Transferable interactions of Li+ and Mg2+ ions in polarizable models

State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms

In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.

Balancing Group I Monatomic Ion-Polar Compound Interactions for Condensed Phase Simulation in the Polarizable Drude Force Field

Molecular dynamics (MD) simulations are a commonly used method for investigating molecular behavior at the atomic level. Achieving reliable MD simulation results necessitates the use of an accurate force field. In the present work, we present a protocol to enhance the quality of group 1 monatomic ions (specifically Li+, Na+, K+, Rb+, and Cs+) with respect to their interactions with common polar model compounds in biomolecules in condensed phases in the context of the Drude polarizable force field. Instead of adjusting preexisting individual parameters for ions, model compounds, and water, we employ atom-pair specific Lennard-Jones (LJ) (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) terms to fine-tune the balance of ion-model compound, ion-water, and model compound-water interactions. This involved establishing a protocol for the optimization of NBFIX and NBTHOLE parameters targeting the difference between molecular mechanical (MM) and quantum mechanical (QM) potential energy scans (PES). It is shown that targeting PES involving complexes that include multiple model compounds and/or ions as trimers and tetramers yields parameters that produce condensed phase properties in agreement with experimental data. Validation of this protocol involved the reproduction of experimental thermodynamic benchmarks, including solvation free energies of ions in methanol and N-methylacetamide, osmotic pressures, ionic conductivities, and diffusion coefficients within the condensed phase. These results show the importance of including more complex ion-model compound complexes beyond dimers in the QM target data to account for many-body effects during parameter fitting. The presented parameters represent a significant refinement of the Drude polarizable force field, which will lead to improved accuracy for modeling ion-biomolecular interactions.

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Linear-Scaling Local Natural Orbital CCSD(T) Approach for Open-Shell Systems: Algorithms, Benchmarks, and Large-Scale Applications

The extension of the highly optimized local natural orbital (LNO) coupled cluster (CC) with single-, double-, and perturbative triple excitations [LNO-CCSD(T)] method is presented for high-spin open-shell molecules based on restricted open-shell references. The techniques enabling the outstanding efficiency of the closed-shell LNO-CCSD(T) variant are adopted, including the iteration- and redundancy-free second-order Møller-Plesset and (T) formulations as well as the integral-direct, memory- and disk use-economic, and OpenMP-parallel algorithms. For large molecules, the efficiency of our open-shell LNO-CCSD(T) method approaches that of its closed-shell parent method due to the application of restricted orbital sets for demanding integral transformations and a novel approximation for higher-order long-range spin-polarization effects. The accuracy of open-shell LNO-CCSD(T) is extensively tested for radicals and reactions thereof, ionization processes, as well as spin-state splittings, and transition-metal compounds. At the size range where the canonical CCSD(T) reference is accessible (up to 20-30 atoms), the average open-shell LNO-CCSD(T) correlation energies are found to be 99.9 to 99.95% accurate, which translates into average absolute deviations of a few tenths of kcal/mol in the investigated energy differences already with the default settings. For more extensive molecules, the local errors may grow, but they can be estimated and decreased via affordable systematic convergence studies. This enables the accurate modeling of large systems with complex electronic structures, as illustrated on open-shell organic radicals and transition-metal complexes of up to 179 atoms as well as on challenging biochemical systems, including up to 601 atoms and 11,000 basis functions. While the protein models involve difficulties for local approximations, such as the spin states of a bounded iron ion or an extremely delocalized singly occupied orbital, the corresponding single-node LNO-CCSD(T) computations were feasible in a matter of days with 10s to 100 GB of memory use. Therefore, the new LNO-CCSD(T) implementation enables highly accurate computations for open-shell systems of unprecedented size and complexity with widely accessible hardware.

