Force field bias in protein folding simulations

GFP's mechanical intermediate states

Green fluorescent protein (GFP) mutants have become the most widely used fluorescence markers in the life sciences, and although they are becoming increasingly popular as mechanical force or strain probes, there is little direct information on how their fluorescence changes when mechanically stretched. Here we derive high-resolution structural models of the mechanical intermediate states of stretched GFP using steered molecular dynamics (SMD) simulations. These structures were used to produce mutants of EGFP and EYFP that mimic GFP's different mechanical intermediates. A spectroscopic analysis revealed that a population of EGFP molecules with a missing N-terminal α-helix was significantly dimmed, while the fluorescence lifetime characteristic of the anionic chromophore state remained unaffected. This suggests a mechanism how N-terminal deletions can switch the protonation state of the chromophore, and how the fluorescence of GFP molecules in response to mechanical disturbance might be turned off.

Context and force field dependence of the loss of protein backbone entropy upon folding using realistic denatured and native state ensembles

The loss of conformational entropy is the largest unfavorable quantity affecting a protein's stability. We calculate the reduction in the number of backbone conformations upon folding using the distribution of backbone dihedral angles (ϕ,ψ) obtained from an experimentally validated denatured state model, along with all-atom simulations for both the denatured and native states. The average loss of entropy per residue is TΔS(BB)(U-N) = 0.7, 0.9, or 1.1 kcal·mol(-1) at T = 298 K, depending on the force field used, with a 0.6 kcal·mol(-1) dispersion across the sequence. The average equates to a decrease of a factor of 3-7 in the number of conformations available per residue (f = Ω(Denatured)/Ω(Native)) or to a total of f(tot) = 3(n)-7(n) for an n residue protein. Our value is smaller than most previous estimates where f = 7-20, that is, our computed TΔS(BB)(U-N) is smaller by 10-100 kcal mol(-1) for n = 100. The differences emerge from our use of realistic native and denatured state ensembles as well as from the inclusion of accurate local sequence preferences, neighbor effects, and correlated motions (vibrations), in contrast to some previous studies that invoke gross assumptions about the entropy in either or both states. We find that the loss of entropy primarily depends on the local environment and less on properties of the native state, with the exception of α-helical residues in some force fields.

Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles

While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large number of applications, limitations in the model with respect to the equilibrium between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non Gly, Pro) backbone CMAP potential has been refined against experimental solution NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mechanical energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mechanical energy surfaces, followed by additional empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against data not used to guide parametrization: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equilibrium folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for the modeling and simulation studies of proteins, including studies of protein folding, assembly and functionally relevant conformational changes.

Comparison of Secondary Structure Formation Using 10 Different Force Fields in Microsecond Molecular Dynamics Simulations

We have compared molecular dynamics (MD) simulations of a β-hairpin forming peptide derived from the protein Nrf2 with 10 biomolecular force fields using trajectories of at least 1 μs. The total simulation time was 37.2 μs. Previous studies have shown that different force fields, water models, simulation methods, and parameters can affect simulation outcomes. The MD simulations were done in explicit solvent with a 16-mer Nrf2 β-hairpin forming peptide using Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, GROMOS96 53a6, CHARMM27, and OPLS-AA/L force fields. The effects of charge-groups, terminal capping, and phosphorylation on the peptide folding were also examined. Despite using identical starting structures and simulation parameters, we observed clear differences among the various force fields and even between replicates using the same force field. Our simulations show that the uncapped peptide folds into a native-like β-hairpin structure at 310 K when Amber ff99SB-ILDN, Amber ff99SB*-ILDN, Amber ff99SB, Amber ff99SB*, Amber ff03, Amber ff03*, GROMOS96 43a1p, or GROMOS96 53a6 were used. The CHARMM27 simulations were able to form native hairpins in some of the elevated temperature simulations, while the OPLS-AA/L simulations did not yield native hairpin structures at any temperatures tested. Simulations that used charge-groups or peptide capping groups were not largely different from their uncapped counterparts with single atom charge-groups. On the other hand, phosphorylation of the threonine residue located at the β-turn significantly affected the hairpin formation. To our knowledge, this is the first study comparing such a large set of force fields with respect to β-hairpin folding. Such a comprehensive comparison will offer useful guidance to others conducting similar types of simulations.

