Towards a consistent modeling of protein thermodynamic and kinetic cooperativity: how applicable is the transition state picture to folding and unfolding?

To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplified protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits protein-like calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable conformational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single-exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.     

Protein stabilization by osmolytes from hyperthermophiles: effect of mannosylglycerate on the thermal unfolding of recombinant nuclease a from Staphylococcus aureus studied by picosecond time-resolved fluorescence and calorimetry

2-O-alpha-Mannosylglycerate, a negatively charged osmolyte widely distributed among (hyper)thermophilic microorganisms, is known to provide notable protection to proteins against thermal denaturation. To study the mechanism responsible for protein stabilization, pico-second time-resolved fluorescence spectroscopy was used to characterize the thermal unfolding of a model protein, Staphylococcus aureus recombinant nuclease A (SNase), in the presence or absence of mannosylglycerate. The fluorescence decay times are signatures of the protein state, and the pre-exponential coefficients are used to evaluate the molar fractions of the folded and unfolded states. Hence, direct determination of equilibrium constants of unfolding from molar fractions was carried out. Van't Hoff plots of the equilibrium constants provided reliable thermodynamic data for SNase unfolding. Differential scanning calorimetry was used to validate this thermodynamic analysis. The presence of 0.5 m potassium mannosylglycerate caused an increase of 7 degrees C in the SNase melting temperature and a 2-fold increase in the unfolding heat capacity. Despite the considerable degree of stabilization rendered by this solute, the nature and population of protein states along unfolding were not altered in the presence of mannosylglycerate, denoting that the unfolding pathway of SNase was unaffected. The stabilization of SNase by mannosylglycerate arises from decreased unfolding entropy up to 65 degrees C and from an enthalpy increase above this temperature. In molecular terms, stabilization is interpreted as resulting from destabilization of the denatured state caused by preferential exclusion of the solute from the protein hydration shell upon unfolding, and stabilization of the native state by specific interactions. The physiological significance of charged solutes in hyperthermophiles is discussed.     

Interleukin-1 beta folding between pH 5 and 7: experimental evidence for three-state folding behavior and robust transition state positions late in folding

The thermodynamic stability and folding kinetics of the all beta-sheet protein interleukin-1beta were measured between 0 and 4 M GdmCl concentrations and pH 5-7. Native interleukin-1beta undergoes a 3.5 kcal/mol decrease in thermodynamic stability, Delta, as pH is increased from 5 to 7. The native state parameter m(NU), measuring protein destabilization/[GdmCl], remains constant between pH 5 and 7, indicating that the solvent-exposed surface area difference between the native state and unfolded ensemble is unchanged across this pH range. Similarly, pH changes between 5 and 7 decrease only the thermodynamic stability, DeltaG(H)2(O), and not the m-values, of the kinetic intermediate and transition states. This finding is shown to be consistent with transition state configurations which continue to be the high-energy configurations of the transition state in the face of changing stability conditions. A three-state folding mechanism U right arrow over left arrow I right arrow over left arrow N is shown to be sufficient in characterizing IL-1beta folding under all conditions studied. The m-values of refolding transitions are much larger than the m-values of unfolding transitions, indicating that that the fast, T(2) (U right arrow over left arrow I), and slow, T(1) (I right arrow over left arrow N), transition states are highly similar to the intermediate I and native state N, respectively. Many of the folding properties of interleukin-1beta are shared among other members of the beta-trefoil protein family, although clear differences can exist.     

Early events during folding of wild-type staphylococcal nuclease and a single-tryptophan variant studied by ultrarapid mixing

A continuous-flow mixing device with a dead time of 100 micros coupled with intrinsic tryptophan and 1-anilinonaphthalene-8-sulfonate (ANS) fluorescence was used to monitor structure formation during early stages of the folding of staphylococcal nuclease (SNase). A variant with a unique tryptophan fluorophore in the N-terminal beta-barrel domain (Trp76 SNase) was obtained by replacing the single Trp140 in wild-type SNase with His in combination with Trp substitution of Phe76. A common background of P47G, P117G and H124L mutations was chosen in order to stabilize the protein and prevent accumulation of cis proline isomers under native conditions. In contrast to WT(*) SNase, which shows no changes in tryptophan fluorescence prior to the rate-limiting folding step ( approximately 100 ms), the F76W/W140H variant shows additional changes (enhancement) during an early folding phase with a time constant of 75 micros. Both proteins exhibit a major increase in ANS fluorescence and identical rates for this early folding event. These findings are consistent with the rapid accumulation of an ensemble of states containing a loosely packed hydrophobic core involving primarily the beta-barrel domain while the specific interactions in the alpha-helical domain involving Trp140 are formed only during the final stages of folding. The fact that both variants exhibit the same number of kinetic phases with very similar rates confirms that the folding mechanism is not perturbed by the F76W/W140H mutations. However, the Trp at position 76 reports on the rapid formation of a hydrophobic cluster in the N-terminal beta-sheet region while the wild-type Trp140 is silent during this early stage of folding. Quantitative modeling of the (un)folding kinetics and thermodynamics of these two proteins versus urea concentration revealed that the F76W/W140H mutation selectively destabilizes the native state relative to WT(*) SNase while the stability of transient intermediates remains unchanged, leading to accumulation of intermediates under equilibrium conditions at moderate denaturant concentrations.     

