that despite the significant computational cost, FEP calculations may offer an effective strategy to understand the effects of interfacial mutations on protein-protein binding affinities and, hence, in a variety of practical applications such as the optimization of neutralizing antibodies.

Enhancing Hit Discovery in Virtual Screening through Absolute Protein-Ligand Binding Free-Energy Calculations

In the hit identification stage of drug discovery, a diverse chemical space needs to be explored to identify initial hits. Contrary to empirical scoring functions, absolute protein-ligand binding free-energy perturbation (ABFEP) provides a theoretically more rigorous and accurate description of protein-ligand binding thermodynamics and could, in principle, greatly improve the hit rates in virtual screening. In this work, we describe an implementation of an accurate and reliable ABFEP method in FEP+. We validated the ABFEP method on eight congeneric compound series binding to eight protein receptors including both neutral and charged ligands. For ligands with net charges, the alchemical ion approach is adopted to avoid artifacts in electrostatic potential energy calculations. The calculated binding free energies correlate with experimental results with a weighted average of R² = 0.55 for the entire dataset. We also observe an overall root-mean-square error (RMSE) of 1.1 kcal/mol after shifting the zero-point of the simulation data to match the average experimental values. Through ABFEP calculations using apo versus holo protein structures, we demonstrated that the protein conformational and protonation state changes between the apo and holo proteins are the main physical factors contributing to the protein reorganization free energy manifested by the overestimation of raw ABFEP calculated binding free energies using the holo structures of the proteins. Furthermore, we performed ABFEP calculations in three virtual screening applications for hit enrichment. ABFEP greatly improves the hit rates as compared to docking scores or other methods like metadynamics. The good performance of ABFEP in rank ordering compounds demonstrated in this work confirms it as a useful tool to improve the hit rates in virtual screening, thus facilitating hit discovery.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N⁷) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N³ - N⁴) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Predicted and Experimental NMR Chemical Shifts at Variable Temperatures: The Effect of Protein Conformational Dynamics

NMR chemical shifts provide a sensitive probe of protein structure and dynamics. Prediction of shifts, and therefore interpretation of shifts, particularly for the frequently measured amidic 15 N sites, remains a tall challenge. We demonstrate that protein 15 N chemical shift prediction from QM/MM predictions can be improved if conformational variation is included via MD sampling, focusing on the antibiotic target, E. coli Dihydrofolate reductase (DHFR). Variations of up to 25 ppm in predicted 15 N chemical shifts are observed over the trajectory. For solution shifts the average of fluctuations on the low picosecond timescale results in a superior prediction to a single optimal conformation. For low temperature solid state measurements, the histogram of predicted shifts for locally minimized snapshots with specific solvent arrangements sampled from the trajectory explains the heterogeneous linewidths; in other words, the conformations and associated solvent are 'frozen out' at low temperatures and result in inhomogeneously broadened NMR peaks. We identified conformational degrees of freedom that contribute to chemical shift variation. Backbone torsion angles show high amplitude fluctuations during the trajectory on the low picosecond timescale. For a number of residues, including I60, ψ varies by up to 60º within a conformational basin during the MD simulations, despite the fact that I60 (and other sites studied) are in a secondary structure element and remain well folded during the trajectory. Fluctuations in ψ appear to be compensated by other degrees of freedom in the protein, including φ of the succeeding residue, resulting in "rocking" of the amide plane with changes in hydrogen bonding interactions. Good agreement for both room temperature and low temperature NMR spectra provides strong support for the specific approach to conformational averaging of computed chemical shifts.

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

Accurate prediction of the pK_a'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 pK_a values. We begin with an initial set of 191 residues with experimentally determined pK_a 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 pK_a prediction methods can be tested. On this data set, we report an RMSE of 0.76 pK_a units for 35 ASP residues, 0.51 pK_a units for 44 GLU residues, and 0.67 pK_a units for 76 HIS residues.

