Robustness of downhill folding: guidelines for the analysis of equilibrium folding experiments on small proteins

Previously, we identified the protein BBL as a downhill folder. This conclusion was based on the statistical mechanical analysis of equilibrium experiments performed in two variants of BBL, one with a fluorescent label at the N-terminus, and another one labeled at both ends. A recent report has claimed that our results are an artifact of label-induced aggregation and that BBL with no fluorescent labels and a longer N-terminal tail folds in a two-state fashion. Here, we show that singly and doubly labeled BBL do not aggregate, unfold reversibly, and have the same thermodynamic properties when studied under appropriate experimental conditions (e.g., our original conditions (1)). With an elementary analysis of the available data on the nonlabeled BBL (2), we also show that this slightly more stable BBL variant is not a two-state folder. We discuss the problems that led to its previous misclassification and how they can be avoided. Finally, we investigate the equilibrium unfolding of the singly labeled BBL with both ends protected by acetylation and amidation. This variant has the same thermodynamic stability of the nonlabeled BBL and displays all the equilibrium signatures of downhill folding. From all these observations, we conclude that fluorescent labels do not perturb the thermodynamic properties of BBL, which consistently folds downhill regardless of its stability and specific protein tails. The work on BBL illustrates the shortcomings of applying conventional procedures intended to distinguish between two-state and three-state folding models to small fast-folding proteins.     

Observation of noncooperative folding thermodynamics in simulations of 1BBL

One of the predictions of the energy landscape theory of protein folding is the possibility of barrierless, “downhill” folding under certain conditions. The protein 1BBL has been proposed to fold by such a downhill mechanism, though this is a matter of some dispute. We carried out extensive replica exchange molecular dynamics simulations on 1BBL in explicit solvent to address this controversy and provide a microscopic picture of its folding thermodynamics. Our simulations show two distinct structural transitions in the folding of 1BBL. A low-temperature transition involves a disordering of the protein's tertiary structure without loss of secondary structure. A distinct, higher temperature transition involves the complete loss of secondary structure and dissolution of the hydrophobic core. In contrast, control simulations of the 1BBL homolog E3BD show a single high temperature unfolding transition. Further simulations of 1BBL at high ionic strength show a significant destabilization of helix II but not helix I, suggesting that the apparent folding cooperativity of 1BBL may be highly dependent on experimental conditions. Although our simulations cannot provide definitive evidence of downhill folding in 1BBL, they clearly show evidence of a complex, non-two-state folding process.     

Downhill versus Barrier-Limited Folding of BBL: 3. Heterogeneity of the Native State of the BBL Peripheral Subunit Binding Domain and Its Implications for Folding Mechanisms

Protein folding studies are generally predicated on Anfinsen's dogma that there is a unique native state of a protein. However, this is not always the case. NMR measurements of BBL, for example, find a decrease in helicity of helix 2 surrounding His166 on its protonation, which, with other experimental data, suggests that the native state can occupy two or more conformations. Here, we analysed the native structure of BBL as a function of pH, temperature and ionic strength, along with a truncated BBL construct, by extensive all-atom molecular dynamics simulations in explicit solvent, corresponding to at least 400 ns of trajectories collected for each set of conditions. The native state was heterogeneous under a variety of conditions, consisting of two predominant conformations. This equilibrium changed with conditions: protonation of His166 at low pH shifted the equilibrium in favour of a less ordered conformer, while high ionic strength at neutral pH shifted the equilibrium to a more ordered conformer. Furthermore, high temperature and truncation of the sequence also shifted the equilibrium toward the less ordered conformer. Importantly, conformational heterogeneity in a native structure that changes with conditions will lead to deviations from the classic two-state behaviour during the barrier-limited unfolding of a protein. In particular, some regions of the protein will appear to unfold asynchronously and some residues will have anomalous thermal titration curves and unusual baseline behaviour monitored microscopically by NMR spectroscopy and macroscopically by calorimetry and other techniques. Such data could otherwise be interpreted as evidence for barrier-free downhill folding. Any biological significance of downhill folding of BBL appears to be ruled out by recent crystallographic studies on the reaction cycle of the BBL-equivalent domain in a pyruvate dehydrogenase multienzyme complex in which the domain remains of constant structure.     

