Solvent-tuning the collapse and helix formation time scales of lambda(6-85)*

The lambda(6-85)(*) pseudo-wild type of lambda repressor fragment is a fast two-state folder (k(f) approximately 35 microsec(-1) at 58 degrees C). Previously, highly stable lambda(6-85)(*) mutants with k(f) > 30 microsec(-1) have been engineered to fold nearly or fully downhill. Stabilization of the native state by solvent tuning might also tune lambda(6-85)(*) away from two-state folding. We test this prediction by examining the folding thermodynamics and kinetics of lambda(6-85)(*) in a stabilizing solvent, 45% by weight aqueous ethylene glycol at -28 degrees C. Detection of kinetics by circular dichroism at 222 nm (sensitive to helix content) and small angle X-ray scattering (measuring the radius of gyration) shows that refolding from guanidine hydrochloride denatured conditions exhibits very different time scales for collapse and secondary structure formation: the two processes become decoupled. Collapse remains a low-barrier activated process, while the fastest of several secondary structure formation time scales approaches the downhill folding limit. Two-state folding of lambda(6-85)(*) is not a robust process.     

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.     

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.     

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.     

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.     

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.     

Robustness of downhill folding: guidelines for the analysis of equilibrium folding experiments on small proteins

Previously, we identified the protein BBL as a downhill folder. This conclusion was based on the statistical mechanical analysis of equilibrium experiments performed in two variants of BBL, one with a fluorescent label at the N-terminus, and another one labeled at both ends. A recent report has claimed that our results are an artifact of label-induced aggregation and that BBL with no fluorescent labels and a longer N-terminal tail folds in a two-state fashion. Here, we show that singly and doubly labeled BBL do not aggregate, unfold reversibly, and have the same thermodynamic properties when studied under appropriate experimental conditions (e.g., our original conditions (1)). With an elementary analysis of the available data on the nonlabeled BBL (2), we also show that this slightly more stable BBL variant is not a two-state folder. We discuss the problems that led to its previous misclassification and how they can be avoided. Finally, we investigate the equilibrium unfolding of the singly labeled BBL with both ends protected by acetylation and amidation. This variant has the same thermodynamic stability of the nonlabeled BBL and displays all the equilibrium signatures of downhill folding. From all these observations, we conclude that fluorescent labels do not perturb the thermodynamic properties of BBL, which consistently folds downhill regardless of its stability and specific protein tails. The work on BBL illustrates the shortcomings of applying conventional procedures intended to distinguish between two-state and three-state folding models to small fast-folding proteins.     

Using chimeric immunity proteins to explore the energy landscape for alpha-helical protein folding

To address the role of sequence in the folding of homologous proteins, the folding and unfolding kinetics of the all-helical bacterial immunity proteins Im2 and Im9 were characterised, together with six chimeric derivatives of these proteins. We show that both Im2 and Im9 fold rapidly (k(UN)(H(2)O)) approximately 2000 s(-1) at pH 7.0, 25 degrees C) in apparent two-state transitions, through rate-limiting transition states that are highly compact (beta(TS)0.93 and 0.96, respectively). Whilst the folding and unfolding properties of three of the chimeras (Im2 (1-44)(Im9), Im2 (1-64)(Im9 )and Im2 (25-44)(Im9)) are similar to their parental counterparts, in other chimeric proteins the introduced sequence variation results in altered kinetic behaviour. At low urea concentrations, Im2 (1-29)(Im9) and Im2 (56-64)(Im9) fold in two-state transitions via transition states that are significantly less compact (beta(TS) approximately 0.7) than those characterised for the other immunity proteins presented here. At higher urea concentrations, however, the rate-limiting transition state for these two chimeras switches or moves to a more compact species (beta(TS) approximately 0.9). Surprisingly, Im2 (30-64)(Im9) populates a highly collapsed species (beta(I)=0.87) in the dead-time (2.5 ms) of stopped flow measurements. These data indicate that whilst topology may place significant constraints on the folding process, specific inter-residue interactions, revealed here through multiple sequence changes, can modulate the ruggedness of the folding energy landscape.     

