Dynamics of unfolded polypeptide chains in crowded environment studied by fluorescence correlation spectroscopy

Proteins have evolved to fold and function within a cellular environment that is characterized by high macromolecular content. The earliest step of protein folding represents intrachain contact formation of amino acid residues within an unfolded polypeptide chain. It has been proposed that macromolecular crowding can have significant effects on rates and equilibria of biomolecular processes. However, the kinetic consequences on intrachain diffusion of polypeptides have not been tested experimentally, yet. Here, we demonstrate that selective fluorescence quenching of the oxazine fluorophore MR121 by the amino acid tryptophan (Trp) in combination with fast fluorescence correlation spectroscopy (FCS) can be used to monitor end-to-end contact formation rates of unfolded polypeptide chains. MR121 and Trp were incorporated at the terminal ends of polypeptides consisting of repetitive units of glycine (G) and serine (S) residues. End-to-end contact formation and dissociation result in "off" and "on" switching of MR121 fluorescence and underlying kinetics can be revealed in FCS experiments with nanosecond time resolution. We revisit previous experimental studies concerning the dependence of end-to-end contact formation rates on polypeptide chain length, showing that kinetics can be described by Gaussian chain theory. We further investigate effects of solvent viscosity and temperature on contact formation rates demonstrating that intrachain diffusion represents a purely diffusive, entropy-controlled process. Finally, we study the influence of macromolecular crowding on polypeptide chain dynamics. The data presented demonstrate that intrachain diffusion is fast in spite of hindered diffusion caused by repulsive interactions with macromolecules. Findings can be explained by effects of excluded volume reducing chain entropy and therefore accelerating the loop search process. Our results suggest that within a cellular environment the early formation of structural elements in unfolded proteins can still proceed quite efficiently in spite of hindered diffusion caused by high macromolecular content.     

Protein stabilization by urea and guanidine hydrochloride

The urea, guanidine hydrochloride, salt, and temperature dependence of the rate of dissociation of CO from a nonequilibrium state of CO-bound native ferrocytochrome c has been studied at pH 7. The heme iron of ferrocytochrome c in the presence of denaturing concentrations of guanidine hydrochloride (GdnHCl) and urea prepared in 0.1 M phosphate, pH 7, binds CO. When the unfolded protein solution is diluted 101-fold into CO-free folding buffer, the protein chain refolds completely, leaving the CO molecule bonded to the heme iron. Subsequently, slow thermal dissociation of the CO molecule yields to the heme coordination of the native M80 ligand. Thus, the reaction monitors the rate of thermal conversion of the CO-liganded native ferrocytochrome c to the M80-liganded native protein. The rate of this reaction, k(diss), shows a characteristic dependence on the presence of nondenaturing concentrations of the denaturants in the reaction medium. The rate decreases by approximately 1.9-3-fold as the concentration of GdnHCl in the refolding medium increases from nearly 0 to approximately 2.1 M. Similarly, the rate decreases by 1.8-fold as the urea concentration is raised from 0.l to approximately 5 M. At still higher concentrations of the denaturants the denaturing effect sets in, the protein is destabilized, and hence the CO dissociation rate increases sharply. The activation energy of the reaction, E(a), increases when the denaturant concentration in the reaction medium is raised: from 24.1 to 28.3 kcal mol(-1) for a 0.05-2.1 M rise in GdnHCl and from 25.2 to 26.9 kcal mol(-1) for a 0.1-26.9 M increase in urea. Corresponding to these increases in denaturant concentrations are also increases in the activation entropy, S(diss)/R, where R is the gas constant of the reaction. The denaturant dependence of these kinetic and thermodynamic parameters of the CO dissociation reaction suggests that binding interactions with GdnHCl and urea can increase the structural and energetic stability of ferrocytochrome c up to the limit of the subdenaturing concentrations of the additives. NaCl and Na(2)SO(4), which stabilize proteins through their salting-in effect, also decrease the rate with a corresponding increase in activation entropy of CO dissociation from CO-bound native ferrocytochrome c, lending support to the view that low concentrations of GdnHCl and urea stabilize proteins. These results have direct relevance to the understanding and interpretation of the free energy-denaturant relationship and protein folding chevrons.     

