Unfolding Rate Constants Research Articles

Implementation of a k/k0 Method to Identify Long-Range Structure in Transition States during Conformational Folding/Unfolding of Proteins

A previously introduced kinetic-rate constant (k/k(0)) method, where k and k(0) are the folding (unfolding) rate constants in the mutant and the wild-type forms, respectively, of a protein, has been applied to obtain qualitative information about structure in the transition state ensemble (TSE) of bovine pancreatic ribonuclease A (RNase A), which contains four native disulfide bonds. The method compares the folding (unfolding) kinetics of RNase A, with and without a covalent crosslink and tests whether the crosslinked residues are associated in the folding (unfolding) transition state (TS) of the noncrosslinked version. To confirm that the fifth disulfide bond has not introduced a significant structural perturbation, we solved the crystal structure of the V43C-R85C mutant to 1.6 A resolution. Our findings suggest that residues Val43 and Arg85 are not associated, and that residues Ala4 and Val118 may form nonnative contacts, in the folding (unfolding) TSE of RNase A.

Mass spectrometric characterization of conformational preludes to β 2-microglobulin aggregation

Characterization of protein folding and unfolding is an important issue for basic biological science, for understanding the devastating amyloid diseases, and for the manufacture and use of biological therapeutics. Unlike nuclear magnetic resonance spectroscopy, the use of mass spectrometry to monitor amide hydrogen ( 1H/ 2H) exchange kinetics (HX-MS) allows characterization of structural dynamics even when only limited amounts of protein is available. As an adjunct technique, requiring even less material and very well suited for serial monitoring of folding phenomena in a single solution under native conditions capillary electrophoresis may also be very informative. These approaches are here used to examine the small (99 amino acid residues) protein β 2-microglobulin (β 2m) which is prone to amyloidogenic unfolding especially after cleavage at its lysine-58 residue. The propensity for unfolding of native, non-cleaved β 2m and lysine-58 cleaved β 2m variants as well as the effect of acetonitrile on the conformational equilibria could be addressed by these approaches. At physiological conditions, intact β 2m and the lysine-58 cleaved variants undergo a transient unfolding that exhibit an EX1 type hydrogen exchange behaviour. We have measured the unfolding rate constants for the cleaved variant where Lys-58 is removed (ΔK58-β 2m) and the cleaved variant where this residue is preserved (cK58-β 2m) at various temperatures. Below 37 °C, the variant devoid of Lys-58 (ΔK58-β 2m) has a higher unfolding rate than cK58-β 2m and this correlates with the observation that ΔK58-β 2m has a higher propensity to aggregate. The results of our studies provide valuable insight into the early conformational perturbations involved in rendering this protein insoluble and amyloidogenic. The approaches used in this study should be useful also for the characterization of other conformationally unstable proteins.

Spackling the Crack: Stabilizing Human Fibroblast Growth Factor-1 by Targeting the N and C terminus β-Strand Interactions

The β-trefoil protein human fibroblast growth factor-1 (FGF-1) is made up of a six-stranded antiparallel β-barrel closed off on one end by three β-hairpins, thus exhibiting a 3-fold axis of structural symmetry. The N and C terminus β-strands hydrogen bond to each other and their interaction is postulated from both NMR and X-ray structure data to be important in folding and stability. Specific mutations within the adjacent N and C terminus β-strands of FGF-1 are shown to provide a substantial increase in stability. This increase is largely correlated with an increased folding rate constant, and with a smaller but significant decrease in the unfolding rate constant. A series of stabilizing mutations are subsequently combined and result in a doubling of the Δ G value of unfolding. When taken in the context of previous studies of stabilizing mutations, the results indicate that although FGF-1 is known for generally poor thermal stability, the β-trefoil architecture appears capable of substantial thermal stability. Targeting stabilizing mutations within the N and C terminus β-strand interactions of a β-barrel architecture may be a generally useful approach to increase protein stability. Such stabilized mutations of FGF-1 are shown to exhibit significant increases in effective mitogenic potency, and may prove useful as “second generation” forms of FGF-1 for application in angiogenic therapy.

