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.     

Folding kinetics of phage 434 Cro protein

Folding kinetics for phage 434 Cro protein are examined and compared with those reported for lambda(6-85), the N-terminal domain of the repressor of phage lambda. The two proteins have similar all-helical structures consisting of five helices but different stabilities. In contrast to lambda(6-85), sharp and distinct aromatic (1)H NMR signals without exchange broadening characterize the native and urea-denatured 434 Cro forms at equilibrium at 20 degrees C, indicating slow interconversion on the NMR time scale. Stopped-flow fluorescence data using the single 434 Cro tryptophan indicate strongly urea-dependent refolding rates and smaller urea dependencies of the unfolding rates, suggesting a native-like transition state ensemble. Refolding rates are slower and unfolding rates considerably faster at pH 4 than at pH 6. This accounts for the lower stability of 434 Cro at pH 4 and suggests the existence of pH-dependent, possibly salt bridge interactions that are more stabilizing at pH 6. At <2 M urea, decreased folding amplitudes and nonlinear urea dependencies that are apparent at pH 6 indicate deviation from two-state behavior and suggest the formation of an early folding intermediate. The folding behavior of 434 Cro and why it folds 2 orders of magnitude slower than lambda(6-85) are rationalized in terms of the lower intrinsic helix stabilities and putative charge interactions in 434 Cro.     

A Survey of λ Repressor Fragments from Two-State to Downhill Folding

We survey the two-state to downhill folding transition by examining 20 λ_6-85^? mutants that cover a wide range of stabilities and folding rates. We investigated four new λ_6-85^? mutants designed to fold especially rapidly. Two were engineered using the core remodeling of Lim and Sauer, and two were engineered using Ferreiro et al.'s frustratometer. These proteins have probe-dependent melting temperatures as high as 80 °C and exhibit a fast molecular phase with the characteristic temperature dependence of the amplitude expected for downhill folding. The survey reveals a correlation between melting temperature and downhill folding previously observed for the β-sheet protein WW domain. A simple model explains this correlation and predicts the melting temperature at which downhill folding becomes possible. An X-ray crystal structure with a 1.64-Å resolution of a fast-folding mutant fragment shows regions of enhanced rigidity compared to the full wild-type protein.     

Apparent two-state tendamistat folding is a sequential process along a defined route

The small all-beta-sheet protein tendamistat folds and unfolds rapidly in apparent two-state reactions. Kinetic measurements of two tendamistat variants under various solvent conditions reveal, however, that folding occurs in at least two sequential steps through a metastable obligatory intermediate. Depending on the solvent conditions either step can become rate limiting. The activation parameters indicate that the first step represents an enthalpic barrier whereas the second step is an entropic barrier at 25 degrees C. Our results suggest that initial non-specific collapse precedes formation of native secondary and tertiary structure in tendamistat folding. This points at a distinct route in tendamistat folding and indicates that partially folded metastable intermediates might play an important role in the mechanism of apparent two-state folding.     

Folding of circular permutants with decreased contact order: general trend balanced by protein stability.

To examine the influence of contact order and stability on the refolding rate constant for two-state proteins, we have analysed the folding kinetics of the small beta-alpha-beta protein S6 and two of its circular permutants with relative contact orders of 0.19, 0.15 and 0.12. Data reveal a small but significant increase of the refolding rate constant (log k(f)) with decreasing contact order. At the same time, the decreased contact order is correlated to losses in global stability and alterations of the folding nucleus. When the differences in stability are accounted for by addition of Na2SO4 or by comparison of the folding kinetics at the transition mid-point, the dependence between log k(f) and contact order becomes stronger and follows the general correlation for two-state proteins. The observation emphasizes the combined action of topology and stability in controlling the rate constant of protein folding.     

