Transition states and the meaning of Phi-values in protein folding kinetics

What is the mechanism of two-state protein folding? The rate-limiting step is typically explored through a Phi-value, which is the mutation-induced change in the transition state free energy divided by the change in the equilibrium free energy of folding. Phi-values ranging from 0 to 1 have been interpreted as meaning the transition state is denatured-like (0), native-like (1) or in-between. But there is no classical interpretation for the experimental Phi-values that are negative or >1. Using a rigorous method to identity transition states via an exact lattice model, we find that nonclassical Phi-values can arise from parallel microscopic flow processes, such as those in funnel-shaped energy landscapes. Phi < 0 results when a mutation destabilizes a slow flow channel, causing a backflow into a faster flow channel. Phi > 1 implies the reverse: a backflow from a fast channel into a slow one. Using a 'landscape mapping' method, we find that Phi correlates with the acceleration/deceleration of folding induced by mutations, rather than with the degree of nativeness of the transition state.     

Helix nucleation kinetics from molecular simulations in explicit solvent

We study the reversible folding/unfolding of short Ala and Gly-based peptides by molecular dynamics simulations of all-atom models in explicit water solvent. A kinetic analysis shows that the formation of a first alpha-helical turn occurs within 0.1-1 ns, in agreement with the analyses of laser temperature jump experiments. The unfolding times exhibit Arrhenius temperature dependence. For a rapidly nucleating all-Ala peptide, the helix nucleation time depends only weakly on temperature. For a peptide with enthalpically competing turn-like structures, helix nucleation exhibits an Arrhenius temperature dependence, corresponding to the unfolding of enthalpic traps in the coil ensemble. An analysis of structures in a "transition-state ensemble" shows that helix-to-coil transitions occur predominantly through breaking of hydrogen bonds at the helix ends, particularly at the C-terminus. The temperature dependence of the transition-state ensemble and the corresponding folding/unfolding pathways illustrate that folding mechanisms can change with temperature, possibly complicating the interpretation of high-temperature unfolding simulations. The timescale of helix formation is an essential factor in molecular models of protein folding. The rapid helix nucleation observed here suggests that transient helices form early in the folding event.     

Does alpha-helix folding necessarily provide an energy source for the protein-lipid binding?

Lipid-induced alpha-helix folding, which occurs in many lipid surface-binding proteins and peptides such as apolipoproteins and synucleins, has been proposed to provide an energy source for protein-lipid interactions. We propose that in a system comprised of a phospholipid surface and a small polypeptide that is unfolded in solution and binds reversibly to lipid surface, helical folding involves expenditure of free energy as compared to a similar polypeptide that is alpha-helical in solution. This is a consequence of the entropic cost of helix folding that is illustrated in a simple thermodynamic model and exemplifies the general "key-into-lock" paradigm of protein-ligand binding. Even though this simple model does not explicitly address the protein-induced lipid re-arrangement and may not directly apply to large proteins that undergo significant tertiary structural changes upon lipid binding, it suggests that the notion of helix folding as an energy source for lipid binding should be treated with caution.     

The Folding Transition-State Ensemble of a Four-Helix Bundle Protein: Helix Propensity as a Determinant and Macromolecular Crowding as a Probe

The four-helix bundle protein Rd-apocyt b₅₆₂, a redesigned stable variant of apocytochrome b₅₆₂, exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Φ-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Φ-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Φ-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.     

Structural instability of the prion protein upon M205S/R mutations revealed by molecular dynamics simulations

The point mutations M205S and M205R have been demonstrated to severely disturb the folding and maturation process of the cellular prion protein (PrP(C)). These disturbances have been interpreted as consequences of mutation-induced structural changes in PrP, which are suggested to involve helix 1 and its attachment to helix 3, because the mutated residue M205 of helix 3 is located at the interface of these two helices. Furthermore, current models of the prion protein scrapie (PrP(Sc)), which is the pathogenic isoform of PrP(C) in prion diseases, imply that helix 1 disappears during refolding of PrP(C) into PrP(Sc). Based on molecular-dynamics simulations of wild-type and mutant PrP(C) in aqueous solution, we show here that the native PrP(C) structure becomes strongly distorted within a few nanoseconds, once the point mutations M205S and M205R have been applied. In the case of M205R, this distortion is characterized by a motion of helix 1 away from the hydrophobic core into the aqueous environment and a subsequent structural decay. Together with experimental evidence on model peptides, this decay suggests that the hydrophobic attachment of helix 1 to helix 3 at M205 is required for its correct folding into its stable native structure.     