Observation of two families of folding pathways of BBL

BBL is an independent folding domain of a large multienzyme complex, 2-oxoglutarate dehydrogenase. The folding mechanism of BBL is under debate between the views of noncooperative downhill-type and classical two-state. Extensive replica exchange molecular dynamics simulations of BBL in explicit solvent have shown some non-two-state behaviors despite no definitive evidence of downhill folding. In this work, we postprocess the replica exchange data using our roadmap-based MaxFlux reaction path algorithm to reveal atomically detailed folding pathways. A connected graph is used to organize and visualize the folding pathways initiated from random coils. High structural and transition heterogeneity is seen in the early stage of folding. Two main parallel folding pathways emerge in the later stage; one path shows that tertiary contact and helix formation develop at different stages of folding, whereas the other path exhibits concurrence of secondary and tertiary structure formation to some extent. Because the native state of BBL is sensitive to experimental conditions, we speculate that the relative predominance of the two pathways may vary with the protein construct and solvent conditions, possibly leading to the seeming discrepancy of experimental results. Our roadmap-based reaction path algorithm is a general tool to extract path information from replica exchange.     

Criteria for downhill protein folding: calorimetry, chevron plot, kinetic relaxation, and single-molecule radius of gyration in chain models with subdued degrees of cooperativity

Recent investigations of possible downhill folding of small proteins such as BBL have focused on the thermodynamics of non-two-state, "barrierless" folding/denaturation transitions. Downhill folding is noncooperative and thermodynamically "one-state," a phenomenon underpinned by a unimodal conformational distribution over chain properties such as enthalpy, hydrophobic exposure, and conformational dimension. In contrast, corresponding distributions for cooperative two-state folding are bimodal with well-separated population peaks. Using simplified atomic modeling of a three-helix bundle-in a scheme that accounts for hydrophobic interactions and hydrogen bonding-and coarse-grained C(alpha) models of four real proteins with various degrees of cooperativity, we evaluate the effectiveness of several observables at defining the underlying distribution. Bimodal distributions generally lead to sharper transitions, with a higher heat capacity peak at the transition midpoint, compared with unimodal distributions. However, the observation of a sigmoidal transition is not a reliable criterion for two-state behavior, and the heat capacity baselines, used to determine the van't Hoff and calorimetric enthalpies of the transition, can introduce ambiguity. Interestingly we find that, if the distribution of the single-molecule radius of gyration were available, it would permit discrimination between unimodal and bimodal underlying distributions. We investigate kinetic implications of thermodynamic noncooperativity using Langevin dynamics. Despite substantial chevron rollovers, the relaxation of the models considered is essentially single-exponential over an extended range of native stabilities. Consistent with experiments, significant deviations from single-exponential behavior occur only under strongly folding conditions.     

The Effect of Electrostatics on the Marginal Cooperativity of an Ultrafast Folding Protein

Proteins fold up by coordinating the different segments of their polypeptide chain through a network of weak cooperative interactions. Such cooperativity results in unfolding curves that are typically sigmoidal. However, we still do not know what factors modulate folding cooperativity or the minimal amount that ensures folding into specific three-dimensional structures. Here, we address these issues on BBL, a small helical protein that folds in microseconds via a marginally cooperative downhill process (Li, P., Oliva, F. Y., Naganathan, A. N., and Muñoz, V. (2009) Proc. Natl. Acad. Sci. USA. 106, 103–108). Particularly, we explore the effects of salt-induced screening of the electrostatic interactions in BBL at neutral pH and in acid-denatured BBL. Our results show that electrostatic screening stabilizes the native state of the neutral and protonated forms, inducing complete refolding of acid-denatured BBL. Furthermore, without net electrostatic interactions, the unfolding process becomes much less cooperative, as judged by the broadness of the equilibrium unfolding curve and the relaxation rate. Our experiments show that the marginally cooperative unfolding of BBL can still be made twice as broad while the protein retains its ability to fold into the native three-dimensional structure in microseconds. This result demonstrates experimentally that efficient folding does not require cooperativity, confirming predictions from theory and computer simulations and challenging the conventional biochemical paradigm. Furthermore, we conclude that electrostatic interactions are an important factor in determining folding cooperativity. Thus, electrostatic modulation by pH-salt and/or mutagenesis of charged residues emerges as an attractive tool for tuning folding cooperativity.     