High-Dimensional Neural Network Potential for Liquid Electrolyte Simulations

Liquid electrolytes are one of the most important components of Li-ion batteries, which are a critical technology of the modern world. However, we still lack the computational tools required to accurately calculate key properties of these materials (viscosity and ionic diffusivity) from first principles necessary to support improved designs. In this work, we report a machine learning-based force field for liquid electrolyte simulations, which bridges the gap between the accuracy of range-separated hybrid density functional theory and the efficiency of classical force fields. Predictions of material properties made with this force field are quantitatively accurate compared to experimental data. Our model uses the QRNN deep neural network architecture, which includes both long-range interactions and global charge equilibration. The training data set is composed solely of non-periodic density functional theory (DFT), allowing the practical use of an accurate theory (here, ωB97X-D3BJ/def2-TZVPD), which would be prohibitively expensive for generating large data sets with periodic DFT. In this report, we focus on seven common carbonates and LiPF₆, but this methodology has very few assumptions and can be readily applied to any liquid electrolyte system. This provides a promising path forward for large-scale atomistic modeling of many important battery chemistries.

Induced-Fit Docking Enables Accurate Free Energy Perturbation Calculations in Homology Models

Homology models have been used for virtual screening and to understand the binding mode of a known active compound; however, rarely have the models been shown to be of sufficient accuracy, comparable to crystal structures, to support free-energy perturbation (FEP) calculations. We demonstrate here that the use of an advanced induced-fit docking methodology reliably enables predictive FEP calculations on congeneric series across homology models ≥30% sequence identity. Furthermore, we show that retrospective FEP calculations on a congeneric series of drug-like ligands are sufficient to discriminate between predicted binding modes. Results are presented for a total of 29 homology models for 14 protein targets, showing FEP results comparable to those obtained using experimentally determined crystal structures for 86% of homology models with template structure sequence identities ranging from 30 to 50%. Implications for the use and validation of homology models in drug discovery projects are discussed.

A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo

Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low-rank structure of the Coulombic integrals have been successful but exhibit high prefactors, making their utility limited to very large systems. Here we present a complementary cubic-scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to ph-AFQMC. We show that the error due to this approximation, which we term localized-orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable and that the method is computationally favorable even for small systems. We present results demonstrating robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized-orbital-based methods, including the singlet-triplet gaps of the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp)₂. Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp)₂, agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.

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.

Pseudospectral implementations of long-range corrected density functional theory

We have implemented pseudospectral density-functional theory (DFT) with long-range corrected DFT functionals (PS-LRC) in quantum mechanics package Jaguar, and applied it in the calculations of geometry optimizations, dimmer interaction energies, polarizabilities and first-order hyperpolarizabilities, harmonic vibrational frequencies, S₁ and T₁ excitation energies, singlet-triplet gaps, charge transfer numbers, oscillator strengths, reaction barrier heights, electron-transfer couplings, and charge-transfer excitation energies. From our accuracy benchmark analysis, PS grids, PS dealiasing functions, PS atomic corrections, PS multigrid strategy, PS length scales, and PS cutoff scheme perform well in PS DFT with LRC density functionals with very small and ignorable deviations when compared to the conventional spectral (CS) method. The timing benchmark study of S₁ excitation energy calculations of fullerenes (C_n , n up to 540) demonstrates that PS-LRC achieves 1.4-8.4-fold speedups in SCF, 22-32-fold speedups in Tamm-Dancoff approximation, and 6-15-fold speedups in total wall clock time with an average error 0.004 eV of excitation energies compared to the CS method.

Highly efficient implementation of the analytical gradients of pseudospectral time-dependent density functional theory

The accuracy and efficiency of time-dependent density functional theory (TDDFT) excited state gradient calculations using the pseudospectral method are presented. TDDFT excited state geometry optimizations of the G2 test set molecules, the organic fluorophores with large Stokes shifts, and the Pt-complexes show that the pseudospectral method gives average errors of 0.01-0.1 kcal/mol for the TDDFT excited state energy, 0.02-0.06 pm for the bond length, and 0.02-0.12° for the bond angle when compared to the results from conventional TDDFT. TDDFT gradient calculations of fullerenes (C_n, n up to 540) with the B3LYP functional and 6-31G** basis set show that the pseudospectral method provides 8- to 14-fold speedups in the total wall clock time over the conventional methods. The pseudospectral TDDFT gradient calculations with a diffuse basis set give higher speedups than the calculations for the same basis set without diffuse functions included.