Importance of hydrophobic cluster formation through long-range contacts in the folding transition state of two-state proteins

Understanding the folding pathways of proteins is a challenging task. The Phi value approach provides a detailed understanding of transition-state structures of folded proteins. In this work, we have computed the hydrophobicity associated with each residue in the folded state of 16 two-state proteins and compared the Phi values of each mutant residue. We found that most of the residues with high Phi value coincide with local maximum in surrounding hydrophobicity, or have nearby residues that show such maximum in hydrophobicity, indicating the importance of hydrophobic interactions in the transition state. We have tested our approach to different structural classes of proteins, such as alpha-helical, SH3 domains of all-beta proteins, beta-sandwich, and alpha/beta proteins, and we observed a good agreement with experimental results. Further, we have proposed a hydrophobic contact network pattern to relate the Phi values with long-range contacts, which will be helpful to understand the transition-state structures of folded proteins. The present approach could be used to identify potential hydrophobic clusters that may form through long-range contacts during the transition state.     

A model for the coupling of alpha-helix and tertiary contact formation

Peptides corresponding to excised alpha-helical segments of natural proteins can spontaneously form helices in solution. However, peptide helices are usually substantially less stable in solution than in the structural context of a folded protein, because of the additional interactions possible between helices in a protein. Such interactions can be thought of as coupling helix formation and tertiary contact formation. The relative energetic contributions of the two processes to the total energy of the folded state of a protein is a matter of current debate. To investigate this balance, an extended helix-coil model (XHC) that incorporates both effects has been constructed. The model treats helix formation with the Lifson-Roig formalism, which describes helix initiation and propagation through cooperative local interactions. The model postulates an additional parameter representing participation of a site in a tertiary contact. In the model, greater helix stability can be achieved through combinations of these short-range and long-range interactions. For instance, stronger tertiary contacts can compensate for helices with little intrinsic stability. By varying the strength of the nonlocal interactions, the model can exhibit behavior consistent with a variety of qualitative models describing the relative importance of secondary and tertiary structure. Moreover, the model is explicit in that it can be used to fit experimental data to individual peptide sequences, providing a means to quantify the two contributions on a common energetic basis.     

Protein folding simulation with solvent-induced force field: folding pathway ensemble of three-helix-bundle proteins

We propose a coarse-grained model of proteins that take into account solvent effects and apply it for simulating folding of a three-helix-bundle protein. The energy functional form, refined from our previous work (Takada et al., J Chem Phys 1999;110:11616-11629), tries to closely imitate real physico-chemical interactions. In particular, the hydrogen bond that depends on local dielectric constant, the helix capping effect, and side-chain entropic effects are included. With use of the model, we simulate folding of the GA module of an albumin binding domain, 1prb(7-53), finding most trajectories reach at the native topology within 1 micros. In the simulation, helices 1 and 3 are mostly formed earlier accompanied by non-specific collapse, while second helix is intrinsically less stable and is formed with the help of tertiary contacts at later stage. We compute an analog of the transition state ensemble and compare it with those of other three-helix-bundle proteins. The transition state of 1prb(7-53) includes a few specific tertiary contacts of C terminus of helix 3 with the loop region between helices 1 and 2. This resembles, but is not equivalent to, an early formed region of fragment B of staphylococcal protein A, but is quite different from the folding transient structures of a de novo designed three-helix-bundle peptide.     

Conformational and dynamic characterization of the molten globule state of an apomyoglobin mutant with an altered folding pathway.

Kinetic and equilibrium studies of apomyoglobin folding pathways and intermediates have provided important insights into the mechanism of protein folding. To investigate the role of intrinsic helical propensities in the apomyoglobin folding process, a mutant has been prepared in which Asn132 and Glu136 have been substituted with glycine to destabilize the H helix. The structure and dynamics of the equilibrium molten globule state formed at pH 4.1 have been examined using NMR spectroscopy. Deviations of backbone (13)C(alpha) and (13)CO chemical shifts from random coil values reveal high populations of helical structure in the A and G helix regions and in part of the B helix. However, the H helix is significantly destabilized compared to the wild-type molten globule. Heteronuclear [(1)H]-(15)N NOEs show that, although the polypeptide backbone in the H helix region is more flexible than in the wild-type protein, its motions are restricted by transient hydrophobic interactions with the molten globule core. Quench flow hydrogen exchange measurements reveal stable helical structure in the A and G helices and part of the B helix in the burst phase kinetic intermediate and confirm that the H helix is largely unstructured. Stabilization of structure in the H helix occurs during the slow folding phases, in synchrony with the C and E helices and the CD region. The kinetic and equilibrium molten globule intermediates formed by N132G/E136G are similar in structure. Although both the wild-type apomyoglobin and the mutant fold via compact helical intermediates, the structures of the intermediates and consequently the detailed folding pathways differ. Apomyoglobin is therefore capable of compensating for mutations by using alternative folding pathways within a common basic framework. Tertiary hydrophobic interactions appear to play an important role in the formation and stabilization of secondary structure in the H helix of the N132G/E136G mutant. These studies provide important insights into the interplay between secondary and tertiary structure formation in protein folding.     

