Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Comparison of force fields for Alzheimer's A : A case study for intrinsically disordered proteins

Intrinsically disordered proteins are essential for biological processes such as cell signalling, but are also associated to devastating diseases including Alzheimer's disease, Parkinson's disease or type II diabetes. Because of their lack of a stable three‐dimensional structure, molecular dynamics simulations are often used to obtain atomistic details that cannot be observed experimentally. The applicability of molecular dynamics simulations depends on the accuracy of the force field chosen to represent the underlying free energy surface of the system. Here, we use replica exchange molecular dynamics simulations to test five modern force fields, OPLS, AMBER99SB, AMBER99SB*ILDN, AMBER99SBILDN‐NMR and CHARMM22*, in their ability to model Aβ₄₂, an intrinsically disordered peptide associated with Alzheimer's disease, and compare our results to nuclear magnetic resonance (NMR) experimental data. We observe that all force fields except AMBER99SBILDN‐NMR successfully reproduce local NMR observables, with CHARMM22* being slightly better than the other force fields.     

Computer simulations of protein folding by targeted molecular dynamics

We have performed 128 folding and 45 unfolding molecular dynamics runs of chymotrypsin inhibitor 2 (CI2) with an implicit solvation model for a total simulation time of 0.4 microseconds. Folding requires that the three-dimensional structure of the native state is known. It was simulated at 300 K by supplementing the force field with a harmonic restraint which acts on the root-mean-square deviation and allows to decrease the distance to the target conformation. High temperature and/or the harmonic restraint were used to induce unfolding. Of the 62 folding simulations started from random conformations, 31 reached the native structure, while the success rate was 83% for the 66 trajectories which began from conformations unfolded by high-temperature dynamics. A funnel-like energy landscape is observed for unfolding at 475 K, while the unfolding runs at 300 K and 375 K as well as most of the folding trajectories have an almost flat energy landscape for conformations with less than about 50% of native contacts formed. The sequence of events, i.e., secondary and tertiary structure formation, is similar in all folding and unfolding simulations, despite the diversity of the pathways. Previous unfolding simulations of CI2 performed with different force fields showed a similar sequence of events. These results suggest that the topology of the native state plays an important role in the folding process.     

Folding simulations of Trp‐cage mini protein in explicit solvent using biasing potential replica‐exchange molecular dynamics simulations

Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp‐cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near‐native conformations was observed after 30–40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of ～1.3 Å from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp‐cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Ensemble MD simulations restrained via crystallographic data: Accurate structure leads to accurate dynamics

Currently, the best existing molecular dynamics (MD) force fields cannot accurately reproduce the global free‐energy minimum which realizes the experimental protein structure. As a result, long MD trajectories tend to drift away from the starting coordinates (e.g., crystallographic structures). To address this problem, we have devised a new simulation strategy aimed at protein crystals. An MD simulation of protein crystal is essentially an ensemble simulation involving multiple protein molecules in a crystal unit cell (or a block of unit cells). To ensure that average protein coordinates remain correct during the simulation, we introduced crystallography‐based restraints into the MD protocol. Because these restraints are aimed at the ensemble‐average structure, they have only minimal impact on conformational dynamics of the individual protein molecules. So long as the average structure remains reasonable, the proteins move in a native‐like fashion as dictated by the original force field. To validate this approach, we have used the data from solid‐state NMR spectroscopy, which is the orthogonal experimental technique uniquely sensitive to protein local dynamics. The new method has been tested on the well‐established model protein, ubiquitin. The ensemble‐restrained MD simulations produced lower crystallographic R factors than conventional simulations; they also led to more accurate predictions for crystallographic temperature factors, solid‐state chemical shifts, and backbone order parameters. The predictions for ¹⁵N relaxation rates are at least as accurate as those obtained from conventional simulations. Taken together, these results suggest that the presented trajectories may be among the most realistic protein MD simulations ever reported. In this context, the ensemble restraints based on high‐resolution crystallographic data can be viewed as protein‐specific empirical corrections to the standard force fields.     

