Are AMBER Force Fields and Implicit Solvation Models Additive? A Folding Study with a Balanced Peptide Test Set

Assessment of the Topology and Oligomerisation States of Coiled Coils Using Metadynamics with Conformational Restraints

Coiled-coil proteins provide an excellent scaffold for multistate de novo protein design due to their established sequence-to-structure relationships and ability to switch conformations in response to external stimuli, such as changes in pH or temperature. However, the computational design of multistate coiled-coil protein assemblies is challenging, as it requires accurate estimates of the free energy differences between multiple alternative coiled-coil conformations. Here, we demonstrate how this challenge can be tackled using metadynamics simulations with orientational, positional and conformational restraints. We show that, even for subtle sequence variations, our protocol can predict the preferred topology of coiled-coil dimers and trimers, the preferred oligomerization states of coiled-coil dimers, trimers, and tetramers, as well as the switching behavior of a pH-dependent multistate system. Our approach provides a method for predicting the stability of coiled-coil designs and offers a new framework for computing binding free energies in protein-protein and multiprotein complexes.

Differentiable simulation to develop molecular dynamics force fields for disordered proteins

Implicit solvent force fields are computationally efficient but can be unsuitable for running molecular dynamics on disordered proteins. Here I improve the a99SB-disp force field and the GBNeck2 implicit solvent model to better describe disordered proteins. Differentiable molecular simulations with 5 ns trajectories are used to jointly optimise 108 parameters to better match explicit solvent trajectories. Simulations with the improved force field better reproduce the radius of gyration and secondary structure content seen in experiments, whilst showing slightly degraded performance on folded proteins and protein complexes. The force field, called GB99dms, reproduces the results of a small molecule binding study and improves agreement with experiment for the aggregation of amyloid peptides. GB99dms, which can be used in OpenMM, is available at https://github.com/greener-group/GB99dms. This work is the first to show that gradients can be obtained directly from nanosecond-length differentiable simulations of biomolecules and highlights the effectiveness of this approach to training whole force fields to match desired properties.

Transferable Implicit Solvation via Contrastive Learning of Graph Neural Networks

Implicit solvent models are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. Efforts are underway to develop accurate and transferable implicit solvent models and coarse-grained (CG) force fields in general, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to the lack of analytical expressions for the PMF and algorithmic limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent the solvation free energy and potential contrasting for parameter optimization. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside of the training data. Our study offers valuable insights for deriving systematically improvable implicit solvent models and CG force fields from a bottom-up perspective.

Transferable Coarse Graining via Contrastive Learning of Graph Neural Networks

Coarse-grained (CG) force fields are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. These simulations employ simplified models grouping atoms into interaction sites, enabling the study of complex biomolecular systems over biologically relevant timescales. Efforts are underway to develop accurate and transferable CG force fields, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to many-body effects, lack of analytical expressions for the PMF, and limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent CG force fields and potential contrasting for parameterization from atomistic simulation data. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside the training data. Our study offers valuable insights for building accurate coarse-grained models bottom-up.

Generalized Born Implicit Solvent Models Do Not Reproduce Secondary Structures of De Novo Designed Glu/Lys Peptides

We test a range of standard generalized Born (GB) models and protein force fields for a set of five experimentally characterized, designed peptides comprising alternating blocks of glutamate and lysine, which have been shown to differ significantly in α-helical content. Sixty-five combinations of force fields and GB models are evaluated in >800 μs of molecular dynamics simulations. GB models generally do not reproduce the experimentally observed α-helical content, and none perform well for all five peptides. These results illustrate that these models are not usefully predictive in this context. These peptides provide a useful test set for simulation methods.

Forcefield evaluation and accelerated molecular dynamics simulation of Zn(II) binding to N-terminus of amyloid-β

We report conventional and accelerated molecular dynamics simulation of Zn(II) bound to the N-terminus of amyloid-β. By comparison against NMR data for the experimentally determined binding mode, we find that certain combinations of forcefield and solvent model perform acceptably in describing the size, shape and secondary structure, and that there is no appreciable difference between implicit and explicit solvent models. We therefore used the combination of ff14SB forcefield and GBSA solvent model to compare the result of different binding modes of Zn(II) to the same peptide, using accelerated MD to enhance sampling and comparing the free peptide simulated in the same way. We show that Zn(II) imparts significant rigidity to the peptide, disrupts the secondary structure and pattern of salt bridges seen in the free peptide, and induces closer contact between residues. Free energy surfaces in 1 or 2 dimensions further highlight the effect of metal coordination on peptide's spatial extent. We also provide evidence that accelerated MD provides improved sampling over conventional MD by visiting as many or more configurations in much shorter simulation times.