Effect of sequence mutations on the higher order structure of the yeast 5 S rRNA.

Mutant yeast ribosomal 5 S RNAs were probed by enzymatic cleavage and chemical reactivity to define further the higher order structure. Mutations that destabilized helix IV resulted in an altered tertiary structure in which a reduced reactivity to ethylnitrosourea at U90 and G91 could be correlated with greater enzymatic and Fe(II)-EDTA cleavages in helices II and V. The results provide direct evidence for, and a further definition of, a structural juxtaposition between helix II and the end of helix IV and indicate that, in contrast to earlier suggestions, the remaining tertiary structure is sufficiently stable to prevent "pseudoknot-like" interactions between helices III and IV. The data are fully consistent with the "lollipop" model of the tertiary structure.     

Explicit-chain model of native-state hydrogen exchange: implications for event ordering and cooperativity in protein folding

Native-state hydrogen exchange experiments on several proteins have revealed partially unfolded conformations with diverse stabilities. These equilibrium observations have been used to support kinetic arguments that folding proceeds via a sequential "pathway." This interpretative logic is evaluated here by analyzing the relationship between thermodynamic behavior and folding kinetics in a class of simplified lattice protein models. The chain models studied have varying degrees of cooperative interplay (coupling) between local helical conformational preference and favorable nonlocal interactions. When model cooperativity is high, as native conditions are weakened, "isotherms" of free energy of exchange for residues belonging to the same helix merge together before global unfolding. The point of merger depends on the model energetic favorability of the helix. This trend is similar to the corresponding experimental observations. Kinetically, we find that the ordering of helix formation in the very last stage of native core assembly tends to follow the stabilities of their converged isotherms. In a majority (but not all) of folding trajectories, the final assembly of helices that are thermodynamically more stable against exchange precedes that of helices that are less stable against exchange. These model features are in partial agreement with common experimental interpretations. However, the model results also underscore the ensemble nature of the folding process: the kinetics of helix formation is not a discrete, strictly "all-or-none" process as that envisioned by certain non-explicit-chain models. Helices generally undergo many cycles of partial formation and dissolution before their conformations are fixed in the final assembly stage of folding, a kinetic stage that takes up only approximately 2% of the average folding time in the present model; and the ordering of the helices' final assembly in some trajectories can be different from the dominant ordering stipulated by the exchange isotherms.     

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model.

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.     

Determining the 3D structure of human ASC2 protein involved in apoptosis and inflammation

ASC2 structure has been well defined by 1141 NOE experimental restraints. The model consists of five alpha helices. alpha-Helices are connected by short random structure loops. The sole exception is the loop connecting helices 2 and 3, which has a 20-residue length. Folding generally agrees with the folding of recently published death domain structures in which alpha-helix structures have been reported. In spite of structural similarity, amino acid sequence homology with the most similar protein (ASC1) is just 64%. DD, DED, and CASP protein structures present six helices along their sequences; ASC2 presents 5 well-defined helices due to long distance restraints. However, a helical fragment was observed between amino acids 38 and 42 (representing helix 3) in the death domains when constructing the model.     

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.     

