Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

Shape of the free energy barriers for protein folding probed by multiple perturbation analysis

The characterization of the free energy barriers has been a major goal in studies on the mechanism of protein folding. Testing the effect of mutations or denaturants on protein folding reactions revealed that transition state movement is rare, suggesting that folding barriers are robust and narrow maxima on the free energy landscape. Here we demonstrate that the application of multiple perturbations allows the observation of small transition state movements that escape detection in single perturbation experiments. We used tendamistat as a model protein to test the broadness of the free energy barriers. Tendamistat folds over two consecutive transition states and through a high-energy intermediate. Measuring the combined effect of temperature and denaturant on the position of the transition state in the wild-type protein and in several mutants revealed that the early transition state shows significant transition state movement. Its accessible surface area state becomes more native-like with destabilization of the native state by temperature. To the same extent, the entropy of the early transition state becomes more native-like with increasing denaturant concentration, in accordance with Hammond behavior. The position of the late transition state, in contrast, is much less sensitive to the applied perturbations. These results suggest that the barriers in protein folding become increasingly narrow as the folding polypeptide chain approaches the native state.     

A kinetic folding intermediate probed by native state hydrogen exchange

Stopped-flow fluorescence studies on the N-terminal domain of rat CD2 (CD2.d1) have demonstrated that folding from the fully denatured state (U) proceeds via the transient accumulation of an apparent intermediate (I) in a so-called burst phase that precedes the rate-limiting transition leading to the native state (N). A previous pH-dependent equilibrium hydrogen exchange (HX) study identified a subset of amides in CD2.d1 which, under EX2 conditions, exchange from N with free energies greater than or equal to the free energy difference between the N and I states calculated from the stopped-flow data. Under EX1 conditions the rates of HX for these amides tend towards an asymptote that matches the global unfolding rate calculated from the stopped-flow data, suggesting that exchange for these amides requires traversing the N-to-I transition state barrier. Exchange for these amides presumably occurs from exchange-competent forms comprising the kinetic burst phase therefore. To explore this idea further, native state HX (NHX) data have been collected for CD2.d1 under EX2 conditions using denaturant concentrations which span either side of the denaturant concentration where, according to the stopped-flow data, the apparent U and I states are iso-energetic. The data fit to a two-component, sub-global (sg)/global (g) NHX mechanism, yielding Delta G and m value parameters (where the m value is a measure of hydrocarbon solvation). Regression analysis demonstrates that the (m(sg), Delta G(sg)) and (m(g), Delta G(g)) values calculated for this subset of amides correspond with those describing the kinetic burst phase transition. This result confirms the ability of the NHX technique to explore the structural and energetic properties of kinetic folding intermediates.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

Dimensions,energetics, and denaturant effects of the protein unstructured state

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure–function relation of intrinsically disordered proteins. Here, we adopt a coil‐globule transition theory to develop a general scheme to extract interaction and free energy information from single‐molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter‐residue interactions on the denaturant concentration, and are thus compatible under the coil‐globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ‐state are also discussed.     

Thermodynamic strategies for stabilizing intermediate states of proteins

This paper presents three theorems pertaining to thermodynamic properties of the intermediate (e.g., molten globule) state of proteins exhibiting such a conformation in the presence of GuHCl or urea. The theorems are proved for the three-state case using the denaturant binding model and the linear extrapolation model; their utility is illustrated via applications to examples in the literature. Theorem One states that the denaturant activity that maximizes the population of a partly folded conformation is at any temperature independent of the Gibbs free energy difference between the intermediate and native states. This result holds for both models of protein–denaturant interaction. The second theorem claims that the population maximum is independent, of the denaturant association constant for the denaturant binding model. Theorem Three, which also applies to both models considered here, states that at the temperatures corresponding to the extrema in the population of the intermediate, the enthalpy change of the intermediate is equal to the excess enthalpy function, an experimentally accessible quantity. In the absence of denaturant, the enthalpy change of the intermediate state at the population extrema can be written as a function of the thermodynamic parameters of the unfolded state alone. These results, which can be applied to systems of any number of states under certain conditions, should aid in the optimization of conditions employed for experimental studies of partly organized states of proteins. © 1994 John Wiley & Sons, Inc.     