"Big Data" Fast Chemoinformatics Model to Predict Generalized Born Radius and Solvent Accessibility as a Function of Geometry

The Generalized Born (GB) solvent model is offering the best accuracy/computing effort ratio yet requires drastic simplifications to estimate of the Effective Born Radii (EBR) in bypassing a too expensive volume integration step. EBRs are a measure of the degree of burial of an atom and not very sensitive to small changes of geometry: in molecular dynamics, the costly EBR update procedure is not mandatory at every step. This work however aims at implementing a GB model into the Sampler for Multiple Protein-Ligand Entities (S4MPLE) evolutionary algorithm with mandatory EBR updates at each step triggering arbitrarily large geometric changes. Therefore, a quantitative structure-property relationship has been developed in order to express the EBRs as a linear function of both the topological neighborhood and geometric occupancy of the space around atoms. A training set of 810 molecular systems, starting from fragment-like to drug-like compounds, proteins, host-guest systems, and ligand-protein complexes, has been compiled. For each species, S4MPLE generated several hundreds of random conformers. For each atom in each geometry of each species, its "standard" EBR was calculated by numeric integration and associated to topological and geometric descriptors of the atom neighborhood. This training set (EBR, atom descriptors) involving >5 M entries was subjected to a boot-strapping multilinear regression process with descriptor selection. In parallel, the strategy was repurposed to also learn atomic solvent-accessible areas (SA) based on the same descriptors. Resulting linear equations were challenged to predict EBR and SA values for a similarly compiled external set of >2000 new molecular systems. Solvation energies calculated with estimated EBR and SA match "standard" energies within the typical error of a force-field-based approach (a few kilocalories per mole). Given the extreme diversity of molecular systems covered by the model, this simple EBR/SA estimator covers a vast applicability domain.

A hybrid, bottom-up, structurally accurate, Go¯-like coarse-grained protein model

Coarse-grained (CG) protein models in the structural biology literature have improved over the years from being simple tools to understand general folding and aggregation driving forces to capturing detailed structures achieved by actual folding sequences. Here, we ask whether such models can be developed systematically from recent advances in bottom-up coarse-graining methods without relying on bioinformatic data (e.g., protein data bank statistics). We use relative entropy coarse-graining to develop a hybrid CG but Go¯-like CG peptide model, hypothesizing that the landscape of proteinlike folds is encoded by the backbone interactions, while the sidechain interactions define which of these structures globally minimizes the free energy in a unique native fold. To construct a model capable of capturing varied secondary structures, we use a new extended ensemble relative entropy method to coarse-grain based on multiple reference atomistic simulations of short polypeptides with varied α and β character. Subsequently, we assess the CG model as a putative protein backbone forcefield by combining it with sidechain interactions based on native contacts but not incorporating native distances explicitly, unlike standard Go¯ models. We test the model's ability to fold a range of proteins and find that it achieves high accuracy (∼2 Å root mean square deviation resolution for both short sequences and large globular proteins), suggesting the strong role that backbone conformational preferences play in defining the fold landscape. This model can be systematically extended to non-natural amino acids and nonprotein polymers and sets the stage for extensions to non-Go¯ models with sequence-specific sidechain interactions.

Assessing AMBER force fields for protein folding in an implicit solvent

Molecular dynamics (MD) simulation implemented with a state-of-the-art protein force field and implicit solvent model is an attractive approach to investigate protein folding, one of the most perplexing problems in molecular biology. But how well can force fields developed independently of implicit solvent models work together in reproducing diverse protein native structures and measuring the corresponding folding thermodynamics is not always clear. In this work, we performed enhanced sampling MD simulations to assess the ability of six AMBER force fields (FF99SBildn, FF99SBnmr, FF12SB, FF14ipq, FF14SB, and FF14SBonlysc) as coupled with a recently improved pair-wise GB-Neck2 model in modeling the folding of two helical and two β-sheet peptides. Whilst most of the tested force fields can yield roughly similar features for equilibrium conformational ensembles and detailed folding free-energy profiles for short α-helical TC10b in an implicit solvent, the measured counterparts are significantly discrepant in the cases of larger or β-structured peptides (HP35, 1E0Q, and GTT). Additionally, the calculated folding/unfolding thermodynamic quantities can only partially match the experimental data. Although a combination of the force fields and GB-Neck2 implicit model able to describe all aspects of the folding transitions towards the native structures of all the considered peptides was not identified, we found that FF14SBonlysc coupled with the GB-Neck2 model seems to be a reasonably balanced combination to predict peptide folding preferences.

