Mapping the transition state of the WW domain beta-sheet

The folding kinetics of a three-stranded antiparallel beta-sheet (WW domain) have been measured by temperature jump relaxation. Folding and activation free energies were determined as a function of temperature for both the wild-type and the mutant domain, W39F, which modifies the beta(2)-beta(3) hydrophobic interface. The folding rate decreases at higher temperatures as a result of the increase in the activation free energy for folding. Phi-Values were obtained for thermal perturbations allowing the primary features of the folding free energy surface to be determined. The results of this analysis indicate a significant shift from an "early" (Phi(T)=0. 4) to a "late" (Phi(T)=0.8) transition state with increasing temperature. The temperature-dependent Phi-value analysis of the wild-type WW domain and of its more stable W39F hydrophobic cluster mutant reveals little participation of residue 39 in the transition state at lower temperature. As the temperature is raised, hydrophobic interactions at the beta(2)-beta(3) interface gain importance in the transition state and the barrier height of the wild-type, which contains the larger tryptophan residue, increases more slowly than the barrier height of the mutant.     

The contribution of the residues from the main hydrophobic core of ribonuclease A to its pressure-folding transition state

The role of hydrophobic interactions established by the residues that belong to the main hydrophobic core of ribonuclease A in its pressure-folding transition state was investigated using the Phi-value method. The folding kinetics was studied using pressure-jump techniques both in the pressurization and depressurization directions. The ratio between the folding activation volume and the reaction volume (beta p-value), which is an index of the compactness or degree of solvation of the transition state, was calculated. All the positions analyzed presented fractional Phi f-values, and the lowest were those corresponding to the most critical positions for the ribonuclease A stability. The structure of the transition state of the hydrophobic core of ribonuclease A, from the point of view of formed interactions, is a relatively, uniformly expanded form of the folded structure with a mean Phi f-value of 0.43. This places it halfway between the folded and unfolded states. On the other hand, for the variants, the average of beta p-values is 0.4, suggesting a transition state that is 40% native-like. Altogether the results suggest that the pressure-folding transition state of ribonuclease A looks like a collapsed globule with some secondary structure and a weakened hydrophobic core. A good correlation was found between the Phi f-values and the Deltabeta p-values. Although the nature of the transition state inferred from pressure-induced folding studies and the results of the protein engineering method have been reported to be consistent for other proteins, to the best of our knowledge this is the first direct comparison using a set of mutants.     

A semiflexible polymer model applied to loop formation in DNA hairpins

A statistical mechanical "zipper" model is applied to describe the equilibrium melting of short DNA hairpins with poly(dT) loops ranging from 4 to 12 bases in the loop. The free energy of loop formation is expressed in terms of the persistence length of the chain. This method provides a new measurement of the persistence length of single-stranded DNA, which is found to be approximately 1.4 nm for poly(dT) strands in 100 mM NaCl. The free energy of the hairpin relative to the random coil state is found to scale with the loop size with an apparent exponent of > or = 7, much larger than the exponent of approximately 1.5-1.8 expected from considerations of loop entropy alone. This result indicates a strong dependence of the excess stability of the hairpins, from stacking interactions of the bases within the loop, on the size of the loop. We interpret this excess stability as arising from favorable hydrophobic interactions among the bases in tight loops and which diminish as the loops get larger. Free energy profiles along a generalized reaction coordinate are calculated from the equilibrium zipper model. The transition state for hairpin formation is identified as an ensemble of looped conformations with one basepair closing the loop, and with a lower enthalpy than the random coil state. The equilibrium model predicts apparent activation energy of approximately -11 kcal/mol for the hairpin closing step, in remarkable agreement with the value obtained from kinetics measurements.     

Context-dependent effects of proline residues on the stability and folding pathway of ubiquitin.

