Consistent free energy landscapes and thermodynamic properties of small proteins based on a single all-atom force field employing an implicit solvation

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.

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.

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template-based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug-design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr-REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native-like structures from a template and to provide a set of persistent contacts to be employed during re-folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled.

The intrinsic conformational features of amino acids from a protein coil library and their applications in force field development

The local conformational (φ, ψ, χ) preferences of amino acid residues remain an active research area, which are important for the development of protein force fields. In this perspective article, we first summarize spectroscopic studies of alanine-based short peptides in aqueous solution. While most studies indicate a preference for the P(II) conformation in the unfolded state over α and β conformations, significant variations are also observed. A statistical analysis from various coil libraries of high-resolution protein structures is then summarized, which gives a more coherent view of the local conformational features. The φ, ψ, χ distributions of the 20 amino acids have been obtained from a protein coil library, considering both backbone and side-chain conformational preferences. The intrinsic side-chain χ(1) rotamer preference and χ(1)-dependent Ramachandran plot can be generally understood by combining the interaction of the side-chain Cγ/Oγ atom with two neighboring backbone peptide groups. Current all-atom force fields such as AMBER ff99sb-ILDN, ff03 and OPLS-AA/L do not reproduce these distributions well. A method has been developed by combining the φ, ψ plot of alanine with the influence of side-chain χ(1) rotamers to derive the local conformational features of various amino acids. It has been further applied to improve the OPLS-AA force field. The modified force field (OPLS-AA/C) reproduces experimental (3)J coupling constants for various short peptides quite well. It also better reproduces the temperature-dependence of the helix-coil transition for alanine-based peptides. The new force field can fold a series of peptides and proteins with various secondary structures to their experimental structures. MD simulations of several globular proteins using the improved force field give significantly less deviation (RMSD) to experimental structures. The results indicate that the local conformational features from coil libraries are valuable for the development of balanced protein force fields.

Dynamic folding pathway models of the Trp-cage protein

Using action-derived molecular dynamics (ADMD), we study the dynamic folding pathway models of the Trp-cage protein by providing its sequential conformational changes from its initial disordered structure to the final native structure at atomic details. We find that the numbers of native contacts and native hydrogen bonds are highly correlated, implying that the native structure of Trp-cage is achieved through the concurrent formations of native contacts and native hydrogen bonds. In early stage, an unfolded state appears with partially formed native contacts (~40%) and native hydrogen bonds (~30%). Afterward, the folding is initiated by the contact of the side chain of Tyr3 with that of Trp6, together with the formation of the N-terminal α -helix. Then, the C-terminal polyproline structure docks onto the Trp6 and Tyr3 rings, resulting in the formations of the hydrophobic core of Trp-cage and its near-native state. Finally, the slow adjustment processes of the near-native states into the native structure are dominant in later stage. The ADMD results are in agreement with those of the experimental folding studies on Trp-cage and consistent with most of other computational studies.

Combining coarse-grained protein models with replica-exchange all-atom molecular dynamics

We describe a combination of all-atom simulations with CABS, a well-established coarse-grained protein modeling tool, into a single multiscale protocol. The simulation method has been tested on the C-terminal beta hairpin of protein G, a model system of protein folding. After reconstructing atomistic details, conformations derived from the CABS simulation were subjected to replica-exchange molecular dynamics simulations with OPLS-AA and AMBER99sb force fields in explicit solvent. Such a combination accelerates system convergence several times in comparison with all-atom simulations starting from the extended chain conformation, demonstrated by the analysis of melting curves, the number of native-like conformations as a function of time and secondary structure propagation. The results strongly suggest that the proposed multiscale method could be an efficient and accurate tool for high-resolution studies of protein folding dynamics in larger systems.

Conformational dynamics of human IAPP monomers

We study the conformational dynamics of the human Islet Amyloid Polypeptide (hIAPP) molecule - a 37 residue-long peptide associated to type 2 diabetes - using molecular dynamics (MD) simulations. We identify partially structured conformational states of the hIAPP monomer, categorized by both end-to-end distance and secondary structure, as suggested by previous experimental and computational studies. The MD trajectories of hIAPP are analyzed using data-driven methods, in particular principal component analysis, in order to identify preferred conformational states of the amylin monomer and to discuss their relative stability as compared to corresponding states in the amylin dimer. These potential hIAPP conformational states could be further tested and described experimentally, or in conjunction with modern computational analysis tools such as Markov state-based methods for extracting kinetics and thermodynamics from atomistic MD trajectories.

