Ultra-fast barrier-limited folding in the peripheral subunit-binding domain family

We have determined the solution structures, equilibrium properties and ultra-fast folding kinetics for three bacterial homologues of the peripheral subunit-binding domain (PSBD) family. The mesophilic homologue, BBL, was less stable than the thermophilic and hyper-thermophilic variants (E3BD and POB, respectively). The broad unfolding transitions of each PSBD, when probed by different techniques, were essentially superimposable, consistent with co-operative denaturation. Temperature-jump and continuous-flow fluorescence methods were used to measure the folding kinetics for E3BD, POB and BBL. E3BD folded fairly rapidly at 298K (folding half-time approximately 25 micros) and BBL and POB folded even faster (folding half-times approximately 3-5 micros). The variations in equilibrium and kinetic behaviour observed for the PSBD family resembles that of the homeodomain family, where the folding pattern changes from apparent two-state transitions to multi-state kinetics as the denatured state becomes more structured. The faster folding of POB may be a consequence of its higher propensity to form helical structure in the region corresponding to the folding nucleus of E3BD. The ultra-fast folding of BBL appears to be a consequence of residual structure in the denatured ensemble, as with engrailed homeodomain. We discuss issues concerning "one-state", downhill folding, and find no evidence for, and strong evidence against, it occurring in these PSBDs. The shorter construct used previously for BBL was destabilized significantly and the stability further perturbed by the introduction of fluorescent probes. Thermal titrations for 11 side-chains scattered around the protein, when probed by (13)C-NMR experiments, could be fit globally to a common co-operative transition.     

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.     

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.     

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.     

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 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.     

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

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

Folding with downhill behavior and low cooperativity of proteins

The downhill folding observed experimentally for a small protein BBL is studied using off-lattice Gō-like model. Our simulations show that the downhill folding has low cooperativity and is barrierless, which is consistent with the experimental findings. As an example of comparison in detail, the two-state folding behavior of proteins, for example, protein CI2, is also simulated. By observing the formation of contacts between the residues for these two proteins, it is found that the physical origin of the downhill folding is due to the deficiency of nonlocal contacts which determine the folding cooperatively. From a statistics on contacts of the native structures of 17 well-studied proteins and the calculation of their cooperativity factors kappa2 based on folding simulations, a strong correlation between the number of nonlocal contacts per residue NN and the factors kappa2 is obtained. Protein BBL with a value of NN = 0.73 has the lowest cooperativity factor kappa2 = 0.34 among all 17 proteins. A crossover around NNc approximately 0.9 could be defined to separate the two-state folders and the downhill folder roughly. A protein would behave downhill folding when its NN = NNc. For proteins with their NN values are about (or slightly larger than) NNc, the folding behaves with low cooperativity and the barriers are small, showing a weak two-state behavior or a downhill-like behavior. Furthermore, simulations on mutants of a two-state folder show that a mutant becomes a downhill folder when its NN is reduced to a value smaller than NNc. These could enable us to identify the downhill folding or the cooperative two-state folding behavior solely from the native structures of proteins.     

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.     

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.     

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.     

Determining denaturation midpoints in multiprobe equilibrium protein folding experiments

Multiprobe equilibrium unfolding experiments in the downhill regime (i.e., maximal barrier < 3 RT) can resolve the folding process with atomic resolution [ Munoz ( 2002) Int. J. Quantum Chem. 90, 1522 -1528] . Such information is extracted from hundreds of heterogeneous atomic equilibrium unfolding curves, which are characterized according to their denaturation midpoint (e.g., T m for thermal denaturation). Using statistical methods, we analyze T m accuracy when determined from the extremum of the derivative of the unfolding curve and from two-state fits under different sets of simulated experimental conditions. We develop simple procedures to discriminate between real unfolding heterogeneity at the atomic level and experimental uncertainty in the single T m of conventional two-state folding. We apply these procedures to the recently published multiprobe NMR experiments of BBL [ Sadqi et al. ( 2006) Nature 442, 317 -321 ] and conclude that for the 122 single transition atomic unfolding curves reported for this protein the mean T m accuracy is better than 1.8 K for both methods, compared to the 60 K spread in T m determined experimentally. Importantly, we also find that when the pre- or posttransition baseline is incomplete, the two-state fits systematically drift the estimated T m value toward the center of the experimental range. Therefore, the reported 60 K T m spread in BBL is in fact a lower limit. The derivative method is significantly less sensitive to this problem and thus is a better choice for multiprobe experiments with a broad T m distribution. The results we obtain in this work lay the foundations for the quantitative analysis of future multiprobe unfolding experiments in fast-folding proteins.     

