Protein Force Field Research Articles

Building quantum mechanics quality force fields of proteins with the generalized energy-based fragmentation approach and machine learning.

We combined our generalized energy-based fragmentation (GEBF) approach and machine learning (ML) technique to construct quantum mechanics (QM) quality force fields for proteins. In our scheme, the training sets for a protein are only constructed from its small subsystems, which capture all short-range interactions in the target system. The energy of a given protein is expressed as the summation of atomic contributions from QM calculations of various subsystems, corrected by long-range Coulomb and van der Waals interactions. With the Gaussian approximation potential (GAP) method, our protocol can automatically generate training sets with high efficiency. To facilitate the construction of training sets for proteins, we store all trained subsystem data in a library. If subsystems in the library are detected in a new protein, corresponding datasets can be directly reused as a part of the training set on this new protein. With two polypeptides, 4ZNN and 1XQ8 segment, as examples, the energies and forces predicted by GEBF-GAP are in good agreement with those from conventional QM calculations, and dihedral angle distributions from GEBF-GAP molecular dynamics (MD) simulations can also well reproduce those from ab initio MD simulations. In addition, with the training set generated from GEBF-GAP, we also demonstrate that GEBF-ML force fields constructed by neural network (NN) methods can also show QM quality. Therefore, the present work provides an efficient and systematic way to build QM quality force fields for biological systems.

Development and Validation of AMBER-FB15-Compatible Force Field Parameters for Phosphorylated Amino Acids.

Phosphorylation of select amino acid residues is one of the most common biological mechanisms for regulating protein structures and functions. While computational modeling can be used to explore the detailed structural changes associated with phosphorylation, most molecular mechanics force fields developed for the simulation of phosphoproteins have been noted to be inconsistent with experimental data. In this work, we parameterize force fields for the phosphorylated forms of the amino acids serine, threonine, and tyrosine using the ForceBalance software package with the goal of improving agreement with experiments for these residues. Our optimized force field, denoted as FB18, is parameterized using high-quality ab initio potential energy scans and is designed to be fully compatible with the AMBER-FB15 protein force field. When utilized in MD simulations together with the TIP3P-FB water model, we find that FB18 consistently enhances the prediction of experimental quantities such as 3J NMR couplings and intramolecular hydrogen-bonding propensities in comparison to previously published models. As was reported with AMBER-FB15, we also see improved agreement with the reference QM calculations in regions at and away from local minima. We thus believe that the FB18 parameter set provides a promising route for the further investigation of the varied effects of protein phosphorylation.

Modeling lipid-protein interactions for coarse-grained lipid and Cα protein models.

Biological membranes that play major roles in diverse functions are composed of numerous lipids and proteins, making them an important target for coarse-grained (CG) molecular dynamics (MD) simulations. Recently, we have developed the CG implicit solvent lipid force field (iSoLF) that has a resolution compatible with the widely used Cα protein representation [D. Ugarte La Torre and S. Takada, J. Chem. Phys. 153, 205101 (2020)]. In this study, we extended it and developed a lipid-protein interaction model that allows the combination of the iSoLF and the Cα protein force field, AICG2+. The hydrophobic-hydrophilic interaction is modeled as a modified Lennard-Jones potential in which parameters were tuned partly to reproduce the experimental transfer free energy and partly based on the free energy profile normal to the membrane surface from previous all-atom MD simulations. Then, the obtained lipid-protein interaction is tested for the configuration and placement of transmembrane proteins, water-soluble proteins, and peripheral proteins, showing good agreement with prior knowledge. The interaction is generally applicable and is implemented in the publicly available software, CafeMol.

Development of CHARMM Additive Potential Energy Parameters for α-Methyl Amino Acids.

Potential energy parameters for α-methyl amino acids were generated with ab initio calculations on α-methyl-N-acetylalanyl-N'-methylamide (the α-methyl "alanine dipeptide") which served as an input to a grid-based correction to the backbone torsional potential (known as CMAP) consistent with the CHARMM36m additive protein force field. The new parameters were validated by comparison with experimentally determined helicities of the 22 residue C-terminal peptide (H10) from apolipoprotein A1 and five α-methylated variants in water and 0.3:0.7 trifluoroethanol (TFE)/water. Conventional molecular dynamics simulation totaling 30 μs for each peptide is in overall good agreement with the experiment, including the increased helicity in 30% TFE. An additional 500 ns of simulation using two-dimensional dihedral biasing (bpCMAP) replica exchange reduced left-handed conformations, increased right-handed helices, and thereby mostly decreased agreement with the experiment. Analysis of side chain-side chain salt bridges suggests that the overestimation of the helical content may be, in part, due to such interactions. The increased helicity of the peptides in 30% TFE arises from decreased hydrogen bonding of the backbone atoms to water and a concomitant increase in intramolecular backbone hydrogen bonds.

