Protein folding↔unfolding dynamics

Discovery of a tetracyclic indole alkaloid that postpones fibrillation of hen egg white lysozyme protein

Protein aggregation, such as amyloid fibril formation, is molecular hallmark of many neurodegenerative disorders including Alzheimer's, Parkinson's, and Prion disease. Indole alkaloids are well-known as the compounds having the ability to inhibit protein fibrillation. In this study, we experimentally and computationally have investigated the anti-amyloid property of a derivative of a synthesized tetracyclic indole alkaloid (TCIA), possessing capable functional groups. The fibrillation reaction of Hen White Egg Lysozyme (HEWL) was performed in absence and presence of the indole alkaloid. For quantitative analysis, we used Thioflovin T binding assay which showed ~50% reduction in fibril formation in the presence of 20 μM TCIA. Using TEM imaging, we observed a significant morphological change in our model protein in the presence of TCIA. In addition, we exploited FT-IR assay by which Amide I peak's shifting toward lower wavenumber was clearly observed. Using Molecular Docking, the interaction of the inhibitor (TCIA) with the protein's amyloidogenic region was modeled. Also, different biophysical parameters were calculated by Molecular Dynamics (MD) simulation. Various biochemical assays, conformational change, and hydrophobicity exposure of the protein during amyloid formation indicated that the compound assists HEWL to keep its native structure via destabilizing β-sheet structure.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Dynamics-based selective 2D (1)H/(1)H chemical shift correlation spectroscopy under ultrafast MAS conditions

Dynamics plays important roles in determining the physical, chemical, and functional properties of a variety of chemical and biological materials. However, a material (such as a polymer) generally has mobile and rigid regions in order to have high strength and toughness at the same time. Therefore, it is difficult to measure the role of mobile phase without being affected by the rigid components. Herein, we propose a highly sensitive solid-state NMR approach that utilizes a dipolar-coupling based filter (composed of 12 equally spaced 90° RF pulses) to selectively measure the correlation of (1)H chemical shifts from the mobile regions of a material. It is interesting to find that the rotor-synchronized dipolar filter strength decreases with increasing inter-pulse delay between the 90° pulses, whereas the dipolar filter strength increases with increasing inter-pulse delay under static conditions. In this study, we also demonstrate the unique advantages of proton-detection under ultrafast magic-angle-spinning conditions to enhance the spectral resolution and sensitivity for studies on small molecules as well as multi-phase polymers. Our results further demonstrate the use of finite-pulse radio-frequency driven recoupling pulse sequence to efficiently recouple weak proton-proton dipolar couplings in the dynamic regions of a molecule and to facilitate the fast acquisition of (1)H/(1)H correlation spectrum compared to the traditional 2D NOESY (Nuclear Overhauser effect spectroscopy) experiment. We believe that the proposed approach is beneficial to study mobile components in multi-phase systems, such as block copolymers, polymer blends, nanocomposites, heterogeneous amyloid mixture of oligomers and fibers, and other materials.

Structural and dynamic investigation of bovine folate receptor alpha (FOLR1), and role of ultra-high temperature processing on conformational and thermodynamic characteristics of FOLR1-folate complex

The folate receptor alpha (FOLR1) present in milk has widely been studied to investigate the effects of pasteurization, ultra-high temperature (UHT) processing and fermentation on net folate concentration. However, the folate binding mechanism with FOLR1, and effect of temperature on FOLR1-folate complex is poorly explored till now in bovine milk which is a chief resource of folate. Despite of enormous importance of folic acid and the routine intake of bovine milk, folic acid deficiency diseases are common in human race. To understand the folate deficiency in milk after processing, in absence of experimental structure, 3D model of bovine FOLR1 (bvFOLR1) was built followed by 40ns molecular dynamics (MD) simulation. The folate and its derivatives binding sites in bvFOLR1 were anticipated by molecular docking using AutoDock 4.2. Essential MD studies suggested the presence of a longer signal peptide (22 residues) and a short propeptide (7 residues) at the C-terminus that may cleaved during post-translational modification. MD analysis of bvFOLR1-folate complex at 298, 323, 353, 373 and 408K followed by binding energy (BE) calculation showed maximum binding affinity at ∼353K. However, at 373K and UHT (408K), the folate BE is significantly decreased with substantial conformational alteration. Heating at UHT followed by cooling within 298-408K range demoed no structural reformation with temperature reduction, and the folate was displaced from the active site. This study presented the disintegration of folate from bvFOLR1 during high temperature processing and revealed a lower folate concentration in UHT milk and dairy products.