Structural Characterization of λ-Repressor Folding from All-Atom Molecular Dynamics Simulations

The five-helix bundle λ-repressor fragment is a fast-folding protein. A length of 80 amino acid residues puts it on the large end among all known microsecond folders and its size poses a computational challenge for molecular dynamics (MD) studies. We simulated the folding of a novel λ-repressor fast-folding mutant (λ-HG) in explicit solvent using an all-atom description. By means of a recently developed tempering method, we observed reversible folding and unfolding of λ-repressor in a 10-microsecond trajectory. The folding kinetics was also investigated through a set of MD simulations run at different temperatures that together covered more than 125 microseconds. The protein was seen to fold into a native-like topology at intermediate temperature and a slow-folding pathway was identified. The simulations suggest new experimental observables for better monitoring the folding process, and a novel mutation expected to accelerate λ-repressor folding.

Bioinformatics and variability in drug response: a protein structural perspective

Marketed drugs frequently perform worse in clinical practice than in the clinical trials on which their approval is based. Many therapeutic compounds are ineffective for a large subpopulation of patients to whom they are prescribed; worse, a significant fraction of patients experience adverse effects more severe than anticipated. The unacceptable risk-benefit profile for many drugs mandates a paradigm shift towards personalized medicine. However, prior to adoption of patient-specific approaches, it is useful to understand the molecular details underlying variable drug response among diverse patient populations. Over the past decade, progress in structural genomics led to an explosion of available three-dimensional structures of drug target proteins while efforts in pharmacogenetics offered insights into polymorphisms correlated with differential therapeutic outcomes. Together these advances provide the opportunity to examine how altered protein structures arising from genetic differences affect protein-drug interactions and, ultimately, drug response. In this review, we first summarize structural characteristics of protein targets and common mechanisms of drug interactions. Next, we describe the impact of coding mutations on protein structures and drug response. Finally, we highlight tools for analysing protein structures and protein-drug interactions and discuss their application for understanding altered drug responses associated with protein structural variants.

Folding of a helix is critically stabilized by polarization of backbone hydrogen bonds: study in explicit water

Multiple single-trajectory molecular dynamics (MD) simulation at room temperature (300 K) in explicit water was carried out to study the folding dynamics of an α-helix (PDB 2I9M ) using a polarized charge scheme that includes electronic polarization of backbone hydrogen bonds. Starting from an extended conformation, the 17-residue peptide was successfully folded into the native structure (α-helix) between 80 and 130 ns with a root-mean-square deviation of ~1.0 Å. Analysis of the time-dependent trajectories revealed that helix formation of the peptide started at the terminals and progressed toward the center of the peptide. For comparison, MD trajectories generated under various versions of standard AMBER force fields failed to show any significant or stable helix formation in our simulation. Our result shows clear evidence that the electronic polarization of backbone hydrogen bonds energetically stabilizes the helix formation and is critical to the stable folding of the short helix structure.

Systematic validation of protein force fields against experimental data

Molecular dynamics simulations provide a vehicle for capturing the structures, motions, and interactions of biological macromolecules in full atomic detail. The accuracy of such simulations, however, is critically dependent on the force field—the mathematical model used to approximate the atomic-level forces acting on the simulated molecular system. Here we present a systematic and extensive evaluation of eight different protein force fields based on comparisons of experimental data with molecular dynamics simulations that reach a previously inaccessible timescale. First, through extensive comparisons with experimental NMR data, we examined the force fields' abilities to describe the structure and fluctuations of folded proteins. Second, we quantified potential biases towards different secondary structure types by comparing experimental and simulation data for small peptides that preferentially populate either helical or sheet-like structures. Third, we tested the force fields' abilities to fold two small proteins—one α-helical, the other with β-sheet structure. The results suggest that force fields have improved over time, and that the most recent versions, while not perfect, provide an accurate description of many structural and dynamical properties of proteins.