Inclusion of High-Field Target Data in AMOEBA's Calibration Improves Predictions of Protein-Ion Interactions

The reliability of molecular mechanics simulations to predict effects of ion binding to proteins depends on their ability to simultaneously describe ion-protein, ion-water, and protein-water interactions. Force fields (FFs) to describe protein-water and ion-water interactions have been constructed carefully and have also been refined routinely to improve accuracy. Descriptions for ion-protein interactions have also been refined, although in an a posteriori manner through the use of "nonbonded-fix (NB-fix)" approaches in which parameters from default Lennard-Jones mixing rules are replaced with those optimized against some reference data. However, even after NB-fix corrections, there remains a significant need for improvement. This is also true for polarizable FFs that include self-consistent inducible moments. Our recent studies on the polarizable AMOEBA FF suggested that the problem associated with modeling ion-protein interactions could be alleviated by recalibrating polarization models of cation-coordinating functional groups so that they respond better to the high electric fields present near ions. Here, we present such a recalibration of carbonyls, carboxylates, and hydroxyls in the AMOEBA protein FF and report that it does improve predictions substantially─mean absolute errors in Na⁺-protein and K⁺-protein interaction energies decrease from 8.7 to 5.3 and 9.6 to 6.3 kcal/mol, respectively. Errors are computed with respect to estimates from van der Waals-inclusive density functional theory benchmarked against high-level quantum mechanical calculations and experiments. While recalibration does improve ion-protein interaction energies, they still remain underestimated, suggesting that further improvements can be made in a systematic manner through modifications in classical formalism. Nevertheless, we show that by applying our many-body NB-fix correction to Lennard-Jones components, these errors are further reduced to 2.7 and 2.6 kcal/mol, respectively, for Na⁺ and K⁺ ions. Finally, we show that the recalibrated AMOEBA protein FF retains its intrinsic reliability in predicting protein structure and dynamics in the condensed phase.

High-Dimensional Parameter Search Method to Determine Force Field Mixing Terms in Molecular Simulations

Molecular dynamics (MD) force fields for lipids and ions are typically developed independently of one another. In simulations consisting of both lipids and ions, lipid-ion interaction energies are estimated using a predefined set of mixing rules for Lennard-Jones (LJ) interactions. This, however, does not guarantee their reliability. In fact, compared to the quantum mechanical reference data, Lorentz-Berthelot mixing rules substantially underestimate the binding energies of Na⁺ ions with small-molecule analogues of lipid headgroups, yielding errors on the order of 80 and 130 kJ/mol, respectively, for methyl acetate and diethyl phosphate. Previously, errors associated with mixing force fields have been reduced using approaches such as "NB-fix" in which LJ interactions are computed using explicit cross terms rather than those from mixing rules. Building on this idea, we derive explicit lipid-ion cross terms that also may implicitly include many-body cooperativity effects. Additionally, to account for the interdependency between cross terms, we optimize all cross terms simultaneously by performing high-dimensional searches using our ParOpt software. The cross terms we obtain reduce the errors due to mixing rules to below 10 kJ/mol. MD simulation of the lipid bilayer conducted using these optimized cross terms resolves the structural discrepancies between our previous simulations and small-angle X-ray and neutron scattering experiments. These results demonstrate that simulations of lipid bilayers with ions that are accurate up to structural data from scattering experiments can be performed without explicit polarization terms. However, it is worth noting that such NB-fix cross terms are not based on any physical principle; a polarizable lipid model would be more realistic and is still desired. Our approach is generic and can be applied to improve the accuracies of simulations employing mixed force fields.

Rational Design of Nonbonded Point Charge Models for Highly Charged Metal Cations with Lennard-Jones 12-6 Potential

Here, we developed nonbonded point charge models using a simple Lennard-Jones (LJ) 12-6 potential for highly charged metal cations (18 trivalent and 6 tetravalent ions) for use with 11 water models of TIP3P, OPC3, SPC/E, SPC/E_b, TIP3P-FB, a99SB-disp, TIP4P-Ew, OPC, TIP4P/2005, TIP4P-D, and TIP4P-FB. The designed models simultaneously reproduce the hydration free energy (HFE) and ion-oxygen distance (IOD) in the first hydration shell with an error within 1 kcal/mol and 0.01 Å on average, respectively, and yield reasonable coordination numbers for most cations. Such performance is equivalent to the previously reported point charge models using a more complex 12-6-4 LJ-type potential, while the LJ R parameters of our models are much close to Shannon's revised effective ion radii than that of the 12-6-4 models. Our designed models overestimate the diffusion constants of several trivalent ions by 5-68%. The performance in predicting osmotic coefficients of trivalent chlorides in aqueous solution depends on the salt type. A calibration of cation-anion interacting LJ parameters reproduces the experimental osmotic coefficients of an AlCl₃ solution at 0.2-3.0 mol/L. The effectiveness of our new models is further demonstrated by simulating a metalloprotein system with four force field/water combinations. This work facilitates accurate modeling of metal-containing systems by a variety of force fields and water models in aqueous solution.