Equilibrium and Kinetics of the Folding and Unfolding of Canine Milk Lysozyme

The equilibrium and kinetics of canine milk lysozyme folding/unfolding were studied by peptide and aromatic circular dichroism and tryptophan fluorescence spectroscopy. The Ca2+-free apo form of the protein exhibited a three-state equilibrium unfolding, in which the molten globule state is well populated as an unfolding intermediate. A rigorous analysis of holo protein unfolding, including the data from the kinetic refolding experiments, revealed that the holo protein also underwent three-state unfolding with the same molten globule intermediate. Although the observed kinetic refolding curves of both forms were single-exponential, a burst-phase change in the peptide ellipticity was observed in both forms, and the burst-phase intermediates of both forms were identical to each other with respect to their stability, indicating that the intermediate does not bind Ca2+. This intermediate was also shown to be identical to the molten globule state observed at equilibrium. The phi-value analysis, based on the effect of Ca2+ on the folding and unfolding rate constants, showed that the Ca2+-binding site was not yet organized in the transition state of folding. A comparison of the result with that previously reported for alpha-lactalbumin indicated that the folding initiation site is different between canine milk lysozyme and alpha-lactalbumin, and hence, the folding pathways must be different between the two proteins. These results thus provide an example of the phenomenon wherein proteins that are very homologous to each other take different folding pathways. It is also shown that the native state of the apo form is composed of at least two species that interconvert.

An On-pathway Intermediate in the Folding of a PDZ Domain

The folding pathways of some proteins include the population of partially structured species en route to the native state. Identification and characterization of these folding intermediates are particularly difficult as they are often only transiently populated and play different mechanistic roles, being either on-pathway productive species or off-pathway kinetic traps. To define the role of folding intermediates, a quantitative analysis of the folding and unfolding rate constants over a wide range of denaturant concentration is often required. Such a task is further complicated by the reversible nature of the folding reaction, which implies the observed kinetics to be governed by a complex combination of different microscopic rate constants. Here, we tackled this problem by measuring directly the folding rate constant under highly denaturing conditions, namely by inducing the folding of a PDZ domain through a quasi-irreversible binding reaction with a specific peptide. In analogy with previous works based on hydrogen exchange experiments, we present evidence that the folding pathway of the PDZ domain involves the formation of an obligatory on-pathway intermediate. The results presented exemplify a novel type of kinetic test to detect an on-pathway folding intermediate.

Effect of a specific inhibitor on the unfolding and refolding kinetics of dimeric triosephosphate isomerase: Establishing the dimeric and similarly structured nature of the main transition states on the forward and backward reactions

2-Phosphoglycolate (PGA), a strong competitive inhibitor of the dimeric enzyme triosephosphate isomerase (TIM), brings about a large decrease in the unfolding rate constant of the protein. The data set of rate constants versus ligand concentration may be equally well explained by regarding either a monomeric or a dimeric transition state (TS). However, if the thermodynamics for binding of PGA to native TIM is taken into account, it becomes clear that a dimeric TS is the right assumption. Furthermore, by studying the effect of the ligand on the second-order refolding reaction, we found results indicating similar PGA-binding affinities to be present in the transition states for the rate-limiting steps of the forward and backward reactions. Most likely, therefore, both TS resemble each other in respect to the active site architecture. It should be mentioned, however, that our data do not rule out the possible occurrence of an unstable, (partially) folded monomeric intermediate, which would rapidly interconvert with the unfolded monomer.

Site‐specific experiments on folding/unfolding of Jun coiled coils: Thermodynamic and kinetic parameters from spin inversion transfer nuclear magnetic resonance at leucine‐18

