Internal friction controls the speed of protein folding from a compact configuration

Several studies have found millisecond protein folding reactions to be controlled by the viscosity of the solvent: Reducing the viscosity allows folding to accelerate. In the limit of very low solvent viscosity, however, one expects a different behavior. Internal interactions, occurring within the solvent-excluded interior of a compact molecule, should impose a solvent-independent upper limit to folding speed once the bulk diffusional motions become sufficiently rapid. Why has this not been observed? We have studied the effect of solvent viscosity on the folding of cytochrome c from a highly compact, late-stage intermediate configuration. Although the folding rate accelerates as the viscosity declines, it tends toward a finite limiting value approximately 10(5) s(-1) as the viscosity tends toward zero. This limiting rate is independent of the cosolutes used to adjust solvent friction. Therefore, interactions within the interior of a compact denatured polypeptide can limit the folding rate, but the limiting time scale is very fast. It is only observable when the solvent-controlled stages of folding are exceedingly rapid or else absent. Interestingly, we find a very strong temperature dependence in these "internal friction"-controlled dynamics, indicating a large energy scale for the interactions that govern reconfiguration within compact, near-native states of a protein.     

Diffusional barrier crossing in a two-state protein folding reaction.

There has been some debate as to whether protein folding involves diffusive chain motions and thus depends on solvent viscosity. The interpretation of folding kinetics in viscous solvents has remained difficult and controversial, in that viscogenic agents affect folding rates not only by increasing solvent viscosity but also by increasing protein stability. By carefully choosing experimental conditions, we can now eliminate the effect on stability and show that the folding dynamics of the cold shock protein CspB are viscosity dependent. Thus Kramers' theory of reaction rates rather than transition state theory should be used to describe this folding reaction.     

Effects of solvent viscosity and different guanidine salts on the kinetics of ribonuclease A chain folding

The kinetics of folding of the two forms of unfolded ribonuclease A have been measured as a function of solvent viscosity by adding either glycerol or sucrose. The aim is to find out if either reaction is rate limited by segmental motion whose rate depends on external friction. The fast folding reaction (U₂ ? N) is known to be the direct folding process, and the slow folding reaction (U₁ ? N) is known to be rate limited by an interconversion between two forms (U₁ ? U₂) which are present after unfolding in strongly denaturing conditions. No dependence on solvent viscosity is found, either for the direct folding reaction or for the interconversion reaction. Each folding reaction has also been tested to see if its rate depends on the concentration of one or more partly folded intermediates, by adding denaturants destabilize any partly folded structures. Different guanidine salts are used as denaturants to vary the denaturing effectiveness of the salt while holding the guanidinium ion concentration constant. The rates both of the direct folding reaction and of the interconversion reaction decrease in relation to the denaturing effectiveness of the salt. However, there is a basic difference between the responses of the fast and slow folding reactions to low concentrations of denaturants. Although each folding reaction produces native protein, there is an 800-fold decrease in the rate of the fast folding reaction in 1M guanidine thiocyanate and only a 13-fold decrease in the rate of the slow folding reaction. This is consistent with the fast reaction being the direct folding process and the slow reaction being rate limited by the initial conversion of the slowrefolding to the fast-refolding form. Both the lack of viscosity dependence and the effects of denaturants indicate that the formation of structure is rate limiting in the direct folding reaction, U₂ ? N. The failure to find a viscosity dependence for the interconversion reaction, U₁ ? U₂, indicates that in this reaction also friction-limited segmental motion is not the rate-limiting process. Since the U₁ ? U₂ interconversion still occurs when the polypeptide chain is completely unfolded, the surprising result is that its rate in refolding conditions depends significantly on a reaction intermediate which is “denatured” by guanidine salts.     