Temperature-dependent downhill unfolding of ubiquitin. I. Nanosecond-to-millisecond resolved nonlinear infrared spectroscopy

Transient thermal unfolding of ubiquitin is investigated using nonlinear infrared spectroscopy after a nanosecond laser temperature jump (T-jump). The abrupt change in the unfolding free energy surface and the ns time resolution allow us to observe a fast response on ns to micros time-scales, which we attribute to downhill unfolding, before a cross-over to ms kinetics. The downhill unfolding by a sub-population of folded proteins is induced through a shift of the barrier toward the native state. By adjusting the T-jump width, the effect of the initial (T(i)) and final (T(f)) temperature on the unfolding dynamics can be separated. From the amplitude of the fast downhill unfolding, the fractional population prepared at the unfolding transition state is obtained. This population increases with both T(i) and with T(f). A two-state kinetic analysis of the ms refolding provides thermodynamic information about the barrier height. By a combination of the fast and slow unfolding and folding parameters, a quasi-two-state kinetic analysis is performed to calculate the time-dependent population changes of the folded state. This calculation coincides with the experimentally obtained population changes at low temperature but deviations are found in the T-jump from 67 to 78 degrees C. Using temperature-dependent barrier height changes, a temperature Phi value analysis is performed. The result shows a decreasing trend of Phi(T) with temperature, which indicates an increase of the heterogeneity of the transition state. We conclude that ubiquitin unfolds along a well-defined pathway at low temperature which expands with increasing temperature to include multiple routes.     

Multifrequency calorimetry of the folding/unfolding transition of cytochrome c.

The folding-unfolding transition of Fe(III) cytochrome c has been studied with the new technique of multifrequency calorimetry. Multifrequency calorimetry is aimed at measuring directly the dynamics of the energetic events that take place during a thermally induced transition by measuring the frequency dispersion of the heat capacity. This is done by modulating the folding/unfolding equilibrium using a variable frequency, small oscillatory temperature perturbation (approximately 0.05-0.1 degrees C) centered at the equilibrium temperature of the system. Fe(III) cytochrome c at pH 4 undergoes a fully reversible folding/unfolding transition centered at 67.7 degrees C and characterized by an enthalpy change of 81 kcal/mol and heat capacity difference between unfolded and folded states of 0.9 kcal/K*mol. By measuring the temperature dependence of the frequency dispersion of the heat capacity in the frequency range of 0.1-1 Hz it has been possible to examine the time regime of the enthalpic events associated with the transition. The multifrequency calorimetry results indicate that approximately 85% of the excess heat capacity associated with the folding/unfolding transition relaxes with a single relaxation time of 326 +/- 68 ms at the midpoint of the transition region. This is the first time that the time regime in which heat is absorbed and released during protein folding/unfolding has been measured.     

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.     

Thermodynamic analysis of the structural stability of phage 434 Cro protein

Thermodynamic parameters describing the phage 434 Cro protein have been determined by calorimetry and, independently, by far-UV circular dichroism (CD) measurements of isothermal urea denaturations and thermal denaturations at fixed urea concentrations. These equilibrium unfolding transitions are adequately described by the two-state model. The far-UV CD denaturation data yield average temperature-independent values of 0.99 +/- 0.10 kcal mol(-)(1) M(-)(1) for m and 0.98 +/- 0.05 kcal mol(-)(1) K(-)(1) for DeltaC(p)()(,U), the heat capacity change accompanying unfolding. Calorimetric data yield a temperature-independent DeltaC(p)()(,U) of 0.95 +/- 0.30 kcal mol(-)(1) K(-)(1) or a temperature-dependent value of 1.00 +/- 0.10 kcal mol(-)(1) K(-)(1) at 25 degrees C. DeltaC(p)()(,U) and m determined for 434 Cro are in accord with values predicted using known empirical correlations with structure. The free energy of unfolding is pH-dependent, and the protein is completely unfolded at pH 2.0 and 25 degrees C as judged by calorimetry or CD. The stability of 434 Cro is lower than those observed for the structurally similar N-terminal domain of the repressor of phage 434 (R1-69) or of phage lambda (lambda(6)(-)(85)), but is close to the value reported for the putative monomeric lambda Cro. Since a protein's structural stability is important in determining its intracellular stability and turnover, the stability of Cro relative to the repressor could be a key component of the regulatory circuit controlling the levels and, consequently, the functions of the two proteins in vivo.     