The 32-residue leucine zipper subsequence, called here Jun-lz, associates in benign media to form a parallel two-stranded coiled coil. Studies are reported of its thermal unfolding/folding transition by circular dichroism (CD) on samples of natural isotopic abundance and by both equilibrium and spin inversion transfer (SIT) nuclear magnetic resonance (NMR) on samples labeled at the leucine-18 alpha-carbon with 99% 13C. The data cover a wide range of temperature and concentration, and show that Jun-lz unfolds below room temperature, being far less stable than some other leucine zippers such as GCN4. 13C-NMR shows two well-separated resonances. We ascribe the upfield one to 13C spins on unfolded single chains and the downfield one to 13C spins on coiled-coil dimers. Their relative intensities provide a measure of the unfolding equilibrium constant. In SIT NMR, the recovery of the equilibrium magnetization after one resonance is inverted is modulated in part by the unfolding and folding rate constants, which are accessible from the data. Global Bayesian analysis of the equilibrium and SIT NMR data provide values for the standard enthalpy, entropy, and heat capacity of unfolding, and show the latter to be unusually large. The CD results are compatible with the NMR findings. Global Bayesian analysis of the SIT NMR data yields the corresponding activation parameters for unfolding and folding. The results show that both reaction directions are activated processes. Activation for unfolding is entropy driven, enthalpy opposed. Activation for folding is strongly enthalpy opposed and somewhat entropy opposed, falsifying the idea that the barrier for folding is solely due to a purely entropic search for properly registered partners. The activation heat capacity is much larger for folding, so almost the entire overall change is due to the folding direction. This latter finding, if it applies to GCN4 leucine zippers, clears up an extant apparent disagreement between folding rate constants for GCN4 as determined by chevron analysis and NMR in differing temperature regimes.

Unveiling a Hidden Folding Intermediate in c-Type Cytochromes by Protein Engineering

Several investigators have highlighted a correlation between the basic features of the folding process of a protein and its topology, which dictates the folding pathway. Within this conceptual framework we proposed that different members of the cytochrome c (cyt c) family share the same folding mechanism, involving a consensus partially structured state. Pseudomonas aeruginosa cyt c(551) (Pa cyt c(551)) folds via an apparent two-state mechanism through a high energy intermediate. Here we present kinetic evidence demonstrating that it is possible to switch its folding mechanism from two to three state, stabilizing the high energy intermediate by rational mutagenesis. Characterization of the folding kinetics of one single-site mutant of the Pa cyt c(551) (Phe(7) to Ala) indeed reveals an additional refolding phase and a fast unfolding process which are explained by the accumulation of a partially folded species. Further kinetic analysis highlights the presence of two parallel processes both leading to the native state, suggesting that the above mentioned species is a non obligatory on-pathway intermediate. Determination of the crystallographic structure of F7A shows the presence of an extended internal cavity, which hosts three "bound" water molecules and a H-bond in the N-terminal helix, which is shorter than in the wild type protein. These two features allow us to propose a detailed structural interpretation for the stabilization of the native and especially the intermediate states induced by a single crucial mutation. These results show how protein engineering, x-ray crystallography and state-of-the-art kinetics concur to unveil a folding intermediate and the structural determinants of its stability.

Contribution of Structural Peculiarities of Onconase to Its High Stability and Folding Kinetics

Onconase (ONC) from Rana pipiens is the smallest member of the ribonuclease A (RNase A) superfamily. Despite a tertiary structure similar to RNase A, ONC is distinguished by an extremely high thermodynamic stability. In the present paper we have probed the significance of three structural regions, which exhibit structural peculiarities in comparison to RNase A, for the stability of ONC to temperature and guanidine hydrochloride induced denaturation: (i) the N-terminal pyroglutamate residue, (ii) the hydrophobic cluster between helix I and the first beta-sheet, and (iii) the C-terminal disulfide bond. For this purpose, the enzyme variants <E1E-, <E1P-, F28T-, F28A-, F36Y-, and C87A/C104A-ONC were produced and studied in equilibrium and kinetic measurements. The destabilizing influence of the mutations strongly depended on the modified structural region. The exchanges of the N-terminal pyroglutamate (<E1E- and <E1P-ONC) had the smallest impact (DeltaDeltaG([D])50% = 4.2 and 7.0 kJ mol(-)(1)), while interferences in the hydrophobic cluster (F28T-, F28A-, and F36Y-ONC) had larger effects (DeltaDeltaG([D])50% = 22.2, 20.9, and 19.5 kJ mol(-)(1)). The removal of the C-terminal disulfide bond (C87A/C104A-ONC) showed the largest influence on stability (DeltaDeltaG([D])50% = 32.0 kJ mol(-)(1)). As concluded from the comparison of DeltaDeltaG([D])50% and DeltaDeltaG++(U)[D]50%, all destabilization effects were exclusively caused by increased unfolding rate constants except for C87A/C104A-ONC, where unfolding as well as folding was impacted. Of all amino acid residues investigated, Phe28, which is unique for ONC among the ribonucleases, had the greatest importance for rate of unfolding. Our data on the folding and unfolding kinetics indicate that the strong stabilization of ONC in comparison to RNase A is caused by a dramatic deceleration of the unfolding reaction.

