Comprehensive analysis of protein folding activation thermodynamics reveals a universal behavior violated by kinetically stable proteases

Alpha-lytic protease (alpha LP) and Streptomyces griseus protease B (SGPB) are two extracellular serine proteases whose folding is absolutely dependent on the existence of their companion pro regions. Moreover, the native states of these proteins are, at best, marginally stable, with the apparent stability resulting from being kinetically trapped in the native state by large barriers to unfolding. Here, in an effort to understand the physical properties that distinguish kinetically and thermodynamically stable proteins, we study the temperature-dependences of the folding and unfolding kinetics of alpha LP and SGPB without their pro regions, and compare their behavior to a comprehensive set of other proteins. For the folding activation thermodynamics, we find some remarkable universal behaviors in the thermodynamically stable proteins that are violated dramatically by alpha LP. Despite significant variations in deltaC(P,F)++, the maximal folding speed occurs within the narrow biological temperature range for all proteins, except for alpha LP, with its maximal folding speed shifted lower by 200 K. This implies evolutionary pressures on folding speed for typical proteins, but not for alpha LP. In addition, the folding free energy barrier in the biological temperature range for most proteins is predominantly enthalpic, but purely entropic for alpha LP. The unfolding of alpha LP and SGPB is distinguished by three properties: a remarkably large deltaC(P,U)++, a very high deltaG(U)++, and a maximum deltaG(u)++ at the optimal growth temperature for the organism. While other proteins display each of these traits to some approximation, the simultaneous optimization of all three occurs only in the kinetically stable proteins, and appears to be required to maximize their unfolding cooperativity, by suppressing local unfolding events, and slowing the rate of global unfolding. Together, these properties extend the lifetime of these enzymes in the highly proteolytic extracellular environment. Attaining such functional properties seems possible only through the gross perturbation of the folding thermodynamics, which in turn has required the co-evolution of pro regions as folding catalysts.     

The folding landscape of an alpha-lytic protease variant reveals the role of a conserved beta-hairpin in the development of kinetic stability

Most secreted bacterial proteases, including alpha-lytic protease (alphaLP), are synthesized with covalently attached pro regions necessary for their folding. The alphaLP folding landscape revealed that its pro region, a potent folding catalyst, is required to circumvent an extremely large folding free energy of activation that appears to be a consequence of its unique unfolding transition. Remarkably, the alphaLP native state is thermodynamically unstable; a large unfolding free energy barrier is solely responsible for the persistence of its native state. Although alphaLP folding is well characterized, the structural origins of its remarkable folding mechanism remain unclear. A conserved beta-hairpin in the C-terminal domain was identified as a structural element whose formation and positioning may contribute to the large folding free energy barrier. In this article, we characterize the folding of an alphaLP variant with a more favorable beta-hairpin turn conformation (alphaLP(beta-turn)). Indeed, alphaLP(beta-turn) pro region-catalyzed folding is faster than that for alphaLP. However, instead of accelerating spontaneous folding, alphaLP(beta-turn) actually unfolds more slowly than alphaLP. Our data support a model where the beta-hairpin is formed early, but its packing with a loop in the N-terminal domain happens late in the folding reaction. This tight packing at the domain interface enhances the kinetic stability of alphaLP(beta-turn), to nearly the same degree as the change between alphaLP and a faster folding homolog. However, alphaLP(beta-turn) has impaired proteolytic activity that negates the beneficial folding properties of this variant. This study demonstrates the evolutionary limitations imposed by the simultaneous optimization of folding and functional properties.     

Interdependent folding of the N- and C-terminal domains defines the cooperative folding of alpha-lytic protease

Alpha-lytic protease (alphaLP) serves as an important model in achieving a quantitative and physical understanding of protein folding reactions. Synthesized as a pro-protease, alphaLP belongs to an interesting class of proteins that require pro regions to facilitate their proper folding. alphaLP's pro region (Pro) acts as a potent folding catalyst for the protease, accelerating alphaLP folding to its native conformation nearly 10(10)-fold. Structural and mutational studies suggested that Pro's considerable foldase activity is directed toward structuring the alphaLP C-terminal domain (CalphaLP), a seemingly folding-impaired domain, which is believed to contribute significantly to the high-energy folding and unfolding transition states of alphaLP. Pro-mediated nucleation of alphaLP folding within CalphaLP was hypothesized to subsequently enable the alphaLP N-terminal domain (NalphaLP) to dock and fold, completing the formation of native protease. In this paper, we find that ternary folding reactions of Pro and noncovalent NalphaLP and CalphaLP domains are unaffected by the order in which the components are added or by the relative concentrations of the alphaLP domains, indicating that neither discrete CalphaLP structuring nor docking of the two alphaLP domains is involved in the folding transition state. Instead, the rate-limiting step of these folding reactions appears to be a slow and concerted rearrangement of the NalphaLP and CalphaLP domains to form active protease. This cooperative and interdependent folding of both protease domains defines the large alphaLP folding barrier and is an apparent extension of the highly cooperative alphaLP unfolding transition that imparts the protease with remarkable kinetic stability and functional longevity.     