Substitution of trans-proline at three positions in ubiquitin (residues 19, 37 and 38) produces significant context-dependent effects on protein stability (both stabilizing and destabilizing) that reflect changes to a combination of parameters including backbone flexibility, hydrophobic interactions, solvent accessibility to polar groups and intrinsic backbone conformational preferences. Kinetic analysis of the wild-type yeast protein reveals a predominant fast-folding phase which conforms to an apparent two-state folding model. Temperature-dependent studies of the refolding rate reveal thermodynamic details of the nature of the transition state for folding consistent with hydrophobic collapse providing the overall driving force. Br?nsted analysis of the refolding and unfolding rates of a family of mutants with a variety of side chain substitutions for P37 and P38 reveals that the two prolines, which are located in a surface loop adjacent to the C terminus of the main alpha-helix (residues 24-33), are not significantly structured in the transition state for folding and appear to be consolidated into the native structure only late in the folding process. We draw a similar conclusion regarding position 19 in the loop connecting the N-terminal beta-hairpin to the main alpha-helix. The proline residues of ubiquitin are passive spectators in the folding process, but influence protein stability in a variety of ways.     

Folding pathway dependence on energetic frustration and interaction heterogeneity for a three-dimensional hydrophobic protein model

Monte Carlo simulations of a hydrophobic protein model of 40 monomers in the cubic lattice are used to explore the effect of energetic frustration and interaction heterogeneity on its folding pathway. The folding pathway is described by the dependence of relevant conformational averages on an appropriate reaction coordinate, pfold, defined as the probability for a given conformation to reach the native structure before unfolding. We compare the energetically frustrated and heterogeneous hydrophobic potential, according to which individual monomers have a higher or lower tendency to form contacts unspecifically depending on their hydrophobicities, to an unfrustrated homogeneous Go-type potential with uniformly attractive native interactions and neutral non-native interactions (called Go1 in this study), and to an unfrustrated heterogeneous potential with neutral non-native interactions and native interactions having the same energy as the hydrophobic potential (called Go2 in this study). Folding kinetics are slowed down dramatically when energetic frustration increases, as expected and previously observed in a two-dimensional model. Contrary to our previous results in two dimensions, however, it appears that the folding pathway and transition state ensemble can be significantly dependent on the energy function used to stabilize the native structure. The sequence of events along the reaction coordinate, or the order along this coordinate in which different regions of the native conformation become structured, turns out to be similar for the hydrophobic and Go2 potentials, but with analogous events tending to occur at lower pfold values in the first case. In particular, the transition state obtained from the ensemble around pfold = 0.5 is more structured for the hydrophobic potential. For Go1, not only the transition state ensemble but the order of events itself is modified, suggesting that interaction heterogeneity, in addition to energetic frustration, can have significant effects on the folding mechanism, most likely by modifying the probability of different contacts in the unfolded state, the starting point for the folding reaction. Although based on a simple model, these results provide interesting insight into how sequence-dependent switching between folding pathways might occur in real proteins.     

The effect of surface charge balance on thermodynamic stability and kinetics of refolding of firefly luciferase

Thermodynamic stability and refolding kinetics of firefly luciferase and three representative mutants with depletion of negative charge on a flexible loop via substitution of Glu by Arg (ER mutant) or Lys (EK mutant) as well as insertion of another Arg in ER mutants (ERR mutant) was investigated. According to thermodynamic studies, structural stability of ERR and ER mutants are enhanced compared to WT protein, whereas, these mutants become prone to aggregation at higher temperatures. Accordingly, it was concluded that enhanced structural stability of mutants depends on more compactness of folded state, whereas aggregation at higher temperatures in mutants is due to weakening of intermolecular repulsive electrostatic interactions and increase of intermolecular hydrophobic interactions. Kinetic results indicate that early events of protein folding are accelerated in mutants.     

Temperature and driving force dependence of the folding rate of reduced horse heart cytochrome c