Determination of membrane-insertion free energies by molecular dynamics simulations

The accurate prediction of membrane-insertion probability for arbitrary protein sequences is a critical challenge to identifying membrane proteins and determining their folded structures. Although algorithms based on sequence statistics have had moderate success, a complete understanding of the energetic factors that drive the insertion of membrane proteins is essential to thoroughly meeting this challenge. In the last few years, numerous attempts to define a free-energy scale for amino-acid insertion have been made, yet disagreement between most experimental and theoretical scales persists. However, for a recently resolved water-to-bilayer scale, it is found that molecular dynamics simulations that carefully mimic the conditions of the experiment can reproduce experimental free energies, even when using the same force field as previous computational studies that were cited as evidence of this disagreement. Therefore, it is suggested that experimental and simulation-based scales can both be accurate and that discrepancies stem from disparities in the microscopic processes being considered rather than methodological errors. Furthermore, these disparities make the development of a single universally applicable membrane-insertion free energy scale difficult.

Dominant folding pathways of a WW domain

We investigate the folding mechanism of the WW domain Fip35 using a realistic atomistic force field by applying the Dominant Reaction Pathways approach. We find evidence for the existence of two folding pathways, which differ by the order of formation of the two hairpins. This result is consistent with the analysis of the experimental data on the folding kinetics of WW domains and with the results obtained from large-scale molecular dynamics simulations of this system. Free-energy calculations performed in two coarse-grained models support the robustness of our results and suggest that the qualitative structure of the dominant paths are mostly shaped by the native interactions. Computing a folding trajectory in atomistic detail only required about one hour on 48 Central Processing Units. The gain in computational efficiency opens the door to a systematic investigation of the folding pathways of a large number of globular proteins.

Three force fields' views of the 3(10) helix

Slowly but steadily bibliographic evidence is accumulating that the apparent convergence of the various biomolecular force fields as evidenced from simulations of proteins in the folded state does not hold true for folding simulations. Here we add one more example to the growing list of peptides and proteins for which different force fields show irreconcilable differences in their folding predictions, even at such a fundamental level as that of a peptide's secondary structure. We show that for an undecamer peptide that is known from two independent NMR structure determinations to have a mainly 3(10)-helical structure in solution, three mainstream biomolecular force fields give completely disparate predictions: The CHARMM force field (with the CMAP correction) predicts an outstandingly stable α-helical structure, in disagreement not only with the experimental structures, but also with experimental evidence obtained from circular dichroism. OPLS-AA shows an almost totally disordered peptide with the most frequently observed folded conformation corresponding to a β-hairpin-like structure, again in disagreement with all available experimental evidence. Only the AMBER99SB force field appears to qualitatively agree with not only the general structural characteristics of the peptide (on the account of both NMR- and CD-based experiments), but to also correctly predict some of the experimentally observed interactions at the level of side chains. Possible interpretations of these findings are discussed.

Atomistic molecular simulations of protein folding

Theory and experiment have provided answers to many of the fundamental questions of protein folding; a remaining challenge is an accurate, high-resolution picture of folding mechanism. Atomistic molecular simulations with explicit solvent are the most promising method for providing this information, by accounting more directly for the physical interactions that stabilize proteins. Although simulations of folding with such force fields are extremely challenging, they have become feasible as a result of recent advances in computational power, accuracy of the energy functions or 'force fields', and methods for improving sampling of folding events. I review the recent progress in these areas, and highlight future challenges and questions that we may hope to address with these methods. I also attempt to place atomistic models into the context of the energy landscape view of protein folding, and coarse-grained simulations.