Structural dynamics, stability and folding of proteins

The present concepts of protein folding in vitro are reviewed. According to these concepts, amino acid sequence of protein, which has appeared a result of evolutionary selection, determines the native structure of protein, the pathway of protein folding, and the existence of free energy barrier between native and denatured states of protein. The latter means that protein macromolecule can exist in either native or denatured state. And all macromolecules in the native state are identical but for structural fluctuations due to Brownian motion of their atoms. Identity of all molecules in native state is of primary importance for their correct functioning. The dependence of protein stability, which is measured as the difference between free energy of protein in native and denatured states, on temperature and denaturant concentration is discussed. The modern approaches characterizing transition state and nucleation are regarded. The role of intermediate and misfolded states in amorphous aggregate and amyloid fibril formation is discussed.     

Folding pathway of FKBP12 and characterisation of the transition state.

The folding pathway of human FKBP12, a 12 kDa FK506-binding protein (immunophilin), has been characterised. Unfolding and refolding rate constants have been determined over a wide range of denaturant concentrations and data are shown to fit to a two-state model of folding in which only the denatured and native states are significantly populated, even in the absence of denaturant. This simple model for folding, in which no intermediate states are significantly populated, is further supported from stopped-flow circular dichroism experiments in which no fast "burst" phases are observed. FKBP12, with 107 residues, is the largest protein to date which folds with simple two-state kinetics in water (kF=4 s(-1)at 25 degrees C). The topological crossing of two loops in FKBP12, a structural element suggested to cause kinetic traps during folding, seems to have little effect on the folding pathway.The transition state for folding has been characterised by a series of experiments on wild-type FKBP12. Information on the thermodynamic nature of, the solvent accessibility of, and secondary structure in, the transition state was obtained from experiments measuring the unfolding and refolding rate constants as a function of temperature, denaturant concentration and trifluoroethanol concentration. In addition, unfolding and refolding studies in the presence of ligand provided information on the structure of the ligand-binding pocket in the transition state. The data suggest a compact transition state relative to the unfolded state with some 70 % of the surface area buried. The ligand-binding site, which is formed mainly by two loops, is largely unstructured in the transition state. The trifluoroethanol experiments suggest that the alpha-helix may be formed in the transition state. These results are compared with results from protein engineering studies and molecular dynamics simulations (see the accompanying paper).     

Early collapse is not an obligate step in protein folding

The dimensions and secondary structure content of two proteins which fold in a two-state manner are measured within milliseconds of denaturant dilution using synchrotron-based, stopped-flow small-angle X-ray scattering and far-UV circular dichroism spectroscopy. Even upon a jump to strongly native conditions, neither ubiquitin nor common-type acylphosphatase contract prior to the major folding event. Circular dichroism and fluorescence indicate that negligible amounts of secondary and tertiary structures form in the burst phase. Thus, for these two denatured states, collapse and secondary structure formation are not energetically downhill processes even under aqueous, low-denaturant conditions. In addition, water appears to be as good a solvent as that with high concentrations of denaturant, when considering the over-all dimensions of the denatured state. However, the removal of denaturant does subtly alter the distribution of backbone dihedral phi,psi angles, most likely resulting in a shift from the polyproline II region to the helical region of the Ramachandran map. We consider the thermodynamic origins of these behaviors along with implications for folding mechanisms and computer simulations thereof.     

Reliable protein folding on complex energy landscapes: the free energy reaction path

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate r at which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate r is below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.     

Folding of the yeast prion protein Ure2: kinetic evidence for folding and unfolding intermediates.

The Saccharomyces cerevisiae non-Mendelian factor [URE3] propagates by a prion-like mechanism, involving aggregation of the chromosomally encoded protein Ure2. The N-terminal prion domain (PrD) of Ure2 is required for prion activity in vivo and amyloid formation in vitro. However, the molecular mechanism of the prion-like activity remains obscure. Here we measure the kinetics of folding of Ure2 and two N-terminal variants that lack all or part of the PrD. The kinetic folding behaviour of the three proteins is identical, indicating that the PrD does not change the stability, rates of folding or folding pathway of Ure2. Both unfolding and refolding kinetics are multiphasic. An intermediate is populated during unfolding at high denaturant concentrations resulting in the appearance of an unfolding burst phase and "roll-over" in the denaturant dependence of the unfolding rate constants. During refolding the appearance of a burst phase indicates formation of an intermediate during the dead-time of stopped-flow mixing. A further fast phase shows second-order kinetics, indicating formation of a dimeric intermediate. Regain of native-like fluorescence displays a distinct lag due to population of this on-pathway dimeric intermediate. Double-jump experiments indicate that isomerisation of Pro166, which is cis in the native state, occurs late in refolding after regain of native-like fluorescence. During protein refolding there is kinetic partitioning between productive folding via the dimeric intermediate and a non-productive side reaction via an aggregation prone monomeric intermediate. In the light of this and other studies, schemes for folding, aggregation and prion formation are proposed.     