Hydration and packing along the folding pathway of SH3 domains by pressure-dependent NMR

The volumetric properties associated with protein folding transitions reflect changes in protein packing and hydration of the states that participate in the folding reaction. Here, NMR spin relaxation techniques are employed to probe the folding-unfolding kinetics of two SH3 domains as a function of pressure so that the changes in partial molar volumes along the folding pathway can be measured. The two domains fold with rates that differ by approximately 3 orders of magnitude, so their folding dynamics must be probed using different NMR relaxation experiments. In the case of the drkN SH3 domain that folds via a two-state mechanism on a time scale of seconds, nitrogen magnetization exchange spectroscopy is employed, while for the G48M mutant of the Fyn SH3 domain where the folding occurs on the millisecond time scale (three-step reaction), relaxation dispersion experiments are utilized. The NMR methodology is extremely sensitive to even small changes in equilibrium and rate constants, so reliable estimates of partial molar volumes can be obtained using low pressures (1-120 bar), thus minimizing perturbations to any of the states along the folding reaction coordinate. The volumetric data that were obtained are consistent with a similar folding mechanism for both SH3 domains, involving early chain compaction to states that are at least partially hydrated. This work emphasizes the role of NMR spin relaxation in studying dynamic processes over a wide range of time scales.     

Diffusive motions control the folding and unfolding kinetics of the apomyoglobin pH 4 molten globule intermediate

The sperm whale apomyoglobin pH 4 folding intermediate exists in two forms, Ia and Ib, that mimic transient kinetic intermediates in the folding of the native protein at pH 6. To characterize the nature of the kinetic barrier that controls the formation of the earliest intermediate Ia, we have investigated the effects of small viscogenic cosolvents on its folding and unfolding kinetics. The kinetics are measurable by stopped-flow fluorescence and follow a cooperative two-state model in the absence and presence of cosolvents. Small cosolvents stabilize Ia, but, by applying the isostability test to separate the viscogenic effect of the cosolvent from its stabilizing effect, we found that, in both folding and unfolding conditions, the apparent rate constant decreases when solvent viscosity increases. The unitary inverse dependence of the apparent rate constant on solvent viscosity indicates a diffusion-controlled reaction. This result is consistent with the hypothesis that folding of the apomyoglobin pH 4 intermediate obeys a diffusion-collision model. Additionally, the temperature dependence of the reaction rate at constant viscosity indicates that the formation of Ia is also controlled by an energy barrier. Linear free energy relationships show that the transition state of the U <==> Ia reaction is compact and buries 45% of the surface area that is buried in native apomyoglobin. We conclude that the transition state of the U <==> Ia reaction resembles that for the formation of native proteins; namely, it is dry and its compactness is closer to that of the folded (Ia) form than of the unfolded form.     

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).     

Thermodynamics of a diffusional protein folding reaction

The folding reactions of several proteins are well described as diffusional barrier crossing processes, which suggests that they should be analyzed by Kramers' rate theory rather than by transition state theory. For the cold shock protein Bc-Csp from Bacillus caldolyticus, we measured stability and folding kinetics, as well as solvent viscosity as a function of temperature and denaturant concentration. Our analysis indicates that diffusional folding reactions can be treated by transition state theory, provided that the temperature and denaturant dependence of the solvent viscosity is properly accounted for, either at the level of the measured rate constants or of the calculated activation parameters. After viscosity correction the activation barriers for folding become less enthalpic and more entropic. The transition from an enthalpic to an entropic folding barrier with increasing temperature is, however, apparent in the data before and after this correction. It is a consequence of the negative activation heat capacity of refolding, which is independent of solvent viscosity. Bc-Csp and its mesophilic homolog Bs-CspB from Bacillus subtilis differ strongly in stability but show identical enthalpic and entropic barriers to refolding. The increased stability of Bc-Csp originates from additional enthalpic interactions that are established after passage through the activated state. As a consequence, the activation enthalpy of unfolding is increased relative to Bs-CspB.     

Protein folding as a diffusional process.

A protein chain must move relative to the solvent molecules and explore many conformations when it folds from the extended unfolded state to the compact native state. Experimental and theoretical approaches suggest that diffusional processes in fact contribute to the kinetics of protein folding. We describe here how variations of the solvent viscosity can be employed to uncover the diffusional contributions to a folding reaction and assess the use of transition state theory and Kramers' rate theory for the analysis of protein folding reactions.     