Molecular dynamics simulation of β₂-microglobulin in denaturing and stabilizing conditions

β₂‐Microglobulin has been a model system for the study of fibril formation for 20 years. The experimental study of β₂‐microglobulin structure, dynamics, and thermodynamics in solution, at atomic detail, along the pathway leading to fibril formation is difficult because the onset of disorder and aggregation prevents signal resolution in Nuclear Magnetic Resonance experiments. Moreover, it is difficult to characterize conformers in exchange equilibrium. To gain insight (at atomic level) on processes for which experimental information is available at molecular or supramolecular level, molecular dynamics simulations have been widely used in the last decade. Here, we use molecular dynamics to address three key aspects of β₂‐microglobulin, which are known to be relevant to amyloid formation: (1) 60 ns molecular dynamics simulations of β₂‐microglobulin in trifluoroethanol and in conditions mimicking low pH are used to study the behavior of the protein in environmental conditions that are able to trigger amyloid formation; (2) adaptive biasing force molecular dynamics simulation is used to force cis‐trans isomerization at Proline 32 and to calculate the relative free energy in the folded and unfolded state. The native‐like trans‐conformer (known as intermediate 2 and determining the slow phase of refolding), is simulated for 10 ns, detailing the possible link between cis‐trans isomerization and conformational disorder; (3) molecular dynamics simulation of highly concentrated doxycycline (a molecule able to suppress fibril formation) in the presence of β₂‐microglobulin provides details of the binding modes of the drug and a rationale for its effect. Proteins 2011. © 2010 Wiley‐Liss, Inc.     

Shortening a loop can increase protein native state entropy

Protein loops are essential structural elements that influence not only function but also protein stability and folding rates. It was recently reported that shortening a loop in the AcP protein may increase its native state conformational entropy. This effect on the entropy of the folded state can be much larger than the lower entropic penalty of ordering a shorter loop upon folding, and can therefore result in a more pronounced stabilization than predicted by polymer model for loop closure entropy. In this study, which aims at generalizing the effect of loop length shortening on native state dynamics, we use all‐atom molecular dynamics simulations to study how gradual shortening a very long or solvent‐exposed loop region in four different proteins can affect their stability. For two proteins, AcP and Ubc7, we show an increase in native state entropy in addition to the known effect of the loop length on the unfolded state entropy. However, for two permutants of SH3 domain, shortening a loop results only with the expected change in the entropy of the unfolded state, which nicely reproduces the observed experimental stabilization. Here, we show that an increase in the native state entropy following loop shortening is not unique to the AcP protein, yet nor is it a general rule that applies to all proteins following the truncation of any loop. This modification of the loop length on the folded state and on the unfolded state may result with a greater effect on protein stability. Proteins 2015; 83:2137–2146. © 2015 Wiley Periodicals, Inc.     

Improved side‐chain torsion potentials for the Amber ff99SB protein force field

Recent advances in hardware and software have enabled increasingly long molecular dynamics (MD) simulations of biomolecules, exposing certain limitations in the accuracy of the force fields used for such simulations and spurring efforts to refine these force fields. Recent modifications to the Amber and CHARMM protein force fields, for example, have improved the backbone torsion potentials, remedying deficiencies in earlier versions. Here, we further advance simulation accuracy by improving the amino acid side‐chain torsion potentials of the Amber ff99SB force field. First, we used simulations of model alpha‐helical systems to identify the four residue types whose rotamer distribution differed the most from expectations based on Protein Data Bank statistics. Second, we optimized the side‐chain torsion potentials of these residues to match new, high‐level quantum‐mechanical calculations. Finally, we used microsecond‐timescale MD simulations in explicit solvent to validate the resulting force field against a large set of experimental NMR measurements that directly probe side‐chain conformations. The new force field, which we have termed Amber ff99SB‐ILDN, exhibits considerably better agreement with the NMR data. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Folding thermodynamics of β‐hairpins studied by replica‐exchange molecular dynamics simulations