Characterization of the critical state in protein folding. Effects of guanidine hydrochloride and specific Ca2+ binding on the folding kinetics of alpha-lactalbumin

The reversible unfolding and refolding kinetics of alpha-lactalbumin induced by concentration jump of guanidine hydrochloride were measured at pH 7.0 and 25 degrees C using tryptophan absorption at 292 nm, with varying concentrations of the denaturant and free Ca2+. The refolding reaction of alpha-lactalbumin from the fully unfolded (D) state occurs through the two stages: (1) instantaneous formation of a compact intermediate (the A state) that has a native-like secondary structure; (2) tight packing of the preformed secondary structure segments to lead finally to the native structure, this stage being the rate-determining step of the reaction and associated with acquisition of the specific structure necessary for strong Ca2+ binding. Under strongly native conditions, the observed kinetics of refolding is also complicated by the presence of a slow-folding species (10%) in the unfolded state. Considering these facts, the microscopic rate constants in folding and unfolding directions have been evaluated from the observed kinetics and from the equilibrium constants of the transitions among the native (N), A and D states. Close linear relationships have been found in the plots of the activation free energies, obtained from the microscopic rate constants, against the denaturant concentration. They are similar to the linear relationship between the free energy of unfolding and the denaturant concentration. It was demonstrated that the slope of the plots should be approximately proportional to a change in accessible surface area of the protein during the respective activation process, and that only a third of the difference in accessible surface area between A and N is buried in the critical activated state of folding. However, the selective effect of Ca2+ binding on the folding rate constant has been observed also, demonstrating that the specific Ca2+-binding substructure in the N state is already organized in the activated state. Thus, only a part of the protein molecule involving the Ca2+-binding region is organized in the activated state, with the other part of the molecule being left less organized, suggesting that the second stage of folding may be a sequential growing process of organized assemblage of the performed secondary structure segments.     

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

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

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

Refolding of the hyperthermophilic protein Ssh10b involves a kinetic dimeric intermediate

The α/β-mixed dimeric protein Ssh10b from the hyperthermophile Sulfolobus shibatae is a member of the Sac10b family that is thought to be involved in chromosomal organization or DNA repair/recombination. The equilibrium unfolding/refolding of Ssh10b induced by denaturants and heat was fully reversible, suggesting that Ssh10b could serve as a good model for folding/unfolding studies of protein dimers. Here, we investigate the folding/unfolding kinetics of Ssh10b in detail by stopped-flow circular dichroism (SF-CD) and using GdnHCl as denaturant. In unfolding reactions, the native Ssh10b turned rapidly into fully unfolded monomers within the stopped-flow dead time with no detectable kinetic intermediate, agreeing well with the results of equilibrium unfolding experiments. In refolding reactions, two unfolded monomers associate in the burst phase to form a dimeric intermediate that undergoes a further, slower, first-order folding process to form the native dimer. Our results demonstrate that the dimerization is essential for maintaining the native tertiary interactions of the protein Ssh10b. In addition, folding mechanisms of Ssh10b and several other α/β-mixed or pure β-sheet proteins are compared.     

Three-state protein folding: experimental determination of free-energy profile

When considering protein folding with a transient intermediate, a difficulty arises as to determination of the rates of separate transitions. Here we overcome this problem, using the kinetic studies of the unfolding/refolding reactions of the three-state protein apomyoglobin as a model. Amplitudes of the protein refolding kinetic burst phase corresponding to the transition from the unfolded (U) to intermediate (I) state, that occurs prior to the native state (N) formation, allow us to estimate relative populations of the rapidly converting states at various final urea concentrations. On the basis of these proportions, a complicated experimental chevron plot has been deconvolved into the urea-dependent rates of the I<-->N and U<-->N transitions to give the dependence of free energies of the main transition state and of all three (N, I, and U) stable states on urea concentration.