Methyl-Induced Polarization Destabilizes the Noncovalent Interactions of N-Methylated Lysines

Lysine methylation can modify noncovalent interactions by altering lysine's hydrophobicity as well as its electronic structure. Although the ramifications of the former are documented, the effects of the latter remain largely unknown. Understanding the electronic structure is important for determining how biological methylation modulates protein-protein binding, and the impact of artificial methylation experiments in which methylated lysines are used as spectroscopic probes and protein crystallization facilitators. The benchmarked first-principles calculations undertaken here reveal that methyl-induced polarization weakens the electrostatic attraction of amines with protein functional groups - salt bridges, hydrogen bonds and cation-π interactions weaken by as much as 10.3, 7.9 and 3.5 kT, respectively. Multipole analysis shows that weakened electrostatics is due to the altered inductive effects, which overcome increased attraction from methyl-enhanced polarizability and dispersion. Due to their fundamental nature, these effects are expected to be present in many cases. A survey of methylated lysines in protein structures reveals several cases in which methyl-induced polarization is the primary driver of altered noncovalent interactions; in these cases, destabilizations are found to be in the 0.6-4.7 kT range. The clearest case of where methyl-induced polarization plays a dominant role in regulating biological function is that of the PHD1-PHD2 domain, which recognizes lysine-methylated states on histones. These results broaden our understanding of how methylation modulates noncovalent interactions.

Molecular basis for higher affinity of SARS-CoV-2 spike RBD for human ACE2 receptor

Severe acute respiratory syndrome coronavirus‐2 (SARS‐CoV‐2) has caused substantially more infections, deaths, and economic disruptions than the 2002‐2003 SARS‐CoV. The key to understanding SARS‐CoV‐2's higher infectivity lies partly in its host receptor recognition mechanism. Experiments show that the human angiotensin converting enzyme 2 (ACE2) protein, which serves as the primary receptor for both CoVs, binds to the receptor binding domain (RBD) of CoV‐2's spike protein stronger than SARS‐CoV's spike RBD. The molecular basis for this difference in binding affinity, however, remains unexplained from X‐ray structures. To go beyond insights gained from X‐ray structures and investigate the role of thermal fluctuations in structure, we employ all‐atom molecular dynamics simulations. Microseconds‐long simulations reveal that while CoV and CoV‐2 spike‐ACE2 interfaces have similar conformational binding modes, CoV‐2 spike interacts with ACE2 via a larger combinatorics of polar contacts, and on average, makes 45% more polar contacts. Correlation analysis and thermodynamic calculations indicate that these differences in the density and dynamics of polar contacts arise from differences in spatial arrangements of interfacial residues, and dynamical coupling between interfacial and non‐interfacial residues. These results recommend that ongoing efforts to design spike‐ACE2 peptide blockers will benefit from incorporating dynamical information as well as allosteric coupling effects.

Predictive QM/MM Modeling of Modulations in Protein-Protein Binding by Lysine Methylation

Lysine methylation is a key regulator of protein-protein binding. The amine group of lysine can accept up to three methyl groups, and experiments show that protein-protein binding free energies are sensitive to the extent of methylation. These sensitivities have been rationalized in terms of chemical and structural features present in the binding pockets of methyllysine binding domains. However, understanding their specific roles requires an energetic analysis. Here we propose a theoretical framework to combine quantum and molecular mechanics methods, and compute the effect of methylation on protein-protein binding free energies. The advantages of this approach are that it derives contributions from all local non-trivial effects of methylation on induction, polarizability and dispersion directly from self-consistent electron densities, and at the same time determines contributions from well-characterized hydration effects using a computationally efficient classical mean field method. Limitations of the approach are discussed, and we note that predicted free energies of fourteen out of the sixteen cases agree with experiment. Critical assessment of these cases leads to the following overarching principles that drive methylation-state recognition by protein domains. Methylation typically reduces the pairwise interaction between proteins. This biases binding toward lower methylated states. Simultaneously, however, methylation also makes it easier to partially dehydrate proteins and place them in protein-protein complexes. This latter effect biases binding in favor of higher methylated states. The overall effect of methylation on protein-protein binding depends ultimately on the balance between these two effects, which is observed to be tuned via several combinations of local features.