Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

Urea Impedes the Hydrophobic Collapse of Partially Unfolded Proteins

Proteins are denatured in aqueous urea solution. The nature of the molecular driving forces has received substantial attention in the past, whereas the question how urea acts at different phases of unfolding is not yet well understood at the atomic level. In particular, it is unclear whether urea actively attacks folded proteins or instead stabilizes unfolded conformations. Here we investigated the effect of urea at different phases of unfolding by molecular dynamics simulations, and the behavior of partially unfolded states in both aqueous urea solution and in pure water was compared. Whereas the partially unfolded protein in water exhibited hydrophobic collapses as primary refolding events, it remained stable or even underwent further unfolding steps in aqueous urea solution. Further, initial unfolding steps of the folded protein were found not to be triggered by urea, but instead, stabilized. The underlying mechanism of this stabilization is a favorable interaction of urea with transiently exposed, less-polar residues and the protein backbone, thereby impeding back-reactions. Taken together, these results suggest that, quite generally, urea-induced protein unfolding proceeds primarily not by active attack. Rather, thermal fluctuations toward the unfolded state are stabilized and the hydrophobic collapse of partially unfolded proteins toward the native state is impeded. As a result, the equilibrium is shifted toward the unfolded state.     

Ligand binding to a high‐energy partially unfolded protein

The conformational energy landscape of a protein determines populations of all possible conformations of the protein and also determines the kinetics of the conversion between the conformations. Interaction with ligands influences the conformational energy landscapes of proteins and shifts populations of proteins in different conformational states. To investigate the effect of ligand binding on partial unfolding of a protein, we use Escherichia coli dihydrofolate reductase (DHFR) and its functional ligand NADP⁺ as a model system. We previously identified a partially unfolded form of DHFR that is populated under native conditions. In this report, we determined the free energy for partial unfolding of DHFR at varying concentrations of NADP⁺ and found that NADP⁺ binds to the partially unfolded form as well as the native form. DHFR unfolds partially without releasing the ligand, though the binding affinity for NADP⁺ is diminished upon partial unfolding. Based on known crystallographic structures of NADP⁺‐bound DHFR and the model of the partially unfolded protein we previously determined, we propose that the adenosine‐binding domain of DHFR remains folded in the partially unfolded form and interacts with the adenosine moiety of NADP⁺. Our result demonstrates that ligand binding may affect the conformational free energy of not only native forms but also high‐energy non‐native forms.     

Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

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).     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.     

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.     

Ab initio construction of protein tertiary structures using a hierarchical approach

We present a hierarchical method to predict protein tertiary structure models from sequence. We start with complete enumeration of conformations using a simple tetrahedral lattice model. We then build conformations with increasing detail, and at each step select a subset of conformations using empirical energy functions with increasing complexity. After enumeration on lattice, we select a subset of low energy conformations using a statistical residue-residue contact energy function, and generate all-atom models using predicted secondary structure. A combined knowledge-based atomic level energy function is then used to select subsets of the all-atom models. The final predictions are generated using a consensus distance geometry procedure. We test the feasibility of the procedure on a set of 12 small proteins covering a wide range of protein topologies. A rigorous double-blind test of our method was made under the auspices of the CASP3 experiment, where we did ab initio structure predictions for 12 proteins using this approach. The performance of our methodology at CASP3 is reasonably good and completely consistent with our initial tests.     

Single molecule force spectroscopy reveals a weakly populated microstate of the FnIII domains of tenascin

The native states of proteins exist as an ensemble of conformationally similar microstates. The fluctuations among different microstates are of great importance for the functions and structural stability of proteins. Here, we demonstrate that single molecule atomic force microscopy (AFM) can be used to directly probe the existence of multiple folded microstates. We used the AFM to repeatedly stretch and relax a recombinant tenascin fragment TNfnALL to allow the fibronectin type III (FnIII) domains to undergo repeated unfolding/refolding cycles. In addition to the native state, we discovered that some FnIII domains can refold from the unfolded state into a previously unrecognized microstate, N* state. This novel state is conformationally similar to the native state, but mechanically less stable. The native state unfolds at approximately 120 pN, while the N* state unfolds at approximately 50 pN. These two distinct populations of microstates constitute the ensemble of the folded states for some FnIII domains. An unfolded FnIII domain can fold into either one of the two microstates via two distinct folding routes. These results reveal the dynamic and heterogeneous picture of the folded ensemble for some FnIII domains of tenascin, which may carry important implications for the mechanical functions of tenascins in vivo.     