Utilizing the stability difference between the ferro and ferri forms of horse heart cytochrome c (cyt c), folding of reduced cyt c was triggered by laser-induced reduction of unfolded oxidized cyt c. Measurements were made of the kinetics of the main folding phase (1 ms-10 s) in which collapsed reduced cyt c transforms to the native conformation. The folding rates were studied extensively as a function of temperature (5-75 degrees C) and guanidine hydrochloride (GdnHCl) concentration (1.6-4.9 M). At constant [GdnHCl], the Arrhenius plot of the folding rate constant (k) is nonlinear. At temperatures above 40 degrees C, the decrease in protein stability counteracts the expected increase in folding rate. Introducing free energy (DeltaG), derived from protein stability data, into the Eyring and Arrhenius equations leads to: ln k = ln(k(b)T/h) + DeltaS()/R - DeltaH()/RT - theta(m)DeltaG/RT = ln A - E(a)/RT - theta(m)DeltaG/RT, where theta(m) is the ratio between the denaturant dependence of the folding rate and the stability. By using this equation at constant DeltaG [or constant equilibrium constant (K)], linear Arrhenius plots are obtained. For the main folding phase of reduced cyt c, a positive DeltaS() is obtained indicating that the transition state is less ordered than the reactant. A model is proposed in which reduced cyt c first collapses into a compact intermediate, which needs to expand to reach the transition state of the rate-limiting folding reaction.     

Non-native interactions,effective contact order,and protein folding: a mutational investigation with the energetically frustrated hydrophobic model

By Monte Carlo simulations, we explored the effect of single mutations on the thermodynamics and kinetics of the folding of a two-dimensional, energetically frustrated, hydrophobic protein model. Phi-Value analysis, corroborated by simulations beginning from given sets of judiciously chosen initial contacts, suggests that the transition state of the model consists of a limited region of the native structure, that is, a folding nucleus. It seems that the most important contacts in the transition state (large and positive Phi) are not the ones with the highest contact order, because in this case the entropic cost of their formation would be too high, but exactly the ones that decrease the entropic cost of difficult contacts, reducing their effective contact order. Mutations of internal monomers involved in high-order contacts were actually the ones resulting in the fastest kinetics (and Phi < 0), indicating they tend to make low order, non-native contacts of low entropic cost that stabilize the unfolded state with respect to the transition state. Folding acceleration by other non-native interactions was also observed and a simple general mechanism is proposed according to which non-native contacts can act indirectly over the folding nucleus, "chelating" out potentially harmful contacts. The polymer graph of our model, which facilitates the visualization of effective contact orders, successfully suggests the relative kinetic importance of different contacts and is reasonably consistent with analogous graphs for the well characterized family of SH3 domains.     

Sequential barriers and an obligatory metastable intermediate define the apparent two-state folding pathway of the ubiquitin-like PB1 domain of NBR1

The 90-residue N-terminal Phox and Bem1p (PB1) domain of NBR1 forms an α/β ubiquitin-like fold. Kinetic analysis using stopped-flow fluorescence reveals two-state kinetics; however, nonlinear effects in the denaturant dependence of the unfolding data demonstrate changes in the position of the rate-limiting barrier along the folding coordinate as the folding conditions change. The kinetics of wt-PB1 and several mutants show that this curvature is consistent with a single-pathway mechanism involving sequential transition states (TS1 and TS2) separated by a transiently populated high-energy intermediate, rather than movement of the transition state on a broad energy plateau. We show that the two transition states within the sequential model represent structurally and thermodynamically distinct species. TS1 is a collapsed state (α_TS1 = 0.71) with a large enthalpic barrier to formation that is rate-limiting under conditions that strongly favour folding. TS2 is highly native-like (α_TS2 = 0.93) and represents a late entropic barrier to formation of the native state. In support of the sequential transition state mechanism, we show that the G62A helix 2 substitution stabilises TS1 and the intermediate to such an extent that the latter becomes significantly populated, leading to the observation of a fast kinetic phase representing the initial U → I transition, with TS2 (α_TS2 = 0.87) becoming rate-limiting. The folding rate is not retarded by populating an intermediate, which would be expected for a misfold state, but is accelerated, suggesting that the I state is productive and on-pathway. The results show that the apparent two-state folding of the wt-PB1 domain occurs along a well-defined pathway involving structurally and thermodynamically distinct sequential transition states and an obligatory metastable intermediate that represents a productive local minimum in the energy landscape that increases the efficiency of barrier crossing through favourable effects on the entropy of activation.     