Determining denaturation midpoints in multiprobe equilibrium protein folding experiments

Multiprobe equilibrium unfolding experiments in the downhill regime (i.e., maximal barrier < 3 RT) can resolve the folding process with atomic resolution [ Munoz ( 2002) Int. J. Quantum Chem. 90, 1522 -1528] . Such information is extracted from hundreds of heterogeneous atomic equilibrium unfolding curves, which are characterized according to their denaturation midpoint (e.g., T m for thermal denaturation). Using statistical methods, we analyze T m accuracy when determined from the extremum of the derivative of the unfolding curve and from two-state fits under different sets of simulated experimental conditions. We develop simple procedures to discriminate between real unfolding heterogeneity at the atomic level and experimental uncertainty in the single T m of conventional two-state folding. We apply these procedures to the recently published multiprobe NMR experiments of BBL [ Sadqi et al. ( 2006) Nature 442, 317 -321 ] and conclude that for the 122 single transition atomic unfolding curves reported for this protein the mean T m accuracy is better than 1.8 K for both methods, compared to the 60 K spread in T m determined experimentally. Importantly, we also find that when the pre- or posttransition baseline is incomplete, the two-state fits systematically drift the estimated T m value toward the center of the experimental range. Therefore, the reported 60 K T m spread in BBL is in fact a lower limit. The derivative method is significantly less sensitive to this problem and thus is a better choice for multiprobe experiments with a broad T m distribution. The results we obtain in this work lay the foundations for the quantitative analysis of future multiprobe unfolding experiments in fast-folding proteins.     

Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape

An acid-destabilized form of apomyoglobin, the so-called E state, consists of a set of heterogeneous structures that are all characterized by a stable hydrophobic core composed of 30-40 residues at the intersection of the A, G, and H helices of the protein, with little other secondary structure and no other tertiary structure. Relaxation kinetics studies were carried out to characterize the dynamics of core melting and formation in this protein. The unfolding and/or refolding response is induced by a laser-induced temperature jump between the folded and unfolded forms of E, and structural changes are monitored using the infrared amide I' absorbance at 1648-1651 cm(-1) that reports on the formation of solvent-protected, native-like helix in the core and by fluorescence emission changes from apomyoglobin's Trp14, a measure of burial of the indole group of this residue. The fluorescence kinetics data are monoexponential with a relaxation time of 14 micros. However, infrared kinetics data are best fit to a biexponential function with relaxation times of 14 and 59 micros. These relaxation times are very fast, close to the limits placed on folding reactions by diffusion. The 14 micros relaxation time is weakly temperature dependent and thus represents a pathway that is energetically downhill. The appearance of this relaxation time in both the fluorescence and infrared measurements indicates that this folding event proceeds by a concomitant formation of compact secondary and tertiary structures. The 59 micros relaxation time is much more strongly temperature dependent and has no fluorescence counterpart, indicating an activated process with a large energy barrier wherein nonspecific hydrophobic interactions between helix A and the G and H helices cause some helix burial but Trp14 remains solvent exposed. These results are best fit by a multiple-pathway kinetic model when U collapses to form the various folded core structures of E. Thus, the results suggest very robust dynamics for core formation involving multiple folding pathways and provide significant insight into the primary processes of protein folding.     

Stability and physicochemical properties of the bovine brain phosphatidylethanolamine-binding protein.

The equilibrium behaviour of the bovine phosphatidylethanolamine-binding protein (PEBP) has been studied under various conditions of pH, temperature and urea concentration. Far-UV and near-UV CD, fluorescence and Fourier transform infrared spectroscopies indicate that, in its native state, PEBP is mainly composed of beta-sheets, with Trp residues mostly localized in a hydrophobic environment; these results suggest that the conformation of PEBP in solution is similar to the three-dimensional structure determined by X-ray crystallography. The pH-induced conformational changes show a transition midpoint at pH 3.0, implying nine protons in the transition. At neutral pH, the thermal denaturation is irreversible due to protein precipitation, whereas at acidic pH values the protein exhibits a reversible denaturation. The thermal denaturation curves, as monitored by CD, fluorescence and differential scanning calorimetry, support a two-state model for the equilibrium and display coincident values with a melting temperature Tm = 54 degrees C, an enthalpy change DeltaH = 119 kcal.mol-1 and a free energy change DeltaG(H2O, 25 degrees C) = 5 kcal.mol-1. The urea-induced unfolding profiles of PEBP show a midpoint of the two-state unfolding transition at 4.8 M denaturant, and the stability of PEBP is 4.5 kcal.mol-1 at 25 degrees C. Moreover, the surface active properties indicate that PEBP is essentially a hydrophilic protein which progressively unfolds at the air/water interface over the course of time. Together, these results suggest that PEBP is well-structured in solution but that its conformation is weakly stable and sensitive to hydrophobic conditions: the PEBP structure seems to be flexible and adaptable to its environment.     