Urea dependence of thiol-disulfide equilibria in thioredoxin: confirmation of the linkage relationship and a sensitive assay for structure

Thioredoxin contains a single disulfide bond that can be reduced without perturbing significantly the structure of the enzyme. Upon reduction of the disulfide, protein stability decreases. We have experimentally tested the expected linkage relationship between disulfide bond formation and protein stability for thioredoxin. In order to do this, it is necessary to measure the equilibrium constant for disulfide bond formation in both the folded and unfolded states of the protein. Using glutathione as a reference species, we have measured the equilibrium constant for forming the disulfide bond (effective concentration) in thioredoxin as a function of urea concentration. As a control, we show that urea per se does not interfere with our measurements of thiol-disulfide equilibrium constants. Comparison of the values obtained for disulfide bond formation in the folded and unfolded states with the free energies for unfolding oxidized and reduced thioredoxin using circular dichroism confirms the expected linkage relationship. The urea dependence of thiol-disulfide equilibria provides a sensitive assay for folded structure in peptides or proteins. The method should also be useful to evaluate the stabilizing or destabilizing effect of natural or genetically engineered disulfides in proteins. In future work, the effects of amino acid substitutions on disulfide bond formation could be evaluated individually in the native and unfolded states of a protein.     

Membrane adsorption,folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Predicting the equilibrium protein folding pathway: Structure-based analysis of staphylococcal nuclease

The equilibrium folding pathway of staphylococcal nucleas (SNase) has been approximated using a statistical thermodynamic formalism that utilizes the high-resolution structure of the native state as a template to generate a large ensemble of partially folded states. Close to 400,000 different states ranging from the native to the completely unfolded states were included in the analysis. The probability of each state was estimated using an empirical structural parametrization of the folding energetics. It is shown that this formalism predicts accurately the stability of the protein, the cooperativity of the folding/unfolding transition observed by differential scanning calorimetry (DSC) or urea denaturation and the thermodynamic parameters for unfolding. More importantly, this formalism provides a quantitative account of the experimental hydrogen exchange protection factors measured under native conditions for SNase. These results suggest that the computer-generated distribution of states approximates well the ensemble of conformations existing in solution. Furthermore, this formalism represents the first model capable of quantitatively predicting within a unified framework the probability distribution of states seen under native conditions and its change upon unfolding. © 1997 Wiley-Liss, Inc.     

Membrane adsorption, folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.     

Energetic coupling between native-state prolyl isomerization and conformational protein folding

In folded proteins, prolyl peptide bonds are usually thought to be either trans or cis because only one of the isomers can be accommodated in the native folded protein. For the N-terminal domain of the gene-3 protein of the filamentous phage fd (N2 domain), Pro161 resides at the tip of a beta hairpin and was found to be cis in the crystal structure of this protein. Here we show that Pro161 exists in both the cis and the trans conformations in the folded form of the N2 domain. We investigated how conformational folding and prolyl isomerization are coupled in the unfolding and refolding of N2 domain. A combination of single-mixing and double-mixing unfolding and refolding experiments showed that, in unfolded N2 domain, 7% of the molecules contain a cis-Pro161 and 93% of the molecules contain a trans-Pro161. During refolding, the fraction of molecules with a cis-Pro161 increases to 85%. This implies that 10.3 kJ mol(-1) of the folding free energy was used to drive this 75-fold change in the Pro161 cis/trans equilibrium constant during folding. The stabilities of the forms with the cis and the trans isomers of Pro161 and their folding kinetics could be determined separately because their conformational folding is much faster than the prolyl isomerization reactions in the native and the unfolded proteins. The energetic coupling between conformational folding and Pro161 isomerization is already fully established in the transition state of folding, and the two isomeric forms are thus truly native forms. The folding kinetics are well described by a four-species box model, in which the N2 molecules with either isomer of Pro161 can fold to the native state and in which cis/trans isomerization occurs in both the unfolded and the folded proteins.     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

Molecular dynamics simulation of amyloid beta dimer formation

Recent experiments with amyloid beta (Abeta) peptide indicate that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation. 1), We use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations; and 2), we employ all-atom molecular mechanics simulations to estimate thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.