A comparison of the folding of two knotted proteins: YbeA and YibK

The extraordinary topology of proteins belonging to the alpha/beta-knot superfamily of proteins is unexpected, due to the apparent complexities involved in the formation of a deep trefoil knot in a polypeptide backbone. Despite this, an increasing number of knotted structures are being identified; how such proteins fold remains a mystery. Studies on the dimeric protein YibK from Haemophilus influenzae have led to the characterisation of its folding pathway in some detail. To complement research into the folding of YibK, and to address whether folding pathways are conserved for members of the alpha/beta-knot superfamily, the structurally similar knotted protein YbeA from Escherichia coli has been studied. A comprehensive thermodynamic and kinetic analysis of the folding of YbeA is presented here, and compared to that of YibK. Both fold via an intermediate state populated under equilibrium conditions that is monomeric and considerably structured. The unfolding/refolding kinetics of YbeA are simpler than those found for YibK and involve two phases attributed to the formation of a monomeric intermediate state and a dimerisation step. In contrast to YibK, a change in the rate-determining step on the unfolding pathway for YbeA is observed with a changing concentration of urea. Despite this difference, both proteins fold by a mechanism involving at least one sequential monomeric intermediate that has properties similar to that observed during the equilibrium unfolding. The rate of dimerisation observed for YbeA and YibK is very similar, as is the rate constant for formation of the kinetic monomeric intermediate that precedes dimerisation. The findings suggest that relatively slow folding and dimerisation may be common attributes of knotted proteins.     

Branching in the sequential folding pathway of cytochrome c

Previous results indicate that the folding pathways of cytochrome c and other proteins progressively build the target native protein in a predetermined stepwise manner by the sequential formation and association of native-like foldon units. The present work used native state hydrogen exchange methods to investigate a structural anomaly in cytochrome c results that suggested the concerted folding of two segments that have little structural relationship in the native protein. The results show that the two segments, an 18-residue omega loop and a 10-residue helix, are able to unfold and refold independently, which allows a branch point in the folding pathway. The pathway that emerges assembles native-like foldon units in a linear sequential manner when prior native-like structure can template a single subsequent foldon, and optional pathway branching is seen when prior structure is able to support the folding of two different foldons.     

Diffusional barrier in the unfolding of a small protein

To determine how the dynamics of the polypeptide chain in a protein molecule are coupled to the bulk solvent viscosity, the unfolding by urea of the small protein barstar was studied in the presence of two viscogens, xylose and glycerol. Thermodynamic studies of unfolding show that both viscogens stabilize barstar by a preferential hydration mechanism, and that viscogen and urea act independently on protein stability. Kinetic studies of unfolding show that while the rate-limiting conformational change during unfolding is dependent on the bulk solvent viscosity, eta, its rate does not show an inverse dependence on eta, as expected by Kramers' theory. Instead, the rate is found to be inversely proportional to an effective viscosity, eta + xi, where xi is an adjustable parameter which needs to be included in the rate equation. xi is found to have a value of -0.7 cP in xylose and -0.5 cP in glycerol, in the case of unfolding, at constant urea concentration as well as under isostability conditions. Hence, the unfolding protein chain does not experience the bulk solvent viscosity, but instead an effective solvent viscosity, which is lower than the bulk solvent viscosity by either 0.7 cP or 0.5 cP. A second important result is the validation of the isostability assumption, commonly used in protein folding studies but hitherto untested, according to which if a certain concentration of urea can nullify the effect of a certain concentration of viscogen on stability, then the same concentrations of urea and viscogen will also not perturb the free energy of activation of the unfolding of the protein.     

Computer simulation of the folding-unfolding transition of island-model proteins--folding pathway, transition process, and fluctuations

Monte Carlo computer simulations were performed to elucidate the dynamic aspects of the folding and unfolding transitions of island-model protein. Five different types of model proteins were designed, according to characteristics of backbone structure. The computer simulations clearly show that the unfolding and folding transitions are all-or-none processes between the N-and U-states. They are typical Poisson processes. From the Arrhenius plots of rate constants, the activation enthalpies of folding and unfolding were determined. In addition, the folding pathways were determined along the reaction coordinate. Formations of several local structures along a polypeptide chain are almost simultaneous, but the most probable time sequence of events exists at the moment of transition. That is the most probable folding pathway. The unfolding pathway was found to be just the reverse process of the most probable folding pathway. The relationship between the fluctuations in each equilibrium state and the transition process was considered. In contrast to the theory of absolute reaction rate, the transient states are widely distributed along the reaction coordinate. From analysis of the “transient process,” we tried to determine the critical states from which the transient process starts. As a result, we found that the unfolding transition occurs at the stage near the N-state. During the U-state, large joined blocks rarely appear, but they appear in the transient process towards the N-state. However, the “branch point” between the N- and U-states lies near the N-state, and joined blocks tend to unfold prior to passing over the branch point. We concluded that the stability of later folding intermediates is important for selection of the folding pathway, while preferential selection of an early folding intermediate is important in acceleration of the folding rate. The effects of intrachain cross-linking and peptide fragment binding on the rate constants were examined by using computer simulations of model proteins. In general, a small-sized loop formed by cross-linking accelerates the folding rate and a large-sized loop contributes much to the stabilization of the native conformation. We also found that peptide fragment binding contributes little to the acceleration of the folding rate of the residual protein.     