How to strike a conformational balance in protein force fields for molecular dynamics simulations?

AbstractMolecular dynamics (MD) simulation is a powerful tool for exploring the conformational energy landscape of proteins, and the reliability of MD results is crucially dependent on the underlying force field (FF). An accurate FF capable of producing balanced distributions of diverse conformations at multiple levels has been a long‐sought goal. Towards this, several decades of joint efforts have been made to address FF deficiencies, manifested by conformational biases at different levels (local conformations, secondary structures, and global extendedness of polypeptide chain). We first present the major FF biases, then review the strategies to address them separately. Specifically, both nonresidue‐specific and residue‐specific strategies for torsional parameter optimization have been applied to achieve local conformation and secondary structure balances. Significant improvements can be gained with residue‐specific torsional parameters especially when explicit dihedral couplings are considered. Further, the additional balance between protein–protein and protein–water interactions has been optimized via multiple ways to reproduce the global extendedness of polypeptide chains, especially for unfolded or disordered proteins. This review aims to summarize the most valuable experience and lessons gained from the past, which, we hope, can facilitate further improvements of both classical FFs and more sophisticated models such as polarizable FFs.This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Molecular and Statistical Mechanics > Molecular Mechanics

Salt dependent phase behavior of intrinsically disordered proteins from a coarse-grained model with explicit water and ions.

Multivalent proteins and nucleic acids can self-assemble into biomolecular condensates that contribute to compartmentalize the cell interior. Computer simulations offer a unique view to elucidate the mechanisms and key intermolecular interactions behind the dynamic formation and dissolution of these condensates. In this work, we present a novel approach to include explicit water and salt in sequence-dependent coarse-grained (CG) models for proteins and RNA, enabling the study of biomolecular condensate formation in a salt-dependent manner. Our framework combines a reparameterized version of the HPS protein force field with the monoatomic mW water model and the mW-ion potential for NaCl. We show how our CG model qualitatively captures the experimental radius of the gyration trend of a subset of intrinsically disordered proteins and reproduces the experimental protein concentration and water percentage of the human fused in sarcoma (FUS) low-complexity-domain droplets at physiological salt concentration. Moreover, we perform seeding simulations as a function of salt concentration for two antagonist systems: the engineered peptide PR25 and poly-uridine/poly-arginine mixtures, finding good agreement with their reported in vitro phase behavior with salt concentration in both cases. Taken together, our work represents a step forward towards extending sequence-dependent CG models to include water and salt, and to consider their key role in biomolecular condensate self-assembly.

Advanced Sampling Methods for Multiscale Simulation of Disordered Proteins and Dynamic Interactions.

Intrinsically disordered proteins (IDPs) are highly prevalent and play important roles in biology and human diseases. It is now also recognized that many IDPs remain dynamic even in specific complexes and functional assemblies. Computer simulations are essential for deriving a molecular description of the disordered protein ensembles and dynamic interactions for a mechanistic understanding of IDPs in biology, diseases, and therapeutics. Here, we provide an in-depth review of recent advances in the multi-scale simulation of disordered protein states, with a particular emphasis on the development and application of advanced sampling techniques for studying IDPs. These techniques are critical for adequate sampling of the manifold functionally relevant conformational spaces of IDPs. Together with dramatically improved protein force fields, these advanced simulation approaches have achieved substantial success and demonstrated significant promise towards the quantitative and predictive modeling of IDPs and their dynamic interactions. We will also discuss important challenges remaining in the atomistic simulation of larger systems and how various coarse-grained approaches may help to bridge the remaining gaps in the accessible time- and length-scales of IDP simulations.