Reliable and Accurate Solution to the Induced Fit Docking Problem for Protein-Ligand Binding

We present a reliable and accurate solution to the induced fit docking problem for protein-ligand binding by combining ligand-based pharmacophore docking, rigid receptor docking, and protein structure prediction with explicit solvent molecular dynamics simulations. This novel methodology in detailed retrospective and prospective testing succeeded to determine protein-ligand binding modes with a root-mean-square deviation within 2.5 Å in over 90% of cross-docking cases. We further demonstrate these predicted ligand-receptor structures were sufficiently accurate to prospectively enable predictive structure-based drug discovery for challenging targets, substantially expanding the domain of applicability for such methods.

Cryo-EM Structures of SARS-CoV-2 Spike without and with ACE2 Reveal a pH-Dependent Switch to Mediate Endosomal Positioning of Receptor-Binding Domains

The SARS-CoV-2 spike employs mobile receptor-binding domains (RBDs) to engage the human ACE2 receptor and to facilitate virus entry, which can occur through low-pH-endosomal pathways. To understand how ACE2 binding and low pH affect spike conformation, we determined cryo-electron microscopy structures-at serological and endosomal pH-delineating spike recognition of up to three ACE2 molecules. RBDs freely adopted "up" conformations required for ACE2 interaction, primarily through RBD movement combined with smaller alterations in neighboring domains. In the absence of ACE2, single-RBD-up conformations dominated at pH 5.5, resolving into a solitary all-down conformation at lower pH. Notably, a pH-dependent refolding region (residues 824-858) at the spike-interdomain interface displayed dramatic structural rearrangements and mediated RBD positioning through coordinated movements of the entire trimer apex. These structures provide a foundation for understanding prefusion-spike mechanics governing endosomal entry; we suggest that the low pH all-down conformation potentially facilitates immune evasion from RBD-up binding antibody.

In silico prediction of annihilators for triplet-triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.

Cryo-EM Structures Delineate a pH-Dependent Switch that Mediates Endosomal Positioning of SARS-CoV-2 Spike Receptor-Binding Domains

The SARS-CoV-2 spike employs mobile receptor-binding domains (RBDs) to engage the ACE2 receptor and to facilitate virus entry. Antibodies can engage RBD but some, such as CR3022, fail to inhibit entry despite nanomolar spike affinity. Here we show the SARS-CoV-2 spike to have low unfolding enthalpy at serological pH and up to 10-times more unfolding enthalpy at endosomal pH, where we observe significantly reduced CR3022 affinity. Cryo-EM structures -at serological and endosomal pH- delineated spike recognition of up to three ACE2 molecules, revealing RBD to freely adopt the 'up' conformation. In the absence of ACE2, single-RBD-up conformations dominated at pH 5.5, resolving into a locked all-down conformation at lower pH. Notably, a pH-dependent refolding region (residues 824-858) at the spike-interdomain interface displayed dramatic structural rearrangements and mediated RBD positioning and spike shedding of antibodies like CR3022. An endosomal mechanism involving spike-conformational change can thus facilitate immune evasion from RBD-'up'-recognizing antibody.

Multiple Stable Isoprene-Ozone Complexes Reveal Complex Entrance Channel Dynamics in the Isoprene + Ozone Reaction