Phosphatidylglycerol lipids enhance folding of an alpha helical membrane protein

Membrane lipids are increasingly being recognised as active participants in biological events. The precise roles that individual lipids or global properties of the lipid bilayer play in the folding of membrane proteins remain to be elucidated, Here, we find a significant effect of phosphatidylglycerol (PG) on the folding of a trimeric α helical membrane protein from Escherichia coli diacylglycerol kinase. Both the rate and the yield of folding are increased by increasing the amount of PG in lipid vesicles. Moreover, there is a direct correlation between the increase in yield and the increase in rate; thus, folding becomes more efficient in terms of speed and productivity. This effect of PG seems to be a specific requirement for this lipid, rather than a charge effect. We also find an effect of single-chain lyso lipids in decreasing the rate and yield of folding. We compare this to our previous work in which lyso lipids increased the rate and yield of another membrane protein, bacteriorhodopsin. The contrasting effect of lyso lipids on the two proteins can be explained by the different folding reaction mechanisms and key folding steps involved. Our findings provide information on the lipid determinants of membrane protein folding.     

Kinetic consequences of native state optimization of surface-exposed electrostatic interactions in the Fyn SH3 domain

Optimization of surface exposed charge-charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge-charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge-charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture.     

Specificity of the initial collapse in the folding of the cold shock protein

The two-state folding reaction of the cold shock protein from Bacillus caldolyticus (Bc-Csp) is preceded by a rapid chain collapse. A fast shortening of intra-protein distances was revealed by F?rster resonance energy transfer (FRET) measurements with protein variants that carried individual pairs of donor and acceptor chromophores at various positions along the polypeptide chain. Here we investigated the specificity of this rapid compaction. Energy transfer experiments that probed the stretching of strand beta2 and the close approach between the strands beta1 and beta2 revealed that the beta1-beta2 hairpin is barely formed in the collapsed form, although it is native-like in the folding transition state of Bc-Csp. The time course of the collapse could not be resolved by pressure or temperature jump experiments, indicating that the collapsed and extended forms are not separated by an energy barrier. The co-solute (NH4)2SO4 stabilizes both native Bc-Csp and the collapsed form, which suggests that the large hydrated SO4(2-) ions are excluded from the surface of the collapsed form in a similar fashion as they are excluded from folded Bc-Csp. Ethylene glycol increases the stability of proteins because it is excluded preferentially from the backbone, which is accessible in the unfolded state. The collapsed form of Bc-Csp resembles the unfolded form in its interaction with ethylene glycol, suggesting that in the collapsed form the backbone is still accessible to water and small molecules. Our results thus rule out that the collapsed form is a folding intermediate with native-like chain topology. It is better described as a mixture of compact conformations that belong to the unfolded state ensemble. However, some of its structural elements are reminiscent of the native protein.     

Measuring solution viscosity and its effect on enzyme activity

In proteins, some processes require conformational changes involving structural domain diffusion. Among these processes are protein folding, unfolding and enzyme catalysis. During catalysis some enzymes undergo large conformational changes as they progress through the catalytic cycle. According to Kramers theory, solvent viscosity results in friction against proteins in solution, and this should result in decreased motion, inhibiting catalysis in motile enzymes. Solution viscosity was increased by adding increasing concentrations of glycerol, sucrose and trehalose, resulting in a decrease in the reaction rate of the H⁺-ATPase from the plasma membrane ofKluyveromyces lactis. A direct correlation was found between viscosity (η) and the inhibition of the maximum rate of catalysis (V _max). The protocol used to measure viscosity by means of a falling ball type viscometer is described, together with the determination of enzyme kinetics and the application of Kramers’ equation to evaluate the effect of viscosity on the rate of ATP hydrolysis by the H⁺-ATPase. Published: May 1, 2003     