Dynamics of unfolded polypeptide chains as model for the earliest steps in protein folding

The rate of formation of intramolecular interactions in unfolded proteins determines how fast conformational space can be explored during folding. Characterization of the dynamics of unfolded proteins is therefore essential for the understanding of the earliest steps in protein folding. We used triplet-triplet energy transfer to measure formation of intrachain contacts in different unfolded polypeptide chains. The time constants (1/k) for contact formation over short distances are almost independent of chain length, with a maximum value of about 5 ns for flexible glycine-rich chains and of 12 ns for stiffer chains. The rates of contact formation over longer distances decrease with increasing chain length, indicating different rate-limiting steps for motions over short and long chain segments. The effect of the amino acid sequence on local chain dynamics was probed by using a series of host-guest peptides. Formation of local contacts is only sixfold slower around the stiffest amino acid (proline) compared to the most flexible amino acid (glycine). Good solvents for polypeptide chains like EtOH, GdmCl and urea were found to slow intrachain diffusion and to decrease chain stiffness. These data allow us to determine the time constants for formation of the earliest intrachain contacts during protein folding.     

Determination of ultrafast protein folding rates from loop formation dynamics

Quenching of the triplet state of tryptophan by contact with cysteine can be used to measure the kinetics of loop formation in unfolded proteins. Here we show that cysteine quenching dynamics also provide a novel method for measuring folding rates when the exchange between folded and unfolded states is faster than the unquenched triplet lifetime (approximately 100 micros). We use this technique to investigate folding/unfolding kinetics of the 35 residue headpiece subdomain of the protein villin, which contains a single tryptophan residue and was engineered to contain a cysteine residue at the N terminus. At intermediate concentrations of denaturant the time-course of the triplet decay consists of two relaxations, the rates and amplitudes of which reveal the fast kinetics for folding and unfolding of this protein. The folding rates extracted using a simple kinetic model are close to those reported previously from laser-induced temperature-jump experiments that employ the change in tryptophan fluorescence as a probe. However, the results differ significantly from those reported from dynamic NMR line shape analysis on a variant with methionine at the N terminus, an issue that remains to be resolved. The analysis of the triplet quenching kinetics also shows that the quenching rates in the unfolded state increase with decreasing denaturant concentration, indicating a compaction of the unfolded protein.     

Kinetics of intramolecular contact formation in a denatured protein

Quenching of the triplet state of tryptophan by cysteine has provided a new tool for measuring the rate of forming a specific intramolecular contact in disordered polypeptides. Here, we use this technique to investigate contact formation in the denatured state of CspTm, a small cold-shock protein from Thermotoga maritima, engineered to contain a single tryptophan residue (W29) and a single cysteine residue at the C terminus (C67). At all concentrations of denaturant, the decay rate of the W29 triplet of the unfolded protein is more than tenfold faster than the rate observed for the native protein ( approximately 10(4)s(-1)). Experiments on the unfolded protein without the added C-terminal cysteine residue show that this faster rate results entirely from contact quenching by C67. The quenching rate in the unfolded state by C67 increases at concentrations of denaturant that favor folding, indicating a compaction of the unfolded protein as observed previously in single-molecule F?rster resonance energy transfer (FRET) experiments.     