One-state downhill versus conventional protein folding

Classical protein folding invokes a cooperative transition between distinct thermodynamic states that are individually populated at equilibrium and separated by an energy barrier. It has been proposed, however, that the small protein, BBL, undergoes one-step downhill folding whereby it folds non-cooperatively to its native state without encountering an appreciable energy barrier. Only a single conformational ensemble is populated under given conditions, and so the denatured state ensemble progressively changes into the native structure. A wide dispersion of thermal denaturation midpoints that was observed for an extrinsically labelled fragment of BBL is proposed to be evidence for its one-state, downhill folding, a phenomenon that is also suggested to be functionally important for BBL and its homologues. We found, however, that thermal denaturation of unlabelled wild-type BBL was highly cooperative, with very similar transition midpoints for the melting of secondary and tertiary interactions, as well as for individual residues when monitored by NMR. Similar results were also observed for two other homologues, E3BD and POB. Further, the extrinsic fluorophores perturbed the unfolding energetics of labelled BBL, and complicated its equilibrium behaviour. One-step downhill folding may well occur for some proteins that do not have distinct folded states but not for BBL and its well-folded homologues.     

Nonuniform chain collapse during early stages of staphylococcal nuclease folding detected by fluorescence resonance energy transfer and ultrarapid mixing methods

The development of tertiary structure during folding of staphylococcal nuclease (SNase) was studied by time‐resolved fluorescence resonance energy transfer measured using continuous‐ and stopped‐flow techniques. Variants of this two‐domain protein containing intradomain and interdomain fluorescence donor/acceptor pairs (Trp and Cys‐linked fluorophore or quencher) were prepared to probe the intradomain and interdomain structural evolution accompanying SNase folding. The intra‐domain donor/acceptor pairs are within the β‐barrel domain (Trp27/Cys64 and Trp27/Cys97) and the interdomain pair is between the α‐helical domain and the β‐barrel domain (Trp140/Cys64). Time‐resolved energy transfer efficiency accompanying folding and unfolding at different urea concentrations was measured over a time range from 30 μs to ～10 s. Information on average donor/acceptor distances at different stages of the folding process was obtained by using a quantitative kinetic modeling approach. The average distance for the donor/acceptor pairs in the β‐barrel domain decreases to nearly native values whereas that of the interdomain donor/acceptor pairs remains unchanged in the earliest intermediate (<500 μs of refolding). This indicates a rapid nonuniform collapse resulting in an ensemble of heterogeneous conformations in which the central region of the β‐barrel domain is well developed while the C‐terminal α‐helical domain remains disordered. The distance between Trp140 and Cys64 decreases to native values on the 100‐ms time scale, indicating that the α‐helical domain docks onto the preformed β‐barrel at a late stage of the folding. In addition, the unfolded state is found to be more compact under native conditions, suggesting that changes in solvent conditions may induce a nonspecific hydrophobic collapse.     

The native state conformational ensemble of the SH3 domain from alpha-spectrin.

The folding/unfolding equilibrium of the alpha-spectrin SH3 domain has been measured by NMR-detected hydrogen/deuterium exchange and by differential scanning calorimetry. Protection factors against exchange have been obtained under native conditions for more than half of the residues in the domain. Most protected residues are located at the beta-strands, the short 3(10) helix, and part of the long RT loop, whereas the loops connecting secondary structure elements show no measurable protection. Apparent stability constants per residue and their corresponding Gibbs energies have been calculated from the exchange experiments. The most stable region of the SH3 domain is defined by the central portions of the beta-strands. The peptide binding region, on the other hand, is composed of a highly stable region (residues 53-57) and a highly unstable region, the loop between residues 34-41 (n-Src loop). All residues in the domain have apparent Gibbs energies lower than the global unfolding Gibbs energy measured by differential scanning calorimetry, indicating that under our experimental conditions the amide exchange of all residues in the SH3 domain occurs primarily via local unfolding reactions. A structure-based thermodynamic analysis has allowed us to predict correctly the thermodynamics of the global unfolding of the domain and to define the ensemble of conformational states that quantitatively accounts for the observed pattern of hydrogen exchange protection. These results demonstrate that under native conditions the SH3 domain needs to be considered as an ensemble of conformations and that the hydrogen exchange data obtained under those conditions cannot be interpreted by a two-state equilibrium. The observation that specific regions of a protein are able to undergo independent local folding/unfolding reactions indicates that under native conditions the scale of cooperative interactions is regional rather than global.     