Mesophile versus thermophile: insights into the structural mechanisms of kinetic stability

Obtaining detailed knowledge of folding intermediate and transition state (TS) structures is critical for understanding protein folding mechanisms. Comparisons between proteins adapted to survive extreme temperatures with their mesophilic homologs are likely to provide valuable information on the interactions relevant to the unfolding transition. For kinetically stable proteins such as alpha-lytic protease (alphaLP) and its family members, their large free energy barrier to unfolding is central to their biological function. To gain new insights into the mechanisms that underlie kinetic stability, we have determined the structure and high temperature unfolding kinetics of a thermophilic homolog, Thermobifida fusca protease A (TFPA). These studies led to the identification of a specific structural element bridging the N and C-terminal domains of the protease (the "domain bridge") proposed to be associated with the enhanced high temperature kinetic stability in TFPA. Mutagenesis experiments exchanging the TFPA domain bridge into alphaLP validate this hypothesis and illustrate key structural details that contribute to TFPA's increased kinetic thermostability. These results lead to an updated model for the unfolding transition state structure for this important class of proteases in which domain bridge undocking and unfolding occurs at or before the TS. The domain bridge appears to be a structural element that can modulate the degree of kinetic stability of the different members of this class of proteases.     

Disabling the folding catalyst is the last critical step in alpha-lytic protease folding

Alpha-Lytic protease (alphaLP) is an extracellular bacterial pro-protease marked by extraordinary conformational rigidity and a highly cooperative barrier to unfolding. Although these properties successfully limit its proteolytic destruction, thereby extending the functional lifetime of the protease, they come at the expense of foldability (t(1/2) = 1800 yr) and thermodynamic stability (native alphaLP is less stable than the unfolded species). Efficient folding has required the coevolution of a large N-terminal pro region (Pro) that rapidly catalyzes alphaLP folding (t(1/2) = 23 sec) and shifts the thermodynamic equilibrium in favor of folded protease through tight native-state binding. Release of active alphaLP from this stabilizing, but strongly inhibitory, complex requires the proteolytic destruction of Pro. alphaLP is capable of initiating Pro degradation via cleavage of a flexible loop within the Pro C-terminal domain. This single cleavage event abolishes Pro catalysis while maintaining strong native-state binding. Thus, the loop acts as an Achilles' heel by which the Pro foldase machinery can be safely dismantled, preventing Pro-catalyzed unfolding, without compromising alphaLP native-state stability. Once the loop is cleaved, Pro is rapidly degraded, releasing active alphaLP.     

The pro region N-terminal domain provides specific interactions required for catalysis of alpha-lytic protease folding

The extracellular bacterial protease, alpha-lytic protease (alphaLP), is synthesized with a large, two-domain pro region (Pro) that catalyzes the folding of the protease to its native conformation. In the absence of its Pro folding catalyst, alphaLP encounters a very large folding barrier (DeltaG = 30 kcal mol(-1)) that effectively prevents the protease from folding (t(1/2) of folding = 1800 years). Although homology data, mutational studies, and structural analysis of the Pro.alphaLP complex suggested that the Pro C-terminal domain (Pro C-domain) serves as the minimum "foldase" unit responsible for folding catalysis, we find that the Pro N-terminal domain (Pro N-domain) is absolutely required for alphaLP folding. Detailed kinetic analysis of Pro N-domain point mutants and a complete N-domain deletion reveal that the Pro N-domain both provides direct interactions with alphaLP that stabilize the folding transition state and confers stability to the Pro C-domain. The Pro N- and C-domains make conflicting demands upon native alphaLP binding that are alleviated in the optimized interface of the folding transition state complex. From these studies, it appears that the extremely high alphaLP folding barrier necessitates the presence of both the Pro domains; however, alphaLP homologues with less demanding folding barriers may not require both domains, thus possibly explaining the wide variation in the pro region size of related pro-proteases.     