A photoprotection strategy for microsecond-resolution single-molecule fluorescence spectroscopy

Time resolution of current single-molecule fluorescence techniques is limited to milliseconds because of dye blinking and bleaching. Here we introduce a photoprotection strategy that affords microsecond resolution by combining efficient triplet quenching by oxygen and Trolox with minimized bleaching via the oxygen radical scavenger cysteamine. Using this approach we resolved the single-molecule microsecond conformational fluctuations of two proteins: the two-state folder α-spectrin SH3 domain and the ultrafast downhill folder BBL.     

Folding Simulations of a De Novo Designed Protein with a βαβ Fold

βαβ structural motifs are commonly used building blocks in protein structures containing parallel β-sheets. However, to our knowledge, no stand-alone βαβ structure has been observed in nature to date. Recently, for the first time that we know of, a small protein with an independent βαβ structure (DS119) was successfully designed in our laboratory. To understand the folding mechanism of DS119, in the study described here, we carried out all-atom molecular dynamics and coarse-grained simulations to investigate its folding pathways and energy landscape. From all-atom simulations, we successfully observed the folding event and got a stable folded structure with a minimal root mean-square deviation of 2.6 Å with respect to the NMR structure. The folding process can be described as a fast collapse phase followed by rapid formation of the central helix, and then slow formation of a parallel β-sheet. By using a native-centric Gō-like model, the cooperativity of the system was characterized in terms of the calorimetric criterion, sigmoidal transitions, conformation distribution shifts, and free-energy profiles. DS119 was found to be an incipient downhill folder that folds more cooperatively than a downhill folder, but less cooperatively than a two-state folder. This may reflect the balance between the two structural elements of DS119: the rapidly formed α-helix and the slowly formed parallel β-sheet. Folding times estimated from both the all-atom simulations and the coarse-grained model were at microsecond level, making DS119 another fast folder. Compared to fast folders reported previously, DS119 is, to the best of our knowledge, the first that exhibits a parallel β-sheet.     

Heterogeneous folding of the trpzip hairpin: full atom simulation and experiment

The beta-hairpin trpzip2 can be tuned continuously from a two-state folder to folding on a rough energy landscape without a dominant refolding barrier. At high denaturant concentration, this extremely stable peptide exhibits a single apparent "two-state" transition temperature when monitored by different spectroscopic techniques. However, under optimal folding conditions the hairpin undergoes an unusual folding process with three clusters of melting transitions ranging from 15 degrees C to 160 degrees C, as monitored by 12 different experimental and computational observables. We explain this behavior in terms of a rough free energy landscape of the unfolded peptide caused by multiple tryptophan interactions and alternative backbone conformations. The landscape is mapped out by potentials of mean force derived from replica-exchange molecular dynamics simulations. Implications for deducing cooperativity from denaturant titrations, for the origin of folding cooperativity, and for the folding of thermophilic proteins are pointed out. trpzip is an excellent small tunable model system for the glass-like folding transitions predicted by landscape theory.     

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.     

All-atom replica exchange molecular simulation of protein BBL

Downhill folding is one of the most important predictions of energy landscape theory. Recently, the Escherichia coli 2-oxoglutarate dehydrogenase PSBD was described as a first example of global downhill folding (Garcia-Mira et al., Science 2002;298:2191), classification that has been later subject of significant controversy. To help resolve this problem, by using intensive all-atom simulation with explicit water model and the replica exchange method, we sample the phase space of protein BBL and depict the free energy landscape. We give an estimate of the free energy barrier height of 1-2 k(B)T, dependent on the way the energy landscape is projected. We also study the conformational distribution of the transition region and find that the three helices generally take the similar positions as that in the native states whereas their spatial orientations show large variability. We further detect the inconsistency between different signals by individually fitting the thermal denaturation curves of five structural features using two-state model, which gives a wide spread melting temperature of 19 K. All of these features are consistent with a picture of folding with very low cooperativities. Compared with the experimental data (Sadqi et al., Nature 2006; 442:317), our results indicate that the Naf-BBL (pH5.3) may have an even lower barrier height and cooperativity.     