Simulations of multi-directional forced unfolding of titin I27

Mechanical resistance of a protein under external force is known to depend on the amino acid sequence, unfolding rate constant, topology and the direction of force applied. To assess the affect of force direction on mechanical resistance, molecular dynamics (MD) simulations of the partial unfolding of titin I27 have been carried out by applying a ramp of force between the N-terminus and the alpha-carbon of each amino acid, respectively. The results arbitrarily place the amino acids in a hierarchy in terms of the time at which an unfolding intermediate is formed. The onset of unfolding is indeed affected by force direction; directions that give maximum leverage (for the A strand to detach) unfold to the intermediate quicker than directions that give least leverage. Moreover, the change in the time taken to reach the intermediate, hence the change in mechanical resistance, can be attributed to β-strand topology. The simulations indicate that experimentally multi-directional forced unfolding could be used to reveal and study strand topology, and suggests that direction of applied force, topology and mechanical resistance are all closely related.

Thermostability of Irreversible Unfolding α-Amylases Analyzed by Unfolding Kinetics

For most multidomain proteins the thermal unfolding transitions are accompanied by an irreversible step, often related to aggregation at elevated temperatures. As a consequence the analysis of thermostabilities in terms of equilibrium thermodynamics is not applicable, at least not if the irreversible process is fast with respect the structural unfolding transition. In a comparative study we investigated aggregation effects and unfolding kinetics for five homologous alpha-amylases, all from mesophilic sources but with rather different thermostabilities. The results indicate that for all enzymes the irreversible process is fast and the precedent unfolding transition is the rate-limiting step. In this case the kinetic barrier toward unfolding, as measured by unfolding rates as function of temperature, is the key feature in thermostability. The investigated enzymes exhibit activation energies (E(a)) between 208 and 364 kJmol(-1) and pronounced differences in the corresponding unfolding rates. The most thermostable alpha-amylase from Bacillus licheniformis (apparent transition temperature, T(1/2) approximately 100 degrees C) shows an unfolding rate which is four orders of magnitude smaller as compared with the alpha-amylase from pig pancreas (T(1/2) approximately 65 degrees C). Even with respect to two other alpha-amylases from Bacillus species (T(1/2) approximately 86 degrees C) the difference in unfolding rates is still two orders of magnitude.

Kinetic resolution of bimolecular hybridization versus intramolecular folding in nucleic acids by surface plasmon resonance: application to G-quadruplex/duplex competition in human c-myc promoter

The human oncogene c-myc is regulated by G-quadruplex formation within the nuclease hypersensitive element (NHE IIII) in the c-myc promoter, making the quadruplex a strong anti-cancer target. With respect to this, the competing equilibrium between intramolecular quadruplex folding and bimolecular duplex formation is poorly understood and very few techniques have addressed this problem. We present a method for simultaneously determining the kinetic constants for G-quadruplex folding/unfolding and hybridization in the presence of the complementary strand from a single reaction using an optical biosensor based on surface plasmon resonance (SPR). Using this technique, we demonstrate for the first time that quadruplex formation in the c-myc promoter is favored at low strand concentrations. Our results indicate favorable quadruplex folding (equilibrium folding constant KF of 2.09 calculated from the kinetic parameters: folding rate constant, kf = 1.65 × 10−2 s−1 and unfolding rate constant, ku = 7.90 × 10−3 s−1) in 150 mM K+. The hybridization rate constants detected concurrently gave a bimolecular association constant, ka = 1.37 × 105 M−1 s−1 and dissociation constant, kd = 4.94 × 10−5 s−1. Interestingly, in the presence of Na+ we observed that G-quadruplex folding was unfavorable (KF = 0.54). Implication of our results on the c-myc transcription activation model is discussed in light of aberrant c-myc expression observed on destabilization of the G-quadruplex.