The effects of implicit modeling of nonpolar solvation on protein folding simulations

Implicit solvent models, in which the polar and nonpolar solvation free-energies of solute molecules are treated separately, have been widely adopted for molecular dynamics simulation of protein folding. While the development of the implicit models is mainly focused on the methodological improvement and key parameter optimization for polar solvation, nonpolar solvation has been either ignored or described by a simplistic surface area (SA) model. In this work, we performed the folding simulations of multiple β-hairpin and α-helical proteins with varied surface tension coefficients embedded in the SA model to clearly demonstrate the effects of nonpolar solvation treated by a popular SA model on protein folding. The results indicate that the change in the surface tension coefficient does not alter the ability of implicit solvent simulations to reproduce a protein native structure but indeed controls the components of the equilibrium conformational ensemble and modifies the energetic characterization of the folding transition pathway. The suitably set surface tension coefficient can yield explicit solvent simulations and/or experimentally suggested folding mechanism of protein. In addition, the implicit treatment of both polar and nonpolar components of solvation free-energy contributes to the overestimation of the secondary structure in implicit solvent simulations.

Tandem Tetrahydroisoquinoline-4-carboxylic Acid/β-Alanine as a New Construct Able To Induce a Flexible Turn

Tetrahydroisoquinoline-4-carboxylic acid, a constrained β² -amino acid named β-TIC, was synthesised for the first time in enantiopure form. The biocatalytic route applied herein represents one of the few successful examples of enzymatic resolution of β² -amino acids. Model tetrapeptides, namely, Fmoc-l-Ala-β-TIC-β-Ala-l-Val-OBn (Fmoc=fluorenylmethyloxycarbonyl, Bn=benzyl), containing both isomers of β-TIC, were prepared. Both computational and NMR spectroscopy studies were performed. A reverse-turn conformation was observed in the case of (R)-β-TIC enantiomer that was obtained in 99 % enantiomeric excess by enzymatic resolution. The β-TIC/β-Ala construct represents the first example of a flexible turn mimetic containing a cyclic and an acyclic β-amino acid. Furthermore, the presence of an aromatic ring of β-TIC could facilitate non-covalent interactions to increase the potential of this scaffold for the preparation of protein-protein interaction modulators.

Human EGF-derived direct and reverse short linear motifs: conformational dynamics insight into the receptor-binding residues

Short linear motifs (SLiMs) have been recognized to perform diverse functions in a variety of regulatory proteins through the involvement in protein-protein interactions, signal transduction, cell cycle regulation, protein secretion, etc. However, detailed molecular mechanisms underlying their functions including roles of definite amino acid residues remain obscure. In our previous studies, we demonstrated that conformational dynamics of amino acid residues in oligopeptides derived from regulatory proteins such as alpha-fetoprotein (AFP), carcino-embryonic antigen (CEA), and pregnancy specific β1-glycoproteins (PSGs) contributes greatly to their biological activities. In the present work, we revealed the 22-member linear modules composed of direct and reverse AFP_14-20-like heptapeptide motifs linked by CxxGY/FxGx consensus motif within epidermal growth factor (EGF), growth factors of EGF family and numerous regulatory proteins containing EGF-like modules. We showed, first, the existence of similarity in amino acid signatures of both direct and reverse motifs in terms of their physicochemical properties. Second, molecular dynamics (MD) simulation study demonstrated that key receptor-binding residues in human EGF in the aligned positions of the direct and reverse motifs may have similar distribution of conformational probability densities and dynamic behavior despite their distinct physicochemical properties. Third, we found that the length of a polypeptide chain (from 7 to 53 residues) has no effect, while disulfide bridging and backbone direction significantly influence the conformational distribution and dynamics of the residues. Our data may contribute to the atomic level structure-function analysis and protein structure decoding; additionally, they may provide a basis for novel protein/peptide engineering and peptide-mimetic drug design.