Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Effects of force fields on the conformational and dynamic properties of amyloid β(1‐40) dimer explored by replica exchange molecular dynamics simulations

The conformational space and structural ensembles of amyloid beta (Aβ) peptides and their oligomers in solution are inherently disordered and proven to be challenging to study. Optimum force field selection for molecular dynamics (MD) simulations and the biophysical relevance of results are still unknown. We compared the conformational space of the Aβ(1‐40) dimers by 300 ns replica exchange MD simulations at physiological temperature (310 K) using: the AMBER‐ff99sb‐ILDN, AMBER‐ff99sb*‐ILDN, AMBER‐ff99sb‐NMR, and CHARMM22* force fields. Statistical comparisons of simulation results to experimental data and previously published simulations utilizing the CHARMM22* and CHARMM36 force fields were performed. All force fields yield sampled ensembles of conformations with collision cross sectional areas for the dimer that are statistically significantly larger than experimental results. All force fields, with the exception of AMBER‐ff99sb‐ILDN (8.8 ± 6.4%) and CHARMM36 (2.7 ± 4.2%), tend to overestimate the α‐helical content compared to experimental CD (5.3 ± 5.2%). Using the AMBER‐ff99sb‐NMR force field resulted in the greatest degree of variance (41.3 ± 12.9%). Except for the AMBER‐ff99sb‐NMR force field, the others tended to under estimate the expected amount of β‐sheet and over estimate the amount of turn/bend/random coil conformations. All force fields, with the exception AMBER‐ff99sb‐NMR, reproduce a theoretically expected β‐sheet‐turn‐β‐sheet conformational motif, however, only the CHARMM22* and CHARMM36 force fields yield results compatible with collapse of the central and C‐terminal hydrophobic cores from residues 17‐21 and 30‐36. Although analyses of essential subspace sampling showed only minor variations between force fields, secondary structures of lowest energy conformers are different.     

Tackling Force-Field Bias in Protein Folding Simulations: Folding of Villin HP35 and Pin WW Domains in Explicit Water

The ability to fold proteins on a computer has highlighted the fact that existing force fields tend to be biased toward a particular type of secondary structure. Consequently, force fields for folding simulations are often chosen according to the native structure, implying that they are not truly “transferable.” Here we show that, while the AMBER ff03 potential is known to favor helical structures, a simple correction to the backbone potential (ff03^∗) results in an unbiased energy function. We take as examples the 35-residue α-helical Villin HP35 and 37 residue β-sheet Pin WW domains, which had not previously been folded with the same force field. Starting from unfolded configurations, simulations of both proteins in Amber ff03^∗ in explicit solvent fold to within 2.0 Å RMSD of the experimental structures. This demonstrates that a simple backbone correction results in a more transferable force field, an important requirement if simulations are to be used to interpret folding mechanism.     

An Analysis of Biomolecular Force Fields for Simulations of Polyglutamine in Solution

Polyglutamine (polyQ) peptides are a useful model system for biophysical studies of protein folding and aggregation, both for their intriguing aggregation properties and their own relevance to human disease. The genetic expansion of a polyQ tract triggers the formation of amyloid aggregates associated with nine neurodegenerative diseases. Several clearly identifiable and separable factors, notably the length of the polyQ tract, influence the mechanism of aggregation, its associated kinetics, and the ensemble of structures formed. Atomistic simulations are well positioned to answer open questions regarding the thermodynamics and kinetics of polyQ folding and aggregation. The additional, explicit representation of water permits deeper investigation of the role of solvent dynamics, and it permits a direct comparison of simulation results with infrared spectroscopy experiments. The generation of meaningful simulation results hinges on satisfying two essential criteria: achieving sufficient conformational sampling to draw statistically valid conclusions, and accurately reproducing the intermolecular forces that govern system structure and dynamics. In this work, we examine the ability of 12 biomolecular force fields to reproduce the properties of a simple, 30-residue polyQ peptide (Q₃₀) in explicit water. In addition to secondary and tertiary structure, we consider generic structural properties of polymers that provide additional dimensions for analysis of the highly degenerate disordered states of the molecule. We find that the 12 force fields produce a wide range of predictions. We identify AMBER ff99SB, AMBER ff99SB^∗, and OPLS-AA/L to be most suitable for studies of polyQ folding and aggregation.     

