The folding of an enzyme. I. Theory of protein engineering analysis of stability and pathway of protein folding.

The theory, assumptions and limitations are outlined for a simple protein engineering approach to the problem of the stability and pathway of protein folding. It is a general procedure for analysing structure-activity relationships in non-covalent bonding, including enzyme catalysis, that relates experimentally accessible data to changes in non-covalent bonding. Kinetic and equilibrium measurements on the unfolding and refolding of mutant proteins can be used to map the formation of structure in transition states and folding intermediates. For example, the ratio of the changes in the activation energy of unfolding and the free energy of unfolding on mutation is measured to give a parameter phi. There are two extreme values of phi that are often found in practice and may be interpreted in a simple manner. A value of phi = 0 implies that the structure at the site of mutation is as folded in the transition state as it is in the folded state. Conversely, phi = 1 shows that the structure at the site of mutation is as unfolded in the transition state as it is in the unfolded structure. Fractional values of phi are more difficult to interpret and require a more sophisticated approach. The most suitable mutations involve truncation of side-chains to remove moieties that preferably make few interactions with the rest of the protein and do not pair with buried charges. Fractional values of phi found for this type of mutation may imply that there is partial non-covalent bond formation or a mixture of states. The major assumptions of the method are: (1) mutation does not alter the pathway of folding; (2) mutation does not significantly change the structure of the folded state; (3) mutation does not perturb the structure of the unfolded state; and (4) the target groups do not make new interactions with new partners during the course of reaction energy. Assumptions (2) and (3) are not necessarily essential for the simple cases of phi = 0 or 1, the most common values, since effects of disruption of structure can cancel out. Assumption (4) may be checked by the double-mutant cycle procedure, which may be analysed to isolate the effects of just a pair of interactions against a complicated background. This analysis provides the formal basis of the accompanying studies on the stability and pathway of folding of barnase, where it is seen that the theory holds very well in practice.     

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations. Proteins 29:282–291, 1997. © 1997 Wiley-Liss, Inc.     

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.     

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.     

The folding pathway of barnase: the rate-limiting transition state and a hidden intermediate under native conditions

The nature of the rate-limiting transition state at zero denaturant (TS(1)) and whether there are hidden intermediates are the two major unsolved problems in defining the folding pathway of barnase. In earlier studies, it was shown that TS(1) has small phi values throughout the structure of the protein, suggesting that the transition state has either a defined partially folded secondary structure with all side chains significantly exposed or numerous different partially unfolded structures with similar stability. To distinguish the two possibilities, we studied the effect of Gly mutations on the folding rate of barnase to investigate the secondary structure formation in the transition state. Two mutations in the same region of a beta-strand decreased the folding rate by 20- and 50-fold, respectively, suggesting that the secondary structures in this region are dominantly formed in the rate-limiting transition state. We also performed native-state hydrogen exchange experiments on barnase at pD 5.0 and 25 degrees C and identified a partially unfolded state. The structure of the intermediate was investigated using protein engineering and NMR. The results suggest that the intermediate has an omega loop unfolded. This intermediate is more folded than the rate-limiting transition state previously characterized at high denaturant concentrations (TS(2)). Therefore, it exists after TS(2) in folding. Consistent with this conclusion, the intermediate folds with the same rate and denaturant dependence as the wild-type protein, but unfolds faster with less dependence on the denaturant concentration. These and other results in the literature suggest that barnase folds through partially unfolded intermediates that exist after the rate-limiting step. Such folding behavior is similar to those of cytochrome c and Rd-apocyt b(562). Together, we suggest that other small apparently two-state proteins may also fold through hidden intermediates.     

Characterization of the hydrodynamic properties of the folding transition state of an SH3 domain by magnetization transfer NMR spectroscopy

Protein folding kinetic data have been obtained for the marginally stable N-terminal Src homology 3 domain of the Drosophila protein drk (drkN SH3) in an investigation of the hydrodynamic properties of its folding transition state. Due to the presence of NMR resonances of both folded and unfolded states at equilibrium, kinetic data can be derived from NMR magnetization transfer techniques under equilibrium conditions. Kinetic analysis as a function of urea (less than approximately 1 M) and glycerol enables determination of alpha values, measures of the energetic sensitivity of the transition state to the perturbation relative to the end states of the protein folding reaction (the folded and unfolded states). Both end states have previously been studied experimentally by NMR spectroscopic and other biophysical methods in great detail and under nondenaturing conditions. Combining these results with the kinetic folding data obtained here, we can characterize the folding transition state without requiring empirical models for the unfolded state structure. We are thus able to give a reliable measure of the solvent-accessible surface area of the transition state of the drkN SH3 domain (4730 +/- 360 A(2)) based on urea titration data. Glycerol titration data give similar results and additionally demonstrate that folding of this SH3 domain is dependent on solvent viscosity, which is indicative of at least partial hydration of the transition state. Because SH3 domains appear to fold by a common folding mechanism, the data presented here provide valuable insight into the transition states of the drkN and other SH3 domains.     