A study of the structural properties and thermal stability of human Bcl-2 by molecular dynamics simulations

The anti-apoptotic B-cell lymphoma 2 (Bcl-2) protein interacts with several proteins that regulate the apoptotic properties of cells. In this research, we conduct several all-atom molecular dynamics (MD) simulations under high-temperature unfolding conditions, from 400 to 800 K, for 25 ns. These simulations were performed using a model of an engineered Bcl-2 human protein (Bcl-2-Δ22Σ3), which lacks 22 C-terminal residues of the transmembrane domain. The aim of this study is to gain insight into the structural behavior of Bcl-2-Δ22Σ3 by mapping the conformational movements involved in Bcl-2 stability and its biological function. To build a Bcl-2-Δ22Σ3 three-dimensional model, the protein core was built by homology modeling and the flexible loop domain (FLD, residues 33-91) by ab initio methods. Further, the entire protein model was refined by MD simulations. Afterwards, the production MD simulations showed that the FLD at 400 and 500 K has several conformations reaching into the protein core, whereas at 600 K some of the alpha-helices were lost. At 800 K, the Bcl-2 core is destabilized suggesting a possible mechanism for protein unfolding, where the alpha helices 1 and 6 were the most stable, and a reduction in the number of hydrogen bonds initially occurs. In conclusion, the structural changes and the internal protein interactions suggest that the core and the FLD are crucial components of Bcl-2 in its function of regulate ng access to the recognition sites of kinases and caspases.

Thermodynamics and folding pathways of trpzip2: an accelerated molecular dynamics simulation study

In this paper, we apply an enhanced sampling method introduced earlier to study the folding mechanism of a beta-hairpin, trpzip2, using an all-atom potential for the protein and an implicit model for the solvent. The enhanced sampling method allows us to obtain multiple protein folding and unfolding trajectories in relatively short simulations. The sufficient sampling of folding and unfolding events of trpzip2 makes possible a more detailed investigation of its folding landscape and thermodynamics, leading to the identification of folding pathways. The analysis of the thermodynamics involved in the folding of trpzip2 showed that this polypeptide folds by two stages: a downhill hydrophobic collapse followed by formation of native hydrogen bonds. During the hydrogen bond formation, a transition state can be identified with only one native hydrogen bond being formed, which is more consistent with a 'zip-out' mechanism. To address the dynamics in a more reliable way, explicit solvent was used for the estimation of the diffusion constant, which was used in the Kramer's theory, together with the free energy profile calculated using the enhanced sampling and the implicit solvent, to calculate the folding rate. The calculated folding time agrees well with the experimental value of 2.5 micros.

Molecular dynamics simulations of various coronavirus main proteinases

In this study, two homology models (denoted as MproST and MproSH) of main proteinase (Mpro) from the novel coronavirus associated with severe acute respiratory syndrome (SARS-CoV) were constructed based on the crystal structures of Mpro from transmissible gastroenteritis coronavirus (TGEV) (MproT) and human coronavirus HcoV-229E (MproH), respectively. Both MproST and MproSH exhibit similar folds as their respective template proteins. These homology models reveal three distinct functional domains as well as an intervening loop connecting domains II and III as found in both template proteins. A catalytic cleft containing the substrate binding sites S1 and S2 between domains I and II are also observed. S2 undergoes more significant structural fluctuation than S1 during the 400 ps molecular dynamics simulations because it is located at the open mouth of the catalytic cleft, while S1 is situated in the very bottom of this cleft. The thermal unfolding of these proteins begins at domain III, where the structure is least conserved among these proteins. Mpro may still maintain its proteolytic activity while it is partially unfolded. The electrostatic interaction between Arg40 and Asp186 plays an important role in maintaining the structural integrity of both S1 and S2.

The protein folding 'speed limit'

How fast can a protein possibly fold? This question has stimulated experimentalists to seek fast folding proteins and to engineer them to fold even faster. Proteins folding at or near the speed limit are prime candidates for all-atom molecular dynamics simulations. They may also have no free energy barrier, allowing the direct observation of intermediate structures on the pathways from the unfolded to the folded state. Both experimental and theoretical approaches predict a speed limit of approximately N/100micros for a generic N-residue single-domain protein, with alpha proteins folding faster than beta or alphabeta. The predicted limits suggest that most known ultrafast folding proteins can be engineered to fold more than ten times faster.