Ultrafast events in the folding of ferrocytochrome c

Laser flash photolysis and stopped-flow methods have been used to study the dynamic events in the micro- to millisecond time bin in the refolding of horse ferrocytochrome c in the full range of guanidine hydrochloride concentration at pH 12.8 (+/-0.1), 22 degrees C. Under the absolute refolding condition, the earliest relaxation time of the unfolded protein chain is less than 1 micros. The chain then undergoes diffusive dynamics-mediated contraction and expansion, in which intrapolypeptide ligands make transient contacts with the heme iron, giving rise to two distinct kinetic phases of approximately 0.4 and approximately 3 micros. Under moderate to absolute refolding conditions, the rates of these processes show little dependence on the denaturant concentration, indicating the absence of structural element in the incipient or the relaxed state. Chain expansion and contraction events continue until the polypeptide finds a stable and supportive transition state. The crossing of this transition barrier, which rate-limits the folding of alkaline ferrocytochrome c, is characterized by a stopped-flow measured time constant of approximately 3 ms in aqueous solvent. Observed kinetics thus implicate no submillisecond folding structure. The folding kinetics is effectively two state in which the unfolded polypeptide first relaxes to an unstructured chain and then crosses over a late rate-limiting barrier to achieve the native conformation. The experimentally observed rates as a function of guanidine hydrochloride concentration have been simulated by numerically calculated microscopic rates of a simple kinetic model that captures the essential features of folding.     

Ligand exchange during unfolding of cytochrome c.

The productive folding pathway of cytochrome c passes through an obligatory HW intermediate in which the heme is coordinated by a solvent water molecule and a native ligand, His-18, prior to the formation of the folded HM state with both the native His-18 and Met-80 heme coordination. Two off pathway intermediates, a five-coordinated state (5C) and a bis-histidine state (HH), were also identified during the folding reaction. In the present work, the thermodynamics and the kinetics of the unfolding reaction of cytochrome c were investigated with resonance Raman scattering, tryptophan fluorescence spectroscopy, and circular dichroism. The objective of these experiments was to determine if the protein opens up and diverges into the differing heme ligation states through a many pathway mechanism or if it passes through intermediate states analogous to those observed during the folding reaction. Equilibrium unfolding results indicate that, in contrast to 5C, the stability of HH with respect to HW decreases as the concentration of GdnHCl increases. The difference in their response to the denaturant indicates that the polypeptide structure of 5C is relatively loose as compared with HH in which the polypeptide is misfolded. Time-resolved resonance Raman measurements show that strikingly similar ligand exchange reactions occur during unfolding as were observed during folding. Combined with fluorescence data, a kinetic model is proposed in which local structural rearrangements controlled by heme ligand exchange reactions appear prior to the global relaxation of the polypeptide chain.     

The folding pathway of barnase: the rate-limiting transition state and a hidden intermediate under native conditions

The nature of the rate-limiting transition state at zero denaturant (TS(1)) and whether there are hidden intermediates are the two major unsolved problems in defining the folding pathway of barnase. In earlier studies, it was shown that TS(1) has small phi values throughout the structure of the protein, suggesting that the transition state has either a defined partially folded secondary structure with all side chains significantly exposed or numerous different partially unfolded structures with similar stability. To distinguish the two possibilities, we studied the effect of Gly mutations on the folding rate of barnase to investigate the secondary structure formation in the transition state. Two mutations in the same region of a beta-strand decreased the folding rate by 20- and 50-fold, respectively, suggesting that the secondary structures in this region are dominantly formed in the rate-limiting transition state. We also performed native-state hydrogen exchange experiments on barnase at pD 5.0 and 25 degrees C and identified a partially unfolded state. The structure of the intermediate was investigated using protein engineering and NMR. The results suggest that the intermediate has an omega loop unfolded. This intermediate is more folded than the rate-limiting transition state previously characterized at high denaturant concentrations (TS(2)). Therefore, it exists after TS(2) in folding. Consistent with this conclusion, the intermediate folds with the same rate and denaturant dependence as the wild-type protein, but unfolds faster with less dependence on the denaturant concentration. These and other results in the literature suggest that barnase folds through partially unfolded intermediates that exist after the rate-limiting step. Such folding behavior is similar to those of cytochrome c and Rd-apocyt b(562). Together, we suggest that other small apparently two-state proteins may also fold through hidden intermediates.     