Residual structures, conformational fluctuations, and electrostatic interactions in the synergistic folding of two intrinsically disordered proteins

To understand the interplay of residual structures and conformational fluctuations in the interaction of intrinsically disordered proteins (IDPs), we first combined implicit solvent and replica exchange sampling to calculate atomistic disordered ensembles of the nuclear co-activator binding domain (NCBD) of transcription coactivator CBP and the activation domain of the p160 steroid receptor coactivator ACTR. The calculated ensembles are in quantitative agreement with NMR-derived residue helicity and recapitulate the experimental observation that, while free ACTR largely lacks residual secondary structures, free NCBD is a molten globule with a helical content similar to that in the folded complex. Detailed conformational analysis reveals that free NCBD has an inherent ability to substantially sample all the helix configurations that have been previously observed either unbound or in complexes. Intriguingly, further high-temperature unbinding and unfolding simulations in implicit and explicit solvents emphasize the importance of conformational fluctuations in synergistic folding of NCBD with ACTR. A balance between preformed elements and conformational fluctuations appears necessary to allow NCBD to interact with different targets and fold into alternative conformations. Together with previous topology-based modeling and existing experimental data, the current simulations strongly support an “extended conformational selection” synergistic folding mechanism that involves a key intermediate state stabilized by interaction between the C-terminal helices of NCBD and ACTR. In addition, the atomistic simulations reveal the role of long-range as well as short-range electrostatic interactions in cooperating with readily fluctuating residual structures, which might enhance the encounter rate and promote efficient folding upon encounter for facile binding and folding interactions of IDPs. Thus, the current study not only provides a consistent mechanistic understanding of the NCBD/ACTR interaction, but also helps establish a multi-scale molecular modeling framework for understanding the structure, interaction, and regulation of IDPs in general.

Intrinsically disordered proteins (IDPs) are now widely recognized to play fundamental roles in biology and to be frequently associated with human diseases. Although the potential advantages of intrinsic disorder in cellular signaling and regulation have been widely discussed, the physical basis for these proposed phenomena remains sketchy at best. An integration of multi-scale molecular modeling and experimental characterization is necessary to uncover the molecular principles that govern the structure, interaction, and regulation of IDPs. In this work, we characterize the conformational properties of two IDPs involved in transcription regulation at the atomistic level and further examine the roles of these properties in their coupled binding and folding interactions. Our simulations suggest interplay among residual structures, conformational fluctuations, and electrostatic interactions that allows efficient synergistic folding of these two IDPs. In particular, we propose that electrostatic interactions might play an important role in facilitating rapid folding and binding recognition of IDPs, by enhancing the encounter rate and promoting efficient folding upon encounter.

Directional Dependence of Hydrogen Bonds: a Density-based Energy Decomposition Analysis and Its Implications on Force Field Development

One well-known shortcoming of widely-used biomolecular force fields is the description of the directional dependence of hydrogen bonding (HB). Here we aim to better understand the origin of this difficulty and thus provide some guidance for further force field development. Our theoretical approaches center on a novel density-based energy decomposition analysis (DEDA) method [J. Chem. Phys., 131, 164112 (2009)], in which the frozen density energy is variationally determined through constrained search. This unique and most significant feature of DEDA enables us to find that the frozen density interaction term is the key factor in determining the HB orientation, while the sum of polarization and charge-transfer components shows very little HB directional dependence. This new insight suggests that the difficulty for current non-polarizable force fields to describe the HB directional dependence is not due to the lack of explicit polarization or charge-transfer terms. Using the DEDA results as reference, we further demonstrate that the main failure coming from the atomic point charge model can be overcome largely by introducing extra charge sites or higher order multipole moments. Among all the electrostatic models explored, the smeared charge distributed multipole model (up to quadrupole), which also takes account of charge penetration effects, gives the best agreement with the corresponding DEDA results. Meanwhile, our results indicate that the van der Waals interaction term needs to be further improved to better model directional hydrogen bonding.

