Folding Free Energy Surface Research Articles

Zinc Binding Modulates the Entire Folding Free Energy Surface of Human Cu,Zn Superoxide Dismutase

Over 100 amino acid replacements in human Cu,Zn superoxide dismutase (SOD) are known to cause amyotrophic lateral sclerosis, a gain-of-function neurodegenerative disease that destroys motor neurons. Supposing that aggregates of partially folded states are primarily responsible for toxicity, we determined the role of the structurally important zinc ion in defining the folding free energy surface of dimeric SOD by comparing the thermodynamic and kinetic folding properties of the zinc-free and zinc-bound forms of the protein. The presence of zinc was found to decrease the free energies of a peptide model of the unfolded monomer, a stable variant of the folded monomeric intermediate, and the folded dimeric species. The unfolded state binds zinc weakly with a micromolar dissociation constant, and the folded monomeric intermediate and the native dimeric form both bind zinc tightly, with subnanomolar dissociation constants. Coupled with the strong driving force for the subunit association reaction, the shift in the populations toward more well-folded states in the presence of zinc decreases the steady-state populations of higher-energy states in SOD under expected in vivo zinc concentrations (approximately nanomolar). The significant decrease in the population of partially folded states is expected to diminish their potential for aggregation and account for the known protective effect of zinc. The ∼ 100-fold increase in the rate of folding of SOD in the presence of micromolar concentrations of zinc demonstrates a significant role for a preorganized zinc-binding loop in the transition-state ensemble for the rate-limiting monomer folding reaction in this β-barrel protein.

Structural Analysis of Kinetic Folding Intermediates for a TIM Barrel Protein, Indole-3-glycerol Phosphate Synthase, by Hydrogen Exchange Mass Spectrometry and Gō Model Simulation

The structures of partially folded states appearing during the folding of a (βα) 8 TIM barrel protein, the indole-3-glycerol phosphate synthase from Sulfolobus solfataricus (sIGPS), was assessed by hydrogen exchange mass spectrometry (HX-MS) and Gō model simulations. HX-MS analysis of the peptic peptides derived from the pulse-labeled product of the sub-millisecond folding reaction from the urea-denatured state revealed strong protection in the (βα) 4 region, modest protection in the neighboring (βα) 1–3 and (βα) 5β 6 segments and no significant protection in the remaining N and C-terminal segments. These results demonstrate that this species is not a collapsed form of the unfolded state under native-favoring conditions nor is it the native state formed via fast-track folding. However, the striking contrast of these results with the strong protection observed in the (βα) 2–5β 6 region after 5 s of folding demonstrates that these species represent kinetically distinct folding intermediates that are not identical as previously thought. A re-examination of the kinetic folding mechanism by chevron analysis of fluorescence data confirmed distinct roles for these two species: the burst-phase intermediate is predicted to be a misfolded, off-pathway intermediate, while the subsequent 5 s intermediate corresponds to an on-pathway equilibrium intermediate. Comparison with the predictions using a C α Gō model simulation of the kinetic folding reaction for sIGPS shows good agreement with the core of the structure offering protection against exchange in the on-pathway intermediate(s). Because the native-centric Gō model simulations do not explicitly include sequence-specific information, the simulation results support the hypothesis that the topology of TIM barrel proteins is a primary determinant of the folding free energy surface for the productive folding reaction. The early misfolding reaction must involve aspects of non-native structure not detected by the Gō model simulation.