Accurately characterizing isoprene ozonolysis continues to challenge atmospheric chemists. The reaction is believed to be a spontaneous, concerted cycloaddition. However, little information is available about the entrance channel and isoprene-ozone complexes thought to define the long-range portion of the reaction coordinate. Our coupled cluster and auxiliary field quantum Monte Carlo calculations predict multiple stable isoprene-ozone van der Waals complexes for trans-isoprene in the gas phase with moderate association energies. These results indicate that long-range dynamics in the isoprene-ozone entrance channel can impact the overall reaction in the troposphere and provide the spectroscopic information necessary to extend the microwave characterization of isoprene ozonolysis to prereactive complexes. At the air-water interface, Born-Oppenheimer molecular dynamics simulations indicate that the cycloaddition reaction between ozone and trans-isoprene follows a stepwise mechanism, which is quite distinct from our proposed gas-phase mechanism and occurs on a femtosecond time scale. The stepwise nature of isoprene ozonolysis on the aqueous surface is more consistent with the DeMore mechanism than with the Criegee mechanism suggested by the gas-phase calculations, suggesting that the reaction media may play an important role in the reaction. Overall, these predictions aim to provide a missing fundamental piece of molecular insight into isoprene ozonolysis, which has broad tropospheric implications due to its critical role as a nighttime source of hydroxyl radicals.

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).

Relative Binding Affinity Prediction of Charge-Changing Sequence Mutations with FEP in Protein-Protein Interfaces

Building on the substantial progress that has been made in using free energy perturbation (FEP) methods to predict the relative binding affinities of small molecule ligands to proteins, we have previously shown that results of similar quality can be obtained in predicting the effect of mutations on the binding affinity of protein–protein complexes. However, these results were restricted to mutations which did not change the net charge of the side chains due to known difficulties with modeling perturbations involving a change in charge in FEP. Various methods have been proposed to address this problem. Here we apply the co-alchemical water approach to study the efficacy of FEP calculations of charge changing mutations at the protein–protein interface for the antibody–gp120 system investigated previously and three additional complexes. We achieve an overall root mean square error of 1.2 kcal/mol on a set of 106 cases involving a change in net charge selected by a simple suitability filter using side-chain predictions and solvent accessible surface area to be relevant to a biologic optimization project. Reasonable, although less precise, results are also obtained for the 44 more challenging mutations that involve buried residues, which may in some cases require substantial reorganization of the local protein structure, which can extend beyond the scope of a typical FEP simulation. We believe that the proposed prediction protocol will be of sufficient efficiency and accuracy to guide protein engineering projects for which optimization and/or maintenance of a high degree of binding affinity is a key objective.

Modeling the value of predictive affinity scoring in preclinical drug discovery

Drug discovery is widely recognized to be a difficult and costly activity in large part due to the challenge of identifying chemical matter which simultaneously optimizes multiple properties, one of which is affinity for the primary biological target. Further, many of these properties are difficult to predict ahead of expensive and time-consuming compound synthesis and experimental testing. Here we highlight recent work to develop compound affinity prediction models, and extensively investigate the value such models may provide to preclinical drug discovery. We demonstrate that the ability of these models to improve the overall probability of success is crucially dependent on the shape of the error distribution, not just the root-mean-square error. In particular, while scoring more molecule ideas generally improves the probability of project success when the error distribution is Gaussian, fat-tail distributions such as a Cauchy distribution, can lead to a situation where scoring more ideas actually decreases the overall probability of success.

Automated Transition State Search and Its Application to Diverse Types of Organic Reactions

Transition state search is at the center of multiple types of computational chemical predictions related to mechanistic investigations, reactivity and regioselectivity predictions, and catalyst design. The process of finding transition states in practice is, however, a laborious multistep operation that requires significant user involvement. Here, we report a highly automated workflow designed to locate transition states for a given elementary reaction with minimal setup overhead. The only essential inputs required from the user are the structures of the separated reactants and products. The seamless workflow combining computational technologies from the fields of cheminformatics, molecular mechanics, and quantum chemistry automatically finds the most probable correspondence between the atoms in the reactants and the products, generates a transition state guess, launches a transition state search through a combined approach involving the relaxing string method and the quadratic synchronous transit, and finally validates the transition state via the analysis of the reactive chemical bonds and imaginary vibrational frequencies as well as by the intrinsic reaction coordinate method. Our approach does not target any specific reaction type, nor does it depend on training data; instead, it is meant to be of general applicability for a wide variety of reaction types. The workflow is highly flexible, permitting modifications such as a choice of accuracy, level of theory, basis set, or solvation treatment. Successfully located transition states can be used for setting up transition state guesses in related reactions, saving computational time and increasing the probability of success. The utility and performance of the method are demonstrated in applications to transition state searches in reactions typical for organic chemistry, medicinal chemistry, and homogeneous catalysis research. In particular, applications of our code to Michael additions, hydrogen abstractions, Diels-Alder cycloadditions, carbene insertions, and an enzyme reaction model involving a molybdenum complex are shown and discussed.