Polarization of intraprotein hydrogen bond is critical to thermal stability of short helix

Simulation result for protein folding/unfolding is highly dependent on the accuracy of the force field employed. Even for the simplest structure of protein such as a short helix, simulations using the existing force fields often fail to produce the correct structural/thermodynamic properties of the protein. Recent research indicated that lack of polarization is at least partially responsible for the failure to successfully fold a short helix. In this work, we develop a simple formula-based atomic charge polarization model for intraprotein (backbone) hydrogen bonding based on the existing AMBER force field to study the thermal stability of a short helix (2I9M) by replica exchange molecular dynamics simulation. By comparison of the simulation results with those obtained by employing the standard AMBER03 force field, the formula-based atomic charge polarization model gave the helix melting curve in close agreement with the NMR experiment. However, in simulations using the standard AMBER force field, the helix was thermally unstable at the temperature of the NMR experiment, with a melting temperature almost below the freezing point. The difference in observed thermal stability from these two simulations is the effect of backbone intraprotein polarization, which was included in the formula-based atomic charge polarization model. The polarization of backbone hydrogen bonding thus plays a critical role in the thermal stability of helix or more general protein structures.

A direct coupling between global and internal motions in a single domain protein? MD investigation of extreme scenarios

Proteins are not rigid molecules, but exhibit internal motions on timescales ranging from femto- to milliseconds and beyond. In solution, proteins also experience global translational and rotational motions, sometimes on timescales comparable to those of the internal fluctuations. The possibility that internal and global motions may be directly coupled has intriguing implications, given that enzymes and cell signaling proteins typically associate with binding partners and cellular scaffolds. Such processes alter their global motion and may affect protein function. Here, we present molecular dynamics simulations of extreme case scenarios to examine whether a possible relationship exists. In our model protein, a ubiquitin-like RhoGTPase binding domain of plexin-B1, we removed either internal or global motions. Comparisons with unrestrained simulations show that internal and global motions are not appreciably coupled in this single-domain protein. This lack of coupling is consistent with the observation that the dynamics of water around the protein, which is thought to permit, if not stimulate, internal dynamics, is also largely independent of global motion. We discuss implications of these results for the structure and function of proteins.

Substrate binding process and mechanistic functioning of type 1 11β-hydroxysteroid dehydrogenase from enhanced sampling methods

In humans, type 1 11β-hydroxysteroid dehydrogenase (11β-HSD-1) plays a key role in the regulation of the glucocorticoids balance by converting the inactive hormone cortisone into cortisol. Numerous functional aspects of 11β-HSD-1 have been understood thanks to the availability at the Worldwide Protein Data Bank of a number of X-ray structures of the enzyme either alone or in complex with inhibitors, and to several experimental data. However at present, a complete description of the dynamic behaviour of 11β-HSD-1 upon substrate binding is missing. To this aim we firstly docked cortisone into the catalytic site of 11β-HSD-1 (both wild type and Y177A mutant), and then we used steered molecular dynamics and metadynamics to simulate its undocking. This methodology helped shedding light at molecular level on the complex relationship between the enzyme and its natural substrate. In particular, the work highlights a) the reason behind the functional dimerisation of 11β-HSD-1, b) the key role of Y177 in the cortisone binding event, c) the fine tuning of the active site degree of solvation, and d) the role of the S228-P237 loop in ligand recognition.

Iterative Optimization of Molecular Mechanics Force Fields from NMR Data of Full-Length Proteins

High quality molecular mechanics force fields of proteins are key for the quantitative interpretation of experimental data and the predictive understanding of protein function based on computer simulations. A strategy is presented for the optimization of protein force fields based on full-length proteins in their native environment that is guided by experimental NMR chemical shifts and residual dipolar couplings (RDCs). An energy-based reweighting approach is applied to a long molecular dynamics trajectory, performed with a parent force field, to efficiently screen a large number of trial force fields. The force field that yields the best agreement with the experimental data is then used as the new parent force field, and the procedure is repeated until no further improvement is obtained. This method is demonstrated for the optimization of the backbone φ,ψ dihedral angle potential of the Amber ff99SB force field using six trial proteins and another 17 proteins for cross-validation using (13)C chemical shifts with and without backbone RDCs. The φ,ψ dihedral angle potential is systematically improved by the inclusion of correlation effects through the addition of up to 24 bivariate Gaussian functions of variable height, width, and tilt angle. The resulting force fields, termed ff99SB_φψ(g24;CS) and ff99SB_φψ(g8;CS,RDC), perform significantly better than their parent force field in terms of both NMR data reproduction and Cartesian coordinate root-mean-square deviations between the MD trajectories and the X-ray crystal structures. The strategy introduced here represents a powerful addition to force field optimization approaches by overcoming shortcomings of methods that are solely based on quantum-chemical calculations of small molecules and protein fragments in the gas phase.