Structural and mechanistic exploration of acid resistance: kinetic stability facilitates evolution of extremophilic behavior

Kinetically stable proteins are unique in that their stability is determined solely by kinetic barriers rather than by thermodynamic equilibria. To better understand how kinetic stability promotes protein survival under extreme environmental conditions, we analyzed the unfolding behavior and determined the structure of Nocardiopsis alba Protease A (NAPase), an acid-resistant, kinetically stable protease, and compared these results with a neutrophilic homolog, α-lytic protease (αLP). Although NAPase and αLP have the same number of acid-titratable residues, kinetic studies revealed that the height of the unfolding free energy barrier for NAPase is less sensitive to acid than that of αLP, thereby accounting for NAPase's improved tolerance of low pH. A comparison of the αLP and NAPase structures identified multiple salt-bridges in the domain interface of αLP that were relocated to outer regions of NAPase, suggesting a novel mechanism of acid stability in which acid-sensitive electrostatic interactions are rearranged to similarly affect the energetics of both the native state and the unfolding transition state. An acid-stable variant of αLP in which a single interdomain salt-bridge is replaced with a corresponding intradomain NAPase salt-bridge shows a dramatic > 15-fold increase in acid resistance, providing further evidence for this hypothesis. These observations also led to a general model of the unfolding transition state structure for αLP protease family members in which the two domains separate from each other while remaining relatively intact themselves. These results illustrate the remarkable utility of kinetic stability as an evolutionary tool for developing longevity over a broad range of harsh conditions.     

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102–14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape‐based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C‐terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.     

alpha-lytic protease precursor: characterization of a structured folding intermediate

The bacterial alpha-lytic protease (alphaLP) is synthesized as a precursor containing a large N-terminal pro region (Pro) transiently required for correct folding of the protease [Silen, J. L., and Agard, D. A. (1989) Nature 341, 462-464]. Upon folding, the precursor is autocatalyticly cleaved to yield a tight-binding inhibitory complex of the pro region and the fully folded protease (Pro/alphaLP). An in vitro purification and refolding protocol has been developed for production of the disulfide-bonded precursor. A combination of spectroscopic approaches have been used to compare the structure and stability of the precursor with either the Pro/alphaLP complex or isolated Pro. The precursor and complex have significant similarities in secondary structure but some differences in tertiary structure, as well as a dramatic difference in stability. Correlations with isolated Pro suggest that the pro region part of the precursor is fully folded and acts to stabilize and structure the alphaLP region. Precursor folding is shown to be biphasic with the fast phase matching the rate of pro region folding. Further, the rate-limiting step in oxidative folding is formation of the disulfide bonds and autocatalytic processing occurs rapidly thereafter. These studies suggests a model in which the pro region folds first and catalyzes folding of the protease domain, forming the active site and finally causing autocatalytic cleavage of the bond separating pro region and protease. This last processing step is critical as it allows the protease N-terminus to rearrange, providing the majority of net stabilization of the product Pro/alphaLP complex.     

Two energetically disparate folding pathways of alpha-lytic protease share a single transition state

The Lysobacter enzymogenes alpha-lytic protease (alphaLP) is synthesized with a 166 amino acid pro region (Pro) that catalyzes the folding of the 198 amino acid protease into its native conformation. An extraordinary feature of this system is the very high energy barrier (DeltaG = 30 kcal mol-1) that effectively prevents alphaLP from folding in the absence of Pro (t1/2 = 1800 years). A pair of mutations has been isolated in the protease that completely suppresses the catalytic defect incurred in Pro by truncation of its last three amino acids. These mutations also accelerate the folding of alphaLP in the absence of Pro by 400-fold. An energetic analysis of the two folding reactions indicates that the mutations stabilize the transition states of both the catalyzed and uncatalyzed folding reactions by 3 kcal mol-1. This finding points to a single transition state for these two distinct and energetically disparate folding pathways, and raises the possibility that all alphaLP folding pathways share the same transition state.     