Advancing Drug Discovery through Enhanced Free Energy Calculations

A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates, is potentially transformative in enabling hard to drug targets to be attacked, and in facilitating the development of superior compounds, in various dimensions, for a wide range of targets. More effective integration of FEP+ calculations into the drug discovery process will ensure that the results are deployed in an optimal fashion for yielding the best possible compounds entering the clinic; this is where the greatest payoff is in the exploitation of computer driven design capabilities. A key conclusion from the work described is the surprisingly robust and accurate results that are attainable within the conventional classical simulation, fixed charge paradigm. No doubt there are individual cases that would benefit from a more sophisticated energy model or dynamical treatment, and properties other than protein-ligand binding energies may be more sensitive to these approximations. We conclude that an inflection point in the ability of MD simulations to impact drug discovery has now been attained, due to the confluence of hardware and software development along with the formulation of "good enough" theoretical methods and models.

Free Energy Perturbation Calculation of Relative Binding Free Energy between Broadly Neutralizing Antibodies and the gp120 Glycoprotein of HIV-1

Direct calculation of relative binding affinities between antibodies and antigens is a long-sought goal. However, despite substantial efforts, no generally applicable computational method has been described. Here, we describe a systematic free energy perturbation (FEP) protocol and calculate the binding affinities between the gp120 envelope glycoprotein of HIV-1 and three broadly neutralizing antibodies (bNAbs) of the VRC01 class. The protocol has been adapted from successful studies of small molecules to address the challenges associated with modeling protein–protein interactions. Specifically, we built homology models of the three antibody–gp120 complexes, extended the sampling times for large bulky residues, incorporated the modeling of glycans on the surface of gp120, and utilized continuum solvent-based loop prediction protocols to improve sampling. We present three experimental surface plasmon resonance data sets, in which antibody residues in the antibody/gp120 interface were systematically mutated to alanine. The RMS error in the large set (55 total cases) of FEP tests as compared to these experiments, 0.68 kcal/mol, is near experimental accuracy, and it compares favorably with the results obtained from a simpler, empirical methodology. The correlation coefficient for the combined data set including residues with glycan contacts, R² = 0.49, should be sufficient to guide the choice of residues for antibody optimization projects, assuming that this level of accuracy can be realized in prospective prediction. More generally, these results are encouraging with regard to the possibility of using an FEP approach to calculate the magnitude of protein–protein binding affinities.

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Natural bNAbs against HIV-1 are a promising starting point for therapies.

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FEP provides a promising technique to computationally predict antibody structure optimizations.

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We show that FEP applied to bNAb mutations predicts binding affinity changes.

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FEP can provide an efficient method to identify potency-enhancing mutations to bNAbs.

Computational Approach To Large Quam Dynamical Problems

The organizational structure is described for a new program that permits computa tions on a variety of quantum mechanical problems in chemical dynamics and spec troscopy. Particular attention was devoted to developing and using algorithms that exploit the capabilities of current vector supercomputers. A key component in this procedure is the recursive transformation of the large sparse Hamiltonian matrix into a much smaller tridiagonal matrix. An ap plication to time-dependent laser-mole cule energy transfer is presented. Rate of energy deposition in the multimode mole cule for systematic variations in the mo lecular intermode coupling parameters is emphasized.