The folding pathway of an FF domain: characterization of an on-pathway intermediate state under folding conditions by (15)N, (13)C(alpha) and (13)C-methyl relaxation dispersion and (1)H/(2)H-exchange NMR spectroscopy

The FF domain from the human protein HYPA/FBP11 folds via a low-energy on-pathway intermediate (I). Elucidation of the structure of such folding intermediates and denatured states under conditions that favour folding are difficult tasks. Here, we investigated the millisecond time-scale equilibrium folding transition of the 71-residue four-helix bundle wild-type protein by (15)N, (13)C(alpha) and methyl(13)C Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion experiments and by (1)H/(2)H-exchange measurements. The relaxation data for the wild-type protein fitted a simple two-site exchange process between the folded state (F) and I. Destabilization of F in mutants A17G and Q19G allowed the detection of the unfolded state U by (15)N CPMG relaxation dispersion. The dispersion data for these mutants fitted a three-site exchange scheme, U<-->I<-->F, with I populated higher than U. The kinetics and thermodynamics of the folding reaction were obtained via temperature and urea-dependent relaxation dispersion experiments, along with structural information on I from backbone (15)N, (13)C(alpha) and side-chain methyl (13)C chemical shifts, with further information from protection factors for the backbone amide groups from (1)H/(2)H-exchange. Notably, helices H1-H3 are at least partially formed in I, while helix H4 is largely disordered. Chemical shift differences for the methyl (13)C nuclei suggest a paucity of stable, native-like hydrophobic interactions in I. These data are consistent with Phi-analysis of the rate-limiting transition state between I and F. The combination of relaxation dispersion and Phi data can elucidate whole experimental folding pathways.     

Structure and function in bacteriorhodopsin: the effect of the interhelical loops on the protein folding kinetics

The loops connecting the seven transmembrane helices of bacteriorhodopsin have each been replaced in turn by structureless linkers of Gly-Gly-Ser repeat sequences, and the effect on the protein folding kinetics has been determined. An SDS-denatured state of each loop mutant bacterio-opsin was folded in l-alpha-1,2-dihexanoylphosphatidylcholine/l-alpha-1,2-dimyristoylphosphatidylcholine micelles, containing retinal, to give functional bacteriorhodopsin. Stopped-flow mixing was used to initiate the folding reaction, giving a time resolution of milliseconds, and changes in protein fluorescence were used to monitor folding. All loop mutant proteins folded according to the same reaction scheme as wild-type protein. The folding kinetics of the AB, BC and DE loop mutants were the same as wild-type protein, despite the blue-shifted chromophore band of the BC loop mutant bR state. A partially folded apoprotein intermediate state of the AB loop mutant did however appear to decay in the absence of retinal. The most significant effects on the folding kinetics were seen for mutant protein with structureless linkers in place of the CD, EF and FG loops. The rate-limiting apoprotein folding step of the CD loop mutant was about ten times slower than wild-type, whilst that of the EF loop mutant was almost four times slower than wild-type. Wild-type behaviour was observed for the other folding and retinal binding events of the CD and EF loop mutant proteins. These effects of the CD and EF loop mutations on apoprotein folding correlate with the fact that these two loop mutants also have the least stable, partially folded apoprotein intermediate of all the loop mutants, and are the most affected by a decrease in lipid lateral pressure. In contrast, the FG loop mutant exhibited wild-type apoprotein folding, but altered covalent binding of retinal and final folding to bacteriorhodopsin. This correlates with the fact that the FG loop mutant bacteriorhodopsin is the most susceptible to denaturation by SDS of all the loop mutants, but its partially folded apoprotein intermediate is more stable than that of the CD and EF mutants. Thus the CD and EF loops may contribute to the transition state for the rate-limiting apoprotein folding step and the FG loop to that for final folding and covalent binding of retinal.     

Evidence for partial secondary structure formation in the transition state for arc repressor refolding and dimerization