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.     

Molecular basis of co-operativity in protein folding.

The folding/unfolding transition of proteins is a highly co-operative process characterized by the presence of very few or no thermodynamically stable partially folded intermediate states. The purpose of this paper is to present a thermodynamic formalism aimed at describing quantitatively the co-operative folding behavior of proteins. In order to account for this behavior, a hierarchical algorithm aimed at evaluating the folding/unfolding partition function has been developed. This formalism defines the partition function in terms of multiple levels of interacting co-operative folding units. A co-operative folding unit is defined as a protein structural element that exhibits two-state folding/unfolding behavior. At the most fundamental level are those structural elements that behave co-operatively as a result of purely local interactions. Higher-order co-operative folding units are formed through interactions between different structural elements. The hierarchical formalism utilizes the crystallographic structure of the protein as a template to generate partially folded conformations defined in terms of co-operative folding units. The Gibbs free energy of those states and their corresponding statistical weights are then computed using experimental energetic parameters determined calorimetrically. This formalism has been applied to the case of myoglobin. It is shown that the hierarchical partition function correctly predicts the presence, energetics and co-operativity of the heat and cold denaturation transitions. The major contribution to the co-operative folding behavior arises from the solvent exposure of non-polar residues located in regions complementary to those that have undergone unfolding. This entropically uncompensated and energetically unfavorable solvent exposure characterizes all partially folded states but not the unfolded state, thus minimizing the population of partially folded intermediates throughout the folding/unfolding transition.     

Searching for folding initiation sites of staphylococcal nuclease: a study of N-terminal short fragments

The N-terminal short fragments of staphylococcal nuclease (SNase), SNase20, SNase28, and SNase36, corresponding to the sequence regions, Ala1-Gly20, Ala1-Lys28, and Ala1-Leu36, respectively, as well as an 8-residue peptide (Ala17-Ile18-Asp19-Gly20-Asp21-Thr22-Val23-Lys24) have been synthesized. The conformational states of these fragments were investigated using CD and NMR spectroscopy in aqueous solution and in trifluoroethanol (TFE)-H(2)O mixture. SNase20 containing a sequence corresponding to a bent peptide in native SNase shows a transient population of bend-like conformation around Ala12-Thr13-Leu14 in TFE-H(2)O mixture. The sequence region of Ala17-Thr22 of SNase28 displays a localized propensity for turn-like conformation in both aqueous solution and TFE-H(2)O mixture. The conformational ensemble of SNase36 in aqueous solution includes populated turn-like conformations localized in sequence regions Ala17-Thr22 and Tyr27-Gln30. The analysis suggests that these sequence regions, which form the regular secondary structures in native protein, may serve as the folding nucleation sites of SNase fragments of different chain lengths starting from the N-terminal end. Thus, the formation of bend- and turn-like conformations of these sequence regions may be involved in the early folding events of the SNase polypeptide chain in vitro.     

NMR investigations on residue level unfolding thermodynamics in DLC8 dimer by temperature dependent native state hydrogen exchange

Understanding protein stability at residue level detail in the native state ensemble of a protein is crucial to understanding its biological function. At the same time, deriving thermodynamic parameters using conventional spectroscopic and calorimetric techniques remains a major challenge for some proteins due to protein aggregation and irreversibility of denaturation at higher temperature values. In this regard, we describe here the NMR investigations on the conformational stabilities and related thermodynamic parameters such as local unfolding enthalpies, heat capacities and transition midpoints in DLC8 dimer, by using temperature dependent native state hydrogen exchange; this protein aggregates at high (>65°C) temperatures. The stability (free energy) of the native state was found to vary substantially with temperature at every residue. Significant differences were found in the thermodynamic parameters at individual residue sites indicating that the local environments in the protein structure would respond differently to external perturbations; this reflects on plasticity differences in different regions of the protein. Further, comparison of this data with similar data obtained from GdnHCl dependent native state hydrogen exchange indicated many similarities at residue level, suggesting that local unfolding transitions may be similar in both the cases. This has implications for the folding/unfolding mechanisms of the protein. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

What causes hyperfluorescence: folding intermediates or conformationally flexible native states?