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.     

Energetic coupling between native-state prolyl isomerization and conformational protein folding

In folded proteins, prolyl peptide bonds are usually thought to be either trans or cis because only one of the isomers can be accommodated in the native folded protein. For the N-terminal domain of the gene-3 protein of the filamentous phage fd (N2 domain), Pro161 resides at the tip of a beta hairpin and was found to be cis in the crystal structure of this protein. Here we show that Pro161 exists in both the cis and the trans conformations in the folded form of the N2 domain. We investigated how conformational folding and prolyl isomerization are coupled in the unfolding and refolding of N2 domain. A combination of single-mixing and double-mixing unfolding and refolding experiments showed that, in unfolded N2 domain, 7% of the molecules contain a cis-Pro161 and 93% of the molecules contain a trans-Pro161. During refolding, the fraction of molecules with a cis-Pro161 increases to 85%. This implies that 10.3 kJ mol(-1) of the folding free energy was used to drive this 75-fold change in the Pro161 cis/trans equilibrium constant during folding. The stabilities of the forms with the cis and the trans isomers of Pro161 and their folding kinetics could be determined separately because their conformational folding is much faster than the prolyl isomerization reactions in the native and the unfolded proteins. The energetic coupling between conformational folding and Pro161 isomerization is already fully established in the transition state of folding, and the two isomeric forms are thus truly native forms. The folding kinetics are well described by a four-species box model, in which the N2 molecules with either isomer of Pro161 can fold to the native state and in which cis/trans isomerization occurs in both the unfolded and the folded proteins.     

Trehalose favors a cutinase compact intermediate off-folding pathway

The folding of cutinase, an enzyme displaying lipolytic activity, has been studied in the presence of trehalose. Equilibrium unfolding data show that trehalose increases the free energy change between folded and unfolded states. Unfolding kinetics reveal the presence of an intermediate which is ca. 60% folded in terms of solvent exposure. Trehalose stabilizes this intermediate relative to the folded state. In contrast, the intermediate revealed by folding kinetics is more compact than the transition state, as shown by the positive slope observed at low denaturant concentration in the chevron plot, as well as the decrease in the observable rate constant for folding with the increase in trehalose concentration. This intermediate displays more than 50% of area buried from the solvent (relative to the native state) compared to around 40% for the transition state for folding and therefore appears to be off the folding pathway. Trehalose stabilizes and guanidine hydrochloride destabilizes this compact intermediate. Both unfolding and folding kinetics show that compact conformational states are stabilized by trehalose, in agreement with current models on the effect of compatible solutes. This effect occurs even for compact states that decelerate the folding as in the case of the intermediate revealed by folding kinetics.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Free energy landscape and folding mechanism of a beta-hairpin in explicit water: a replica exchange molecular dynamics study

The free energy landscape and the folding mechanism of the C-terminal beta-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a beta-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the beta-hairpin occurs as the sequence: collapse of hydrophobic core --> formation of H-bond --> formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart.     

Correlation between mutational destabilization of phage T4 lysozyme and increased unfolding rates

The thermodynamics and kinetics of unfolding of 28 bacteriophage T4 lysozyme variants were compared by using urea gradient gel electrophoresis. The mutations studied cause a variety of sequence changes at different residues throughout the polypeptide chain and result in a wide range of thermodynamic stabilities. A striking relationship was observed between the thermodynamic and kinetic effects of the amino acid replacements: All the substitutions that destabilized the native protein by 2 kcal/mol or more also increased the rate of unfolding. The observed increases in unfolding rate corresponded to a decrease in the activation energy of unfolding (delta Gu) at least 35% as large as the decrease in thermodynamic stability (delta Gu). Thus, the destabilizing lesions bring the free energy of the native state closer to that of both the unfolded state and the transition state for folding and unfolding. Since a large fraction of the mutational destabilization is expressed between the transition state and the native conformation, the changes in folding energetics cannot be accounted for by effects on the unfolded state alone. The results also suggest that interactions throughout much of the folded structure are altered in the formation of the transition state during unfolding.     

Structure of a partially unfolded form of Escherichia coli dihydrofolate reductase provides insight into its folding pathway

Proteins frequently fold via folding intermediates that correspond to local minima on the conformational energy landscape. Probing the structure of the partially unfolded forms in equilibrium under native conditions can provide insight into the properties of folding intermediates. To elucidate the structures of folding intermediates of Escherichia coli dihydrofolate reductase (DHFR), we investigated transient partial unfolding of DHFR under native conditions. We probed the structure of a high‐energy conformation susceptible to proteolysis (cleavable form) using native‐state proteolysis. The free energy for unfolding to the cleavable form is clearly less than that for global unfolding. The dependence of the free energy on urea concentration (m‐value) also confirmed that the cleavable form is a partially unfolded form. By assessing the effect of mutations on the stability of the partially unfolded form, we found that native contacts in a hydrophobic cluster formed by the F‐G and Met‐20 loops on one face of the central β‐sheet are mostly lost in the partially unfolded form. Also, the folded region of the partially unfolded form is likely to have some degree of structural heterogeneity. The structure of the partially unfolded form is fully consistent with spectroscopic properties of the near‐native kinetic intermediate observed in previous folding studies of DHFR. The findings suggest that the last step of the folding of DHFR involves organization in the structure of two large loops, the F‐G and Met‐20 loops, which is coupled with compaction of the rest of the protein.     