Mapping the Structure of Folding Cores in TIM Barrel Proteins by Hydrogen Exchange Mass Spectrometry: The Roles of Motif and Sequence for the Indole-3-glycerol Phosphate Synthase from Sulfolobus solfataricus

To test the roles of motif and amino acid sequence in the folding mechanisms of TIM barrel proteins, hydrogen-deuterium exchange was used to explore the structure of the stable folding intermediates for the of indole-3-glycerol phosphate synthase from Sulfolobus solfataricus (sIGPS). Previous studies of the urea denaturation of sIGPS revealed the presence of an intermediate that is highly populated at ∼4.5 M urea and contains ∼50% of the secondary structure of the native (N) state. Kinetic studies showed that this apparent equilibrium intermediate is actually comprised of two thermodynamically distinct species, I a and I b. To probe the location of the secondary structure in this pair of stable on-pathway intermediates, the equilibrium unfolding process of sIGPS was monitored by hydrogen-deuterium exchange mass spectrometry. The intact protein and pepsin-digested fragments were studied at various concentrations of urea by electrospray and matrix-assisted laser desorption ionization time-of-flight mass spectrometry, respectively. Intact sIGPS strongly protects at least 54 amide protons from hydrogen-deuterium exchange in the intermediate states, demonstrating the presence of stable folded cores. When the protection patterns and the exchange mechanisms for the peptides are considered with the proposed folding mechanism, the results can be interpreted to define the structural boundaries of I a and I b. Comparison of these results with previous hydrogen-deuterium exchange studies on another TIM barrel protein of low sequence identify, α-tryptophan synthase (αTS), indicates that the thermodynamic states corresponding to the folding intermediates are better conserved than their structures. Although the TIM barrel motif appears to define the basic features of the folding free energy surface, the structures of the partially folded states that appear during the folding reaction depend on the amino acid sequence. Markedly, the good correlation between the hydrogen-deuterium exchange patterns of sIGPS and αTS with the locations of hydrophobic clusters defined by isoleucine, leucine, and valine residues suggests that branch aliphatic side-chains play a critical role in defining the structures of the equilibrium intermediates.

Mapping the Folding Free Energy Surface for Metal-free Human Cu,Zn Superoxide Dismutase

Mutations at many different sites in the gene encoding human Cu,Zn superoxide dismutase (SOD) are known to be causative agents in amyotrophic lateral sclerosis (ALS). One explanation for the molecular basis of this pathology is the aggregation of marginally soluble, partially structured states whose populations are enhanced in the protein variants. As a benchmark for testing this hypothesis, the equilibrium and kinetic properties of the reversible folding reaction of a metal-free variant of SOD were investigated. Reversibility was achieved by replacing the two non-essential cysteine residues with non-oxidizable analogs, C6A/C111S, to produce apo-AS-SOD. The metal-free pseudo-wild-type protein is folded and dimeric in the absence of chemical denaturants, and its equilibrium folding behavior is well described by an apparent two-state mechanism involving the unfolded monomer and the native dimer. The apparent free energy of folding in the absence of denaturant and at standard state is − 20.37( ± 1.04) kcal (mol dimer) − 1 . A global analysis of circular dichroism kinetic traces for both unfolding and refolding reactions, combined with results from small angle X-ray scattering and time-resolved fluorescence anisotropy measurements, supports a sequential mechanism involving the unfolded monomer, a folded monomeric intermediate, and the native dimer. The rate-limiting monomer folding reaction is followed by a near diffusion-limited self-association reaction to form the native dimer. The relative population of the folded monomeric intermediate is predicted not to exceed 0.5% at micromolar concentrations of protein under equilibrium and both strongly unfolding and refolding conditions for metal-free pseudo-wild-type SOD.

Thermodynamics and kinetics of downhill protein folding investigated with a simple statistical mechanical model

AbstractThe possibility of downhill protein folding is one of the most intriguing predictions of the energy landscape approach. Finding examples of downhill folding has important practical implications because in the absence of a free energy barrier the mechanism of folding is amenable to experimental observation. Here, a simple statistical mechanical model of protein folding is used to analyze the thermodynamic and kinetic properties of downhill and two‐state folding. Folding free energy surfaces with and without a barrier separating denatured and native states can be generated with this model by simply modifying the curvature of the energy as a function of the order parameter, i.e., number of amino acids in incorrect conformation. Thermodynamic and kinetic analysis of surfaces with a barrier show the typical properties of two‐state folding: a first‐order equilibrium unfolding transition and exponential biphasic folding kinetics. In contrast, in downhill surfaces the unfolding process is noncooperative, and the apparent transition depends on the structural probe used to measure it. Therefore, this inherent behavior can be used as an experimental criterion for the identification of downhill folding. Surprisingly, the kinetics of downhill folding do not greatly deviate from exponential behavior unless the effective diffusion coefficient is assumed to decrese as folding progresses, exemplifying the increase in the roughness of the landscape. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Quantifying protein folding transition States with φ(t).