Kinetic folding mechanism of PDZ2 from PTP-BL

PDZ domains represent a large family of protein-interaction modules associated with a variety of unrelated proteins with different functions. We report a complete characterization of the kinetic folding mechanism of a fluorescent variant of PDZ2 from PTP-BL, investigated under a variety of different experimental conditions. For this purpose, we engineered a fluorescent variant of this protein Y43W (called pseudo-wild-type, pWT43). The results suggest the presence of a high-energy intermediate in the folding of PDZ2, as revealed by a pronounced non-linear dependence of the unfolding rate constant on denaturant concentration. Such an intermediate may or may not be detectable depending on the experimental conditions, giving rise to apparent two-state folding under stabilizing conditions (e.g. in the presence of sodium sulfate). Interestingly, even under these conditions, three-state folding can be restored by selectively destabilizing the native-like rate-limiting barrier by one specific mutation (V44A). Finally, we show that data taken on pWT43 under different experimental conditions (e.g. different pH values from 2.1 to 8.0 or in the presence of a stabilizing salt) and also data on a site-directed conservative mutant can be rationalized in terms of a simple reaction scheme involving a single set of intermediates and transition states.

Charge–charge interactions in the denatured state influence the folding kinetics of ribonuclease Sa

Gaining a better understanding of the denatured state ensemble of proteins is important for understanding protein stability and the mechanism of protein folding. We studied the folding kinetics of ribonuclease Sa (RNase Sa) and a charge-reversal variant (D17R). The refolding kinetics are similar, but the unfolding rate constant is 10-fold greater for the variant. This suggests that charge-charge interactions in the denatured state and the transition state ensembles are more favorable in the variant than in RNase Sa, and shows that charge-charge interactions can influence the kinetics and mechanism of protein folding.

An Obligatory Intermediate in the Folding Pathway of Cytochromec552 from Hydrogenobacterthermophilus

The folding mechanism of many proteins involves the population of partially organized structures en route to the native state. Identification and characterization of these intermediates is particularly difficult, as they are often only transiently populated and may play different mechanistic roles, being either on-pathway productive species or off-pathway kinetic traps. Following different spectroscopic probes, and employing state-of-the-art kinetic analysis, we present evidence that the folding mechanism of the thermostable cytochrome c552 from Hydrogenobacter thermophilus does involve the presence of an elusive, yet compact, on-pathway intermediate. Characterization of the folding mechanism of this cytochrome c is particularly interesting for the purpose of comparative folding studies, because H. thermophilus cytochrome c552 shares high sequence identity and structural homology with its homologue from the mesophilic bacterium Pseudomonas aeruginosa cytochrome c551, which refolds through a broad energy barrier without the accumulation of intermediates. Analysis of the folding kinetics and correlation with the three-dimensional structure add new evidence for the validity of a consensus folding mechanism in the cytochrome c family.

Folding Thermodynamics and Kinetics of YNMG RNA Hairpins: Specific Incorporation of 8-Bromoguanosine Leads to Stabilization by Enhancement of the Folding Rate

Modified nucleotides allow fundamental energetic and kinetic properties of nucleic acids to be probed. Here, we demonstrate that an RNA hairpin containing the nucleotide analogue 8-bromoguanosine (8BrG or G), gcUUCGgc, has enhanced stability relative to the unmodified hairpin, with DeltaDeltaG(37)(degrees)= -0.69 +/- 0.15 kcal mol(-1) and DeltaT(M) = +6.8 +/- 1.4 degrees C. NMR spectroscopic data suggest that the enhanced stability of gcUUCGgc does not arise from the native state; laser temperature-jump experiments support this notion, as gcUUCGgc and gcUUCGgc have similar unfolding rate constants, but the folding rate constant of gcUUCGgc is 4.1-fold faster at 37.5 degrees C and 2.8-fold faster under isoenergetic conditions. On the basis of these findings, we propose that 8BrG reduces the conformational entropy of the denatured state, resulting in an accelerated conformational search for the native state and enhanced stability.

Determining the folding and unfolding rate constants of nucleic acids by biosensor. Application to telomere G-quadruplex.