Rate-temperature relationships in lambda-repressor fragment lambda 6-85 folding

Two classes of lambda(6-85) mutants (those richer in alanine, and those richer in glycine) have very similar slopes in an Arrhenius plot of the unfolding rates but very different temperature dependencies of the folding rates. Temperature-dependent interactions (e.g., hydrophobicity) play a large role in the initial stages of folding but not in the initial stages of unfolding of lambda(6-85). Placement of the transition state in terms of its surface exposure and entropy shows that at least two reaction coordinates are required to describe folding of all mutants over the full temperature range. The unusual Arrhenius plots of the very fastest mutant provide an additional kinetic signature for downhill folding.     

The folding of staphylococcal nuclease in the presence of methanol or guanidine thiocyanate

The effect of methanol on the folding of staphylococcal nuclease has been investigated. Equilibrium thermal unfolding transitions were monitored by fluorescence emission. The transition was very sensitive to the presence of methanol (at pH 7.0), the Tm decreased from above 50 degrees C for aqueous solution to below 0 degree C for 70% methanol. The transitions were fully reversible and conformed to two-state behavior. A linear relationship was observed between the hydrophobicity of the solvent and both the Tm and the change in delta G for unfolding. The effect of pH on the transition in 50% methanol at 0 degree C was essentially the same as for aqueous solution, with a cooperative transition in the vicinity of apparent pH (pH*) 4. The unfolding transition was determined as a function of guanidine thiocyanate in aqueous and 50% methanol solvents. The midpoints of the transitions were 0.30 and 0.20 M, respectively, at 2.1 degrees C. The kinetics of folding at 0 degree C were compared in aqueous, 50% methanol and 0.30 M guanidine thiocyanate solvents, by monitoring changes in the tryptophan fluorescence intensity. Triphasic kinetics for refolding in both aqueous and 50% methanol solutions were observed in stopped-flow experiments. In both solvent systems the slowest phase is ascribed to proline isomerization. The kinetics of refolding were monitored at subzero temperatures in 50% methanol at pH* 7.0 in manual mixing experiments. Biphasic kinetics were observed at temperatures between 0 and -35 degrees C. A third, faster phase, was inferred from the missing amplitude. The energies of activation were 20.0 and 17.2 kcal mol-1, respectively, for the two slower phases. At -33.8 degrees C, the observed pseudo first-order rate constants were 1.2 x 10(-3) and 2.1 x 10(-5) s-1. At temperatures above -35 degrees C, the sum of the observed amplitudes was essentially constant at 70-75% of the expected total amplitude. At lower temperatures the amplitude of the refolding reaction decreased, and the native state was not formed (unless the temperature was increased), due to the formation of a trapped intermediate state. This intermediate has circular dichroism and fluorescence properties consistent with a compact state with some molten globule characteristics.     

Folding of a designed simple ankyrin repeat protein

Ankyrin repeats (AR) are 33-residue motifs containing a beta-turn, followed by two alpha-helices connected by a loop. AR occur in tandem arrangements and stack side-by-side to form elongated domains involved in very different cellular tasks. Recently, consensus libraries of AR repeats were constructed. Protein E1_5 represents a member of the shortest library, and consists of only a single consensus repeat flanked by designed N- and C-terminal capping repeats. Here we present a biophysical characterization of this AR domain. The protein is compactly folded, as judged from the heat capacity of the native state and from the specific unfolding enthalpy and entropy. From spectroscopic data, thermal and urea-induced unfolding can be modeled by a two-state transition. However, scanning calorimetry experiments reveal a deviation from the two-state behavior at elevated temperatures. Folding and unfolding at 5 degrees C both follow monoexponential kinetics with k(folding) = 28 sec(-1) and k(unfolding) = 0.9 sec(-1). Kinetic and equilibrium unfolding parameters at 5 degrees C agree very well. We conclude that E1_5 folds in a simple two-state manner at low temperatures while equilibrium intermediates become populated at higher temperatures. A chevron-plot analysis indicates that the protein traverses a very compact transition state along the folding/unfolding pathway. This work demonstrates that a designed minimal ankyrin repeat protein has the thermodynamic and kinetic properties of a compactly folded protein, and explains the favorable properties of the consensus framework.     