Microsecond simulations of mdm2 and its complex with p53 yield insight into force field accuracy and conformational dynamics

The p53‐MDM2 complex is both a major target for cancer drug development and a valuable model system for computational predictions of protein‐ligand binding. To investigate the accuracy of molecular simulations of MDM2 and its complex with p53, we performed a number of long (200 ns to 1 µs) explicit‐solvent simulations using a range of force fields. We systematically compared nine popular force fields (AMBER ff03, ff12sb, ff14sb, ff99sb, ff99sb‐ildn, ff99sb‐ildn‐nmr, ff99sb‐ildn‐phi, CHARMM22*, and CHARMM36) against experimental chemical shift data, and found similarly accurate results, with microsecond simulations achieving better agreement compared to 200‐ns trajectories. Although the experimentally determined apo structure has a closed binding cleft, simulations in all force fields suggest the apo state of MDM2 is highly flexible, and able to sample holo‐like conformations, consistent with a conformational selection model. Initial structuring of the MDM2 lid region, known to competitively bind the binding cleft, is also observed in long simulations. Taken together, these results show molecular simulations can accurately sample conformations relevant for ligand binding. We expect this study to inform future computational work on folding and binding of MDM2 ligands. Proteins 2015; 83:1665–1676. © 2015 Wiley Periodicals, Inc.     

Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER

To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.     

Speed of Conformational Change: Comparing Explicit and Implicit Solvent Molecular Dynamics Simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.     

Flexibility of the Bacterial Chaperone Trigger Factor in Microsecond-Timescale Molecular Dynamics Simulations

The bacterial chaperone trigger factor (TF) is the first chaperone to be encountered by a nascent protein chain as it emerges from the ribosome exit tunnel. Experimental results suggest that TF possesses considerable conformational flexibility, and in an attempt to provide an atomic-level view of this flexibility, we have performed independent 1.5-μs molecular dynamics simulations of TF in explicit solvent using two different simulation force fields (OPLS-AA/L and AMBER ff99SB-ILDN). Both simulations indicate that TF possesses tremendous flexibility, with huge excursions from the crystallographic conformation caused by reorientations of the protein’s constituent domains; both simulations also predict the formation of extensive contacts between TF’s PPIase domain and the Arm 1 domain that is involved in nascent-chain binding. In the OPLS simulation, however, TF rapidly settles into a very compact conformation that persists for at least 1 μs, whereas in the AMBER simulation, it remains highly dynamic; additional simulations in which the two force fields were swapped suggest that these differences are at least partly attributable to sampling issues. The simulation results provide potential rationalizations of a number of experimental observations regarding TF’s conformational behavior and have implications for using simulations to model TF’s function on translating ribosomes.     

The sequence TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase displays structural ambivalence and interconverts between alpha-helical and beta-hairpin conformations mediated by collapsed conformational states.

The peptide TGAAKAVALVL from glyceraldehyde-3-phosphate dehydrogenase adopts a helical conformation in the crystal structure and is a site for two hydrated helical segments, which are thought to be helical folding intermediates. Overlapping sequences of four to five residues from the peptide, sample both helical and strand conformations in known protein structures, which are dissimilar to glyceraldehyde-3-phosphate dehydrogenase suggesting that the peptide may have a structural ambivalence. Molecular dynamics simulations of the peptide sequence performed for a total simulation time of 1.2 micros, starting from the various initial conformations using GROMOS96 force field under NVT conditions, show that the peptide samples a large number of conformational forms with transitions from alpha-helix to beta-hairpin and vice versa. The peptide, therefore, displays a structural ambivalence. The mechanism from alpha-helix to beta-hairpin transition and vice versa reveals that the compact bends and turns conformational forms mediate such conformational transitions. These compact structures including helices and hairpins have similar hydrophobic radius of gyration (Rgh) values suggesting that similar hydrophobic interactions govern these conformational forms. The distribution of conformational energies is Gaussian with helix sampling lowest energy followed by the hairpins and coil. The lowest potential energy of the full helix may enable the peptide to take up helical conformation in the crystal structure of the glyceraldehyde-3-phosphate dehydrogenase, even though the peptide has a preference for hairpin too. The relevance of folding and unfolding events observed in our simulations to hydrophobic collapse model of protein folding are discussed.     