Solvation effects and driving forces for protein thermodynamic and kinetic cooperativity: how adequate is native-centric topological modeling?

What energetic and solvation effects underlie the remarkable two-state thermodynamics and folding/unfolding kinetics of small single-domain proteins? To address this question, we investigate the folding and unfolding of a hierarchy of continuum Langevin dynamics models of chymotrypsin inhibitor 2. We find that residue-based additive Gō-like contact energies, although native-centric, are by themselves insufficient for protein-like calorimetric two-state cooperativity. Further native biases by local conformational preferences are necessary for protein-like thermodynamics. Kinetically, however, even models with both contact and local native-centric energies do not produce simple two-state chevron plots. Thus a model protein's thermodynamic cooperativity is not sufficient for simple two-state kinetics. The models tested appear to have increasing internal friction with increasing native stability, leading to chevron rollovers that typify kinetics that are commonly referred to as non-two-state. The free energy profiles of these models are found to be sensitive to the choice of native contacts and the presumed spatial ranges of the contact interactions. Motivated by explicit-water considerations, we explore recent treatments of solvent granularity that incorporate desolvation free energy barriers into effective implicit-solvent intraprotein interactions. This additional feature reduces both folding and unfolding rates vis-à-vis that of the corresponding models without desolvation barriers, but the kinetics remain non-two-state. Taken together, our observations suggest that interaction mechanisms more intricate than simple Gō-like constructs and pairwise additive solvation-like contributions are needed to rationalize some of the most basic generic protein properties. Therefore, as experimental constraints on protein chain models, requiring a consistent account of protein-like thermodynamic and kinetic cooperativity can be more stringent and productive for some applications than simply requiring a model heteropolymer to fold to a target structure.     

Predicting protein folding rates from geometric contact and amino acid sequence

Protein folding speeds are known to vary over more than eight orders of magnitude. Plaxco, Simons, and Baker (see References) first showed a correlation of folding speed with the topology of the native protein. That and subsequent studies showed, if the native structure of a protein is known, its folding speed can be predicted reasonably well through a correlation with the "localness" of the contacts in the protein. In the present work, we develop a related measure, the geometric contact number, N (alpha), which is the number of nonlocal contacts that are well-packed, by a Voronoi criterion. We find, first, that in 80 proteins, the largest such database of proteins yet studied, N (alpha) is a consistently excellent predictor of folding speeds of both two-state fast folders and more complex multistate folders. Second, we show that folding rates can also be predicted from amino acid sequences directly, without the need to know the native topology or other structural properties.     

Slow Proton Transfer Coupled to Unfolding Explains the Puzzling Results of Single-Molecule Experiments on BBL,a Paradigmatic Downhill Folding Protein