Equilibrium unfolding of dimeric human prostatic acid phosphatase involves an inactive monomeric intermediate

Guanidine hydrochloride (GdnHCl)-induced unfolding of human prostatic acid phosphatase (hPAP), a homodimer of 50 kDa subunit molecular weight, was investigated with activity measurements, size exclusion HPLC, tryptophan fluorescence, 1-anilinonaphtalene-8-sulfonate (ANS) binding and reactivity with 2-(4'-maleimidoanilino)naphthalene-6-sulfonate (MIANS). Equilibrium analysis was performed to shed light on the role of dimerization in the folding and stability of the catalytically active oligomeric protein. Unfolding was reversible, as verified by activity measurements and tryptophan fluorescence. The noncoincidence of the unfolding curves obtained by different techniques suggests the occurrence of a multiphasic process.The reaction of hPAP inactivation is accompanied by dissociation of the dimer into two monomers. The midpoint of this transition is at 0.65 M GdnHCl with 4.24+/-0.12 kcalmol(-1) free energy change. Binding of ANS to the inactive phosphatase monomer, especially remarkable in the region from 0.8 to 1.25M GdnHCl, suggests that the hydrophobic probe indicates exposition of the intersubunit hydrophobic surface and a loosening of the monomer's tertiary structure. Strong fluorescence of thiol group derivatives, the products of their reaction with MIANS, appears in a limited range of GdnHCl concentrations (1.2-1.6M). This shows that in the relaxed structure of the intermediate, the reagent is allowed to penetrate into the hydrophobic environment of the partially hidden thiol groups.The equilibrium unfolding reaction of hPAP, as monitored by tryptophan fluorescence, does not depend on the protein concentration and displays a single transition curve with a midpoint at 1.7 M GdnHCl and value of DeltaG(unf)(H(2)O)=3.38+/-0.08 kcalmol(-1) per monomer, a result implying that this transition is related to the conformational change of the earlier dissociated and already inactive subunit of the protein.     

Equilibrium and kinetic analysis of folding of ketosteroid isomerase from Comamonas testosteroni

Equilibrium and kinetic analyses have been carried out to elucidate the folding mechanism of homodimeric ketosteroid isomerase (KSI) from Comamonas testosteroni. The folding of KSI was reversible since the activity as well as the fluorescence and CD spectra was almost completely recovered after refolding. The equilibrium unfolding transitions monitored by fluorescence and CD measurements were almost coincident with each other, and the transition midpoint increased with increasing protein concentration. This suggests that the KSI folding follows a simple two-state mechanism consisting of native dimer and unfolded monomer without any thermodynamically stable intermediates. Sedimentation equilibrium analysis and size-exclusion chromatography of KSI at different urea concentrations supported the two-state model without any evidence of folded monomeric intermediates. Consistent with the two-state model, (1)H-(15)N HSQC spectra obtained for KSI in the unfolding transition region could be reproduced by a simple addition of the spectra of the native and the unfolded KSI. The KSI refolding kinetics as monitored by fluorescence intensity could be described as a fast first-order process followed by a second-order and a subsequent slow first-order processes with rate constants of 60 s(-)(1), 5.4 x 10(4) M(-)(1).s(-)(1), and 0.017 s(-)(1), respectively, at 0.62 M urea, suggesting that there may be a monomeric folding intermediate. After a burst phase that accounts for >83% of the total amplitude, the negative molar ellipticity at 225 nm increased slowly in a single phase at a rate comparable to that of the bimolecular intermediate step. The kinetics of activity recovery from the denatured state were markedly dependent upon the protein concentration, implying that the monomers are not fully active. Taken together, our results demonstrate that the dimerization induces KSI to fold into the complete structure and is crucial for maintaining the tertiary structure to perform efficient catalysis.     

The folding pathway of spectrin R17 from experiment and simulation: using experimentally validated MD simulations to characterize States hinted at by experiment

We present an experimental and computational analysis of the folding pathway of the 17th domain of chicken brain alpha-spectrin, R17. Wild-type R17 folds in a two-state manner and the chevron plot (plot of the logarithm of the observed rate constant against concentration of urea) shows essentially linear folding and unfolding arms. A number of mutant proteins, however, show a change in slope of the unfolding arm at high concentration of denaturant, hinting at complexity in the folding landscape. Through a combination of mutational studies and high temperature molecular dynamics simulations we show that the folding of R17 can be described by a model with two sequential transition states separated by an intermediate species. The rate limiting transition state for folding in water has been characterized both through experimental Phi-value analysis and by simulation. In contrast, a detailed analysis of the transition state predicted to dominate under highly denaturing conditions is only possible by simulation.