Dissecting the non-specific and specific components of the initial folding reaction of barstar by multi-site FRET measurements

Initial polypeptide chain collapse plays a major role in the development of subsequent structure during protein folding, but it has been difficult to elucidate the coupling between its cooperativity and specificity. To better understand this important aspect of protein folding, nine different intramolecular distances in the protein have been measured by fluorescence resonance energy transfer (FRET) in the product(s) of the initial, sub-millisecond collapse reaction during the folding of barstar, under different folding conditions. All nine distances contract in these initial folding products, when the denaturant concentration is reduced. Two of these distances were also measured in peptides corresponding to sequence segments 38-55 and 51-69 of the protein. Surprisingly, both distances do not contract in the peptides which remain fully unfolded when the denaturant concentration is reduced. This suggests that the contraction of at least some segments of the polypeptide chain may be facilitated only by contraction of other segments. In the case of the initial product of folding of the protein, the dependence on denaturant concentration of the relative change in each distance suggests that there are two components to the initial folding reaction. One is a nonspecific component, which appears to be driven by the change in denaturant concentration that is used to initiate refolding. This component corresponds to the collapse of completely unfolded protein (U) to unfolded protein in refolding conditions (U(C)). The extent of nonspecific collapse can be predicted by the response of completely unfolded protein to a change in denaturant concentration. All distances undergo such solvent-induced contraction, but each distance contracts to a different extent. There is also a specific component to initial sub-millisecond folding, in which some distances (but not all) contract more than that predicted by solvent-induced contraction. The observation that only some of the distances undergo contraction over and above solvent-induced contraction, suggest that this specific component is associated with the formation of a specific intermediate (I(E)). FRET efficiency and distance change differently for the different donor-acceptor pairs, with a change in denaturant concentration, indicating that the formation or dissolution of structure in U(C) and I(E) does not happen in a synchronized manner across different regions of the protein molecule. Also, all nine FRET efficiencies and intramolecular distances in the product(s) of sub-ms folding, change continuously with a change in denaturant concentration. Hence, it appears that the transitions from U to U(C) and to I(E) are gradual transformations, and not all-or-none structural transitions. Nevertheless, the product of these gradual transitions, I(E), possesses specific structure.     

Fast coordination changes in cytochrome c do not necessarily imply folding

Folding of globular proteins occurs with rates that range from microseconds to minutes; consequently, it has been necessary to develop new strategies to follow the faster processes that exceed stopped-flow capabilities. Rapid photochemical methods have been employed to study the rate of folding of reduced cytochrome c. In this protein, the iron of the covalently bound heme binds a His and a Met, proximal and distal. Unfolding by guanidine or urea weakens the Fe-Met bond, and the reduced unfolded cytochrome c easily binds CO and other heme ligands, which would react slowly or not at all with the native protein. Therefore in the presence of CO, reduced cytochrome c unfolds at lower denaturant concentrations than in the absence of this ligand, and rapid photochemical removal of CO from unfolded cytochrome c, is expected to trigger at least an incomplete refolding. This approach is complicated by the breakage of the proximal His-Fe bond that may occur as a consequence of CO photodissociation in the unfolded cytochrome c because of the so-called base elimination mechanism. Rebinding of CO to the four-coordinate heme yields kinetic intermediates unrelated to folding. Our hypothesis is supported by parallel observations carried out with protoheme and microperoxidase.     

Rapid intrachain binding of histidine-26 and histidine-33 to heme in unfolded ferrocytochrome C.