Stability and folding kinetics of a ubiquitin mutant with a strong propensity for nonnative beta-hairpin conformation in the unfolded state

A F45W mutant of yeast ubiquitin has been used as a model system to examine the effects of nonnative local interactions on protein folding and stability. Mutating the native TLTGK G-bulged type I turn in the N-terminal beta-hairpin to NPDG stabilizes a nonnative beta-strand alignment in the isolated peptide fragment. However, NMR structural analysis of the native and mutant proteins shows that the NPDG mutant is forced to adopt the native beta-strand alignment and an unfavorable type I NPDG turn. The mutant is significantly less stable (approximately 9 kJ mol(-1)) and folds 30 times slower than the native sequence, demonstrating that local interactions can modulate protein stability and that attainment of a nativelike beta-hairpin conformation in the transition state ensemble is frustrated by the turn mutations. Surprising, alcoholic cosolvents [5-10% (v/v) TFE] are shown to accelerate the folding rate of the NPDG mutant. We conclude, backed-up by NMR data on the peptide fragments, that even though nonnative states in the denatured ensemble are highly populated and their stability further enhanced in the presence of cosolvents, the simultaneous increase in the proportion of nativelike secondary structure (hairpin or helix), in rapid equilibrium with nonnative states, is sufficient to accelerate the folding process. It is evident that modulating local interactions and increasing nonnative secondary structure propensities can change protein stability and folding kinetics. However, nonlocal contacts formed in the global cooperative folding event appear to determine structural specificity.     

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.     

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.     

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.     

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.     

The stability and folding process of amyloidogenic mutant human lysozymes.

Amyloid deposits are frequently formed by mutant proteins that have a lower stability than the wild-type proteins. Some reports, however, have shown that mutant-induced thermodynamic destabilization is not always a general mechanism of amyloid formation. To obtain a better understanding of the mechanism of amyloid fibril formation, we show in this study that equilibrium and kinetic refolding-unfolding reaction experiments with two amyloidogenic mutant human lysozymes (I56T and D67H) yield folding pathways that can be drawn as Gibbs energy diagrams. The equilibrium stabilities between the native and denatured states of both mutant proteins were decreased, but the degrees of instability were different. The Gibbs energy diagrams of the folding process reveal that the Gibbs energy change between the native and folding intermediate states was similar for both proteins, and also that the activation Gibbs energy change from the native state to the transition state decreased. Our results confirm that the tendency to favor the intermediate of denaturation facilitates amyloid formation by the mutant human lysozymes more than equilibrium destabilization between the native and completely denatured states does.     

Carboxyl pKa Values and Acid Denaturation of BBL

The protein BBL undergoes structural transitions and acid denaturation between pH 1.2 and 8.0. Using NMR spectroscopy, we measured the pK_a values of all the carboxylic residues in this pH range. We employed ¹³C direct-detection two-dimensional IPAP (in-phase antiphase) CACO NMR spectroscopy to monitor the ionization state of different carboxylic groups and demonstrated its advantages over other NMR techniques in measuring pK_a values of carboxylic residues. The two residues Glu161 and Asp162 had significantly lowered pK_a values, showing that these residues are involved in a network of stabilizing electrostatic interactions, as is His166. The other carboxylates had unperturbed values. The pH dependence of the free energy of denaturation was described quantitatively by the ionizations of those three residues of perturbed pK_a, and, using thermodynamic cycles, we could calculate their pK_as in the native and denatured states as well as the equilibrium constants for denaturation of the different protonation states. We also measured ¹³C^α chemical shifts of individual residues as a function of pH. These shifts sense structural transitions rather than ionizations, and they titrated with pH consistent with the change in equilibrium constant for denaturation. Kinetic measurements of the folding of BBL E161Q indicated that, at pH 7, the stabilizing interactions with Glu161 are formed mainly in the transition state. We also found that local interactions still exist in the acid-denatured state of BBL, which attenuate somewhat the flexibility of the acid-denatured state.