Viscosity and transient solvent accessibility of Trp-63 in the native conformation of lysozyme

We have measured the rates of isotope exchange at the nitrogen of the indole ring of Trp-63 of lysozyme and of L-tryptophan as a function of solution viscosity. We have used two cosolvents, glycerol and ethylene glycol, to modify the relative viscosity. We have derived the appropriate kinetic equations for the alternative possibilities that the exchange takes place either in solution or in the intact protein matrix. Because we chose to study the proton-catalyzed exchange reaction, the rate of it is not expected to be diffusion-limited. We confirmed this by measuring the exchange from tryptophan. These results and the known effects of glycerol and ethylene glycol on the solvation of indole allow us to predict that if the exchange reaction takes place in a protein matrix the effects of the two cosolvents when compared under isoviscous conditions should be identical. This is what we find for Trp-63 in lysozyme at 15, 20 and 26 degrees C. The slope of the linear plot of log k vs. log relative viscosity is 0.6. This strongly supports a model for conformational fluctuations where transient solvation takes place without major changes in protein folding. The most interesting feature of our findings is the fact that a slow reaction admittedly not diffusion-limited shows, when taking place in a protein matrix, a linear dependence on solution viscosity. We suggest that what we observe is the effect of damping of movement of the side chain expressed as a change in the friction along the reaction coordinate in the corresponding phase space. The presence of such effects stresses the validity and usefulness of Kramers model of rate processes for reactions taking place in a protein matrix. Such behavior is predicted by several of the recently proposed general mechanisms of enzyme catalysis.     

How do chemical denaturants affect the mechanical folding and unfolding of proteins?

We present the first single-molecule atomic force microscopy study on the effect of chemical denaturants on the mechanical folding/unfolding kinetics of a small protein GB1 (the B1 immunoglobulin-binding domain of protein G from Streptococcus). Upon increasing the concentration of the chemical denaturant guanidinium chloride (GdmCl), we observed a systematic decrease in the mechanical stability of GB1, indicating the softening effect of the chemical denaturant on the mechanical stability of proteins. This mechanical softening effect originates from the reduced free-energy barrier between the folded state and the unfolding transition state, which decreases linearly as a function of the denaturant concentration. Chemical denaturants, however, do not alter the mechanical unfolding pathway or shift the position of the transition state for mechanical unfolding. We also found that the folding rate constant of GB1 is slowed down by GdmCl in mechanical folding experiments. By combining the mechanical folding/unfolding kinetics of GB1 in GdmCl solution, we developed the “mechanical chevron plot” as a general tool to understand how chemical denaturants influence the mechanical folding/unfolding kinetics and free-energy diagram in a quantitative fashion. This study demonstrates great potential in combining chemical denaturation with single-molecule atomic force microscopy techniques to reveal invaluable information on the energy landscape underlying protein folding/unfolding reactions.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Productive folding to the native state by a group II intron ribozyme.

Group II introns are large catalytic RNA molecules that fold into compact structures essential for the catalysis of splicing and intron mobility reactions. Despite a growing body of information on the folded state of group II introns at equilibrium, there is currently no information on the folding pathway and little information on the ionic requirements for folding. Folding isotherms were determined by hydroxyl radical footprinting for the 32 individual protections that are distributed throughout a group II intron ribozyme derived from intron ai5gamma. The isotherms span a similar range of Mg(2+) concentrations and share a similar index of cooperativity. Time-resolved hydroxyl radical footprinting studies show that all regions of the ribozyme fold slowly and with remarkable synchrony into a single catalytically active structure at a rate comparable to those of other ribozymes studied thus far. The rate constants for the formation of tertiary contacts and recovery of catalytic activity are identical within experimental error. Catalytic activity analyses in the presence of urea provide no evidence that the slow folding of the ai5gamma intron is attributable to the presence of unproductive kinetic traps along the folding pathway. Taken together, the data suggest that the rate-limiting step for folding of group II intron ai5gamma occurs early along the reaction pathway. We propose that this behavior resembles protein folding that is limited in rate by high contact order, or the need to form key tertiary interactions from partners that are located far apart in the primary or secondary structure.