Prediction of Protein-Ligand Binding Poses via a Combination of Induced Fit Docking and Metadynamics Simulations

Ligand docking is a widely used tool for lead discovery and binding mode prediction based drug discovery. The greatest challenges in docking occur when the receptor significantly reorganizes upon small molecule binding, thereby requiring an induced fit docking (IFD) approach in which the receptor is allowed to move in order to bind to the ligand optimally. IFD methods have had some success but suffer from a lack of reliability. Complementing IFD with all-atom molecular dynamics (MD) is a straightforward solution in principle but not in practice due to the severe time scale limitations of MD. Here we introduce a metadynamics plus IFD strategy for accurate and reliable prediction of the structures of protein-ligand complexes at a practically useful computational cost. Our strategy allows treating this problem in full atomistic detail and in a computationally efficient manner and enhances the predictive power of IFD methods. We significantly increase the accuracy of the underlying IFD protocol across a large data set comprising 42 different ligand-receptor systems. We expect this approach to be of significant value in computationally driven drug design.

Successful application of the DBLOC method to the hydroxylation of camphor by cytochrome p450

The activation barrier for the hydroxylation of camphor by cytochrome P450 was computed using a mixed quantum mechanics/molecular mechanics (QM/MM) model of the full protein-ligand system and a fully QM calculation using a cluster model of the active site at the B3LYP/LACVP*/LACV3P** level of theory, which consisted of B3LYP/LACV3P** single point energies computed at B3LYP/LACVP* optimized geometries. From the QM/MM calculation, a barrier height of 17.5 kcal/mol was obtained, while the experimental value was known to be less than or equal to 10 kcal/mol. This process was repeated using the D3 correction for hybrid DFT in order to investigate whether the inadequate treatment of dispersion interaction was responsible for the overestimation of the barrier. While the D3 correction does reduce the computed barrier to 13.3 kcal/mol, it was still in disagreement with experiment. After application of a series of transition metal optimized localized orbital corrections (DBLOC) and without any refitting of parameters, the barrier was further reduced to 10.0 kcal/mol, which was consistent with the experimental results. The DBLOC method to CH bond activation in methane monooxygenase (MMO) was also applied, as a second, independent test. The barrier in MMO was known, by experiment, to be 15.4 kcal/mol. After application of the DBLOC corrections to the MMO barrier compute by B3LYP, in a previous study, and accounting for dispersion with Grimme's D3 method, the unsigned deviation from experiment was improved from 3.2 to 2.3 kcal/mol. These results suggested that the combination of dispersion plus localized orbital corrections could yield significant quantitative improvements in modeling the catalytic chemistry of transition-metal containing enzymes, within the limitations of the statistical errors of the model, which appear to be on the order of approximately 2 kcal/mole.

Leveraging Data Fusion Strategies in Multireceptor Lead Optimization MM/GBSA End-Point Methods

Accurate and efficient affinity calculations are critical to enhancing the contribution of in silico modeling during the lead optimization phase of a drug discovery campaign. Here, we present a large-scale study of the efficacy of data fusion strategies to leverage results from end-point MM/GBSA calculations in multiple receptors to identify potent inhibitors among an ensemble of congeneric ligands. The retrospective analysis of 13 congeneric ligand series curated from publicly available data across seven biological targets demonstrates that in 90% of the individual receptor structures MM/GBSA scores successfully identify subsets of inhibitors that are more potent than a random selection, and data fusion strategies that combine MM/GBSA scores from each of the receptors significantly increase the robustness of the predictions. Among nine different data fusion metrics based on consensus scores or receptor rankings, the SumZScore (i.e., converting MM/GBSA scores into standardized Z-Scores within a receptor and computing the sum of the Z-Scores for a given ligand across the ensemble of receptors) is found to be a robust and physically meaningful metric for combining results across multiple receptors. Perhaps most surprisingly, even with relatively low to modest overall correlations between SumZScore and experimental binding affinities, SumZScore tends to reliably prioritize subsets of inhibitors that are at least as potent as those that are prioritized from a "best" single receptor identified from known compounds within the congeneric series.