Time-resolved spectroscopic studies of unfolded horse iron(II) cytochrome c have suggested that the imidazole side chains of His26 and His33 bind transiently to the heme iron on microsecond time scales, after photodissociation of a carbon monoxide ligand from the heme. Our studies of four variants of cytochrome c (horse wild type, horse H33N, horse H33N/H26Q, and tuna wild type), unfolded in guanidine hydrochloride at pH 6.5, demonstrate that these side chains are responsible for the observed microsecond spectral changes. As His33 and then His26 are eliminated from the horse wild-type sequence, transient optical absorption spectra show systematic suppression of a rapid (approximately 10-100 micros) Soret absorbance change that follows photolysis of CO. Transient binding of these histidine side chains to the heme therefore generates one of the fast kinetic phases observed in previous photochemically triggered spectroscopic studies of dynamics in unfolded iron(II) cytochrome c. Furthermore, both His33 and His26 appear to contribute to a similar extent in these early kinetics. Thus, the stiffness of the polypeptide chain creates a deviation from Gaussian chain behavior by impeding, although not preventing, the formation of short (<10 peptide bonds) intrachain loops around the heme group.     

Conformational equilibration time of unfolded protein chains and the folding speed limit

The speed with which the conformers of unfolded protein chains interconvert is a fundamental question in the study of protein folding. Kinetic evidence is presented here for the time constant for interconversion of disparate unfolded chain conformations of a small globular protein, cytochrome c, in the presence of guanidine hydrochloride denaturant. The axial binding reactions of histidine and methionine residues with the Fe(II) heme cofactor were monitored with time-resolved magnetic circular dichroism spectroscopy after photodissociation of the CO complexes of unfolded protein obtained from horse and tuna and from several histidine mutants of the horse protein. A kinetic model fitting both the reaction rate constants and spectra of the intermediates was used to obtain a quantitative estimate of the conformational diffusion time. The latter parameter was approximated as a first-order time constant for exchange between conformational subensembles presenting either a methionine or a histidine residue to the heme iron for facile binding. The mean diffusional time constant of the wild type and variants was 3 +/- 2 mus, close to the folding "speed limit". The implications of the relatively rapid conformational equilibration time observed are discussed in terms of the energy landscape and classical pathway time regimes of folding, for which the conformational diffusion time can be considered a pivot point.     

Kinetics of internal-loop formation in polypeptide chains: a simulation study

The speed of simple diffusional motions, such as the formation of loops in the polypeptide chain, places one physical limit on the speed of protein folding. Many experimental studies have explored the kinetics of formation of end-to-end loops in polypeptide chains; however, protein folding more often requires the formation of contacts between interior points on the chain. One expects that, for loops of fixed contour length, interior loops will form more slowly than end-to-end loops, owing to the additional excluded volume associated with the "tails". We estimate the magnitude of this effect by generating ensembles of randomly coiled, freely jointed chains, and then using the theory of Szabo, Schulten, and Schulten to calculate the corresponding contact formation rates for these ensembles. Adding just a few residues, to convert an end-to-end loop to an internal loop, sharply decreases the contact rate. Surprisingly, the relative change in rate increases for a longer loop; sufficiently long tails, however, actually reverse the effect and accelerate loop formation slightly. Our results show that excluded volume effects in real, full-length polypeptides may cause the rates of loop formation during folding to depart significantly from the values derived from recent loop-formation experiments on short peptides.     

Conformational properties of the iso-1-cytochrome C denatured state: dependence on guanidine hydrochloride concentration