On the unfolding of alpha-lytic protease and the role of the pro region

Molecular dynamics simulations of alpha-lytic protease (alphaLP) alone and complexed with its pro region (PRO) are performed to understand the origin of its high unfolding (and folding) barrier when it is alone and how the pro region lowers this barrier. At room temperature, alphaLP exhibits lower dynamic fluctuations than alpha-chymotrypsin. Simulation of PRO alone led to reorientation of its N terminal helix and collapse to a more compact state. A model for the uncleaved proenzyme was built and found to be stable in the time scale of the simulations. Energetic analysis suggests that the origin of strain in the uncleaved proenzyme compared with the cleaved complex is in the intramolecular backbone electrostatic interactions of the cleaved strand. In high temperature simulations, the interaction of the long beta hairpin of the enzyme with the C terminal beta sheet of PRO is among the most stable in the complex and a likely "nucleation site" for folding. In the course of unfolding, the C terminal tail of PRO is sometimes observed to intervene between the long hairpin and the aspartate loop of the enzyme, perhaps thereby lowering the energy barrier for separation of the two hairpins. Tighter interactions at the interface between the enzyme and its pro region are also occasionally observed, providing an additional mechanism for unfolding catalysis. Simulations of a mutant enzyme where the buried ion pair residues R102 and D142 were replaced by W and L, respectively, did not display any distinguishable behavior compared with the wild type.     

The Folding Free-Energy Surface of HIV-1 Protease: Insights into the Thermodynamic Basis for Resistance to Inhibitors

Spontaneous mutations at numerous sites distant from the active site of human immunodeficiency virus type 1 protease enable resistance to inhibitors while retaining enzymatic activity. As a benchmark for probing the effects of these mutations on the conformational adaptability of this dimeric β-barrel protein, the folding free-energy surface of a pseudo-wild-type variant, HIV-PR^?, was determined by a combination of equilibrium and kinetic experiments on the urea-induced unfolding/refolding reactions. The equilibrium unfolding reaction was well described by a two-state model involving only the native dimeric form and the unfolded monomer. The global analysis of the kinetic folding mechanism reveals the presence of a fully folded monomeric intermediate that associates to form the native dimeric structure. Independent analysis of a stable monomeric version of the protease demonstrated that a small-amplitude fluorescence phase in refolding and unfolding, not included in the global analysis of the dimeric protein, reflects the presence of a transient intermediate in the monomer folding reaction. The partially folded and fully folded monomers are only marginally stable with respect to the unfolded state, and the dimerization reaction provides a modest driving force at micromolar concentrations of protein. The thermodynamic properties of this system are such that mutations can readily shift the equilibrium from the dimeric native state towards weakly folded states that have a lower affinity for inhibitors but that could be induced to bind to their target proteolytic sites. Presumably, subsequent secondary mutations increase the stability of the native dimeric state in these variants and, thereby, optimize the catalytic properties of the resistant human immunodeficiency virus type 1 protease.     

Elucidating quantitative stability/flexibility relationships within thioredoxin and its fragments using a distance constraint model

Numerous quantitative stability/flexibility relationships, within Escherichia coli thioredoxin (Trx) and its fragments are determined using a minimal distance constraint model (DCM). A one-dimensional free energy landscape as a function of global flexibility reveals Trx to fold in a low-barrier two-state process, with a voluminous transition state. Near the folding transition temperature, the native free energy basin is markedly skewed to allow partial unfolded forms. Under native conditions the skewed shape is lost, and the protein forms a compact structure with some flexibility. Predictions on ten Trx fragments are generally consistent with experimental observations that they are disordered, and that complementary fragments reconstitute. A hierarchical unfolding pathway is uncovered using an exhaustive computational procedure of breaking interfacial cross-linking hydrogen bonds that span over a series of fragment dissociations. The unfolding pathway leads to a stable core structure (residues 22-90), predicted to act as a kinetic trap. Direct connection between degree of rigidity within molecular structure and non-additivity of free energy is demonstrated using a thermodynamic cycle involving fragments and their hierarchical unfolding pathway. Additionally, the model provides insight about molecular cooperativity within Trx in its native state, and about intermediate states populating the folding/unfolding pathways. Native state cooperativity correlation plots highlight several flexibly correlated regions, giving insight into the catalytic mechanism that facilitates access to the active site disulfide bond. Residual native cooperativity correlations are present in the core substructure, suggesting that Trx can function when it is partly unfolded. This natively disordered kinetic trap, interpreted as a molten globule, has a wide temperature range of metastability, and it is identified as the "slow intermediate state" observed in kinetic experiments. These computational results are found to be in overall agreement with a large array of experimental data.     