Three-body interactions improve the prediction of rate and mechanism in protein folding models

Here we study the effects of many-body interactions on rate and mechanism in protein folding by using the results of molecular dynamics simulations on numerous coarse-grained Calpha-model single-domain proteins. After adding three-body interactions explicitly as a perturbation to a Gō-like Hamiltonian with native pairwise interactions only, we have found (i) a significantly increased correlation with experimental phi values and folding rates, (ii) a stronger correlation of folding rate with contact order, matching the experimental range in rates when the fraction of three-body energy in the native state is approximately 20%, and (iii) a considerably larger amount of three-body energy present in chymotripsin inhibitor than in the other proteins studied.

Folding and misfolding of the papillomavirus E6 interacting peptide E6ap

All-atom Langevin dynamics simulations have been performed to study the folding pathways of the 18-residue binding domain fragment E6ap of the human papillomavirus E6 interacting peptide. Six independent folding trajectories, with a total duration of nearly 2 micros, all lead to the same native state in which the E6ap adopts a fluctuating alpha-helix structure in the central portion (Ser-4-Leu-13) but with very flexible N and C termini. Simulations starting from different core configurations exhibit the E6ap folding dynamics as either a two- or three-state folder with an intermediate misfolded state. The essential leucine hydrophobic core (Leu-9, Leu-12, and Leu-13) is well conserved in the native-state structure but absent in the intermediate structure, suggesting that the leucine core is not only essential for the binding activity of E6ap but also important for the stability of the native structure. The free energy landscape reveals a significant barrier between the basins separating the native and misfolded states. We also discuss the various underlying forces that drive the peptide into its native state.

Molecular dynamics simulations of the unfolding of the starch binding domain from Aspergillus niger glucoamylase

The 600 ps molecular dynamics simulations to investigate the unfolding of the starch binding domain from Aspergillus niger glucoamylase were conducted in vacuum as well as in an external field with the dielectric constant of 80 with temperature jump technique. Electrostatic interactions play an important role in determining the stability of the beta-strands in this domain. The starch binding site 1 is less stable than site 2 since it is more exposed to the surface. The disulfide bond between C509 and C604 is unstable since these two residues are located near the flexible linker domain and in the mobile loop region between beta-strands 6 and 7, respectively. The melting temperature, at which the total residual beta-strand content is 50% that of the solution structure, is about 544K for the simulations with dielectric constant of 80, leading to the estimated unfolding timescale of 0.48 ms in vitro. In addition, the unfolding of the starch binding domain is proposed to initiate from the interior region by the lost of the integrity of the secondary structure.

Molecular dynamics simulations of the unfolding mechanism of the catalytic domain from Aspergillus awamori var. X100 glucoamylase

In this study, 200 ps molecular dynamics simulations were conducted to investigate the unfolding mechanism of the catalytic domain of glucoamylase from Aspergillus awamori var. X100. The unfolding of this domain was suggested to follow a putative hierarchical manner, in which the heavily O-glycosylated belt region from residues T440 to A471 acted as the initiation site, followed by the alpha-helix secondary structure destruction, and then the collapse of the catalytic center pocket. The O-glycosylated belt region surrounded the surface of the catalytic domain in its native state at low temperature, whereas it was extended and is more suitable to be classified as part of the subsequent linker domain at high temperatures due to its high flexibility. The inner set helices of the (alpha/alpha)(6)-barrel seemed to exhibit higher helical content than the outer set ones at all temperatures examined. The distances between the C(alpha) of the three Cys residue pairs fluctuated rapidly at higher temperatures, indicating that these disulfide bonds have little effect on the structural stabilization. The melting temperature, at which the residual total helicity of the catalytic domain is 50%, is much lower than the critical temperature, at which the catalytic center pocket has lost its structural integrity.

Steered molecular dynamics investigations of protein function

Molecular recognition and mechanical properties of proteins govern molecular processes in the cell that can cause disease and can be targeted for drug design. Single molecule measurement techniques have greatly advanced knowledge but cannot resolve enough detail to be interpreted in terms of protein structure. We seek to complement the observations through so-called Steered Molecular Dynamics (SMD) simulations that link directly to experiments and provide atomic-level descriptions of the underlying events. Such a research program has been initiated in our group and has involved, for example, studies of elastic properties of immunoglobulin and fibronectin domains as well as the binding of biotin and avidin. In this article we explain the SMD method and suggest how it can be applied to the function of three systems that are the focus of modern molecular biology research: force transduction by the muscle protein titin and extracellular matrix protein fibronectin, recognition of antibody-antigene pairs, and ion selective conductivity of the K+ channel.

