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.

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.

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.

Improved description of ligand polarization enhances transferability of ion-ligand interactions.

The reliability of molecular mechanics (MM) simulations in describing biomolecular ion-driven processes depends on their ability to accurately model interactions of ions simultaneously with water and other biochemical groups. In these models, ion descriptors are calibrated against reference data on ion-water interactions, and it is then assumed that these descriptors will also satisfactorily describe interactions of ions with other biochemical ligands. The comparison against the experiment and high-level quantum mechanical data show that this transferability assumption can break down severely. One approach to improve transferability is to assign cross terms or separate sets of non-bonded descriptors for every distinct pair of ion type and its coordinating ligand. Here, we propose an alternative solution that targets an error-source directly and corrects misrepresented physics. In standard model development, ligand descriptors are never calibrated or benchmarked in the high electric fields present near ions. We demonstrate for a representative MM model that when the polarization descriptors of its ligands are improved to respond to both low and high fields, ligand interactions with ions also improve, and transferability errors reduce substantially. In our case, the overall transferability error reduces from 3.3 kcal/mol to 1.8 kcal/mol. These improvements are observed without compromising on the accuracy of low-field interactions of ligands in gas and condensed phases. Reference data for calibration and performance evaluation are taken from the experiment and also obtained systematically from "gold-standard" CCSD(T) in the complete basis set limit, followed by benchmarked vdW-inclusive density functional theory.

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

Therapeutic implications of Li+, in many cases, stem from its ability to inhibit certain Mg2+-dependent enzymes, where it interacts with or substitutes for Mg2+. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li+ and Mg2+ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

Effect of Zn(2+) ions on the assembly of amylin oligomers: insight into the molecular mechanisms.

Amylin is an endocrine hormone and is a member of the family of amyloid peptides and proteins that emerge as potential scaffolds by self-assembly processes. Zn(2+) ions can bind to amylin peptides to form self-assembled Zn(2+)-amylin oligomers. In the current work the binding sites of Zn(2+) ions in the self-assembled amylin oligomers at various concentrations of zinc have been investigated. Our results yield two conclusions. First, in the absence of Zn(2+) ions polymorphic states (i.e. various classes of amylin oligomers) are obtained, but when Zn(2+) ions bind to amylin peptides to form Zn(2+)-amylin oligomers, the polymorphism is decreased, i.e. Zn(2+) ions bind only to specific classes of amylin. At low concentrations of Zn(2+) ions the polymorphism is smaller than at high concentrations. Second, the structural features of the self-assembled amylin oligomers are not affected by the presence of Zn(2+) ions. This study proposes new molecular mechanisms of the self-assembly of Zn(2+)-amylin oligomers.

The removal of disulfide bonds in amylin oligomers leads to the conformational change of the 'native' amylin oligomers.

The α-helical structure of the N-terminus of the 'native' amylin Lys1-Cys7 consists of a disulfide bond between Cys2 and Cys7. The 'native' amylin oligomers demonstrate polymorphic states. Removal of the disulfide bonds in the 'native' amylin oligomers decreases the polymorphism and induces the formation of longer stable cross-ß strands in the N-termini.

Mutagenic induction of an ultra-fast water-chain proton wire.

Replacement of the hydroxyl group of a hydrophilic sidechain by an H atom in the proton wire of GFP induces formation of a water-chain proton wire. Surprisingly, this "non-native" water chain functions as a proton wire with response times within 10 ps of the wild type protein. This remarkable rate retention is understood as a natural consequence of the well-known Grotthuss mechanism of proton transfer in water.

Orientations of residues along the ß-arch of self-assembled amylin fibril-like structures lead to polymorphism.

Amylin is an endocrine hormone peptide that consists of 37 residues and is the main component of extracellular amyloid deposits found in the pancreas of most type 2 diabetes patients. Amylin peptides are self-assembled to form oligomers and fibrils. So far, four different molecular structures of the self-assembled amylin fibrils have been observed experimentally: two ssNMR models and two crystal models. This study reveals, for the first time, that there are four self-assembled amylin forms that differ in the orientations of the side chains along the ß-arch and are all derived from the two ssNMR models. The two ssNMR models are composed of these four different self-assembled forms of amylin, and the two crystal models are composed of two different self-assembled forms of amylin. This study illustrates at the atomic level the differences among the four experimental models and proposes eight new models of self-assembled amylin that are also composed of the four different self-assembled forms of amylin. Our results show polymorphism of the self-assembled fibril-like amylin, with a slight preference of some of the newly constructed models over the experimental models. Finally, we propose that two different self-assembled fibril-like forms of amylin can interact to form a new fibril-like amylin. We investigated this argument and found that some fibril-like amylin prefers to interact to form stable fibril-like structures, whereas others disfavor it. Our work provides new insights that may suggest strategies for future pharmacological studies that aim to find ways to ameliorate the interactions between polymorphic oligomers and fibrils of amylin.

Insight into the structure and the mechanism of the slow proton transfer in the GFP double mutant T203V/S205A.