Hammond behavior versus ground state effects in protein folding: evidence for narrow free energy barriers and residual structure in unfolded states

Apparent transition state movement upon mutation or changes in solvent conditions is frequently observed in protein folding and is often interpreted in terms of Hammond behavior. This led to the conclusion that barrier regions in protein folding are broad maxima on the free energy landscape. Here, we use the concept of self-interaction and cross-interaction parameters to test experimental data of 21 well-characterized proteins for Hammond behavior. This allows us to characterize the origin of transition state movements along different reaction coordinates. Only one of the 21 proteins shows a small but coherent transition state movement in agreement with the Hammond postulate. In most proteins the structure of the transition state is insensitive to changes in protein stability. The apparent change in the position of the transition state upon mutation, which is frequently observed in phi-value analysis, is in most cases due to ground-state effects caused by structural changes in the unfolded state. This argues for significant residual structure in unfolded polypeptide chains of many proteins. Disruption of these residual interactions by mutation often leads to decreased folding rates, which implies that these interactions are still present in the transition state. The failure to detect Hammond behavior shows that the free energy barriers encountered by a folding polypeptide chain are generally rather narrow and robust maxima for all experimentally explorable reaction coordinates.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Progressive stabilization of intermediate and transition states in protein folding reactions by introducing surface hydrophobic residues

It can be argued from the principle of solvent exclusion that the introduction of hydrophobic residues onto the surface of a protein will not destabilize the folded state because the nonpolar side chain will be at least as exposed in the unfolded state as it is when the protein chain is folded. A comparison of the folding pathway of wild type and 11 site-directed mutants of CD2.d1 shows this to be true. In fact, owing to partial burial of nonpolar groups as folding proceeds, we find that the rapidly formed intermediate state and, to a greater extent, the transition state are generally stabilized by hydrophobic surface mutations. This effect is slightly moderated in the folded state presumably by the perturbation of van der Waals' contacts and/or local electrostatic interactions that have a greater influence in this fully compact structure. The fact that in all but one case we find that stabilization of the rapidly collapsed intermediate is accompanied by a faster acquisition of the folded state refutes the argument that I states are generally "off pathway" conformations or ensembles that lead to the inhibition of otherwise more rapid folding trajectories.     

How, when and why proteins collapse: the relation to folding

Unfolded proteins under strongly denaturing conditions are highly expanded. However, when the conditions are more close to native, an unfolded protein may collapse to a compact globular structure distinct from the folded state. This transition is akin to the coil-globule transition of homopolymers. Single-molecule FRET experiments have been particularly conducive in revealing the collapsed state under conditions of coexistence with the folded state. The collapse can be even more readily observed in natively unfolded proteins. Time-resolved studies, using FRET and small-angle scattering, have shown that the collapse transition is a very fast event, probably occurring on the submicrosecond time scale. The forces driving collapse are likely to involve both hydrophobic and backbone interactions. The loss of configurational entropy during collapse makes the unfolded state less stable compared to the folded state, thus facilitating folding.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Exploring subdomain cooperativity in T4 lysozyme II: uncovering the C-terminal subdomain as a hidden intermediate in the kinetic folding pathway

Intermediates along a protein's folding pathway can play an important role in its biology. Previous kinetics studies have revealed an early folding intermediate for T4 lysozyme, a small, well-characterized protein composed of an N-terminal and a C-terminal subdomain. Pulse-labeling hydrogen exchange studies suggest that residues from both subdomains contribute to the structure of this intermediate. On the other hand, equilibrium native state hydrogen experiments have revealed a high-energy, partially unfolded form of the protein that has an unstructured N-terminal subdomain and a structured C-terminal subdomain. To resolve this discrepancy between kinetics and equilibrium data, we performed detailed kinetics analyses of the folding and unfolding pathways of T4 lysozyme, as well as several point mutants and large-scale variants. The data support the argument for the presence of two distinct intermediates, one present on each side of the rate-limiting transition state barrier. The effects of circular permutation and site-specific mutations in the wild-type and circular permutant background, as well as a fragment containing just the C-terminal subdomain, support a model for the unfolding intermediate with an unfolded N-terminal and a folded C-terminal subdomain. Our results suggest that the partially unfolded form identified by native state hydrogen exchange resides on the folded side of the rate-limiting transition state and is, therefore, under most conditions, a "hidden" intermediate.