A battery of thermodynamic, kinetic, and structural approaches has indicated that the small α-helical protein BBL folds-unfolds via the one-state downhill scenario. Yet, single-molecule fluorescence spectroscopy offers a more conflicting view. Single-molecule experiments at pH 6 show a unique half-unfolded conformational ensemble at mid denaturation, whereas other experiments performed at higher pH show a bimodal distribution, as expected for two-state folding. Here we use thermodynamic and laser T-jump kinetic experiments combined with theoretical modeling to investigate the pH dependence of BBL stability, folding kinetics and mechanism within the pH 6–11 range. We find that BBL unfolding is tightly coupled to the protonation of one of its residues with an apparent pK_a of ∼7. Therefore, in chemical denaturation experiments around neutral pH BBL unfolds gradually, and also converts in binary fashion to the protonated species. Moreover, under the single-molecule experimental conditions (denaturant midpoint and 279 K), we observe that proton transfer is much slower than the ∼15 microseconds folding-unfolding kinetics of BBL. The relaxation kinetics is distinctly biphasic, and the overall relaxation time (i.e. 0.2–0.5 ms) becomes controlled by the proton transfer step. We then show that a simple theoretical model of protein folding coupled to proton transfer explains quantitatively all these results as well as the two sets of single-molecule experiments, including their more puzzling features. Interestingly, this analysis suggests that BBL unfolds following a one-state downhill folding mechanism at all conditions. Accordingly, the source of the bimodal distributions observed during denaturation at pH 7–8 is the splitting of the unique conformational ensemble of BBL onto two slowly inter-converting protonation species. Both, the unprotonated and protonated species unfold gradually (one-state downhill), but they exhibit different degree of unfolding at any given condition because the native structure is less stable for the protonated form.     

Folding of the protein domain hbSBD

The folding of the alpha-helix domain hbSBD of the mammalian mitochondrial branched-chain alpha-ketoacid dehydrogenase complex is studied by the circular dichroism technique in absence of urea. Thermal denaturation is used to evaluate various thermodynamic parameters defining the equilibrium unfolding, which is well described by the two-state model with the folding temperature T(F) = 317.8 +/- 1.95 K and the enthalpy change DeltaH(G) = 19.67 +/- 2.67 kcal/mol. The folding is also studied numerically using the off-lattice coarse-grained Go model and the Langevin dynamics. The obtained results, including the population of the native basin, the free-energy landscape as a function of the number of native contacts, and the folding kinetics, also suggest that the hbSBD domain is a two-state folder. These results are consistent with the biological function of hbSBD in branched-chain alpha-ketoacid dehydrogenase.     

On the relation between native geometry and conformational plasticity

In protein folding the term plasticity refers to the number of alternative folding pathways encountered in response to free energy perturbations such as those induced by mutation. Here we explore the relation between folding plasticity and a gross, generic feature of the native geometry, namely, the relative number of local and non-local native contacts. The results from our study, which is based on Monte Carlo simulations of simple lattice proteins, show that folding to a structure that is rich in local contacts is considerably more plastic than folding to a native geometry characterized by having a very large number of long-range contacts (i.e., contacts between amino acids that are separated by more than 12 units of backbone distance). The smaller folding plasticity of native geometries is probably a direct consequence of their higher folding cooperativity that renders the folding reaction more robust against single- and multiple-point mutations.     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

Downhill versus Barrier-Limited Folding of BBL 2: Mechanistic Insights from Kinetics of Folding Monitored by Independent Tryptophan Probes

Barrier-free downhill folding has been proposed for the peripheral subunit-binding domain BBL. To date, ultrafast kinetic experiments on BBL, which are crucial for a mechanistic understanding of folding, have been hampered by the lack of good intrinsic spectroscopic probes. Here, we present a detailed kinetic characterization of three single-point tryptophan mutants of BBL that have suitable fluorescence properties for following microsecond and nanosecond folding kinetics using temperature jump fluorescence spectroscopy. Experiments were performed at pH 7, which is optimal for stability and minimizes complications that arise from the presence of an alternative native-state conformation of BBL at lower pH. We examined the dependence of rate and equilibrium constants on concentration of denaturant and found that they follow well-established laws allowing kinetic transients to be related to events in folding and compared with equilibrium data. Logarithms of rate constants versus denaturant concentration yielded plots (chevrons) that are characteristic of barrier-limited folding for all mutants investigated, including a truncated sequence that was previously used in the proposal of downhill folding. The thermodynamic quantities calculated from the rate constants were in excellent agreement with those directly determined from equilibrium denaturation based on empirical two-state equations. We found that sequence truncation of BBL as used in studies proposing downhill folding leads to a large loss in helical content and protein stability, which were exacerbated at the low pH used in those studies. The kinetics and equilibria of folding of BBL fit to conventional barrier-limited kinetics.     

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.