Rearrangement of partially ordered stacked conformations contributes to the rugged energy landscape of a small RNA hairpin

We have studied the fast relaxation kinetics of a small RNA hairpin tetraloop using time-resolved infrared spectroscopy. A laser-induced temperature jump initiated the relaxation by rapidly perturbing the thermal equilibrium of the sample. We probed the relaxation kinetics at two different wavenumbers, 1574 and 1669 cm (-1). The latter is due to the C6O6 carbonyl stretch of the base guanine and is a direct measure of guanine base pairing. The former is assigned to a ring vibration of guanine and tracks structure by sensing base stacking interactions. Overall, the kinetics at 1574 cm (-1) are faster than those observed at 1669 cm (-1). When relaxation occurs at the melting temperature, the kinetics at both wavenumbers are biexponential. When relaxation occurs at a temperature that is higher than the melting temperature, the data at 1669 cm (-1) are still biexponential while only a single fast phase is resolved in the data at 1574 cm (-1). The fast phases are in the range of microseconds, while the slower phases are in the range of tens of microseconds. At both wavenumbers, a portion of the relaxation is not resolved, indicating the existence of a very fast, sub-100 ns phase. Our results provide additional evidence that small, fast folding hairpin loops are characterized by a rugged energy landscape. Furthermore, our data suggest that single-strand stacking interactions and stacking interactions in the loop contribute significantly to the ruggedness of the energy landscape. This work also demonstrates the utility of time-resolved infrared spectroscopy in studying RNA folding.     

Kinetic studies of the folding of heterodimeric monellin: evidence for switching between alternative parallel pathways

Determining whether or not a protein uses multiple pathways to fold is an important goal in protein folding studies. When multiple pathways are present, defined by transition states that differ in their compactness and structure but not significantly in energy, they may manifest themselves by causing the dependence on denaturant concentration of the logarithm of the observed rate constant of folding to have an upward curvature. In this study, the folding mechanism of heterodimeric monellin [double-chain monellin (dcMN)] has been studied over a range of protein and guanidine hydrochloride (GdnHCl) concentrations, using the intrinsic tryptophan fluorescence of the protein as the probe for the folding reaction. Refolding is shown to occur in multiple kinetic phases. In the first stage of refolding, which is silent to any change in intrinsic fluorescence, the two chains of monellin bind to one another to form an encounter complex. Interrupted folding experiments show that the initial encounter complex folds to native dcMN via two folding routes. A productive folding intermediate population is identified on one route but not on both of these routes. Two intermediate subpopulations appear to form in a fast kinetic phase, and native dcMN forms in a slow kinetic phase. The chevron arms for both the fast and slow phases of refolding are shown to have upward curvatures, suggesting that at least two pathways each defined by a different intermediate are operational during these kinetic phases of structure formation. Refolding switches from one pathway to the other as the GdnHCl concentration is increased.     

Confirmation of the hierarchical folding of RNase H: a protein engineering study.

The kinetic intermediate of RNase H is structured in a core region of the protein. To probe the role of this intermediate in the folding of RNase H, the folding kinetics of mutant proteins with altered native state stabilities were investigated. Mutations within the folding core destabilize the kinetic intermediate and slow refolding in a manner consistent with an obligatory intermediate model. Mutations outside of the folding core, however, do not affect the stability of the kinetic intermediate but do perturb the native state and transition state. These results indicate that interactions formed in the intermediate persist in the transition and native states and that RNase H folds through a hierarchical mechanism.     