Solvent effects on the conformational transition of a model polyalanine peptide

We have investigated the folding of polyalanine by combining discontinuous molecular dynamics simulation with our newly developed off-lattice intermediate-resolution protein model. The thermodynamics of a system containing a single Ac-KA(14)K-NH(2) molecule has been explored by using the replica exchange simulation method to map out the conformational transitions as a function of temperature. We have also explored the influence of solvent type on the folding process by varying the relative strength of the side-chain's hydrophobic interactions and backbone hydrogen bonding interactions. The peptide in our simulations tends to mimic real polyalanine in that it can exist in three distinct structural states: alpha-helix, beta-structures (including beta-hairpin and beta-sheet-like structures), and random coil, depending upon the solvent conditions. At low values of the hydrophobic interaction strength between nonpolar side-chains, the polyalanine peptide undergoes a relatively sharp transition between an alpha-helical conformation at low temperatures and a random-coil conformation at high temperatures. As the hydrophobic interaction strength increases, this transition shifts to higher temperatures. Increasing the hydrophobic interaction strength even further induces a second transition to a beta-hairpin, resulting in an alpha-helical conformation at low temperatures, a beta-hairpin at intermediate temperatures, and a random coil at high temperatures. At very high values of the hydrophobic interaction strength, polyalanines become beta-hairpins and beta-sheet-like structures at low temperatures and random coils at high temperatures. This study of the folding of a single polyalanine-based peptide sets the stage for a study of polyalanine aggregation in a forthcoming paper.     

Flexibility of the Bacterial Chaperone Trigger Factor in Microsecond-Timescale Molecular Dynamics Simulations

The bacterial chaperone trigger factor (TF) is the first chaperone to be encountered by a nascent protein chain as it emerges from the ribosome exit tunnel. Experimental results suggest that TF possesses considerable conformational flexibility, and in an attempt to provide an atomic-level view of this flexibility, we have performed independent 1.5-μs molecular dynamics simulations of TF in explicit solvent using two different simulation force fields (OPLS-AA/L and AMBER ff99SB-ILDN). Both simulations indicate that TF possesses tremendous flexibility, with huge excursions from the crystallographic conformation caused by reorientations of the protein’s constituent domains; both simulations also predict the formation of extensive contacts between TF’s PPIase domain and the Arm 1 domain that is involved in nascent-chain binding. In the OPLS simulation, however, TF rapidly settles into a very compact conformation that persists for at least 1 μs, whereas in the AMBER simulation, it remains highly dynamic; additional simulations in which the two force fields were swapped suggest that these differences are at least partly attributable to sampling issues. The simulation results provide potential rationalizations of a number of experimental observations regarding TF’s conformational behavior and have implications for using simulations to model TF’s function on translating ribosomes.     

DNA polymorphism: a comparison of force fields for nucleic acids

The improvements of the force fields and the more accurate treatment of long-range interactions are providing more reliable molecular dynamics simulations of nucleic acids. The abilities of certain nucleic acid force fields to represent the structural and conformational properties of nucleic acids in solution are compared. The force fields are AMBER 4.1, BMS, CHARMM22, and CHARMM27; the comparison of the latter two is the primary focus of this paper. The performance of each force field is evaluated first on its ability to reproduce the B-DNA decamer d(CGATTAATCG)(2) in solution with simulations in which the long-range electrostatics were treated by the particle mesh Ewald method; the crystal structure determined by Quintana et al. (1992) is used as the starting point for all simulations. A detailed analysis of the structural and solvation properties shows how well the different force fields can reproduce sequence-specific features. The results are compared with data from experimental and previous theoretical studies.     

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.     