From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding

Beginning with simplified lattice and continuum "minimalist" models and progressing to detailed atomic models, simulation studies have augmented and directed development of the modern landscape perspective of protein folding. In this review we discuss aspects of detailed atomic simulation methods applied to studies of protein folding free energy surfaces, using biased-sampling free energy methods and temperature-induced protein unfolding. We review studies from each on systems of particular experimental interest and assess the strengths and weaknesses of each approach in the context of "exact" results for both free energies and kinetics of a minimalist model for a beta-barrel protein. We illustrate in detail how each approach is implemented and discuss analysis methods that have been developed as components of these studies. We describe key insights into the relationship between protein topology and the folding mechanism emerging from folding free energy surface calculations. We further describe the determination of detailed "pathways" and models of folding transition states that have resulted from unfolding studies. Our assessment of the two methods suggests that both can provide, often complementary, details of folding mechanism and thermodynamics, but this success relies on (a) adequate sampling of diverse conformational regions for the biased-sampling free energy approach and (b) many trajectories at multiple temperatures for unfolding studies. Furthermore, we find that temperature-induced unfolding provides representatives of folding trajectories only when the topology and sequence (energy) provide a relatively funneled landscape and "off-pathway" intermediates do not exist.

Exploring the energy landscape of a beta hairpin in explicit solvent

We studied the energy landscape of the peptide Ace-GEWTYDDATKTFTVTE-Nme, taken from the C-terminal fragment (41-56) of protein G, in explicit aqueous solution by a highly parallel replica-exchange approach that combines molecular dynamics trajectories with a temperature exchange Monte Carlo process. The combined trajectories in T and configurational space allow a replica to overcome a free energy barrier present at one temperature by increasing T, changing configurations, and cooling in a self-regulated manner, thus allowing sampling of broad regions of configurational space in short (nanoseconds) time scales. The free energy landscape of this system over a wide range of temperatures shows that the system preferentially adopts a beta hairpin structure. However, the peptide also samples other stable ensembles where the peptide adopts helices and helix-turn-helix states, among others. The helical states become increasingly stable at low temperatures, but are slightly less stable than the beta turn ensemble. The energy landscape is rugged at low T, where substates are separated by large energy barriers. These barriers disappear at higher T (approximately 330 K), where the system preferentially adopts a "molten globule" state with structures similar to the beta hairpin.

The initial step of the thermal unfolding of 3-isopropylmalate dehydrogenase detected by the temperature-jump Laue method

A temperature-jump (T-jump) time-resolved X-ray crystallographic technique using the Laue method was developed to detect small, localized structural changes of proteins in crystals exposed to a temperature increase induced by laser irradiation. In a chimeric protein between thermophilic and mesophilic 3-isopropylmalate dehydrogenases (2T2M6T), the initial structural change upon T-jump to a denaturing temperature (approximately 90 degrees C) was found to be localized at a region which includes a beta-turn and a loop located between the two domains of the enzyme. A mutant, 2T2M6T-E110P/S111G/S113E, having amino acid replacements in this beta-turn region with the corresponding residues of the thermophilic enzyme, showed greater stability than the original chimera (increase of T:(m) by approximately 10 degrees C) and no T-jump-induced structural change in this region was detected by our method. These results indicate that thermal unfolding of the original chimeric enzyme, 2T2M6T, is triggered in this beta-turn region.

Dissecting the stability of a beta-hairpin peptide that folds in water: NMR and molecular dynamics analysis of the beta-turn and beta-strand contributions to folding