A number of reaction coordinates have been proposed for reduced-dimensionalityrepresentations of a protein's folding free energy surface. We discuss in detail the entropic reaction coordinate Φ(T) = Δ S(†)ΔS, recently introduced to quantify the conservation of mutations and the location of the folding transition state based on experimental temperature-tuning data. Numerical simulations illustrate the advantages as well as the limitations of Φ(T). Φ(T) can be determined from experiment,computation, and analytical theory; Φ(T) can also be used to investigate structurally localized perturbations of the free energy surface. However, Φ(T) is only a relative reaction cordinate; furthermore, proteins undergo cold denaturation at sufficiently low temperatures, and care must be taken ininterpreting Φ(T) near the region where ∂ΔG/∂T = 0, particularly if the heat capacity change upon folding is small.

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.

Comparative Study of the Folding Free Energy Landscape of a Three-Stranded β-Sheet Protein with Explicit and Implicit Solvent Models

We present a molecular dynamics (MD) simulation study of the folding thermodynamics for the three-stranded β-sheet protein Betanova. The protein was explicitly described by employing an all-atom model. The solvation was accounted for by two different solvent models: explicit TIP3P water and implicit Generalized Born (GB) with an exterior dielectric of 80. An umbrella sampling technique was utilized to probe thermodynamically relevant states at different stages of folding. The generated data were combined with the weighted histogram method to produce the two-dimensional folding free energy landscape. Sampling of conformational space was carried out in explicit solvent at 275 K and in implicit solvent at 275, 350, and 400 K. The folding free energy surface of Betanova at 275 K was found to be consistent with that in explicit solvent. In particular, the two models agree with regard to the location of the global minimum, the absence of a significant barrier for folding on the folding free energy surface, and...

Free Energy Surface of the Helical Peptide Y(MEARA)6

The folding of the helical peptide Y(MEARA)6 was studied by a series of molecular dynamics simulations with an implicit solvation model that allowed sampling of a total of more than 4 μs. In the 44 runs at 360 K started from all-coil conformations the peptide assumed an α-helical structure within the first 30 ns, with an average folding time of 10 ns. The free energy surface shows that the coil to helix transition has a small barrier at the helix nucleation step which consists of two to three i, i + 4 hydrogen bonds and does not show a strong preference along the sequence. On the helix side of the barrier, there is a very broad basin corresponding to conformations having more than one helical turn. Although the α-helical content is predominant, there is a nonnegligible percentage of conformations with one or more π-helical turns stabilized in part by interactions between Met side chains. Control simulations with two different helical sequences, a 31-residue polyalanine and A5 (AAARA)3 A, did not reveal a significant π-helix population, which indicates that the π-helical content of Y(MEARA)6 is not an artifact of the force field and solvation model. The folding mechanism and free energy surface presented here are in agreement with previous theoretical models and experimental data on different helical sequences, which suggest that they may be valid for the folding of helical peptides, in general.

Mapping the transition state of the WW domain β-sheet

The folding kinetics of a three-stranded antiparallel β-sheet (WW domain) have been measured by temperature jump relaxation. Folding and activation free energies were determined as a function of temperature for both the wild-type and the mutant domain, W39F, which modifies the β 2-β 3 hydrophobic interface. The folding rate decreases at higher temperatures as a result of the increase in the activation free energy for folding. Φ-Values were obtained for thermal perturbations allowing the primary features of the folding free energy surface to be determined. The results of this analysis indicate a significant shift from an “early” (Φ T = 0.4) to a “late” (Φ T = 0.8) transition state with increasing temperature. The temperature-dependent Φ-value analysis of the wild-type WW domain and of its more stable W39F hydrophobic cluster mutant reveals little participation of residue 39 in the transition state at lower temperature. As the temperature is raised, hydrophobic interactions at the β 2-β 3 interface gain importance in the transition state and the barrier height of the wild-type, which contains the larger tryptophan residue, increases more slowly than the barrier height of the mutant.