Microscopic events in β-hairpin folding from alternative unfolded ensembles

We have performed the first unbiased folding simulations of the GB1 hairpin in explicit solvent, using hundreds of microsecond-long molecular dynamics simulations (total time: 0.7 ms). Our simulations are initiated from two sets of structures. Starting from an equilibrium unfolded state, we obtain single-exponential folding kinetics with rate coefficients in good agreement (T=350 K) or within an order of magnitude (T=300 K) of the experimental values. However, simulations initiated from unfolded configurations lacking secondary structure result in biexponential kinetics with an additional fast nanosecond kinetic mode. This mode can strongly bias the folding rate estimated from the mean first passage time, when the trials are much shorter than the folding time. We find that the mechanism of the hairpin folding is insensitive to the details of the initial unfolded ensemble and is initiated by correct formation of the turn of the hairpin, followed by the formation of the native hydrogen bonds and hydrophobic contacts, consistent with experimental -value analysis. Subsequent native interactions can be formed either from the turn or from the hairpin termini, helping to explain an apparent discrepancy in experimental results. From our simulations, we also obtain the transition path durations, a critical parameter for single molecule experiments aiming to resolve events along folding pathways. The lengths of transition paths span a wide range, from 50 ps to 140 ns, at 300 K.

Free-energy landscape of the GB1 hairpin in all-atom explicit solvent simulations with different force fields: Similarities and differences

Although it is now possible to fold peptides and miniproteins in molecular dynamics simulations, it is well appreciated that force fields are not all transferable to different proteins. Here, we investigate the influence of the protein force field and the solvent model on the folding energy landscape of a prototypical two-state folder, the GB1 hairpin. We use extensive replica-exchange molecular dynamics simulations to characterize the free-energy surface as a function of temperature. Most of these force fields appear similar at a global level, giving a fraction folded at 300 K between 0.2 and 0.8 in all cases, which is a difference in stability of 2.8 kT, and are generally consistent with experimental data at this temperature. The most significant differences appear in the unfolded state, where there are different residual secondary structures which are populated, and the overall dimensions of the unfolded states, which in most of the force fields are too collapsed relative to experimental Förster Resonance Energy Transfer (FRET) data.

Folding of a helix at room temperature is critically aided by electrostatic polarization of intraprotein hydrogen bonds

We report direct folding of a 17-residue helix protein (pdb:2I9M) by standard molecular dynamics simulation (single trajectory) at room temperature with implicit solvent. Starting from a fully extended structure, 2I9M successfully folds into the native conformation within 16 ns using adaptive hydrogen bond-specific charges to take into account the electrostatic polarization effect. Cluster analysis shows that conformations in the native state cluster have the highest population (78.4%) among all sampled conformations. Folding snapshots and the secondary structure analysis demonstrate that the folding of 2I9M begins at terminals and progresses toward the center. A plot of the free energy landscape indicates that there is no significant free energy barrier during folding, which explains the observed fast folding speed. For comparison, exactly the same molecular dynamics simulation but carried out under existing AMBER charges failed to fold 2I9M into native-like structures. The current study demonstrates that electrostatic polarization of intraprotein hydrogen bonding, which stabilizes the helix, is critical to the successful folding of 2I9m.

On the origins of the weak folding cooperativity of a designed ββα ultrafast protein FSD-1

FSD-1, a designed small ultrafast folder with a ββα fold, has been actively studied in the last few years as a model system for studying protein folding mechanisms and for testing of the accuracy of computational models. The suitability of this protein to describe the folding of naturally occurring α/β proteins has recently been challenged based on the observation that the melting transition is very broad, with ill-resolved baselines. Using molecular dynamics simulations with the AMBER protein force field (ff96) coupled with the implicit solvent model (IGB = 5), we shed new light into the nature of this transition and resolve the experimental controversies. We show that the melting transition corresponds to the melting of the protein as a whole, and not solely to the helix-coil transition. The breadth of the folding transition arises from the spread in the melting temperatures (from ∼325 K to ∼302 K) of the individual transitions: formation of the hydrophobic core, β-hairpin and tertiary fold, with the helix formed earlier. Our simulations initiated from an extended chain accurately predict the native structure, provide a reasonable estimate of the transition barrier height, and explicitly demonstrate the existence of multiple pathways and multiple transition states for folding. Our exhaustive sampling enables us to assess the quality of the Amber ff96/igb5 combination and reveals that while this force field can predict the correct native fold, it nonetheless overstabilizes the α-helix portion of the protein (Tm = ∼387K) as well as the denatured structures.