Protein simulation in supercritical CO2: The challenge of force field

Supercritical CO2 is one of the most important green solvents for biotechnological applications. Due to the high-pressure conditions and gas–liquid properties of the fluid, the structural investigations of the biological macromolecules such as proteins and enzymes in supercritical conditions is problematic. Molecular dynamics simulation has emerged as a good tool to study the molecular-levels phenomena in macromolecule/supercritical CO2 environments. Many unsolved aspects of such systems have been explored by this method in recent years. One of the most important challenges in biomolecular simulations in supercritical CO2 is the applied force field for the bio-macromolecules. Most of simulations in supercritical CO2 have been performed by united-atoms and GROMOS96-based force fields for proteins and enzymes. The reliability of the obtained results should be examined by applying the other protein force fields. There is no comprehensive work about the effect of the force field on a single protein model in supercritical CO2. In this work, I have applied four famous biomolecular force fields including: GROMOS96 (43a1), CHARMM (27), AMBER (03) and OPLS-AA for simulation of chymotrypsin inhibitor 2 as a model protein in supercritical CO2 and also in the aqueous conditions. Different structural properties of protein have been examined using the different force fields. Results show that all of the force fields confirm the structural deviations of the protein structure from its native state in supercritical CO2. GROMOS43a1, similar to the previous simulations, showed the higher flexibility of protein backbone in scCO2 in comparison to the aqueous condition. In contrast, in simulations with all-atom force fields, the protein flexibility was almost identical in two solvents. Simulations by all of the force fields confirm the previously proposed mechanism for protein denaturation in scCO2 which states that the changing of the interaction pattern of protein destabilizes the conformation in supercritical CO2. However, the extent of changes was different among the force fields. While united-atom force field show higher changes and deviations from the native state, all-atom force fields, in agreement with each other, show moderate changes and deviations.

Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins.

Finding optimal parameters for force fields used in molecular simulation is a challenging and time-consuming task, partly due to the difficulty of tuning multiple parameters at once. Automatic differentiation presents a general solution: run a simulation, obtain gradients of a loss function with respect to all the parameters, and use these to improve the force field. This approach takes advantage of the deep learning revolution whilst retaining the interpretability and efficiency of existing force fields. We demonstrate that this is possible by parameterising a simple coarse-grained force field for proteins, based on training simulations of up to 2,000 steps learning to keep the native structure stable. The learned potential matches chemical knowledge and PDB data, can fold and reproduce the dynamics of small proteins, and shows ability in protein design and model scoring applications. Problems in applying differentiable molecular simulation to all-atom models of proteins are discussed along with possible solutions and the variety of available loss functions. The learned potential, simulation scripts and training code are made available at https://github.com/psipred/cgdms.

Coarse-Grained Modeling and Molecular Dynamics Simulations of Ca2+-Calmodulin.

Calmodulin (CaM) is a calcium-binding protein that transduces signals to downstream proteins through target binding upon calcium binding in a time-dependent manner. Understanding the target binding process that tunes CaM’s affinity for the calcium ions (Ca2+), or vice versa, may provide insight into how Ca2+-CaM selects its target binding proteins. However, modeling of Ca2+-CaM in molecular simulations is challenging because of the gross structural changes in its central linker regions while the two lobes are relatively rigid due to tight binding of the Ca2+ to the calcium-binding loops where the loop forms a pentagonal bipyramidal coordination geometry with Ca2+. This feature that underlies the reciprocal relation between Ca2+ binding and target binding of CaM, however, has yet to be considered in the structural modeling. Here, we presented a coarse-grained model based on the Associative memory, Water mediated, Structure, and Energy Model (AWSEM) protein force field, to investigate the salient features of CaM. Particularly, we optimized the force field of CaM and that of Ca2+ ions by using its coordination chemistry in the calcium-binding loops to match with experimental observations. We presented a “community model” of CaM that is capable of sampling various conformations of CaM, incorporating various calcium-binding states, and carrying the memory of binding with various targets, which sets the foundation of the reciprocal relation of target binding and Ca2+ binding in future studies.

Force Field Benchmark of Amino Acids. 3. Hydration with Scaled Lennard-Jones Interactions.

Classical protein force fields were reported with too weak protein-water interactions relative to protein-protein interactions, leading to more compact structures and artificial protein aggregation. Here we investigated the impacts of scaled Lennard-Jones (LJ) interactions on the hydration of amino acids and the simulation of folded and intrinsically disordered proteins (IDPs). The obtained optimal scaling parameters reproduce accurately hydration free energies of neutral amino acid side chain analogues and do not affect the compactness and structural stability of folded proteins significantly. The scaling leads to less compact IDPs and varies from case to case. Strengthening the interactions between protein and water oxygen or hydrogen atoms by increasing the interacting LJ well depth (ε) appears more effective than weakening protein-protein interactions by reducing the interacting dispersion coefficients (C6). We demonstrate that weakening water-water interactions is a solution as well to obtaining more favorable protein-water interactions in an indirect way, although modern force fields like Amber ff19SB and a99SB-disp tend to use water models with strong water-water interactions. This is likely a compromise between strong protein-protein interactions and strong water-water interactions. Independent optimization of protein force fields and water models is therefore needed to make both interactions more close to reality, leading to good accuracy without bias or scaling.