NMR studies of the folding and conformational properties of a beta-hairpin peptide, several peptide fragments of the hairpin, and sequence-modified analogues, have enabled the various contributions to beta-hairpin stability in water to be dissected. Temperature and pH-induced unfolding studies indicate that the folding-unfolding equilibrium approximates to a two-state model. The hairpin is highly resistant to denaturation and is still significantly folded in 7 M urea at 298 K. Thermodynamic analysis shows the hairpin to fold in water with a significant change in heat capacity, however, DeltaCp degrees in 7 M urea is reduced. V/Y-->A mutations on one strand of the hairpin reduce folding to <10 %, consistent with a hydrophobic stabilisation model. We show that in a truncated peptide (residues 6-16) lacking the hydrophobic residues on one beta-strand, the type I' Asn-Gly turn in the sequence SINGKK is significantly populated in water in the absence of interstrand hydrophobic contacts. Unrestrained molecular dynamics simulations of unfolding, using an explicit solvation model, show that the conformation of the NG turn persists for longer than the AG analogue, which has a much lower propensity for type I' turn formation from a data base analysis of preferred turns. The origin of the high stability of the Asn-Gly turn is not entirely clear; data base analysis of 66 NG turns, together with molecular dynamics simulations, reveals no participation of the Asn side-chain in turn-stabilising interactions with the peptide backbone. However, hydration analysis of the molecular dynamics simulations reveals a pocket of "high density" water bridging between the Asn side-chain and peptide main-chain that suggests solvent-mediated interactions may play an important role in modulating phi,psi propensities in the NG turn region.

Non-native interactions in protein folding intermediates: molecular dynamics simulations of hen lysozyme

Molecular dynamics simulations of protein denaturation can complement and extend experimental studies of protein folding by providing atomic-level structural information about conformational transitions and any conformational states along the unfolding pathway. Previous unfolding simulations of hen egg-white lysozyme have resulted in intermediate structures with an unfolded alpha-domain and a structured beta-domain, which is inconsistent with experiment. In contrast, the beta-domain unfolded first in the two simulations presented here leaving a structured alpha-domain. Following this, intermediate states were identified that differ with respect to the packing of the helices and the elements of non-native structure adopted. The non-native structure is critical for explaining many of the experimental observations. Overall, the pooled ensemble of these intermediates is in agreement with the experimental data for the major kinetic intermediate, suggesting that the kinetic intermediate may be made up of distinct, but rapidly interconverting, partially folded conformations distinguished primarily by differences in helix packing.

Pathways to a protein folding intermediate observed in a 1-microsecond simulation in aqueous solution

An implementation of classical molecular dynamics on parallel computers of increased efficiency has enabled a simulation of protein folding with explicit representation of water for 1 microsecond, about two orders of magnitude longer than the longest simulation of a protein in water reported to date. Starting with an unfolded state of villin headpiece subdomain, hydrophobic collapse and helix formation occur in an initial phase, followed by conformational readjustments. A marginally stable state, which has a lifetime of about 150 nanoseconds, a favorable solvation free energy, and shows significant resemblance to the native structure, is observed; two pathways to this state have been found.

The early stage of folding of villin headpiece subdomain observed in a 200-nanosecond fully solvated molecular dynamics simulation

A new approach in implementing classical molecular dynamics simulation for parallel computers has enabled a simulation to be carried out on a protein with explicit representation of water an order of magnitude longer than previously reported and will soon enable such simulations to be carried into the microsecond time range. We have used this approach to study the folding of the villin headpiece subdomain, a 36-residue small protein consisting of three helices, from an unfolded structure to a molten globule state, which has a number of features of the native structure. The time development of the solvation free energy, the radius of gyration, and the mainchain rms difference from the native NMR structure showed that the process can be seen as a 60-nsec "burst" phase followed by a slow "conformational readjustment" phase. We found that the burial of the hydrophobic surface dominated the early phase of the folding process and appeared to be the primary driving force of the reduction in the radius of gyration in that phase.

Brownian dynamics simulations of protein folding: access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion-collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion-collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Simulations of protein folding and unfolding

The 'new view' of protein folding is based on a statistical analysis of the landscape for protein folding. This perspective leads to the investigation of the statistical distributions of protein conformations as the folding protein approaches the native state from unfolded states. Molecular dynamics simulations of both the thermodynamics of protein folding and the kinetics of unfolding are beginning to explore the statistical nature of these distributions. They also provide connections between the theory of protein folding landscapes and the experimental observations of the properties of key ensembles of the conformations populated as folding progresses.

A free energy analysis by unfolding applied to 125-mers on a cubic lattice

BACKGROUND

A common approach to the protein folding problem involves computer simulation of folding using lattice models of amino acid sequences. Key factors for good performance in such models are the correct choice of the temperature and the average interaction energy between residues. In order to push the lattice approach to its limit it is important to have a method to adjust these parameters for optimal folding that is not limited by our ability to successfully simulate folding in a reasonable time.