Biomolecularmodeling and simulation: a field coming of age

We assess the progress in biomolecular modeling and simulation, focusing on structure prediction and dynamics, by presenting the field’s history, metrics for its rise in popularity, early expressed expectations, and current significant applications. The increases in computational power combined with improvements in algorithms and force fields have led to considerable success, especially in protein folding, specificity of ligand/biomolecule interactions, and interpretation of complex experimental phenomena (e.g. NMR relaxation, protein-folding kinetics and multiple conformational states) through the generation of structural hypotheses and pathway mechanisms. Although far from a general automated tool, structure prediction is notable for proteins and RNA that preceded the experiment, especially by knowledge-based approaches. Thus, despite early unrealistic expectations and the realization that computer technology alone will not quickly bridge the gap between experimental and theoretical time frames, ongoing improvements to enhance the accuracy and scope of modeling and simulation are propelling the field onto a productive trajectory to become full partner with experiment and a field on its own right.

The energy computation paradox and ab initio protein folding

The routine prediction of three-dimensional protein structure from sequence remains a challenge in computational biochemistry. It has been intuited that calculated energies from physics-based scoring functions are able to distinguish native from nonnative folds based on previous performance with small proteins and that conformational sampling is the fundamental bottleneck to successful folding. We demonstrate that as protein size increases, errors in the computed energies become a significant problem. We show, by using error probability density functions, that physics-based scores contain significant systematic and random errors relative to accurate reference energies. These errors propagate throughout an entire protein and distort its energy landscape to such an extent that modern scoring functions should have little chance of success in finding the free energy minima of large proteins. Nonetheless, by understanding errors in physics-based score functions, they can be reduced in a post-hoc manner, improving accuracy in energy computation and fold discrimination.

Structural dynamics of neuropeptide hPYY

We have employed a combination of experiment and simulation to characterize the ensemble of structures sampled by human Peptide YY (hPYY), an important member of the neuropeptide Y family. Experimental structural characterization carried out with far UV circular dichroism spectroscopy and Fourier Transform-Infrared measurements confirmed that the major feature of the secondary structure of hPYY is the α-helix, encompassing about half the peptide residues, with smaller contributions from turn and β-sheet like structures. The peptide undergoes thermal denaturation characterized by a melting temperature of 48°C with an enthalpy change of -24.5 kcal/mol and entropy change of -76.2 cal/(mol K). In our computational studies, based on a 4-μsec MD trajectory generated with the AMBER03 potential, we found excellent agreement of the predicted features with experimental data, including a stable C-terminal helix, a central turn and conservation of about 80% of measured long-range NOE contacts. The main structural fluctuations involved partial helix unwinding and large-scale motions of the N-terminal. Our joint experimental/computational approach leads to several insights into the biological function of PYY. We conclude that the C-terminal helix is crucial for the structural integrity of PYY. The structures and motions found in the simulations suggest microscopic explanations for observed changes in biological activity of the peptide upon mutation and truncation. We also performed microsecond-length MD and replica-exchange simulations of hPYY with the OPLS-AA force field, for which computed structures did not agree well with experimental data, predicting significant loss of helicity and NOE contacts.

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.