Structural examination of phi-value analysis in protein folding

Protein folding intermediates and transition states are commonly characterized using a protein engineering procedure (Phi-value analysis) based on several assumptions, including (1) intermediates and transition states have native-like conformations and (2) single mutations from larger hydrophobic residues to smaller ones do not perturb their structures. Although Phi-value analysis has been widely used, these assumptions have not been tested to date because of the lack of high-resolution structures of intermediates and transition states. We recently have determined the structure of a folding intermediate for a four-helix bundle protein (Rd-apocytochrome b(562)) using NMR. The intermediate has the N-terminal helix unfolded. The other three helices fold in a native-like topology with extensive non-native hydrophobic interactions. Here, we have determined the Phi values for 14 hydrophobic core residues, including those with significant non-native interactions. All of the Phi values are in the normal range from 0 to 1, indicating that these non-native interactions cannot be identified by the common Phi-value analysis, and therefore, the first assumption is not valid for this intermediate. We also determined the structure of a mutant (F65A) of the intermediate and found that the structure of the intermediate is not perturbed by the mutation, supporting the second assumption. Together, these results suggest that Phi-value analysis may be valid for characterizing the energetics of the interactions between the mutated residue and others, but not for determining the detailed structures of intermediates and transition states because non-native interactions may exist and may not be identifiable by the common Phi-value analysis.     

A role for transmembrane domains V and VI in ligand binding and maturation of the angiotensin II AT1 receptor

Several studies have proposed that angiotensin II (Ang II) binds to its receptor AT1 through interactions with residues in helices V and VI, suggesting that the distance between these helices is crucial for ligand binding. Based on a 3D model of AT1 in which the C-terminus of Ang II is docked, we identified the hydrophobic residues of TM V and VI pointing towards the external face of the helices, which may play a role in the structure of the binding pocket and in the structural integrity of the receptor. We performed a systematic mutagenesis study of these residues and examined the binding, localization, maturation, and dimerization of the mutated receptors. We found that mutations of hydrophobic residues to alanine in helix V do not alter binding, whereas mutations to glutamate lead to loss of binding without a loss in cell surface expression, suggesting that the external face of helix V may not directly participate in binding, but may rather contribute to the structure of the binding pocket. In contrast, mutations of hydrophobic residues to glutamate in helix VI lead to a loss in cell surface expression, suggesting that the external surface of helix VI plays a structural role and ensures correct folding of the receptor.     

RNA tertiary interactions mediate native collapse of a bacterial group I ribozyme

Large RNAs collapse into compact intermediates in the presence of counterions before folding to the native state. We previously found that collapse of a bacterial group I ribozyme correlates with the formation of helices within the ribozyme core, but occurs at Mg2+ concentrations too low to support stable tertiary structure and catalytic activity. Here, using small-angle X-ray scattering, we show that Mg2+-induced collapse is a cooperative folding transition that can be fit by a two-state model. The Mg2+ dependence of collapse is similar to the Mg2+ dependence of helix assembly measured by partial ribonuclease T1 digestion and of an unfolding transition measured by UV hypochromicity. The correspondence between multiple probes of RNA structure further supports a two-state model. A mutation that disrupts tertiary contacts between the L9 tetraloop and its helical receptor destabilized the compact state by 0.8 kcal/mol, while mutations in the central triplex were less destabilizing. These results show that native tertiary interactions stabilize the compact folding intermediates under conditions in which the RNA backbone remains accessible to solvent.     

Folding propensities of synthetic peptide fragments covering the entire sequence of phage 434 Cro protein.

The phage 434 Cro protein, the N-terminal domain of its repressor (R1-69) and that of phage lambda (lambda6-85) constitute a group of small, monomeric, single-domain folding units consisting of five helices with striking structural similarity. The intrinsic helix stabilities in lambda6-85 have been correlated to its rapid folding behavior, and a residual hydrophobic cluster found in R1-69 in 7 M urea has been proposed as a folding initiation site. To understand the early events in the folding of 434 Cro, and for comparison with R1-69 and lambda6-85, we examined the conformational behavior of five peptides covering the entire 434 Cro sequence in water, 40% (by volume) TFE/water, and 7 M urea solutions using CD and NMR. Each peptide corresponds to a helix and adjacent residues as identified in the native 434 Cro NMR and crystal structures. All are soluble and monomeric in the solution conditions examined except for the peptide corresponding to the 434 Cro helix 4, which has low water solubility. Helix formation is observed for the 434 Cro helix 1 and helix 2 peptides in water, for all the peptides in 40% TFE and for none in 7 M urea. NMR data indicate that the helix limits in the peptides are similar to those in the native protein helices. The number of side-chain NOEs in water and TFE correlates with the helix content, and essentially none are observed in 7 M urea for any peptide, except that for helix 5, where a hydrophobic cluster may be present. The low intrinsic folding propensities of the five helices could account for the observed stability and folding behavior of 434 Cro and is, at least qualitatively, in accord with the results of the recently described diffusion-collision model incorporating intrinsic helix propensities.     

The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.