A New Computational Approach for Mechanical Folding Kinetics of RNA Hairpins

Based on an ensemble of kinetically accessible conformations, we propose a new analytical model for RNA folding kinetics. The model gives populational kinetics, kinetic rates, transition states, and pathways from the rate matrix. Applications of the new kinetic model to mechanical folding of RNA hairpins such as trans-activation-responsive RNA reveal distinct kinetic behaviors in different force regimes, from zero force to forces much stronger than the critical force for the folding-unfolding transition. In the absence of force or a low force, folding can be initiated (nucleated) at any position by forming the first base stack and there exist many pathways for the folding process. In contrast, for a higher force, the folding/unfolding would predominantly proceed along a single zipping/unzipping pathway. Studies for different hairpin-forming sequences indicate that depending on the nucleotide sequence, a kinetic intermediate can emerge in the low force regime but disappear in high force regime, and a new kinetic intermediate, which is absent in the low and high force regimes, can emerge in the medium force range. Variations of the force lead to changes in folding cooperativity and rate-limiting steps. The predicted network of pathways for trans-activation-responsive RNA suggests two parallel dominant pathways. The rate-limiting folding steps (at f = 8 pN) are the formation of specific basepairs that are 2-4 basepairs away from the loop. At a higher force (f = 11 pN), the folding rate is controlled by the formation of the bulge loop. The predicted rates and transition states are in good agreement with the experimental data for a broad force regime.     

Folding of staphylococcal nuclease A studied by equilibrium and kinetic circular dichroism spectra

The urea-induced unfolding of staphylococcal nuclease A has been studied by circular dichroism both at equilibrium and by the kinetics of unfolding and refolding (pH 7.0 and 4.5 degrees C), as a function of Ca2+ and thymidine 3',5'-diphosphate (pdTp) concentration. The results are as follows. (1) The unfolding transition is shifted to higher concentrations of urea by Ca2+ and pdTp, and the presence of both ligands further stabilizes the protein. (2) In the first stage of kinetic refolding, the peptide ellipticity changes rapidly within the dead time of stopped-flow measurement (15 ms), indicating accumulation of a transient intermediate. This intermediate is remarkably less stable than those of other globular proteins previously studied. (3) Dependence of the folding and unfolding rate constants on urea concentration indicates that the critical activated state of folding ("transition state") has considerable structural organization. The transition state does not, however, have the capacity to bind Ca2+ and pdTp, as indicated by the effects of these ligands on the unfolding rate constant. (4) There are at least four different phases in the refolding kinetics in native conditions below 1 M urea. In the absence of pdTp, there are two phases in unfolding, while in the presence of pdTp the unfolding kinetics show a single phase. Some characteristics of the transient intermediate and of the transition state for folding are discussed.     

Structural Rearrangements Linked to Global Folding Pathways of the Azoarcus Group I Ribozyme

Stable RNAs must fold into specific three-dimensional structures to be biologically active, yet many RNAs form metastable structures that compete with the native state. Our previous time-resolved footprinting experiments showed that Azoarcus group I ribozyme forms its tertiary structure rapidly (τ < 30 ms) without becoming significantly trapped in kinetic intermediates. Here, we use stopped-flow fluorescence spectroscopy to probe the global folding kinetics of a ribozyme containing 2-aminopurine in the loop of P9. The modified ribozyme was catalytically active and exhibited two equilibrium folding transitions centered at 0.3 and 1.6 mM Mg²⁺, consistent with previous results. Stopped-flow fluorescence revealed four kinetic folding transitions with observed rate constants of 100, 34, 1, and 0.1 s^− 1 at 37 °C. From comparison with time-resolved Fe(II)-ethylenediaminetetraacetic acid footprinting of the modified ribozyme under the same conditions, these folding transitions were assigned to formation of the I_C intermediate, tertiary folding and docking of the nicked P9 tetraloop, reorganization of the P3 pseudoknot, and refolding of nonnative conformers, respectively. The footprinting results show that 50-60% of the modified ribozyme folds in less than 30 ms, while the rest of the RNA population undergoes slow structural rearrangements that control the global folding rate. The results show how small perturbations to the structure of the RNA, such as a nick in P9, populate kinetic folding intermediates that are not observed in the natural ribozyme.     