Multiple folding pathways for the P4-P6 RNA domain

We recently described site-specific pyrene labeling of RNA to monitor Mg(2+)-dependent equilibrium formation of tertiary structure. Here we extend these studies to follow the folding kinetics of the 160-nucleotide P4-P6 domain of the Tetrahymena group I intron RNA, using stopped-flow fluorescence with approximately 1 ms time resolution. Pyrene-labeled P4-P6 was prepared using a new phosphoramidite that allows high-yield automated synthesis of oligoribonucleotides with pyrene incorporated at a specific 2'-amino-2'-deoxyuridine residue. P4-P6 forms its higher-order tertiary structure rapidly, with k(obs) = 15-31 s(-1) (t(1/2) approximately 20-50 ms) at 35 degrees C and [Mg(2+)] approximately 10 mM in Tris-borate (TB) buffer. The folding rate increases strongly with temperature from 4 to 45 degrees C, demonstrating a large activation enthalpy DeltaH(double dagger) approximately 26 kcal/mol; the activation entropy DeltaS(double dagger) is large and positive. In low ionic strength 10 mM sodium cacodylate buffer at 35 degrees C, a slow (t(1/2) approximately 1 s) folding component is also observed. The folding kinetics are both ionic strength- and temperature-dependent; the slow phase vanishes upon increasing [Na(+)] in the cacodylate buffer, and the kinetics switch completely from fast at 30 degrees C to slow at 40 degrees C. Using synchrotron hydroxyl radical footprinting, we confirm that fluorescence monitors the same kinetic events as hydroxyl radical cleavage, and we show that the previously reported slow P4-P6 folding kinetics apply only to low ionic strength conditions. One model to explain the fast and slow folding kinetics postulates that some tertiary interactions are present even without Mg(2+) in the initial state. The fast kinetic phase reflects folding that is facilitated by these interactions, whereas the slow kinetics are observed when these interactions are disrupted at lower ionic strength and higher temperature.     

Probing the folding intermediate of Rd-apocyt b562 by protein engineering and infrared T-jump

Small proteins often fold in an apparent two-state manner with the absence of detectable early-folding intermediates. Recently, using native-state hydrogen exchange, intermediates that exist after the rate-limiting transition state have been identified for several proteins. However, little is known about the folding kinetics from these post-transition intermediates to their corresponding native states. Herein, we have used protein engineering and a laser-induced temperature-jump (T-jump) technique to investigate this issue and have applied it to Rd-apocyt b(562) , a four-helix bundle protein. Previously, it has been shown that Rd-apocyt b(562) folds via an on-pathway hidden intermediate, which has only the N-terminal helix unfolded. In the present study, a double mutation (V16G/I17A) in the N-terminal helix of Rd-apocyt b(562) was made to further increase the relative population of this intermediate state at high temperature by selectively destabilizing the native state. In the circular dichroism thermal melting experiment, this mutant showed apparent two-state folding behavior. However, in the T-jump experiment, two kinetic phases were observed. Therefore, these results are in agreement with the idea that a folding intermediate is populated on the folding pathway of Rd-apocyt b(562) . Moreover, it was found that the exponential growth rate of the native state from this intermediate state is roughly (25 microsec)(-1) at 65 degrees C.     

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.     