Production of seven single surface histidine variants of yeast iso-1-cytochrome c allowed measurement of the apparent pK(a), pK(a)(obs), for histidine-heme loop formation for loops of nine to 83 amino acid residues under varying denaturing conditions (2 M to 6 M guanidine hydrochloride, gdnHCl). A linear correlation between pK(a)(obs) and the log of the loop size is expected for a random coil, pK(a)(obs) proportional to k log(n), where k is a scaling factor and n is the number of monomers in the loop. For small loops of nine, 16, and 22 monomers, no dependence of pK(a)(obs) on loop size was observed at any denaturant concentration indicating effects from chain stiffness. For larger loops of 37, 56, 72, and 83 monomers, the dependence of pK(a)(obs) on log(n) was linear and the slope of that dependence decreased with increasing concentration of denaturant. The scaling factor obtained at 5 M and 6 M gdnHCl for the larger loop sizes was approximately -2.0, close to the value of -2.2 expected for a random coil with excluded volume. However, scaling factors obtained under less harsh denaturing conditions (2 M to 4.5 M gdnHCl) deviated strongly from that expected for a random coil, being in the range -3 to -4. The gdnHCl dependence of pK(a)(obs) at each loop size was also evaluated to obtain denaturant m-values. Short loops where chain stiffness dominates had similar m-values of approximately 0.25 kcal/mol M. For larger loops m-values decrease with increasing loop size indicating that less hydrophobic area is sequestered when larger loops form. It is known that the earliest events in protein folding involve the formation of simple loops. The data from these studies provide direct insight into the relative probability with which loops of different sizes will form, as well as the factors which affect loop formation.     

Effects of denaturants on amide proton exchange rates: a test for structure in protein fragments and folding intermediates

A method for detecting structure in marginally stable forms of a protein is described. The principle is to measure amide proton exchange rates in the absence and presence of varying concentrations of a denaturant. Unfolding of structure by the denaturant is reflected by an acceleration of amide proton exchange rates, after correction for the effects of the denaturant on the intrinsic rate of exchange. This exchange-rate test for structure makes no assumptions about the rate of exchange in the unfolded state. The effects of 0-8 M urea and 0-6 M guanidinium chloride (GdmCl) on acid- and base-catalyzed exchange from model compounds have been calibrated. GdmCl does not appear to be well-suited for use in the exchange-rate test; model compound studies show that the effects of GdmCl on intrinsic exchange rates are complicated. In contrast, the effects of urea are a more uniform function of denaturant concentration. Urea increases acid-catalyzed, and decreases base-catalyzed, rates in model compounds. The exchange-rate test is used here to study structure formation in the S-protein (residues 21-124 of ribonuclease A). In conditions where an equilibrium folding intermediate of S-protein (I3) is known to be populated (pH 1.7, 0 degree C), the exchange-rate test for structure is positive. At higher temperatures (greater than 32 degrees C) I3 is unfolded, but circular dichroism data suggest that residual structure remains [Labhardt, A. M. (1982) J. Mol. Biol. 157, 357-371].(ABSTRACT TRUNCATED AT 250 WORDS)     

Effects of denaturants on the dynamics of loop formation in polypeptides

Quenching of the triplet state of tryptophan by close contact with cysteine has been used to measure the reaction-limited and diffusion-limited rates of loop formation in disordered polypeptides having the sequence cys-(ala-gly-gln)j-trp (j=1-9). The decrease in the length-dependence of the reaction-limited rate for short chains in aqueous buffer, previously attributed to chain stiffness, is not observed at high concentrations of chemical denaturant (6 M GdmCl and 8 M urea), showing that denaturants increase chain flexibility. For long chains, both reaction-limited and diffusion-limited rates are significantly smaller in denaturant and exhibit a steeper length dependence. The results can be explained using end-to-end distributions from a wormlike chain model in which excluded volume interactions are incorporated by associating a 0.4-0.5 nm diameter hard sphere with the end of each virtual peptide bond. Fitting the data with this model shows that the denaturants reduce the persistence length from approximately 0.6 nm to approximately 0.4 nm, only slightly greater than the length of a peptide bond. The same model also describes the reported length dependence for the radii of gyration of chemically denatured proteins containing 50-400 residues. The end-to-end diffusion coefficients obtained from the diffusion-limited rates are smaller than the sum of the monomer diffusion coefficients and exhibit significant temperature dependence, suggesting that diffusion is slowed by internal friction arising from barriers to backbone conformational changes.     