Hyperfluorescent intensity maxima during protein unfolding titrations are often taken as a sign for a thermodynamic folding intermediate. Here we explore another possibility: that hyperfluorescence could be the signature of a "pretransition" conformationally loosened native state. To model such native states, we study mutants of a fluorescent ubiquitin variant, placing cavities at various distances from the tryptophan fluorophore. We examine the correlation between protein flexibility and enhanced fluorescence intensity by using circular dichroism, fluorescence intensity unfolding titrations, fluorescence anisotropy measurements, and molecular dynamics. Based on experiment and simulation, we propose a simple model for hyperfluorescence in terms of static and dynamic conformational properties of the native state during unfolding. Apomyoglobin denaturant unfolding and phosphoglycerate kinase cold denaturation are discussed as examples. Our results do not preclude the existence of thermodynamic intermediates but do raise caution that by itself, hyperfluorescence during unfolding titrations is not conclusive proof of thermodynamic folding intermediates.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

Aggregation of granulocyte colony stimulating factor under physiological conditions: characterization and thermodynamic inhibition

We have investigated the aggregation of recombinant human granulocyte colony stimulating factor (rhGCSF), a protein that rapidly aggregates and precipitates at pH 6.9 and 37 degrees C. We observed that native monomeric rhGCSF reversibly forms a dimer under physiological conditions and that this dimeric species does not participate in the irreversible aggregation process. Sucrose, a thermodynamic stabilizer, inhibits the aggregation of rhGCSF. We postulate that sucrose acts by reducing the concentration of structurally expanded species, consistent with the hypothesis that preferential exclusion favors most compact species in the native state ensemble. Thermodynamic stability data from unfolding curves and hydrogen-deuterium exchange experimental results support the above hypothesis. Thus, the strategy of stabilizing the native state of the protein under physiological conditions using thermodynamic stabilizers, especially ligands binding with high affinity to the native state, is expected to protect against protein aggregation occurring under such nonperturbing solution conditions.     

Compact dimension of denatured states of staphylococcal nuclease

Fluorescence and circular dichroism stopped-flow have been widely used to determine the kinetics of protein folding including folding rates and possible folding pathways. Yet, these measurements are not able to provide spatial information of protein folding/unfolding. Especially, conformations of denatured states cannot be elaborated in detail. In this study, we apply the method of fluorescence energy transfer with a stopped-flow technique to study global structural changes of the staphylococcal nuclease (SNase) mutant K45C, where lysine 45 is replaced by cysteine, during folding and unfolding. By labeling the thiol group of cysteine with TNB (5,5'-dithiobis-2-nitrobenzoic acid) as an energy acceptor and the tryptophan at position 140 as a donor, distance changes between the acceptor and the donor during folding and unfolding are measured from the efficiency of energy transfer. Results indicate that the denatured states of SNase are highly compact regardless of how the denatured states (pH-induced or GdmCl-induced) are induced. The range of distance changes between two probes is between 25.6 and 25.4 A while it is 20.4 A for the native state. Furthermore, the folding process consists of three kinetic phases while the unfolding process is a single phase. These observations agree with our previous sequential model: N(0) left arrow over right arrow D(1) left arrow over right arrow D(2) left arrow over right arrow D(3) (Chen et al., J Mol Biol 1991;220:771-778). The efficiency of protein folding may be attributed to initiating the folding process from these compact denatured structures.     

Deconvoluting Protein (Un)folding Structural Ensembles Using X-Ray Scattering,Nuclear Magnetic Resonance Spectroscopy and Molecular Dynamics Simulation

The folding and unfolding of protein domains is an apparently cooperative process, but transient intermediates have been detected in some cases. Such (un)folding intermediates are challenging to investigate structurally as they are typically not long-lived and their role in the (un)folding reaction has often been questioned. One of the most well studied (un)folding pathways is that of Drosophila melanogaster Engrailed homeodomain (EnHD): this 61-residue protein forms a three helix bundle in the native state and folds via a helical intermediate. Here we used molecular dynamics simulations to derive sample conformations of EnHD in the native, intermediate, and unfolded states and selected the relevant structural clusters by comparing to small/wide angle X-ray scattering data at four different temperatures. The results are corroborated using residual dipolar couplings determined by NMR spectroscopy. Our results agree well with the previously proposed (un)folding pathway. However, they also suggest that the fully unfolded state is present at a low fraction throughout the investigated temperature interval, and that the (un)folding intermediate is highly populated at the thermal midpoint in line with the view that this intermediate can be regarded to be the denatured state under physiological conditions. Further, the combination of ensemble structural techniques with MD allows for determination of structures and populations of multiple interconverting structures in solution.     