Nucleic acid molecules may fold into secondary structures, and the formation of such structures is involved in many biological processes and technical applications. The folding and unfolding rate constants define the kinetics of conformation interconversion and the stability of these structures and is important in realizing their functions. We developed a method to determine these kinetic parameters using an optical biosensor based on surface plasmon resonance. The folding and unfolding of a nucleic acid is coupled with a hybridization reaction by immobilization of the target nucleic acid on a sensor chip surface and injection of a complementary probe nucleic acid over the sensor chip surface. By monitoring the time course of duplex formation, both the folding and unfolding rate constants for the target nucleic acid and the association and dissociation rate constants for the target-probe duplex can all be derived from the same measurement. We applied this method to determine the folding and unfolding rate constants of the G-quadruplex of human telomere sequence (TTAGGG)(4) and its association and dissociation rate constants with the complementary strand (CCCTAA)(4). The results show that both the folding and unfolding occur on the time scale of minutes at physiological concentration of K(+). We speculate that this property might be important for telomere elongation. A complete set of the kinetic parameters for both of the structures allows us to study the competition between the formation of the quadruplex and the duplex. Calculations indicate that the formation of both the quadruplex and the duplex is strand concentration-dependent, and the quadruplex can be efficiently formed at low strand concentration. This property may provide the basis for the formation of the quadruplex in vivo in the presence of a complementary strand.

Simulation of the mechanical unfolding of ubiquitin: probing different unfolding reaction coordinates by changing the pulling geometry.

Motivated by the recent experimental atomic force microscopy (AFM) measurements of the mechanical unfolding of proteins pulled in different directions [D. J. Brockwell et al., Nat. Struct. Biol. 10, 731 (2003); M. Carrion-Vazquez et al., ibid 10, 738 (2003)] we have computed the unfolding free energy profiles for the ubiquitin domain when it is stretched between its (A) N and C termini, (B) Lys48 and C terminus, (C) Lys11 and C terminus, and (D) N terminus and Lys63. Our results for cases (A) and (B) are in good agreement with the experimental unfolding forces measured for the N-C and Lys48-C linked polyubiquitin, in particular, indicating a considerably lower unfolding force in the latter case. Mechanical unfolding in case (A) involves longitudinal shearing of the terminal parallel strands while in case (C) the same strands are "unzipped" by the force. The computed unfolding forces in case (C) are found to be very low, less than 50 pN for pulling rates typical of AFM experiments. The unfolding free energy barrier found in case (C) is approximately 13 kcal/mol, which corresponds to a zero-force unfolding rate constant that is comparable to the rate of chemical unfolding extrapolated to zero denaturant concentration. The unfolding barrier calculated in case (A) in the limit of zero force is much higher, suggesting that mechanical unfolding in this case follows a pathway that is different from that of thermal/chemical denaturation.

Slow unfolding explains high stability of thermostable ferredoxins: common mechanism governing thermostability?

The role of kinetics in governing exceptional stability of thermophilic ferredoxins has been explored. Strikingly, unfolding-rate constants (pH 7, 20 °C) are over eight (log 10) orders of magnitude slower for the thermophiles than for a large set of unrelated mesophilic proteins. Also at low pH, where ionic interactions are diminished, unfolding of the thermophilic ferredoxins is significantly slower than unfolding of the mesophiles at pH 7, emphasizing the importance of hydrophobic interactions. A kinetic barrier towards unfolding may be a common strategy used by many proteins to withstand extreme conditions.

The side chain of aspartic acid 69 dictates the folding mechanism of Bacillus subtilis HPr.

Many small, single-domain proteins show equilibrium and kinetic folding mechanisms that appear to be adequately described as two state. The two-state model makes several predictions that can be tested experimentally. First, the conformational stability determined at or extrapolated to a set of reference conditions should be independent of the measurement method (thermal or solvent denaturation or hydrogen exchange). Second, model-independent measures of the cardinal thermodynamic parameters (T(m), DeltaH) as determined from direct calorimetric means should be identical to those determined from the two-state analysis of thermal unfolding data. Third, the ratio of the kinetic folding and unfolding rate constants should be equal to K(eq) determined from an equilibrium measurement under the same conditions. Here, we show that the wild-type HPr protein from Bacillus subtilis does not meet all of these criteria under our standard conditions. However, if we replace the side chain of Asp69, or add moderate concentrations of salt, we find excellent two-state behavior in both equilibrium and kinetic folding. Thus, for this protein and possibly others, very subtle changes in the primary structure or in the solution conditions can dramatically alter the relative stabilities of the native intermediate, and unfolded ensembles can cause an observable change in the nature of the folding mechanism.