Unfolding rates of barstar determined in native and low denaturant conditions indicate the presence of intermediates

The folding and unfolding rates of the small protein, barstar, have been monitored using stopped-flow measurements of intrinsic tryptophan fluorescence at 25 degrees C, pH 8.5, and have been compared over a wide range of urea and guanidine hydrochloride (GdnHCl) concentrations. When the logarithms of the rates of folding from urea and from GdnHCl unfolded forms are extrapolated linearly with denaturant concentration, the same rate is obtained for folding in zero denaturant. Similar linear extrapolations of rates of unfolding in urea and GdnHCl yield, however, different unfolding rates in zero denaturant, indicating that such linear extrapolations are not valid. It has been difficult, for any protein, to determine unfolding rates under nativelike conditions in direct kinetic experiments. Using a novel strategy of coupling the reactivity of a buried cysteine residue with 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) to the unfolding reaction of barstar, the global unfolding and refolding rates have now been determined in low denaturant concentrations. The logarithms of unfolding rates obtained at low urea and GdnHCl concentrations show a markedly nonlinear dependence on denaturant concentration and converge to the same unfolding rate in the absence of denaturant. It is shown that the native protein can sample the fully unfolded conformation even in the absence of denaturant. The observed nonlinear dependences of the logarithms of the refolding and unfolding rates observed for both denaturants are shown to be due to the presence of (un)folding intermediates and not due to movements in the position of the transition state with a change in denaturant concentration.     

Folding and stability of trp aporepressor from Escherichia coli

Equilibrium and kinetic studies of the urea-induced unfolding of trp aporepressor from Escherichia coli were performed to probe the folding mechanism of this intertwined, dimeric protein. The equilibrium unfolding transitions at pH 7.6 and 25 degrees C monitored by difference absorbance, fluorescence, and circular dichroism spectroscopy are coincident within experimental error. All three transitions are well described by a two-state model involving the native dimer and the unfolded monomer; the free energy of folding in the absence of denaturant and under standard-state conditions is estimated to be 23.3 +/- 0.9 kcal/mol of dimer. The midpoint of the equilibrium unfolding transition increases with increasing protein concentration in the manner expected from the law of mass action for the two-state model. We find no evidence for stable folding intermediates. Kinetic studies reveal that unfolding is governed by a single first-order reaction whose relaxation time decreases exponentially with increasing urea concentration and also decreases with increasing protein concentration in the transition zone. Refolding involves at least three phases that depend on both the protein concentration and the final urea concentration in a complex manner. The relaxation time of the slowest of these refolding phases is identical with that for the single phase in unfolding in the transition zone, consistent with the results expected for a reaction that is kinetically reversible. The two faster refolding phases are presumed to arise from slow isomerization reactions in the unfolded form and reflect parallel folding channels.     