The cross-road between the mechanisms of protein folding and aggregation; study of human stefin B and its H75W mutant

The role of the aromatic residue at site 75 to protein stability, the mechanism of folding and the mechanism of amyloid-fibril formation were investigated for the human stefin B variant (bearing Y at site 31) and its point mutation H75W. With an aim to reveal the conformation at the cross-road between folding and aggregation, first, the kinetics of folding and oligomer formation by human stefin B(Y31) variant were studied. It was found to fold in three kinetic phases at pH 4.8 and 10% TFE; the pH and solvent conditions that transform the protein into amyloid fibrils at longer times. The same pH leads to the formation of native-like intermediate (known from previous studies of this variant), meaning that the process of folding and amyloid-fibril formation share the same structural intermediate, which is in this case native-like and dimeric. At pH 5.8 and 7.0 stefin B folded to the native state in four kinetic phases over two intermediates. In distinction, the mutant H75W did not fold to completion, ending in intermediate states at all pH values studied: 4.8, 5.8 and 7.0. At pH 4.8 and 5.8, the mutant folded in one kinetic phase to the intermediate of the “molten globule” type, which leads to the conclusion that its mechanism of folding differs from the one of the parent stefin B at the same pH. At pH 7.0 the mutant H75W folded in three kinetic phases to a native-like intermediate, analogous to folding of stefin B at pH 4.8.     

Multiple interactions of a DNA-binding protein in vivo. II. Effects of host mutations on DNA replication of phage T4 gene 32 mutants.

A quantitative analysis has been made of the kinetics of disulphide bond formation, breakage, and rearrangement which occur during the folding and unfolding of the pancreatic trypsin inhibitor. The results have been used to infer the energetics of the protein conformational transitions which accompany each step.The folding transition is shown to be a co-operative process in which all intermediate states with one or two disulphide bonds are unstable relative to the unfolded, reduced protein and that in the fully folded conformation with three disulphide bonds. The approximate two-state nature of the transition at equilibrium was demonstrated experimentally. The folding transition of the inhibitor which has been determined kinetically is therefore analogous to that observed generally with other globular proteins.     

Exploring the folding pathway of green fluorescent protein through disulfide engineering

We have introduced two disulfide crosslinks into the loop regions on opposite ends of the beta barrel in superfolder green fluorescent protein (GFP) in order to better understand the nature of its folding pathway. When the disulfide on the side opposite the N/C‐termini is formed, folding is 2× faster, unfolding is 2000× slower, and the protein is stabilized by 16 kJ/mol. But when the disulfide bond on the side of the termini is formed we see little change in the kinetics and stability. The stabilization upon combining the two crosslinks is approximately additive. When the kinetic effects are broken down into multiple phases, we observe Hammond behavior in the upward shift of the kinetic m‐value of unfolding. We use these results in conjunction with structural analysis to assign folding intermediates to two parallel folding pathways. The data are consistent with a view that the two fastest transition states of folding are "barrel closing" steps. The slower of the two phases passes through an intermediate with the barrel opening occurring between strands 7 and 8, while the faster phase opens between 9 and 4. We conclude that disulfide crosslink‐induced perturbations in kinetics are useful for mapping the protein folding pathway.     

Kinetic coupling between protein folding and prolyl isomerization. II. Folding of ribonuclease A and ribonuclease T1.

The folding and unfolding kinetics within the transition region were measured for RNase A and for RNase T1. The data were used to evaluate the theoretical models for the influence of prolyl isomerization on the observed folding kinetics. These two proteins were selected, since the folding reaction of RNase A is faster than prolyl isomerization, whereas in RNase T1, folding is slower than isomerization in the transition region. Folding of RNase T1 was investigated for three variants with different numbers of cis prolyl residues. The results indicate that in the transition region the folding rates are indeed strongly dependent on the number of prolyl residues. The variant of RNase T1 that contains only one cis prolyl residue folds about ten times faster than two variants that contain two cis prolyl residues. For both RNase A and RNase T1, the apparent rates of folding and unfolding as well as the corresponding amplitudes depend on the concentration of denaturant in a manner that was predicted by the model calculations. When refolding was started from the fast-folding species, additional kinetic phases could be observed in the transition region for both proteins. The obtained values could be used to calculate the microscopic rate constants of folding and isomerization on the basis of theoretical models.     