Validating the CHARMM36m protein force field with LJ-PME reveals altered hydrogen bonding dynamics under elevated pressures

The pressure-temperature phase diagram is important to our understanding of the physics of biomolecules. Compared to studies on temperature effects, studies of the pressure dependence of protein dynamic are rather limited. Molecular dynamics (MD) simulations with fine-tuned force fields (FFs) offer a powerful tool to explore the influence of thermodynamic conditions on proteins. Here we evaluate the transferability of the CHARMM36m (C36m) protein force field at varied pressures compared with NMR data using ubiquitin as a model protein. The pressure dependences of J couplings for hydrogen bonds and order parameters for internal motion are in good agreement with experiment. We demonstrate that the C36m FF combined with the Lennard-Jones particle-mesh Ewald (LJ-PME) method is suitable for simulations in a wide range of temperature and pressure. As the ubiquitin remains stable up to 2500 bar, we identify the mobility and stability of different hydrogen bonds in response to pressure. Based on those results, C36m is expected to be applied to more proteins in the future to further investigate protein dynamics under elevated pressures.

Modeling structural interconversion in Alzheimers’ amyloid beta peptide with classical and intrinsically disordered protein force fields

A comprehensive understanding of the aggregation mechanism in amyloid beta 42 (Aβ42) peptide is imperative for developing therapeutic drugs to prevent or treat Alzheimer’s disease. Because of the high flexibility and lack of native tertiary structures of Aβ42, molecular dynamics (MD) simulations may help elucidate the peptide’s dynamics with atomic details and collectively improve ensembles not seen in experiments. We applied microsecond-timescale MD simulations to investigate the dynamics and conformational changes of Aβ42 by using a newly developed Amber force field (ff14IDPSFF). We compared the ff14IDPSFF and the regular ff14SB force field by examining the conformational changes of two distinct Aβ42 monomers in explicit solvent. Conformational ensembles obtained by simulations depend on the force field and initial structure, Aβ42α-helix or Aβ42β-strand. The ff14IDPSFF sampled a high ratio of disordered structures and diverse β-strand secondary structures; in contrast, ff14SB favored helicity during the Aβ42α-helix simulations. The conformations obtained from Aβ42β-strand simulations maintained a balanced content in the disordered and helical structures when simulated by ff14SB, but the conformers clearly favored disordered and β-sheet structures simulated by ff14IDPSFF. The results obtained with ff14IDPSFF qualitatively reproduced the NMR chemical shifts well. In-depth peptide and cluster analysis revealed some characteristic features that may be linked to early onset of the fibril-like structure. The C-terminal region (mainly M35-V40) featured in-registered anti-parallel β-strand (β-hairpin) conformations with tested systems. Our work should expand the knowledge of force field and structure dependency in MD simulations and reveals the underlying structural mechanism–function relationship in Aβ42 peptides. Communicated by Ramaswamy H. Sarma

Developing and Assessing Nonbonded Dummy Models of Magnesium Ion with Different Hydration Free Energy References.

A large diversity in the targeted hydration free energies (HFEs) during model parameterization of metal ions was reported in the literature with a difference by dozens of kcal/mol. Here, we developed a series of nonbonded dummy models of the Mg2+ ion targeting different HFE references in TIP3P water, followed by assessments of the designed models in the simulations of MgCl2 solution and biological systems. Together with the comparison of existing models, we conclude that the difference in the targeted HFEs has a limited influence on the model performance, while the usability of these models differs from case to case. The feasibility of reproducing more properties of Mg2+ such as diffusion constants and water exchange rates using a nonbonded dummy model is demonstrated. Underestimated activity derivative and osmotic coefficient of MgCl2 solutions in high concentration reveal a necessity for further optimization of ion-pair interactions. The developed dummy models are applicable to metal coordination with Asp, Glu, and His residues in metalloenzymes, and the performance in predicting monodentate or bidentate binding modes of Asp/Glu residues depends on the complexity of metal centers and the choice of protein force fields. When both the binding modes coexist, the nonbonded dummy models outperform point charge models, probably in need of considering polarization of metal-binding residues by, for instance, charge calibration in classical force fields. This work is valuable for the use and further development of magnesium ion models for simulations of metal-containing systems with good accuracy.

Machine learning builds full-QM precision protein force fields in seconds.

