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

Abstract

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.

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

“…The NMA and acetate parameters are taken from our earlier work that perform better at reproducing high-field reference data. 36 In both strategies, we use the Nelder−Mead algorithm for optimizing LJ crossterms using a parameter range of [3.0, 4.2] Å and [0.1, 0.9] kcal/mol for R 0 and ϵ, respectively. We carried out 100 different optimizations starting with different seeds, which produced 100 different sets of parameters.…”

“…Previously, we had chosen to do this using protein clusters, as the multipoles in small molecules slightly differ from their representative chemical groups in proteins. 36 We use the interaction energies from the 6-fold PDB clusters as target data and determine R ij 0 and ϵ ij such that they minimize the root-mean-square error (RMSE) to this target. The best parameter set obtained after the exhaustive search is provided in Table S3 of the Supporting Information.…”

“…The other issue concerns whether LJ cross-terms should be determined by using small-molecule representatives of proteins or directly from protein clusters. Previously, we had chosen to do this using protein clusters, as the multipoles in small molecules slightly differ from their representative chemical groups in proteins . We use the interaction energies from the 6-fold PDB clusters as target data and determine R ij 0 and ϵ ij such that they minimize the root-mean-square error (RMSE) to this target.…”

“…In recent years, errors in ion–protein interactions have been reduced to some extent in an a posteriori manner through the so-called “Nonbonded-fix (NB-fix)”-type approaches. In NB-fix, the parameters for ion–protein interactions obtained from mixing rules are substituted with those obtained from fitting to reference data on interactions of ions with small molecules representative of protein chemical groups. − ,− However, even after including NB-fix corrections, and in MM models whose multipoles can adjust to a local electric field (polarizable MM models), errors in interactions of proteins with monovalent and divalent cations can exceed 10 and 20 kcal/mol, respectively. , This implies that to further improve accuracies, we need to look beyond NB-fix corrections.…”

Exploring Routes to Enhance the Calculation of Free Energy Differences via Nonequilibrium Work SQM/MM Switching Simulations by Using Hybrid Charge Intermediates Between MM and SQM Level of Theory or Non-linear Switching Schemes

“…Even if one is not interested in studying chemical reactions, the neglect of induced electronic polarization in classical force fields may lead to problems even for seemingly simple applications, such as computing relative free energies of hydration of mono-or bivalent ions. [12][13][14] In such situations, hybrid quantum-mechanical / molecular mechanical (QM/MM) Hamiltonians Version March 27, 2023 submitted to Molecules 2 of 25 are called for. However, even when using only semiempirical quantum chemical methods (henceforth abbreviated as SQM) for the core region, i.e., the part of the system one is particularly interested in, the computational cost can quickly become prohibitive.…”