Using simplified protein representation as a reference potential for all-atom calculations of folding free energy

An effective approach for evaluating folding free-energy surfaces of explicit all-atom models is developed and examined. This approach is based on using the potential of a simplified protein model as a reference potential for calculating the free energy of the corresponding explicit model. Preliminary results are presented for the folding free energy of a 12-residue helix. The potential of the method for studies of protein-folding processes is discussed, emphasizing the ability to determine the difference between the results of simplified and explicit models. This can help in establishing the validity of simplified folding models.

Folding Free Energy Surface of a Three-Stranded β-Sheet Protein

We present a molecular dynamics (MD) simulation study of the folding thermodynamics of the three-stranded β-sheet protein Betanova. The protein and solvent are explicitly described by employing all atom models. An umbrella sampling technique was employed to probe thermodynamically relevant states at different stages of folding. A database for the sampling was generated by conducting four high-temperature simulations. The initial conditions for the umbrella sampling were selected from this database of structures by employing hierarchical clustering. Sampling of conformational space was then carried out at 275 K and the generated data were combined with the weighted histogram method to produce the two-dimensional folding free energy landscape. We found that the folding of the protein Betanova occurs in two collapse stages. The first collapse brings the protein into a basin that contains various structures differing in their size and elements of secondary structure. At the transition state from this basin of collapsed states to the native basin, the protein adopts a native-like fold and size and forms ≈60% of native contacts. Thus the formation of native-like structure is concurrent with the secondary collapse. The overall stability of protein Betanova is found to be about 1 kcal/mol, in agreement with the experimental estimate. We found that the native side chain contacts are the primary factor in driving Betanova folding and stabilizing its native three-stranded β-sheet conformation. By contrast, hydrogen bonding is found to play a minor role in the folding of Betanova. Solvent is observed to be present in the protein core until late in folding.

Variational Theory for Site Resolved Protein Folding Free Energy Surfaces

We present a microscopic variational theory for the free energy surface of a fast folding protein that allows folding kinetics to be resolved to the residue level using Debye-Waller factors as local order parameters. We apply the method to lambda-repressor and compare with site directed mutagenesis experiments. The formation of native structure and the free energy profile along the folding route are shown to be well described by the capillarity approximation but with some fine structure due to local folding topology.

Exploring the folding free energy surface of a three-helix bundle protein.

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50-70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg approximately 12 A), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

Solvent, force field, temperature and quantum effects on the folding free energy surface of blocked alanine tripeptide

Une etude par simulation numerique du tri-peptide bloque Ac-(Ala) 3 -NHMe, en solution aqueuse et en phase gazeuse a ete realise a T = 300K et T = 600K. La dependance en temperature de l'energie libre de repliement du peptide ainsi que les effets provenant d'un traitement quantique ont ete determine par la methode dite umbrella sampling. La coordonnee de reaction volumetrique utilisee correspond a la distance entre l'atome d'hydrogrene lie au carbone du groupement amide bloquant et l'atome d'oxygene du groupement ester bloquant Ac.

Constant-temperature free energy surfaces for physical and chemical processes

A comparison between two methods for combining data from molecular simulations to generate free energy surfaces for physical and chemical processes is presented. The conventional «splicing» method is compared with a recently introduced histogram-based technique for the calculation of the free energy surface for folding a short peptide in vacuo. We present an extension of the weighted histogram analysis method, described recently by Kumar et al. (J. Comput. Chem. 1992, 13, 1101-1021), which is specialized to the case of constant-temperature simulations and generalized to multiple dimensions. Our data indicate that both methods produce identical results, at the qualitative level, for the folding free energy surface