Full-quantum mechanics (QM) calculations are extraordinarily precise but difficult to apply to large systems, such as biomolecules. Motivated by the massive demand for efficient calculations for large systems at the full-QM level and by the significant advances in machine learning, we have designed a neural network-based two-body molecular fractionation with conjugate caps (NN-TMFCC) approach to accelerate the energy and atomic force calculations of proteins. The results show very high precision for the proposed NN potential energy surface models of residue-based fragments, with energy root-mean-squared errors (RMSEs) less than 1.0kcal/mol and force RMSEs less than 1.3kcal/mol/Å for both training and testing sets. The proposed NN-TMFCC method calculates the energies and atomic forces of 15 representative proteins with full-QM precision in 10-100s, which is thousands of times faster than the full-QM calculations. The computational complexity of the NN-TMFCC method is independent of the protein size and only depends on the number of residue species, which makes this method particularly suitable for rapid prediction of large systems with tens of thousands or even hundreds of thousands of times acceleration. This highly precise and efficient NN-TMFCC approach exhibits considerable potential for performing energy and force calculations, structure predictions and molecular dynamics simulations of proteins with full-QM precision.

Multi-body effects in a coarse-grained protein force field

The use of coarse-grained (CG) models is a popular approach to study complex biomolecular systems. By reducing the number of degrees of freedom, a CG model can explore long time- and length-scales inaccessible to computational models at higher resolution. If a CG model is designed by formally integrating out some of the system's degrees of freedom, one expects multi-body interactions to emerge in the effective CG model's energy function. In practice, it has been shown that the inclusion of multi-body terms indeed improves the accuracy of a CG model. However, no general approach has been proposed to systematically construct a CG effective energy that includes arbitrary orders of multi-body terms. In this work, we propose a neural network based approach to address this point and construct a CG model as a multi-body expansion. By applying this approach to a small protein, we evaluate the relative importance of the different multi-body terms in the definition of an accurate model. We observe a slow convergence in the multi-body expansion, where up to five-body interactions are needed to reproduce the free energy of an atomistic model.

Kirkwood–Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of KBFF20.

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

Configurational Entropy of Folded Proteins and Its Importance for Intrinsically Disordered Proteins.

Many pairwise additive force fields are in active use for intrinsically disordered proteins (IDPs) and regions (IDRs), some of which modify energetic terms to improve the description of IDPs/IDRs but are largely in disagreement with solution experiments for the disordered states. This work considers a new direction—the connection to configurational entropy—and how it might change the nature of our understanding of protein force field development to equally well encompass globular proteins, IDRs/IDPs, and disorder-to-order transitions. We have evaluated representative pairwise and many-body protein and water force fields against experimental data on representative IDPs and IDRs, a peptide that undergoes a disorder-to-order transition, for seven globular proteins ranging in size from 130 to 266 amino acids. We find that force fields with the largest statistical fluctuations consistent with the radius of gyration and universal Lindemann values for folded states simultaneously better describe IDPs and IDRs and disorder-to-order transitions. Hence, the crux of what a force field should exhibit to well describe IDRs/IDPs is not just the balance between protein and water energetics but the balance between energetic effects and configurational entropy of folded states of globular proteins.

Drude Polarizable Simulations of the p53 Transactivation Domain with Different Binding Partners

Intrinsically disordered proteins (IDPs) and intrinsically disordered protein regions (IDRs) do not follow the canonical structure-function paradigm of adopting a dominant fold, instead interconverting among multiple structures that are accessible along a rugged, shallow free energy surface. This structural plasticity is exploited to facilitate binding to structurally diverse partners, including both proteins and nucleic acids. Given that IDPs often serve critical regulatory roles in a range of cellular functions such as signal transduction and cell cycle checkpoints, it is crucial to understand the dynamics and interactions of these abundant proteins. Previous molecular dynamics studies of IDPs have primarily used additive force fields, which approximate polarization effects assuming a uniform dielectric medium. This approximation may fall short in IDPs, for which cooperative, induced effects such as hydrogen bonding, are particularly important in dictating the balance of secondary structure. Here, we apply the Drude-2019 polarizable protein force field for the first time to simulations of the p53 transactivation domain (TAD) alone and in complex with two binding partners: MDM2, a protein with well-defined tertiary structure, and the nuclear coactivator domain of CBP, an IDR. p53 is a widely studied protein and is a prototypical protein with IDRs, thus the TAD is a useful model IDP to examine the role of side-chain and backbone electronic polarization in the nucleation of secondary structure upon complexation. We focus our analysis on properties that are only attainable using a polarizable force field, such as individual molecular dipole moments of different protein moieties. We find that side-chain dipole moments are perturbed upon burial in the protein-protein complexes and that these depolarization effects are almost entirely confined to the interface between the p53 TAD and the binding partners, with aliphatic residues being the most impacted.