Mechanisms of the multiphasic kinetics in the folding and unfolding of globular proteins

The multiphasic kinetics of the protein folding and unfolding processes are examined for a “cluster model” with only two thermodynamically stable macroscopic states, native (N) and denatured (D), which are essentially distributions of microscopic states. The simplest kinetic schemes consistent with the model are: N-(fast) → I-(slow) → D for unfolding and N ← (fast)-D₂ ← (slow)-D₁ for refolding. The fast phase during the unfolding process can be visualized as the redistribution of the native population N to I within its free energy valley. Then, this population crosses over the free energy barrier to the denatured state D in the slow phase. Therefore, the macrostate I is a kinetic intermediate which is not stable at equilibrium. For the refolding process, the initial equilibrium distribution of the denatured state D appears to be separated into D₁ and D₂ in the final condition because of the change in position of the free energy barrier. The fast refolding species D₂ is due to the “leak” from the broadly distributed D state, while the rest is the slow refolding species D₁, which must overpass the free energy barrier to reach N. At an early stage of the folding process the amino acid chain is considered to be composed of several locally ordered regions, which we call clusters, connected by random coil chain parts. Thus, the denatured state contains different sizes and distributions of clusters depending on the external condition. A later stage of the folding process is the association of smaller clusters. The native state is expressed by a maximum-size cluster with possible fluctuation sites reflecting this association. A general discussion is given of the correlation between the kinetics and thermodynamics of proteins from the overall shape of the free energy function. The cluster model provides a conceptual link between the folding kinetics and the structural patterns of globular proteins derived from the X-ray crystallographic data.     

Positive selection dictates the choice between kinetic and thermodynamic protein folding and stability in subtilases

Subtilisin E (SbtE) is a member of the ubiquitous superfamily of serine proteases called subtilases and serves as a model for understanding propeptide-mediated protein folding mechanisms. Unlike most proteins that adopt thermodynamically stable conformations, the native state of SbtE is trapped into a kinetically stable conformation. While kinetic stability offers distinct functional advantages to the native state, the constraints that dictate the selection between kinetic and thermodynamic folding and stability remain unknown. Using highly conserved subtilases, we demonstrate that adaptive evolution of sequence dictates selection of folding pathways. Intracellular and extracellular serine proteases (ISPs and ESPs, respectively) constitute two subfamilies within the family of subtilases that have highly conserved sequences, structures, and catalytic activities. Our studies on the folding pathways of subtilisin E (SbtE), an ESP, and its homologue intracellular serine protease 1 (ISP1), an ISP, show that although topology, contact order, and hydrophobicity that drive protein folding reactions are conserved, ISP1 and SbtE fold through significantly different pathways and kinetics. While SbtE absolutely requires the propeptide to fold into a kinetically trapped conformer, ISP1 folds to a thermodynamically stable state more than 1 million times faster and independent of a propeptide. Furthermore, kinetics establish that ISP1 and SbtE fold through different intermediate states. An evolutionary analysis of folding constraints in subtilases suggests that observed differences in folding pathways may be mediated through positive selection of specific residues that map mostly onto the protein surface. Together, our results demonstrate that closely related subtilases can fold through distinct pathways and mechanisms, and suggest that fine sequence details can dictate the choice between kinetic and thermodynamic folding and stability.     

Redesigning the hydrophobic core of a four-helix-bundle protein.

Rationally redesigned variants of the 4-helix-bundle protein Rop are described. The novel proteins have simplified, repacked, hydrophobic cores and yet reproduce the structure and native-like physical properties of the wild-type protein. The repacked proteins have been characterized thermodynamically and their equilibrium and kinetic thermal and chemical unfolding properties are compared with those of wild-type Rop. The equilibrium stability of the repacked proteins to thermal denaturation is enhanced relative to that of the wild-type protein. The rate of chemically induced folding and unfolding of wild-type Rop is extremely slow when compared with other small proteins. Interestingly, although the repacked proteins are more thermally stable than the wild type, their rates of chemically induced folding and unfolding are greatly increased in comparison to wild type. Perhaps as a consequence of this, their equilibrium stabilities to chemical denaturants are slightly reduced in comparison to the wild type.     