Multiscale Optimization of a Truncated Newton Minimization Algorithm and Application to Proteins and Protein-Ligand Complexes

We optimize a truncated Newton (TN) minimization algorithm and computer package, TNPACK, developed for macromolecular minimizations by applying multiscale methods, analogous to those used in molecular dynamics (e.g., r-RESPA). The molecular mechanics forces are divided into short- and long-range components, with the long-range forces updated only intermittently in the iterative evaluations. This algorithm, which we refer to as MSTN, is implemented as a modification to the TNPACK package and is tested on energy minimizations of protein loops, entire proteins, and protein-ligand complexes and compared with the unmodified truncated Newton algorithm, a quasi-Newton algorithm (LBFGS), and a conjugate gradient algorithm (CG+). In vacuum minimizations, the speedup of MSTN relative to the unmodified TN algorithm (TNPACK) depends on system size and the distance cutoffs used for defining the short- and long-range interactions and the long-range force updating frequency, but it is 4 to 5 times greater in the work reported here. This algorithm works best for the minimization of small portions of a protein and shows some degradation (speedup factor of 2-3) for the minimization of entire proteins. The MSTN algorithm is faster than the quasi-Newton and conjugate gradient algorithms by approximately 1 order of magnitude. We also present a modification of the algorithm which permits minimizations with a generalized Born implicit solvent model, using a self-consistent procedure that increases the computational expense, relative to a vacuum, by only a small factor (∼3-4).

OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins

The parametrization and validation of the OPLS3 force field for small molecules and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addition of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chemical space, OPLS3 employs over an order of magnitude more reference data and associated parameter types relative to other commonly used small molecule force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small molecule conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a number of proteins. Together, the improvements made to both the small molecule and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.

Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field

Designing tight-binding ligands is a primary objective of small-molecule drug discovery. Over the past few decades, free-energy calculations have benefited from improved force fields and sampling algorithms, as well as the advent of low-cost parallel computing. However, it has proven to be challenging to reliably achieve the level of accuracy that would be needed to guide lead optimization (∼5× in binding affinity) for a wide range of ligands and protein targets. Not surprisingly, widespread commercial application of free-energy simulations has been limited due to the lack of large-scale validation coupled with the technical challenges traditionally associated with running these types of calculations. Here, we report an approach that achieves an unprecedented level of accuracy across a broad range of target classes and ligands, with retrospective results encompassing 200 ligands and a wide variety of chemical perturbations, many of which involve significant changes in ligand chemical structures. In addition, we have applied the method in prospective drug discovery projects and found a significant improvement in the quality of the compounds synthesized that have been predicted to be potent. Compounds predicted to be potent by this approach have a substantial reduction in false positives relative to compounds synthesized on the basis of other computational or medicinal chemistry approaches. Furthermore, the results are consistent with those obtained from our retrospective studies, demonstrating the robustness and broad range of applicability of this approach, which can be used to drive decisions in lead optimization.

Conformational preferences underlying reduced activity of a thermophilic ribonuclease H

The conformational basis for reduced activity of the thermophilic ribonuclease HI enzyme from Thermus thermophilus, compared to its mesophilic homolog from Escherichia coli, is elucidated using a combination of NMR spectroscopy and molecular dynamics (MD) simulations. Explicit-solvent all-atom MD simulations of the two wild-type proteins and an E. coli mutant in which a glycine residue is inserted after position 80 to mimic the T. thermophilus protein reproduce the differences in conformational dynamics determined from (15)N spin-relaxation NMR spectroscopy of three loop regions that surround the active site and contain functionally important residues: the glycine-rich region, the handle region, and the β5/αE loop. Examination of the MD trajectories indicates that the thermophilic protein samples conformations productive for substrate binding and activity less frequently than the mesophilic enzyme, although these differences may manifest as either increased or decreased relative flexibility of the different regions. Additional MD simulations indicate that mutations increasing activity of the T. thermophilus enzyme at mesophilic temperatures do so by reconfiguring the local environments of the mutated sites to more closely resemble active conformations. Taken together, the results show that both locally increased and decreased flexibility contribute to an overall reduction in activity of T. thermophilus ribonuclease H compared to its mesophilic E. coli homolog.