RESULTS

In this study, we adopt a simple cubic-lattice model and present a method for calculating the free energy of a chain as a function of the number of native contacts. This does not require that we are able to fold the sequence by simulation and it provides a method of estimating the folding transition temperature. For a given set of parameters, the free energy analysis also allows an estimate of foldability. By applying the method to sequences with 27 and 125 residues, we show that optimal folding occurs near the folding transition temperature and at either zero or small negative average interaction energy. We find ourselves able to fold only 125-mers that have significant short-range native contacts.

CONCLUSIONS

A free energy analysis during unfolding is a useful tool for the study of foldability and should be applicable to a variety of folding models. In this way we are able to fold some 125-mer designed sequences and our results confirm the finding that short-range contacts contribute to foldability.

Molecular dynamics simulation of the unfolding of barnase: characterization of the major intermediate

The folding/unfolding pathway of barnase has been studied extensively using the protein engineering method, which has provided indirect structural information for the transition state and the major folding intermediate. To further characterize the structural properties of the intermediate, we have simulated the thermal denaturation of barnase beginning from the average NMR structure. Our results indicate that there are at least two intermediates on the unfolding pathway. The three hydrophobic cores are partially formed in the major intermediate (I1), with core1 and core3 being slightly stronger than core2. Helix alpha 1 is substantially formed, with the center being stronger than the termini. The first turn of alpha 2 is lost and alpha 3 is unfolded. The center of the beta-sheet is substantially formed, but the edges are disrupted. These structural characteristics are in good qualitative agreement with the experimental data. For semi-quantitative comparison with experimental data, the extent of native structure of individual residues is characterized by a structure index, S, that reflects both secondary and tertiary structure. There is good agreement between S and the experimentally measured phi values, which are based on energetics, except for three residues. These residues are polar and non-conservative mutations were made to obtain phi values, which can complicate structural interpretations. These residues make strong side-chain interactions in I1, but the backbone structure is disrupted, leading to low S values. Thus, this discordance highlights possible limitations in both the phi value and S value analyses: strong polar interactions in the intermediate may give rise to high phi values that are not reflective of structure per se; however, due to sampling limitations, any one simulation is not expected to capture all of the features of the true conformational ensemble. In any case, these simulations provide an experimentally testable, atomic-level structural model for the major folding intermediate of barnase, as well as the detailed pathway from the native to the intermediate state.

A desolvation barrier to hydrophobic cluster formation may contribute to the rate-limiting step in protein folding

To gain insight into the free energy changes accompanying protein hydrophobic core formation, we have used computer simulations to study the formation of small clusters of nonpolar solutes in water. A barrier to association is observed at the largest solute separation that does not allow substantial solvent penetration. The barrier reflects an effective increase in the size of the cavity occupied by the expanded but water-excluding cluster relative to both the close-packed cluster and the fully solvated separated solutes; a similar effect may contribute to the barrier to protein folding/unfolding. Importantly for the simulation of protein folding without explicit solvent, we find that the interactions between nonpolar solutes of varying size and number can be approximated by a linear function of the molecular surface, but not the solvent-accessible surface of the solutes. Comparison of the free energy of cluster formation to that of dimer formation suggests that the assumption of pair additivity implicit in current protein database derived potentials may be in error.

The Levinthal paradox: yesterday and today

A change in the perception of the protein folding problem has taken place recently. The nature of the change is outlined and the reasons for it are presented. An essential element is the recognition that a bias toward the native state over much of the effective energy surface may govern the folding process. This has replaced the random search paradigm of Levinthal and suggests that there are many ways of reaching the native state in a reasonable time so that a specific pathway does not have to be postulated. The change in perception is due primarily to the application of statistical mechanical models and lattice simulations to protein folding. Examples of lattice model results on protein folding are presented. It is pointed out that the new optimism about the protein folding problem must be complemented by more detailed studies to determine the structural and energetic factors that introduce the biases which make possible the folding of real proteins.