Mg2+-dependent folding of a large ribozyme without kinetic traps

The folding kinetics of the catalytic domain of Bacillus subtilis ribonuclease P is analyzed here by fluorescence and catalytic activity. The folding pathway is apparently free of kinetic traps, as indicated by a decrease in folding rates upon the addition of urea. We apply Mg2+ and urea chevron analysis to fully describe the folding and unfolding kinetics of this ribozyme. A folding scheme containing two kinetic intermediates completely accounts for the free energy, the Mg2+ Hill coefficient and the surface buried in the equilibrium transition. At saturating Mg 2+concentrations, folding is limited by a barrier that is independent of Mg2+ and urea. These results describe the first trap-free folding pathway of a large ribozyme and indicate that kinetic traps are not an obligate feature of RNA folding.     

Multiple folding pathways of the SH3 domain

Experimental observations suggest that proteins follow different folding pathways under different environmental conditions. We perform molecular dynamics simulations of a model of the c-Crk SH3 domain over a broad range of temperatures, and identify distinct pathways in the folding transition. We determine the kinetic partition temperature-the temperature for which the c-Crk SH3 domain undergoes a rapid folding transition with minimal kinetic barriers-and observe that below this temperature the model protein may undergo a folding transition by multiple folding pathways via only one or two intermediates. Our findings suggest the hypothesis that the SH3 domain, a protein fold for which only two-state folding kinetics was observed in previous experiments, may exhibit intermediate states under conditions that strongly stabilize the native state.     

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.     

Pathway modulation, circular permutation and rapid RNA folding under kinetic control

The thermodynamics and folding kinetics of a circularly permuted construct of the ribozyme from Bacillus subtilis RNase P are analyzed and compared with the folding properties of the wild-type ribozyme using optical spectroscopy and catalytic activity. The folding of the wild-type ribozyme is slow due to the rearrangement of kinetically trapped species containing misfolded structures. To test whether any misfolded structure arises from interactions between the two independently folding domains of the RNase P RNA, a circular permuted form was created where one of the two phosphodiester bonds connecting these domains is broken. This construct folds approximately 15-fold faster (t1/2 approximately nine seconds) than the wild-type ribozyme at 37 degreesC. While the complete folding of both domains is kinetically indistinguishable in the wild-type ribozyme, one domain folds much faster than the other domain in the circularly permuted construct. Hence, the major kinetic trap in the folding of the wild-type RNase P RNA involves interdomain interactions. This kinetic trap is avoidable at 37 degreesC in the circularly permuted RNA. However, at temperatures below 30 degreesC or when refolding begins from an equilibrium intermediate stabilized by submillimolar concentrations of Mg2+, a subpopulation containing an interdomain misfold still forms. These results indicate that the folding pathway of this large RNA is highly malleable and can be under kinetic control.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

Solvation and desolvation dynamics in apomyoglobin folding monitored by time-resolved infrared spectroscopy

Solvation and desolvation dynamics around helices during the kinetic folding process of apomyoglobin (apoMb) were investigated by using time-resolved infrared (IR) spectroscopy based on continuous-flow rapid mixing devices and an IR microscope. The folding of apoMb can be described by the collapse and search mechanism, in which the initial collapse occurring within several hundreds of microseconds is followed by the search for the correct secondary and tertiary structures. The time-resolved IR measurements showed a significant increase in solvated helix possessing a component of amide I' at 1633 cm(-1) within 100 mus after initiating the folding by a pD jump from pD2.2 to 6.0. In contrast, there was a minor increase in buried helices having amide I' at 1652 cm(-1) in this time domain. The observations demonstrate that the initially collapsed conformation of apoMb possesses a large amount of solvated helices, and suggest that much water is retained inside the collapsed domain. The contents of solvated and buried helices decrease and increase, respectively, in the time domain after the collapse, showing that the stepwise desolvation around helices is associated with the conformational search process. Interestingly, the largest changes in solvated and buried helices were observed at the final rate-limiting step of the apoMb folding. The persistence of the solvated helix until the final stage of apoMb folding suggests that the dissociation of hydrogen bonds between water and main-chain amides contributes to the energy barrier in the rate-determining step of the folding.     

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments (for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.