Simulations of a protein crystal with a high resolution X-ray structure: evaluation of force fields and water models

We use classical molecular dynamics and 16 combinations of force fields and water models to simulate a protein crystal observed by room-temperature X-ray diffraction. The high resolution of the diffraction data (0.96 Å) and the simplicity of the crystallization solution (nearly pure water) make it possible to attribute any inconsistencies between the crystal structure and our simulations to artifacts of the models rather than inadequate representation of the crystal environment or uncertainty in the experiment. All simulations were extended for 100 ns of production dynamics, permitting some long-time scale artifacts of each model to emerge. The most noticeable effect of these artifacts is a model-dependent drift in the unit cell dimensions, which can become as large as 5% in certain force fields; the underlying cause is the replacement of native crystallographic contacts with non-native ones, which can occur with heterogeneity (loss of crystallographic symmetry) in simulations with some force fields. We find that the AMBER FF99SB force field maintains a lattice structure nearest that seen in the X-ray data, and produces the most realistic atomic fluctuations (by comparison to crystallographic B-factors) of all the models tested. We find that the choice of water model has a minor effect in comparison to the choice of protein model. We also identify a number of artifacts that occur throughout all of the simulations: excessive formation of hydrogen bonds or salt bridges between polar groups and loss of hydrophobic interactions. This study is intended as a foundation for future work that will identify individual parameters in each molecular model that can be modified to improve their representations of protein structure and thermodynamics.

Equilibrium sampling in biomolecular simulations

Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to parallelization to novel uses of hardware. Special focus is placed on classifying algorithms--most of which are underpinned by a few key ideas--in order to understand their fundamental strengths and limitations. Although algorithms have proliferated, progress resulting from novel hardware use appears to be more clear-cut than from algorithms alone, due partly to the lack of widely used sampling measures.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

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 alpha-helical Villin HP35 and 37 residue beta-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 A 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.

Challenges in protein folding simulations: Timescale, representation, and analysis

Experimental studies of protein folding processes are frequently hampered by the fact that only low resolution structural data can be obtained with sufficient temporal resolution. Molecular dynamics simulations offer a complementary approach, providing extremely high resolution spatial and temporal data on folding processes. The effectiveness of such simulations is currently hampered by continuing questions regarding the ability of molecular dynamics force fields to reproduce the true potential energy surfaces of proteins, and ongoing difficulties with obtaining sufficient sampling to meaningfully comment on folding mechanisms. We review recent progress in the simulation of three common model systems for protein folding, and discuss how recent advances in technology and theory are allowing protein folding simulations to address their current shortcomings.

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.

The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe

The four-helix bundle protein Rd-apocyt b(562), a redesigned stable variant of apocytochrome b(562), exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Phi-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Phi-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Phi-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.

Force field-dependent structural divergence revealed during long time simulations of Calbindin d9k

The structural and the dynamic features of the Calbindin (CaB) protein in its holo and apo states are compared using molecular dynamics simulations under nine different force fields (FFs) (G43a1, G53a6, Opls-AA, Amber94, Amber99, Amber99p, AmberGS, AmberGSs, and Amber99sb). The results show that most FFs reproduce reasonably well the majority of the experimentally derived features of the CaB protein. However, in several cases, there are significant differences in secondary structure properties, root mean square deviations (RMSDs), root mean square fluctuations (RMSFs), and S(2) order parameters among the various FFs. What is more, in certain cases, these parameters differed from the experimentally derived values. Some of these deviations became noticeable only after 50 ns. A comparison with experimental data indicates that, for CaB, the Amber94 shows overall best agreement with the measured values, whereas several others seem to deviate from both crystal and nuclear magnetic resonance data.

Multiscale coarse-graining of the protein energy landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.

Conformational preferences of a 14-residue fibrillogenic peptide from acetylcholinesterase

A 14-residue fragment from near the C-terminus of the enzyme acetylcholinesterase (AChE) is believed to have a neurotoxic/neurotrophic effect acting via an unknown pathway. While the peptide is α-helical in the full-length enzyme, the structure and association mechanism of the fragment are unknown. Using multiple molecular dynamics simulations, starting from a tetrameric complex of the association domain of AChE and systematically disassembled subsets that include the peptide fragment, we show that the fragment is incapable of retaining its helicity in solution. Extensive replica exchange Monte Carlo folding and unfolding simulations in implicit solvent with capped and uncapped termini failed to converge to any consistent cluster of structures, suggesting that the fragment remains largely unstructured in solution under the conditions considered. Furthermore, extended molecular dynamics simulations of two steric zipper models show that the peptide is likely to form a zipper with antiparallel sheets and that peptides with mutations known to prevent fibril formation likely do so by interfering with this packing. The results demonstrate how the local environment of a peptide can stabilize a particular conformation.