Structure formation and dimerization are concerted processes in the refolding of Arc repressor. The integrity of secondary structure in the transition state of Arc refolding has been investigated here by determining the changes in equilibrium stability and refolding/unfolding kinetics for a set of Ala --> Gly mutations at residues that are solvent-exposed in the native Arc dimer. At some sites, reduced stability was caused primarily by faster unfolding, indicating that secondary structure at these positions is largely absent in the transition state. However, most of the Ala --> Gly substitutions in the alpha-helices of Arc and a triple mutant in the beta-sheet also resulted in decreased refolding rates, in some cases, accounting for the major fraction of thermodynamic destabilization. Overall, these results suggest that some regions of native secondary structure are present but incompletely formed in the transition state of Arc refolding and dimerization. Consolidation of this secondary structure, like close packing of the hydrophobic core, seems to occur later in the folding process. On average, Phi(F) values for the Ala --> Gly mutations were significantly larger than Phi(F) values previously determined for alanine-substitution mutants, suggesting that backbone interactions in the transition state may be stronger than side chain interactions. Mutations causing significant reductions in the Arc refolding rate were found to cluster in the central turn of alpha-helix A and in the first two turns of alpha-helix B. In the Arc dimer, these elements pack together in a compact structure, which might serve as nucleus for further folding.     

Effects of mutation, truncation, and temperature on the folding kinetics of a WW domain

The purpose of this work is to show how mutation, truncation, and change of temperature can influence the folding kinetics of a protein. This is accomplished by principal component analysis of molecular-dynamics-generated folding trajectories of the triple β-strand WW domain from formin binding protein 28 (FBP28) (Protein Data Bank ID: 1E0L) and its full-size, and singly- and doubly-truncated mutants at temperatures below and very close to the melting point. The reasons for biphasic folding kinetics [i.e., coexistence of slow (three-state) and fast (two-state) phases], including the involvement of a solvent-exposed hydrophobic cluster and another delocalized hydrophobic core in the folding kinetics, are discussed. New folding pathways are identified in free-energy landscapes determined in terms of principal components for full-size mutants. Three-state folding is found to be a main mechanism for folding the FBP28 WW domain and most of the full-size and truncated mutants. The results from the theoretical analysis are compared to those from experiment. Agreements and discrepancies between the theoretical and experimental results are discussed. Because of its importance in understanding protein kinetics and function, the diffusive mechanism by which the FBP28 WW domain and its full-size and truncated mutants explore their conformational space is examined in terms of the mean-square displacement and principal component analysis eigenvalue spectrum analyses. Subdiffusive behavior is observed for all studied systems.     

Transition-states in protein folding kinetics: the structural interpretation of Phi values

Phi values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is what structural information Phi values give about the transition-state of folding. Traditionally, a Phi value is interpreted as representing the "nativeness" of a mutated residue in the transition-state. However, this interpretation is often problematic. We present here a better structural interpretation of Phi values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free energy contributions of helical residues. From a linear fit of the model to experimental data, we obtain two structural parameters: the extent of helix formation in the transition-state, and the nativeness of tertiary interactions in the transition-state. We apply the model to all proteins with well-characterized helices for which more than 10 Phi values are available: protein A, CI2, and protein L. The model is simple to apply to experimental data, captures nonclassical Phi values <0 or >1 in these helices, and explains how different mutations at a given site can lead to different Phi values.     

Exploring the temperature-pressure phase diagram of staphylococcal nuclease

The temperature dependence of the pressure-induced equilibrium unfolding of staphylococcal nuclease (Snase) was determined by fluorescence of the single tryptophan residue, FTIR absorption for the amide I' and tyrosine O-H bands, and small-angle X-ray scattering (SAXS). The results from these three techniques were similar, although the stability as measured by fluorescence was slightly lower than that measured by FTIR and SAXS. The resulting phase diagram exhibits the well-known curvature for heat and cold denaturation of proteins, due to the large decrease in heat capacity upon folding. The volume change for unfolding became less negative with increasing temperatures, consistent with a larger thermal expansivity for the unfolded state than for the folded state. Fluorescence-detected pressure-jump kinetics measurements revealed that the curvature in the phase diagram is due primarily to the rate constant for folding, indicating a loss in heat capacity for the transition state relative to the unfolded state. The similar temperature dependence of the equilibrium and activation volume changes for folding indicates that the thermal expansivities of the folded and transition states are similar. This, along with the fact that the activation volume for folding is positive over the temperature range examined, the nonlinear dependence of the folding rate constant upon temperature implicates significant dehydration in the rate-limiting step for folding of Snase.     