The protein folding process, in which a linear chain of amino acids reaches its biologically active three-dimensional shape, is fundamental to life. Small “ultrafast” folders, proteins that fold in microseconds, have received considerable attention, because these proteins serve as model systems for the folding of larger proteins, and thus permit a testing of the accuracy of computational models as well as an assessment of protein folding theories. FSD-1, a designed small ultrafast folder with a ββα fold, has been actively studied in the last few years as a model system for mixed α/β fold proteins. The suitability of this protein to describe the folding of naturally occurring proteins has however recently been challenged based on the observation that the melting transition is very broad, with ill-resolved baselines. Prior simulations have not been successful in providing an interpretation of this broad melting transition. In the present study, our extensive molecular dynamics simulations using the AMBER protein force field (ff96) coupled with the implicit solvent model (IGB = 5) shed new light on the nature of the folding transition of this protein, as well as reveal the strengths and weaknesses of the force field in predicting the thermodynamics and kinetics of folding.

Balance between alpha and beta structures in ab initio protein folding

Despite initial successes in folding of proteins by molecular simulation, it is becoming increasingly evident that current energy functions (force fields) tend to favor either alpha or beta secondary structure, such that the choice of force field is governed by the structural class of the protein. Here, we study the folding of peptides with either predominantly alpha (Trp cage) or beta (GB1 hairpin) structure with a modified version of the Amber ff03 force field, optimized to reproduce structural propensity in a helix-forming peptide. Using extensive replica exchange molecular dynamics simulations starting from completely unfolded configurations, we obtain the correct folded structure for each peptide, in close agreement with the experimental native structure (<1.5 A all-atom root-mean-square deviation). We obtain converged equilibrium distributions, with folded populations at standard conditions (approximately 300 K), in remarkable accord with experiment. Further comparison to experimental data from NMR spectroscopy and FRET suggests that although the folded structures are accurately reproduced, the unfolded state remains too structured and compact. Our results suggest that the backbone correction results in a force field that is transferable to the folding of proteins from different structural classes.

All-atom ab initio native structure prediction of a mixed fold (1FME): a comparison of structural and folding characteristics of various beta beta alpha miniproteins

We performed an all-atom ab initio native structure prediction of 1FME, which is one of the computationally challenging mixed fold beta beta alpha miniproteins, by combining a novel conformational search algorithm (multiplexed Q-replica exchange molecular dynamics scheme) with a well-balanced all-atom force field employing a generalized Born implicit solvation model (param99MOD5/GBSA). The nativelike structure of 1FME was identified from the lowest free energy minimum state and in excellent agreement with the NMR structure. Based on the interpretation of the free energy landscape, the structural properties as well as the folding behaviors of 1FME were compared with other beta beta alpha miniproteins (1FSD, 1PSV, and BBA5) that we have previously studied with the same force field. Our simulation showed that the 28-residue beta beta alpha miniproteins (1FME, 1FSD, and 1PSV) share a common feature of the free energy topography and exhibit the three local minimum states on each computed free energy map, but the 23-residue miniprotein (BBA5) follows a downhill folding with a single minimum state. Also, the structure and stability changes resulting from the two point mutation (Gln1-->Glu1 and Ile7-->Tyr7) of 1FSD were investigated in details for direct comparison with the experiment. The comparison shows that upon mutation, the experimentally observed turn type switch from an irregular turn (1FSD) to type I(') turn (1FME) was well reproduced with the present simulation.

All-atom level direct folding simulation of a betabetaalpha miniprotein

We performed ab initio folding simulation for a betabetaalpha peptide BBA5 (PDB code 1T8J) with a modified param99 force field using the generalized Born solvation model (param99MOD5/GBSA). For efficient conformational sampling, we extended a previously developed novel Q-replica exchange molecular dynamics (Q-REMD) into a multiplexed Q-REMD. Starting from a fully extended conformation, we were able to locate the nativelike structure in the global free minimum region at 280 K. The current approach, which combines the more balanced force field with the efficient sampling scheme, demonstrates a clear advantage in direct folding simulation at all-atom level.