We study the differences in folding stability of β‐hairpin peptides, including GB1 hairpin and a point mutant GB1 K10G, as well as tryptophan zippers (TrpZips): TrpZip1, TrpZip2, TrpZip3‐1, and TrpZip4. By performing replica‐exchange molecular dynamics simulations with Amber03* force field (a modified version of Amber ff03) in explicit solvent, we observe ab initio folding of all the peptides except TrpZip3‐1, which is experimentally known to be the least stable among the peptides studied here. By calculating the free energies of unfolding of the peptides at room temperature and folding midpoint temperatures for thermal unfolding of peptides, we find that TrpZip4 and GB1 K10G peptides are the most stable β‐hairpins followed by TrpZip1, GB1, and TrpZip2 in the given order. Hence, the proposed K10G mutation of GB1 peptide results in enhanced stability compared to wild‐type GB1. An important goal of our study is to test whether simulations with Amber 03* model can reproduce experimentally predicted folding stability differences between these peptides. While the stabilities of GB1 and TrpZip1 yield close agreement with experiment, TrpZip2 is found to be less stable than predicted by experiment. However, as heterogenous folding of TrpZip2 may yield divergent thermodynamic parameters by different spectroscopic methods, mismatching of results with previous experimental values are not conclusive of model shortcomings. For most of the cases, molecular simulations with Amber03* can successfully reproduce experimentally known differences between the mutated peptides, further highlighting the predictive capabilities of current state‐of‐the‐art all‐atom protein force fields. Proteins 2015; 83:1307–1315. © 2015 Wiley Periodicals, Inc.     

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.     

Direct observation of microscopic reversibility in single-molecule protein folding

Both folded and unfolded conformations should be observed for a protein at its melting temperature (T(m)), where DeltaG between these states is zero. In an all-atom molecular dynamics simulation of chymotrypsin inhibitor 2 (CI2) at its experimental T(m), the protein rapidly loses its low-temperature native structure; it then unfolds before refolding to a stable, native-like conformation. The initial unfolding follows the unfolding pathway described previously for higher-temperature simulations: the hydrophobic core is disrupted, the beta-sheet pulls apart and the alpha-helix unravels. The unfolded state reached under these conditions maintains a kernel of structure in the form of a non-native hydrophobic cluster. Refolding simply reverses this path, the side-chain interactions shift, the helix refolds, and the native packing and hydrogen bonds are recovered. The end result of this refolding is not the initial crystal structure; it contains the proper topology and the majority of the native contacts, but the structure is expanded and the contacts are long. We believe this to be the native state at elevated temperature, and the change in volume and contact lengths is consistent with experimental studies of other native proteins at elevated temperature and the chemical denaturant equivalent of T(m).     

Temperature and urea induced denaturation of the TRP‐cage mini protein TC5b: A simulation study consistent with experimental observations

The effects of temperature and urea denaturation (6M urea) on the dominant structures of the 20‐residue Trp‐cage mini‐protein TC5b are investigated by molecular dynamics simulations of the protein at different temperatures in aqueous and in 6M urea solution using explicit solvent degrees of freedom and the GROMOS force‐field parameter set 45A3. In aqueous solution at 278 K, TC5b is stable throughout the 20 ns of MD simulation and the trajectory structures largely agree with the NMR‐NOE atom–atom distance data available. Raising the temperature to 360 K and to 400 K, the protein denatures within 22 ns and 3 ns, showing that the denaturation temperature is well below 360 K using the GROMOS force field. This is 40–90 K lower than the denaturation temperatures observed in simulations using other much used protein force fields. As the experimental denaturation temperature is about 315 K, the GROMOS force field appears not to overstabilize TC5b, as other force fields and the use of continuum solvation models seem to do. This feature may directly stem from the GROMOS force‐field parameter calibration protocol, which primarily involves reproduction of condensed phase thermodynamic quantities such as energies, densities, and solvation free energies of small compounds representative for protein fragments. By adding 6M urea to the solution, the onset of denaturation is observed in the simulation, but is too slow to observe a particular side‐chain side‐chain contact (Trp6‐Ile4) that was experimentally observed to be characteristic for the denatured state. Interestingly, using temperature denaturation, the process is accelerated and the experimental data are reproduced.     