Protein folding: the endgame

The last stage of protein folding, the "endgame," involves the ordering of amino acid side-chains into a well defined and closely packed configuration. We review a number of topics related to this process. We first describe how the observed packing in protein crystal structures is measured. Such measurements show that the protein interior is packed exceptionally tightly, more so than the protein surface or surrounding solvent and even more efficiently than crystals of simple organic molecules. In vitro protein folding experiments also show that the protein is close-packed in solution and that the tight packing and intercalation of side-chains is a final and essential step in the folding pathway. These experimental observations, in turn, suggest that a folded protein structure can be described as a kind of three-dimensional jigsaw puzzle and that predicting side-chain packing is possible in the sense of solving this puzzle. The major difficulty that must be overcome in predicting side-chain packing is a combinatorial "explosion" in the number of possible configurations. There has been much recent progress towards overcoming this problem, and we survey a variety of the approaches. These approaches differ principally in whether they use ab initio (physical) or more knowledge-based methods, how they divide up and search conformational space, and how they evaluate candidate configurations (using scoring functions). The accuracy of side-chain prediction depends crucially on the (assumed) positioning of the main-chain. Methods for predicting main-chain conformation are, in a sense, not as developed as that for side-chains. We conclude by surveying these methods. As with side-chain prediction, there are a great variety of approaches, which differ in how they divide up and search space and in how they score candidate conformations.

The role of protein-solvent interactions in protein unfolding

Protein unfolding occurs when the balance of forces between the protein's interaction with itself and the protein's interaction with its environment is disrupted. The disruption of this balance of forces may be as simple as a perturbance of the normal water structure around the protein. A decrease in the normal water-water interaction will result in an increase in the relative interaction of water with the protein. An increase in the number of interactions between water and the protein may initiate a protein's unfolding. This model for protein unfolding is supported by a range of recent experimental and computational data.

The concept of a random coil. Residual structure in peptides and denatured proteins

Non-native states of proteins are of increasing interest because of their relevance to issues such as protein folding, translocation and stability. A framework for interpreting the wealth of experimental data for non-native states emerging from rapid advances in experimental techniques involves comparison with a "random coll' state, which possesses no structure except that inherent in the local interactions. We review here the concept of a random coil, from its global to its local properties. In particular, we focus on the description of a random coil in terms of statistical distributions in psi, phi space. We show that such a model, in combination with experimental data, provides insight into the structural properties of polypeptide chains and has significance for understanding protein folding and for molecular design.

First-principles calculation of the folding free energy of a three-helix bundle protein

The folding and unfolding of a three-helix bundle protein were explored with molecular-dynamics simulations, cluster analysis, and weighted-histogram techniques. The folding-unfolding process occurs by means of a "folding funnel," in which a uniform and broad distribution of conformational states is accessible outside of the native manifold. This distribution narrows near a transition region and becomes compact within the native manifold. Key thermodynamic steps in folding include initial interactions around the amino-terminal helix-turn-helix motif, interactions between helices I and II, and, finally, the docking of helix III onto the helix I-II subdomain. A metastable minimum in the calculated free-energy surface is observed at approximately 1.5 times the native volume. Folding-unfolding thermodynamics are dominated by the opposing influences of protein-solvent energy, which favors unfolding, and the overall entropy, which favors folding by means of the hydrophobic effect.

Computational approaches to study protein unfolding: hen egg white lysozyme as a case study

Four methods are compared to drive the unfolding of a protein: (1) high temperature (T-run), (2) high pressure (P-run), (3) by imposing a gradual increase in the mean radius of the protein using a penalty function added to the physical interaction function (F-run, radial force driven unfolding), and (4) by weak coupling of the difference between the temperature of the radially outward moving atoms and the radially inward moving atoms to an external temperature bath (K-run, kinetic energy driven unfolding). The characteristic features of the four unfolding pathways are analyzed in order to detect distortions due to the size or the type of the applied perturbation, as well as the features that are common to all of them. Hen egg white lysozyme is used as a test system. The simulations are analyzed and compared to experimental data like 1H-NMR amide proton exchange-folding competition, heat capacity, and compressibility measurements.

Theoretical studies of protein folding and unfolding

The mechanism of protein folding is being investigated theoretically by the use of both simplified and all-atom models of the polypeptide chain. Lattice heteropolymer simulations of the folding process have led to proposals for the folding mechanism and for the resolution of the Levinthal paradox. Both stability and rapid folding have been shown in model studies to result from the presence of a pronounced global energy minimum corresponding to the native state. Concomitantly, molecular dynamics simulations with detailed atomic models have been used to analyze the initial stages of protein unfolding. Results concerning possible folding intermediates and the role of water in the unfolding process have been obtained. The two types of theoretical approaches are providing information essential for an understanding of the mechanism of protein folding and are useful for the design of experiments to study the mechanism in different proteins.