Kinetically robust monomeric protein from a hyperthermophile

Equilibrium and kinetic studies were carried out under denaturation conditions to clarify the energetic features of the high stability of a monomeric protein, ribonuclease HII, from a hyperthermophile, Thermococcus kodakaraensis (Tk-RNase HII). Guanidine hydrochloride (GdnHCl)-induced unfolding and refolding were measured with circular dichroism at 220 nm, and heat-induced denaturation was studied with differential scanning calorimetry. Both GdnHCl- and heat-induced denaturation are very reversible. It was difficult to obtain the equilibrated unfolding curve of Tk-RNase HII below 40 degrees C, because of the remarkably slow unfolding. The two-state unfolding and refolding reactions attained equilibrium at 50 degrees C after 2 weeks. The Gibbs energy change of GdnHCl-induced unfolding (DeltaG(H(2)O)) at 50 degrees C was 43.6 kJ mol(-1). The denaturation temperature in the DSC measurement shifted as a function of the scan rate; the denaturation temperature at a scan rate of 90 degrees C h(-1) was higher than at a scan rate of 5 degrees C h(-1). The unfolding and refolding kinetics of Tk-RNase HII were approximated as a first-order reaction. The ln k(u) and ln k(r) values depended linearly on the denaturant concentration between 10 and 50 degrees C. The DeltaG(H(2)O) value obtained from the rate constant in water using the two-state model at 50 degrees C, 44.5 kJ mol(-1), was coincident with that from the equilibrium study, 43.6 kJ mol(-1), suggesting the two-state folding of Tk-RNase HII. The values for the rate constant in water of the unfolding for Tk-RNase HII were much smaller than those of E. coli RNase HI and Thermus thermophilus RNase HI, which has a denaturation temperature similar to that of Tk-RNase HII. In contrast, little difference was observed in the refolding rates among these proteins. These results indicate that the stabilization mechanism of monomeric protein from a hyperthermophile, Tk-RNase HII, with reversible two-state folding is characterized by remarkably slow unfolding.     

Folding with downhill behavior and low cooperativity of proteins

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

Cytochrome c folds through a smooth funnel

A dominant feature of folding of cytochrome c is the presence of nonnative His-heme kinetic traps, which either pre-exist in the unfolded protein or are formed soon after initiation of folding. The kinetically trapped species can constitute the majority of folding species, and their breakdown limits the rate of folding to the native state. A temperature jump (T-jump) relaxation technique has been used to compare the unfolding/folding kinetics of yeast iso-2 cytochrome c and a genetically engineered double mutant that lacks His-heme kinetic traps, H33N,H39K iso-2. The results show that the thermodynamic properties of the transition states are very similar. A single relaxation time tau(obs) is observed for both proteins by absorbance changes at 287 nm, a measure of solvent exclusion from aromatic residues. At temperatures near Tm, the midpoint of the thermal unfolding transitions, tau(obs) is four to eight times faster for H33N,H39K iso-2 (tau(obs) approximately 4-10 ms) than for iso-2 (tau(obs) approximately 20-30 ms). T-jumps show that there are no kinetically unresolved (tau < 1-3 micros T-jump dead time) "burst" phases for either protein. Using a two-state model, the folding (k(f)) and unfolding (k(u)) rate constants and the thermodynamic activation parameters standard deltaGf, standard deltaGu, standard deltaHf, standard deltaHu, standard deltaSf, standard deltaSu are evaluated by fitting the data to a function describing the temperature dependence of the apparent rate constant k(obs) (= tau(obs)(-1)) = k(f) + k(u). The results show that there is a small activation enthalpy for folding, suggesting that the barrier to folding is largely entropic. In the "new view," a purely entropic kinetic barrier to folding is consistent with a smooth funnel folding landscape.     

Defining folding and unfolding reactions of apocytochrome b5 using equilibrium and kinetic fluorescence measurements.