Folding of horse cytochrome c in the reduced state

Equilibrium and kinetic folding studies of horse cytochrome c in the reduced state have been carried out under strictly anaerobic conditions at neutral pH, 10 degrees C, in the entire range of aqueous solubility of guanidinium hydrochloride (GdnHCl). Equilibrium unfolding transitions observed by Soret heme absorbance, excitation energy transfer from the lone tryptophan residue to the ferrous heme, and far-UV circular dichroism (CD) are all biphasic and superimposable, implying no accumulation of structural intermediates. The thermodynamic parameters obtained by two-state analysis of these transitions yielded DeltaG(H2O)=18.8(+/-1.45) kcal mol(-1), and C(m)=5.1(+/-0.15) M GdnHCl, indicating unusual stability of reduced cytochrome c. These results have been used in conjunction with the redox potential of native cytochrome c and the known stability of oxidized cytochrome c to estimate a value of -164 mV as the redox potential of the unfolded protein. Stopped-flow kinetics of folding and unfolding have been recorded by Soret heme absorbance, and tryptophan fluorescence as observables. The refolding kinetics are monophasic in the transition region, but become biphasic as moderate to strongly native-like conditions are approached. There also is a burst folding reaction unobservable in the stopped-flow time window. Analyses of the two observable rates and their amplitudes indicate that the faster of the two rates corresponds to apparent two-state folding (U<-->N) of 80-90 % of unfolded molecules with a time constant in the range 190-550 micros estimated by linear extrapolation and model calculations. The remaining 10-20 % of the population folds to an off-pathway intermediate, I, which is required to unfold first to the initial unfolded state, U, in order to refold correctly to the native state, N (I<-->U<-->N). The slower of the two observable rates, which has a positive slope in the linear functional dependence on the denaturant concentration indicating that an unfolding process under native-like conditions indeed exists, originates from the unfolding of I to U, which rate-limits the overall folding of these 10-20 % of molecules. Both fast and slow rates are independent of protein concentration and pH of the refolding milieu, suggesting that the off-pathway intermediate is not a protein aggregate or trapped by heme misligation. The nature or type of unfolded-state heme ligation does not interfere with refolding. Equilibrium pH titration of the unfolded state yielded coupled ionization of the two non-native histidine ligands, H26 and H33, with a pK(a) value of 5.85. A substantial fraction of the unfolded population persists as the six-coordinate form even at low pH, suggesting ligation of the two methionine residues, M65 and M80. These results have been used along with the known ligand-binding properties of unfolded cytochrome c to propose a model for heme ligation dynamics. In contrast to refolding kinetics, the unfolding kinetics of reduced cytochrome c recorded by observation of Soret absorbance and tryptophan fluorescence are all slow, simple, and single-exponential. In the presence of 6.8 M GdnHCl, the unfolding time constant is approximately 300(+/-125) ms. There is no burst unfolding reaction. Simulations of the observed folding-unfolding kinetics by numerical solutions of the rate equations corresponding to the three-state I<-->U<-->N scheme have yielded the microscopic rate constants.     

Pressure-jump studies of the folding/unfolding of trp repressor.

The dimeric protein, trp apo-repressor of Escherichia coli has been subjected to high hydrostatic pressure under a variety of conditions, and the effects have been monitored by fluorescence spectroscopic and infra-red absorption techniques. Under conditions of micromolar protein concentration and low, non-denaturing concentrations of guanidinium hydrochloride (GuHCl), tryptophan and 8-anilino-1-naphthalene sulfonate (ANS) fluorescence detected high pressure profiles demonstrate that pressures below 3 kbar result in dissociation of the dimer to a monomeric species that presents no hydrophobic binding sites for ANS. The FTIR-detected high pressure profile obtained under significantly different solution conditions (30 mM trp repressor in absence of denaturant) exhibits a much smaller pressure dependence than the fluorescence detected profiles. The pressure-denatured form obtained under the FTIR conditions retains about 50 % alpha-helical structure. From this we conclude that the secondary structure present in the high pressure state achieved under the conditions of the fluorescence experiments is at least as disrupted as that achieved under FTIR conditions. Fluorescence-detected pressure-jump relaxation studies in the presence of non-denaturing concentrations of GuHCl reveal a positive activation volume for the association/folding reaction and a negative activation volume for dissociation/unfolding reaction, implicating dehydration as the rate-limiting step for association/folding and hydration as the rate-limiting step for unfolding. The GuHCl concentration dependence of the kinetic parameters place the transition state at least half-way along the reaction coordinate between the unfolded and folded states. The temperature dependence of the pressure-jump fluorescence-detected dissociation/unfolding reaction in the presence of non-denaturing GuHCl suggests that the curvature in the temperature dependence of the stability arises from non-Arrhenius behavior of the folding rate constant, consistent with a large decrease in heat capacity upon formation of the transition state from the unfolded state. The decrease in the equilibrium volume change for folding with increasing temperature (due to differences in thermal expansivity of the folded and unfolded states) arises from a decrease in the absolute value for the activation volume for unfolding, thus indicating that the thermal expansivity of the transition state is similar to that of the unfolded state.