Free energy landscape and folding mechanism of a beta-hairpin in explicit water: a replica exchange molecular dynamics study

The free energy landscape and the folding mechanism of the C-terminal beta-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a beta-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the beta-hairpin occurs as the sequence: collapse of hydrophobic core --> formation of H-bond --> formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart.     

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. Proteins 2015; 83:2279–2292. © 2015 Wiley Periodicals, Inc.     

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Molecular dynamics simulation reveals a surface salt bridge forming a kinetic trap in unfolding of truncated Staphylococcal nuclease

Surface salt bridges are ubiquitous in globular proteins. Their contribution to protein stability has been extensively debated in the past decade. Here, molecular dynamics simulations are performed starting from a non-equilibrium state of Staphylococcal nuclease (SNase) with C-terminal truncation (SNaseDelta). The results indicate a key role in the unfolding of the surface salt bridge between arginine 105 and glutamate 135. Experimentally, SNaseDelta is known to be partially unfolded. However, in simulations over 1 ns at 300 K and over 500 ps at 400 K, SNaseDelta remains stable in the native-like folded conformation, the salt bridge hindering unfolding. When the potential function is altered so as to selectively weaken the salt bridge, which then breaks rapidly at 430 K, the protein starts to unfold. The results suggest that breaking of this salt bridge presents a significant barrier to the unfolding transition of SNaseDelta from a native-like state to the unfolded state. Potential of mean force calculations indicate that the barrier height for this transition is approximately 7 kcal/mol.     

Are Current Molecular Dynamics Force Fields too Helical?

Accurate force fields are essential for the success of molecular dynamics simulations. In apparent contrast to the conformational preferences of most force fields, recent NMR experiments suggest that short polyalanine peptides in water populate the polyproline II structure almost exclusively. To investigate this apparent contradiction, with its ramifications for the assessment of molecular force fields and the structure of unfolded proteins, we performed extensive simulations of Ala₅ in water (∼5 μs total time), using twelve different force fields and three different peptide terminal groups. Using either empirical or density-functional-based Karplus relations for the J-couplings, we find that most current force fields do overpopulate the α-region, with quantitative results depending on the choice of Karplus relation and on the peptide termini. Even after reweighting to match experiment, we find that Ala₅ retains significant α- and β-populations. In fact, several force fields match the experimental data well before reweighting and have a significant helical population. We conclude that radical changes to the best current force fields are not necessary, based on the NMR data. Nevertheless, experiments on short peptides open the way toward the systematic improvement of current simulation models.     

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.     

A shorter peptide model from staphylococcal nuclease for the folding-unfolding equilibrium of a beta-hairpin shows that unfolded state has significant contribution from compact conformational states

It is important to understand the conformational features of the unfolded state in equilibrium with folded state under physiological conditions. In this paper, we consider a short peptide model LMYKGQPM from staphylococcal nuclease to model the conformational equilibrium between a hairpin conformation and its unfolded state using molecular dynamics simulation under NVT conditions at 300K using GROMOS96 force field. The free energy landscape has overall funnel-like shape with hairpin conformations sampling the minima. The "unfolded" state has a higher free energy of approximately 12kJ/mol with respect to native hairpin minimum and occupies a plateau region. We find that the unfolded state has significant contributions from compact conformations. Many of these conformations have hairpin-like topology. Further, these compact conformational forms are stabilized by hydrophobic interactions. Conversion between native and non-native hairpins occurs via unfolded states. Frequent conversions between folded and unfolded hairpins are observed with single exponential kinetics. We compare our results with the emerging picture of unfolded state from both experimental and theoretical studies.