Highly divergent dihydrofolate reductases conserve complex folding mechanisms.

To test the hypothesis that protein folding mechanisms are better conserved than amino acid sequences, the mechanisms for dihydrofolate reductases (DHFR) from human (hs), Escherichia coli (ec) and Lactobacillus casei (lc) were elucidated and compared using intrinsic Trp fluorescence and fluorescence-detected 8-anilino-1-naphthalenesulfonate (ANS) binding. The development of the native state was monitored using either methotrexate (absorbance at 380 nm) or NADPH (extrinsic fluorescence) binding. All three homologs displayed complex unfolding and refolding kinetic mechanisms that involved partially folded states and multiple energy barriers. Although the pairwise sequence identities are less than 30 %, folding to the native state occurs via parallel folding channels and involves two types of on-pathway kinetic intermediates for all three homologs. The first ensemble of kinetic intermediates, detected within a few milliseconds, has significant secondary structure and exposed hydrophobic cores. The second ensemble is obligatory and has native-like side-chain packing in a hydrophobic core; however, these intermediates are unable to bind active-site ligands. The formation of the ensemble of native states occurs via three channels for hsDHFR, and four channels for lcDHFR and ecDHFR. The binding of active-site ligands (methotrexate and NADPH) accompanies the rate-limiting formation of the native ensemble. The conservation of the fast, intermediate and slow-folding events for this complex alpha/beta motif provides convincing evidence for the hypothesis that evolutionarily related proteins achieve the same fold via similar pathways.     

Structural analysis of the rate-limiting transition states in the folding of Im7 and Im9: similarities and differences in the folding of homologous proteins

The bacterial immunity proteins Im7 and Im9 fold with mechanisms of different kinetic complexity. Whilst Im9 folds in a two-state transition at pH 7.0 and 10 degrees C, Im7 populates an on-pathway intermediate under these conditions. In order to assess the role of sequence versus topology in the folding of these proteins, and to analyse the effect of populating an intermediate on the landscape for folding, we have determined the conformational properties of the rate-limiting transition state for Im9 folding/unfolding using Phi(F)-value analysis and have compared the results with similar data obtained previously for Im7. The data show that the rate-limiting transition states for Im9 and Im7 folding/unfolding are similar: both are compact (beta(T)=0.94 and 0.89, respectively) and contain three of the four native helices docked around a specific hydrophobic core. Significant differences are observed, however, in the magnitude of the Phi(F)-values obtained for the two proteins. Of the 20 residues studied in both proteins, ten have Phi(F)-values in Im7 that exceed those in Im9 by more than 0.2, and of these five differ by more than 0.4. The data suggest that the population of an intermediate in Im7 results in folding via a transition state ensemble that is conformationally restricted relative to that of Im9. The data are consistent with the view that topology is an important determinant of folding. Importantly, however, they also demonstrate that while the folding transition state may be conserved in homologous proteins that fold with two and three-state kinetics, the population of an intermediate can have a significant effect on the breadth of the transition state ensemble.     

Thermal unfolding simulations of a multimeric protein--transition state and unfolding pathways

The folding of an oligomeric protein poses an extra challenge to the folding problem because the protein not only has to fold correctly; it has to avoid nonproductive aggregation. We have carried out over 100 molecular dynamics simulations using an implicit solvation model at different temperatures to study the unfolding of one of the smallest known tetramers, p53 tetramerization domain (p53tet). We found that unfolding started with disruption of the native tetrameric hydrophobic core. The transition state for the tetramer to dimer transition was characterized as a diverse ensemble of different structures using Phi value analysis in quantitative agreement with experimental data. Despite the diversity, the ensemble was still native-like with common features such as partially exposed tetramer hydrophobic core and shifts in the dimer-dimer arrangements. After passing the transition state, the secondary and tertiary structures continued to unfold until the primary dimers broke free. The free dimer had little secondary structure left and the final free monomers were random-coil like. Both the transition states and the unfolding pathways from these trajectories were very diverse, in agreement with the new view of protein folding. The multiple simulations showed that the folding of p53tet is a mixture of the framework and nucleation-condensation mechanisms and the folding is coupled to the complex formation. We have also calculated the entropy and effective energy for the different states along the unfolding pathway and found that the tetramerization is stabilized by hydrophobic interactions.