Contribution of glycine 146 to a conserved folding module affecting stability and refolding of human glutathione transferase p1-1

In human glutathione transferase P1-1 (hGSTP1-1) position 146 is occupied by a glycine residue, which is located in a bend of a long loop that together with the alpha6-helix forms a substructure (GST motif II) maintained in all soluble GSTs. In the present study G146A and G146V mutants were generated by site-directed mutagenesis in order to investigate the function played by this conserved residue in folding and stability of hGSTP1-1. Crystallographic analysis of the G146V variant, expressed at the permissive temperature of 25 degrees C, indicates that the mutation causes a substantial change of the backbone conformation because of steric hindrance. Stability measurements indicate that this mutant is inactivated at a temperature as low as 32 degrees C. The structure of the G146A mutant is identical to that of the wild type with the mutated residue having main-chain bond angles in a high energy region of the Ramachandran plot. However even this Gly --> Ala substitution inactivates the enzyme at 37 degrees C. Thermodynamic analysis of all variants confirms, together with previous findings, the critical role played by GST motif II for overall protein stability. Analysis of reactivation in vitro indicates that any mutation of Gly-146 alters the folding pathway by favoring aggregation at 37 degrees C. It is hypothesized that the GST motif II is involved in the nucleation mechanism of the protein and that the substitution of Gly-146 alters this transient substructure. Gly-146 is part of the buried local sequence GXXh(T/S)XXDh (X is any residue and h is a hydrophobic residue), conserved in all GSTs and related proteins that seems to behave as a characteristic structural module important for protein folding and stability.     

Tuning lambda6-85 towards downhill folding at its melting temperature

The five-helix bundle lambda6-85* is a fast two-state folder. Several stabilized mutants have been reported to fold kinetically near-downhill or downhill. These mutants undergo a transition to two-state folding kinetics when heated. It has been suggested that this transition is caused by increased hydrophobicity at higher temperature. Here we investigate two histidine-containing mutants of lambda6-85* to see if a weaker hydrophobic core can extend the temperature range of downhill folding. The very stable lambdaHA is the fastest-folding lambda repressor to date (k(f)(-1) approximately k(obs)(-1)=2.3 micros at 44 degrees C). It folds downhill at low temperature, but transits back to two-state folding at its unfolding midpoint. lambdaHG has a weakened hydrophobic core. It is less stable than some slower folding mutants of lambda6-85*, and it has more exposed hydrophobic surface area in the folded state. This mutant nonetheless folds very rapidly, and has the non-exponential folding kinetics of an incipient downhill folder even at the unfolding midpoint (k(m)(-1) approximately 2 micros, k(a)(-1)=15 micros at 56 degrees C). We also compare the thermodynamic melting transition of lambdaHG with the nominal two-state folding mutant lambdaQG, which has a similar melting temperature. Unlike lambdaQG, lambdaHG yields fluorescence wavelength-dependent cooperativities and probe-dependent melting temperatures. This result combined with previous work shows that the energy landscapes of lambda repressor mutants support all standard folding mechanisms.     

The relationship between conservation, thermodynamic stability, and function in the SH3 domain hydrophobic core

To investigate the relationships between sequence conservation, protein stability, and protein function, we have measured the thermodynamic stability, folding kinetics, and in vitro peptide-binding activity of a large number of single-site substitutions in the hydrophobic core of the Fyn SH3 domain. Comparison of these data to that derived from an analysis of a large alignment of SH3 domain sequences revealed a very good correlation between the distinct pattern of conservation observed at each core position and the thermodynamic stability of mutants. Conservation was also found to correlate well with the unfolding rates of mutants, but not to the folding rates, suggesting that evolution selects more strongly for optimal native state packing interactions than for maximal folding rates. Structural analysis suggests that residue-residue core packing interactions are very similar in all SH3 domains, which provides an explanation for the correlation between conservation and mutant stability effects studied in a single SH3 domain. We also demonstrate a correlation between stability and the in vivo activity of mutants, and between conservation and activity. However, the relationship between conservation and activity was very strong only for the three most conserved hydrophobic core positions. The weaker correlation between activity and conservation seen at the other seven core positions indicates that maintenance of protein stability is the dominant selective pressure at these positions. In general, the pattern of conservation at hydrophobic core positions appears to arise from conserved packing constraints, and can be effectively utilized to predict the destabilizing effects of amino acid substitutions.