Molecular dynamics guided study of salt bridge length dependence in both fluorinated and non-fluorinated parallel dimeric coiled-coils

The alpha-helical coiled-coil is one of the most common oligomerization motifs found in both native and engineered proteins. To better understand the stability and dynamics of the coiled-coil motifs, including those modified by fluorination, several fluorinated and nonfluorinated parallel dimeric coiled-coil protein structures were designed and modeled. We also attempt to investigate how changing the length and geometry of the important stabilizing salt bridges influences the coiled-coil protein structure. Molecular dynamics (MD) and free energy simulations with AMBER used a particle mesh Ewald treatment of the electrostatics in explicit TIP3P solvent with balanced force field treatments. Preliminary studies with legacy force fields (ff94, ff96, and ff99) show a profound instability of the coiled-coil structures in short MD simulation. Significantly, better behavior is evident with the more balanced ff99SB and ff03 protein force fields. Overall, the results suggest that the coiled-coil structures can readily accommodate the larger acidic arginine or S-2,7-diaminoheptanedoic acid mutants in the salt bridge, whereas substitution of the smaller L-ornithine residue leads to rapid disruption of the coiled-coil structure on the MD simulation time scale. This structural distortion of the secondary structure allows both the formation of large hydration pockets proximal to the charged groups and within the hydrophobic core. Moreover, the increased structural fluctuations and movement lead to a decrease in the water occupancy lifetimes in the hydration pockets. In contrast, analysis of the hydration in the stable dimeric coiled-coils shows high occupancy water sites along the backbone residues with no water occupancy in the hydrophobic core, although transitory water interactions with the salt bridge residues are evident. The simulations of the fluorinated coiled-coils suggest that in some cases fluorination electrostatically stabilizes the intermolecular coiled-coil salt bridges. Structural analyses also reveal different side chain rotamer preferences for leucine when compared with 5,5,5,5',5',5'-hexafluoroleucine mutants. These observed differences in the side chain rotamer populations suggest differential changes in the side chain conformational entropy upon coiled-coil formation when the protein is fluorinated. The free energy of hydration of the isolated 5,5,5,5',5',5'-hexafluoroleucine amino acid is calculated to be 1.1 kcal/mol less stable than leucine; this hydrophobic penalty in the monomer may provide a driving force for coiled-coil dimer formation. Estimation of the ellipticity at 222 nm from a series of snapshots from the MD simulations with DicroCalc shows distinct increases in the ellipticity when the coiled-coil is fluorinated, which suggests that the helicity in the folded coiled-coils is greater when fluorinated.     

Structural equilibrium of DNA represented with different force fields.

We have recently indicated preliminary evidence of different equilibrium average structures with the CHARMM and AMBER force fields in explicit solvent molecular dynamics simulations on the DNA duplex d(C5T5) . d(A5G5) (Feig, M. and B.M. Pettitt, 1997, Experiment vs. Force Fields: DNA conformation from molecular dynamics simulations. J. Phys. Chem. B. (101:7361-7363). This paper presents a detailed comparison of DNA structure and dynamics for both force fields from extended simulation times of 10 ns each. Average structures display an A-DNA base geometry with the CHARMM force field and a base geometry that is intermediate between A- and B-DNA with the AMBER force field. The backbone assumes B form on both strands with the AMBER force field, while the CHARMM force field produces heterogeneous structures with the purine strand in A form and the pyrimidine strand in dynamical equilibrium between A and B conformations. The results compare well with experimental data for the cytosine/guanine part but fail to fully reproduce an overall B conformation in the thymine/adenine tract expected from crystallographic data, particularly with the CHARMM force field. Fluctuations between A and B conformations are observed on the nanosecond time scale in both simulations, particularly with the AMBER force field. Different dynamical behavior during the first 4 ns indicates that convergence times of several nanoseconds are necessary to fully establish a dynamical equilibrium in all structural quantities on the time scale of the simulations presented here.     

Determination method of the balance of the secondary-structure-forming tendencies of force fields

We propose a new method of optimisation of backbone torsion-energy parameters in the force field for molecular simulations of protein systems. This method is based on the idea of balancing the secondary-structure-forming tendencies, namely, those of α-helix and β-sheet structures. We perform a minimisation of the backbone dihedral angle-based root-mean-square deviation of the helix and β structure regions in many protein structures. As an example, we optimised the backbone torsion-energy parameters of AMBER parm96 force field using 100 protein molecules from the Protein Data Bank. We then performed folding simulations of α-helical and β-hairpin peptides, using the optimised force field. The results imply that the new force-field parameters give structures more consistent with the experimental implications than the original AMBER parm96 force field.