Computing free energies of protein conformations from explicit solvent simulations

We report a fully general technique addressing a long standing challenge of calculating conformational free energy differences between various states of a polymer chain from simulations using explicit solvent force fields. The main feature of our method is a special mapping variable, a path coordinate, which continuously connects two conformations. The path variable has been designed to preserve locality in the phase space near the path endpoints. We avoid the problem of sampling the unfolded states by creating an artificial confinement "tube" in the phase space that prevents the molecule from unfolding without affecting the calculation of the desired free energy difference. We applied our technique to compute the free energy difference between two native-like conformations of the small protein Trp-cage using the CHARMM force field with explicit solvent. We verified this result by comparing it with an independent, significantly more expensive calculation. Overall, the present study suggests that the new method of computing free energy differences between polymer chain conformations is accurate and highly computationally efficient.

(Un)Folding mechanisms of the FBP28 WW domain in explicit solvent revealed by multiple rare event simulation methods

We report a numerical study of the (un)folding routes of the truncated FBP28 WW domain at ambient conditions using a combination of four advanced rare event molecular simulation techniques. We explore the free energy landscape of the native state, the unfolded state, and possible intermediates, with replica exchange molecular dynamics. Subsequent application of bias-exchange metadynamics yields three tentative unfolding pathways at room temperature. Using these paths to initiate a transition path sampling simulation reveals the existence of two major folding routes, differing in the formation order of the two main hairpins, and in hydrophobic side-chain interactions. Having established that the hairpin strand separation distances can act as reasonable reaction coordinates, we employ metadynamics to compute the unfolding barriers and find that the barrier with the lowest free energy corresponds with the most likely pathway found by transition path sampling. The unfolding barrier at 300 K is approximately 17 k(B)T approximately 42 kJ/mol, in agreement with the experimental unfolding rate constant. This work shows that combining several powerful simulation techniques provides a more complete understanding of the kinetic mechanism of protein folding.

Common structural transitions in explicit-solvent simulations of villin headpiece folding

Molecular dynamics simulations of protein folding can provide very high-resolution data on the folding process; however, due to computational challenges most studies of protein folding have been limited to small peptides, or made use of approximations such as Gō potentials or implicit solvent models. We have performed a set of molecular dynamics simulations totaling >50 micros on the villin headpiece subdomain, one of the most stable and fastest-folding naturally occurring proteins, in explicit solvent. We find that the wild-type villin headpiece reliably folds to a native conformation on timescales similar to experimentally observed folding, but that a fast folding double-norleucine mutant shows significantly more heterogeneous behavior. Along with other recent simulation studies, we note the occurrence of nonnative structures intermediates, which may yield a nativelike signal in the fluorescence measurements typically used to study villin folding. Based on the wild-type simulations, we propose alternative approaches to measure the formation of the native state.

Discovery through the computational microscope

All-atom molecular dynamics simulations have become increasingly popular as a tool to investigate protein function and dynamics. However, researchers are concerned about the short time scales covered by simulations, the apparent impossibility to model large and integral biomolecular systems, and the actual predictive power of the molecular dynamics methodology. Here we review simulations that were in the past both hotly disputed and considered key successes, namely of proteins with mainly mechanical functions (titin, fibrinogen, ankyrin, and cadherin). The simulation work covered shows how state-of-the-art modeling alleviates some of the prior concerns and how unrefuted discoveries are made through the "computational microscope."

Biomolecular Structure and Modeling: Historical Perspective

physics, chemistry, and biology have been connected by a web of causal explanation organized by induction-based theories that telescope into one another. … Thus, quantum theory underlies atomic physics, which is the foundation of reagent chemistry and its specialized offshoot biochemistry, which interlock with molecular biology — essentially, the chemistry of organic macromolecules — and hence, through successively higher levels of organization, cellular, organismic, and evolutionary biology. … Such is the unifying and highly productive understanding of the world that has evolved in the natural sciences.