Mutations near the fluorescing chromophore of the green fluorescent protein (GFP) have direct effects on the absorption and emission spectra. Some mutants have significant band shifts and most of the mutants exhibit a loss of fluorescence intensity. In this study we continue our investigation of the factors controlling the excited state proton transfer (PT) process of GFP, in particular to study the effects of modifications to the key side chain Ser205 in wt-GFP, proposed to participate in the proton wire. To this aim we combined mutagenesis, X-ray crystallography, steady-state spectroscopy, time-resolved emission spectroscopy and all-atom explicit molecular dynamics (MD) simulations to study the double mutant T203V/S205A. Our results show that while in the previously described GFP double mutant T203V/S205V the PT process does not occur, in the T203V/S205A mutant the PT process does occur, but with a 350 times slower rate than in wild-type GFP (wt-GFP). Furthermore, the kinetic isotope effect in the GFP double mutant T203V/S205A is twice smaller than in the wt-GFP and in the GFP single mutant S205V, which forms a novel PT pathway. On the other hand, the crystal structure of GFP T203V/S205A does not reveal a viable proton transfer pathway. To explain PT in GFP T203V/S205A, we argue on the basis of the MD simulations for an alternative, novel proton-wire pathway which involves the phenol group of the chromophore and water molecules infrequently entering from the bulk. This alternative pathway may explain the dramatically slow PT in the GFP double mutant T203V/S205A compared to wt-GFP.

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.

Unique Inversion Events of Residues around the Backbone in the Turn Domain of ß-Arches in Amylin Fibrils.

Orientational inversion events of residues along the turn domains of amylin fibrils have been detected. This exceptional phenomenon has been observed in isolated amylin fibrils and in the cross-seeding amylin-Aß and amylin-NAC fibrils. These new findings provide new avenues for detection of side chain flipping and side chain inversion events in turn domains and loops of various proteins.

Ion-Hydroxyl Interactions: From High-Level Quantum Benchmarks to Transferable Polarizable Force Fields.

Ion descriptors in molecular mechanics models are calibrated against reference data on ion-water interactions. It is then typically assumed that these descriptors will also satisfactorily describe interactions of ions with other functional groups, such as those present in biomolecules. However, several studies now demonstrate that this transferability assumption produces, in many different cases, large errors. Here we address this issue in a representative polarizable model and focus on transferability of cationic interactions from water to a series of alcohols. Both water and alcohols use hydroxyls for ion-coordination, and, therefore, this set of molecules constitutes the simplest possible case of transferability. We obtain gas phase reference data systematically from "gold-standard" quantum Monte Carlo and CCSD(T) methods, followed by benchmarked vdW-corrected DFT. We learn that the original polarizable model yields large gas phase water → alcohol transferability errors - the RMS and maximum errors are 2.3 and 5.1 kcal/mol, respectively. These errors are, nevertheless, systematic in that ion-alcohol interactions are overstabilized, and systematic errors typically imply that some essential physics is either missing or misrepresented. A comprehensive analysis shows that when both low- and high-field responses of ligand dipole polarization are described accurately, then transferability improves significantly - the RMS and maximum errors in the gas phase reduce, respectively, to 0.9 and 2.5 kcal/mol. Additionally, predictions of condensed phase transfer free energies also improve. Nevertheless, within the limits of the extrathermodynamic assumptions necessary to separate experimental estimates of salt dissolution into constituent cationic and anionic contributions, we note that the error in the condensed phase is systematic, which we attribute, at least, partially to the parametrization in long-range electrostatics. Overall, this work demonstrates a rational approach to boosting transferability of ionic interactions that will be applicable broadly to improving other polarizable and nonpolarizable models.

Insight into a New Binding Site of Zinc Ions in Fibrillar Amylin.

Amylin peptides are secreted together with insulin and zinc ions from pancreatic ß-cells. Under unknown conditions, the amylin peptides aggregate to produce oligomers and fibrils, and in some cases Zn2+ ions can bind to amylin peptides to form Zn2+-aggregate complexes. Consequently, these aggregates lead to the death of the ß-cells and a decrease in insulin, which is one of the symptoms of type-2 diabetes (T2D). Therefore, it is crucial to investigate the binding sites of the Zn2+ ions in fibrillary amylin. It was previously found by in vitro and simulation studies that Zn2+ ion binds to two or four His residues in the turn domain of fibrillary amylin. In the current study, we present a new Zn2+ binding site in the N-terminus of fibrillary amylin with three different coordination modes. Our simulations showed that Zn2+ ions bind to polymorphic amylin fibrils with a preference to bind to four Cys residues rather than two Cys residues of two neighboring amylin monomers. The new binding site leads to conformational changes, increases the number of polymorphic states, and demonstrates the existence of competition between various binding sites. Our study provides insight into the molecular mechanisms through which Zn2+ ions that play a critical role in amylin aggregation can bind to amylin and promote amylin aggregation in T2D.