Oxidative folding and structural analyses of a Kunitz-related inhibitor and its disulfide intermediates: functional implications

Tick-derived protease inhibitor (TdPI) is a tight-binding Kunitz-related inhibitor of human tryptase β with a unique structure and disulfide-bond pattern. Here we analyzed its oxidative folding and reductive unfolding by chromatographic and disulfide analyses of acid-trapped intermediates. TdPI folds through a stepwise generation of heterogeneous populations of one-disulfide, two-disulfide, and three-disulfide intermediates, with a major accumulation of the nonnative three-disulfide species IIIa. The rate-limiting step of the process is disulfide reshuffling within the three-disulfide population towards a productive intermediate that oxidizes directly into the native four-disulfide protein. TdPI unfolds through a major accumulation of the native three-disulfide species IIIb and the subsequent formation of two-disulfide and one-disulfide intermediates. NMR characterization of the acid-trapped and further isolated IIIa intermediate revealed a highly disordered conformation that is maintained by the presence of the disulfide bonds. Conversely, the NMR structure of IIIb showed a native-like conformation, with three native disulfide bonds and increased flexibility only around the two free cysteines, thus providing a molecular basis for its role as a productive intermediate. Comparison of TdPI with a shortened variant lacking the flexible prehead and posthead segments revealed that these regions do not contribute to the protein conformational stability or the inhibition of trypsin but are important for both the initial steps of the folding reaction and the inhibition of tryptase β. Taken together, the results provide insights into the mechanism of oxidative folding of Kunitz inhibitors and pave the way for the design of TdPI variants with improved properties for biomedical applications.     

Osmolyte effects on kinetics of FKBP12 C22A folding coupled with prolyl isomerization

Unfolding and refolding kinetics of human FKBP12 C22A were monitored by fluorescence emission over a wide range of urea concentration in the presence and absence of protecting osmolytes glycerol, proline, sarcosine and trimethylamine-N-oxide (TMAO). Unfolding is well described by a mono-exponential process, while refolding required a minimum of two exponentials for an adequate fit throughout the urea concentration range considered. The bi-exponential behavior resulted from complex coupling between protein folding, and prolyl isomerization in the denatured state in which the urea-dependent rate constant for folding was greater than, equal to, and less than the rate constants for prolyl isomerization within the urea concentration range of zero to five molar. Amplitudes and the observed folding and unfolding rate constants were fitted to a reversible three-state model composed of two sequential steps involving the native state and a folding-competent denatured species thermodynamically linked to a folding-incompetent denatured species. Excellent agreement between thermodynamic parameters for FKBP12 C22A folding calculated from the kinetic parameters and those obtained directly from equilibrium denaturation assays provides strong support for the applicability of the mechanism, and provides evidence that FKBP12 C22A folding/unfolding is two-state, with prolyl isomer heterogeneity in the denatured ensemble. Despite the chemical diversity of the protecting osmolytes, they all exhibit the same kinetic behavior of increasing the rate constant of folding and decreasing the rate constant for unfolding. Osmolyte effects on folding/unfolding kinetics are readily explained in terms of principles established in understanding osmolyte effects on protein stability. These principles involve the osmophobic effect, which raises the Gibbs energy of the denatured state due to exposure of peptide backbone, thereby increasing the folding rate. This effect also plays a key role in decreasing the unfolding rate when, as is often the case, the activated complex exposes more backbone than is exposed in the native state.     

Phi-analysis at the experimental limits: mechanism of beta-hairpin formation

The 37-residue Formin-binding protein, FBP28, is a canonical three-stranded beta-sheet WW domain. Because of its small size, it is so insensitive to chemical denaturation that it is barely possible to determine accurately a denaturation curve, as the transition spans 0-7 M guanidinium hydrochloride (GdmCl). It is also only marginally stable, with a free energy of denaturation of just 2.3 kcal/mol at 10 degrees Celsius so only small changes in energy upon mutation can be tolerated. But these properties and relaxation times for folding of 25 micros-400 micros conspire to allow the rapid acquisition of accurate and reproducible kinetic data for Phi-analysis using classical temperature-jump methods. The transition state for folding is highly polarized with some regions having Phi-values of 0 and others 1, as readily seen in chevron plots, with Phi-values of 0 having the refolding arms overlaying and those of 1 the unfolding arms superimposable. Good agreement is seen with transition state structures identified from independent molecular dynamics (MD) simulations at 60, 75, and 100 degrees Celsius, which allows us to explore further the details of the folding and unfolding pathway of FBP28. The first beta-turn is near native-like in the transition state for folding (experimental) and unfolding (MD and experiment). The simulations show that there are transient contacts between the aromatic side-chains of the beta-strands in the denatured state and that these interactions provide the driving force for folding of the first beta-hairpin of this three-stranded sheet. Only after the backbone hydrogen bonds are formed between beta1 and beta2 does a hydrogen bond form to stabilize the intervening turn, or the first beta-turn.