The refolding and unfolding kinetics of a soluble domain of apocytochrome b5 extending from residue 1 to 104 have been characterized using stopped flow and equilibrium-based fluorescence methods. The isolated apoprotein unfolds reversibly in the presence of GuHCl. From cooperative unfolding curves, the conformational stability (Delta G(uw)), in the absence of denaturant, is estimated to be 11.6 +/- 1.5 kJ mol-1 at 10 degrees C. The stability of apocytochrome b5 is lower than that of the corresponding form of the holoprotein (Delta G approximately 25 kJ mol-1) and exhibits a transition midpoint at 1.6 M GuHCl. Kinetic studies support the concept of a two-state model with both unfolding and refolding rates showing an exponential dependence on denaturant concentration with no evidence of the formation of transient intermediates in either limb of the chevron plot. Apocytochrome b5 is therefore an example of a protein in which both kinetics and equilibria associated with folding are described by a two-state model. The values of mku and mkf obtained from kinetic analysis are an indication of a transition state (mku/meq of 0.29) that resembles the native form by retaining similar solvent accessibility and many of the noncovalent interactions found in the apoprotein. The changes in heat capacity support a transition state that resembles the apoprotein with a value for Delta Cpf of -3.6 kJ mol-1 K-1 estimated for the refolding reaction. From these measurements, a model of refolding that involves the rapid nucleation of hydrophobic residues around Trp26 is suggested as a major event in the formation of the native apoprotein.     

Observation of two families of folding pathways of BBL

BBL is an independent folding domain of a large multienzyme complex, 2-oxoglutarate dehydrogenase. The folding mechanism of BBL is under debate between the views of noncooperative downhill-type and classical two-state. Extensive replica exchange molecular dynamics simulations of BBL in explicit solvent have shown some non-two-state behaviors despite no definitive evidence of downhill folding. In this work, we postprocess the replica exchange data using our roadmap-based MaxFlux reaction path algorithm to reveal atomically detailed folding pathways. A connected graph is used to organize and visualize the folding pathways initiated from random coils. High structural and transition heterogeneity is seen in the early stage of folding. Two main parallel folding pathways emerge in the later stage; one path shows that tertiary contact and helix formation develop at different stages of folding, whereas the other path exhibits concurrence of secondary and tertiary structure formation to some extent. Because the native state of BBL is sensitive to experimental conditions, we speculate that the relative predominance of the two pathways may vary with the protein construct and solvent conditions, possibly leading to the seeming discrepancy of experimental results. Our roadmap-based reaction path algorithm is a general tool to extract path information from replica exchange.     

Squeezed exponential kinetics to describe a nonglassy downhill folding as observed in a lattice protein model

We previously studied the so-called strange kinetics in the two-dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27-mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two-state-like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or "shrunken") exponential function, exp [-(t/tau)beta] with beta > 1, at temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the nonglassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single-domain proteins may follow the squeezed exponential kinetics at about the room temperature.     

Rapid cooperative two-state folding of a miniature alpha-beta protein and design of a thermostable variant

There is a great deal of interest in developing small stably folded miniature proteins. A limited number of these molecules have been described, however they typically have not been characterized in depth. In particular, almost no detailed studies of the thermodynamics and folding kinetics of these proteins have been reported. Here we describe detailed studies of the thermodynamics and kinetics of folding of a 39 residue mixed alpha-beta protein (NTL9(1-39)) derived from the N-terminal domain of the ribosomal protein L9. The protein folds cooperatively and rapidly in a two-state fashion to a native state typical of those found for normal globular proteins. At pH 5.4 in 20mM sodium acetate, 100mM NaCl the temperature of maximum stability is 6 degrees C, the t(m) is 65.3 degrees C, deltaH degrees (t(m)) is between 24.6 kcalmol(-1) and 26.3 kcalmol(-1), and deltaC(p) degrees is 0.38 kcalmol(-1)deg(-1). The thermodynamic parameters are in the range expected on the basis of per residue values determined from databases of globular proteins. H/2H exchange measurements reveal a set of amides that exchange via global unfolding, exactly as expected for a normal cooperatively folded globular protein. Kinetic measurements show that folding is two-state folding. The folding rate is 640 s(-1) and the value of deltaG degrees calculated from the folding and unfolding rates is in excellent agreement with the equilibrium value. A designed thermostable variant, generated by mutating K12 to M, was characterized and found to have a t(m) of 82 degrees C. Equilibrium and kinetic measurements demonstrate that its folding is cooperative and two-state.