The determinants of pKas in proteins

Although validation studies show that theoretical models for predicting the pKas of ionizable groups in proteins are increasingly accurate, a number of important questions remain: (1) What factors limit the accuracy of current models? (2) How can conformational flexibility of proteins best be accounted for? (3) Will use of solution structures in the calculations, rather than crystal structures, improve the accuracy of the computed pKas? and (4) Why does accurate prediction of protein pKas seem to require that a high dielectric constant be assigned to the protein interior? This paper addresses these and related issues. Among the conclusions are the following: (1) computed pKas averaged over NMR structure sets are more accurate than those based upon single crystal structures; (2) use of atomic parameters optimized to reproduce hydration energies of small molecules improves agreement with experiment when a low protein dielectric constant is assumed; (3) despite use of NMR structures and optimized atomic parameters, pKas computed with a protein dielectric constant of 20 are more accurate than those computed with a low protein dielectric constant; (4) the pKa shifts in ribonuclease A that result from phosphate binding are reproduced reasonably well by calculations; (5) the substantial pKa shifts observed in turkey ovomucoid third domain result largely from interactions among ionized groups; and (6) both experimental data and calculations indicate that proteins tend to lower the pKas of Asp side chains but have little overall effect upon the pKas of other ionizable groups.     

Conformational stability of muscle acylphosphatase: the role of temperature, denaturant concentration, and pH

The conformational stability (delta G) of muscle acylphosphatase, a small alpha/beta globular protein, has been determined as a function of temperature, urea concentration, and pH. A combination of thermally induced and urea-induced unfolding, monitored by far-UV circular dichroism, was used to define the conformational stability over a wide range of temperature. Through analysis of all these data, the heat capacity change upon unfolding (delta Cp) could be estimated, allowing the determination of the temperature dependence of the main thermodynamic functions (delta G, delta H, delta S). Thermal unfolding in the presence of urea made it possible to extend such thermodynamic analysis to examine these parameters as a function of urea concentration. The results indicate that acylphosphatase is a relatively unstable protein with a delta G(H2O) of 22 +/- 1 kJ mol-1 at pH 7 and 25 degrees C. The midpoints of both thermal and chemical denaturation are also relatively low. Urea denaturation curves over the pH range 2-12 have allowed the pH dependence of delta G to be determined and indicate that the maximum stability of the protein occurs near pH 5.5. While the dependence of delta G on urea (the m value) does not vary with temperature, a significant increase has been found at low pH values, suggesting that the overall dimensions of the unfolded state are significantly affected by the number of charges within the polypeptide chain. The comparison of these data with those from other small proteins indicates that the pattern of conformational stability is defined by individual sequences and not by the overall structural fold.     

pKa measurements from nuclear magnetic resonance for the B1 and B2 immunoglobulin G-binding domains of protein G: comparison with calculated values for nuclear magnetic resonance and X-ray structures

Two-dimensional homo- and heteronuclear nuclear magnetic resonance (NMR) spectroscopy was used to determine pKa values for all of the acidic residues in the B1 and B2 immunoglobulin G- (IgG-) binding domains of protein G. Due to the stability of protein G over a wide pH range, estimates of ionization constants were also obtained for some basic residues. These experimentally determined ionization constants were compared with values calculated from both X-ray and NMR-derived structures of B1 and B2 using the UHBD algorithm [Antosiewicz, J., et al. (1994) J. Mol. Biol. 238, 415-436]. This algorithm has been found to be predictive for pKa measurements in proteins and, in combination with experimental measurements, allowed some evaluation of the NMR and X-ray structures. Three regions where significant differences exist between the X-ray and NMR structures are (1) the position of the E56 side chain relative to the backbone amides of K10 and D40, (2) residues 33-37 in the helix, and (3) the Y45 side-chain conformation. For all three cases, the experimental pH titration curves are notably more consistent with the X-ray structures than the NMR structures. In contrast, a number of solvent-accessible side chains have experimental pKas more in agreement with mean pKas calculated from families of NMR structures. The conformations of these side chains may be susceptible to crystal packing effects. From titration experiments under basic conditions, it is noteworthy that the chemical shift of the Y45 C epsilonH resonance is invariant up to pDcorr 12. The Y45 side-chain hydroxyl group appears to maintain a nativelike hydrogen bond with D47 at pDcorr 12, even though the protein is approximately 90% unfolded. These results suggest that this short-range (i, i + 2) interaction, located in the beta3-beta4 hairpin, is present in the high-pH denatured state and may therefore form early in the folding of protein G.     

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

Effect of pH on formation of a nativelike intermediate on the unfolding pathway of a Lys 73 --> His variant of yeast iso-1-cytochrome c

Previous work on a Lys 73 --> His (H73) variant of iso-1-cytochrome c at pH 7.5 [Godbole et al. (1997) Biochemistry 36, 119-126] showed that this variant unfolds through a nativelike intermediate that has properties consistent with replacement of the Met 80 heme ligand by His 73. Here, the pH dependence of the equilibrium unfolding of the wild type (WT) and H73 proteins have been investigated, since a characteristic pH dependence is expected for the stability of an intermediate stabilized by histidine-heme ligation. Stability has been evaluated using guanidine hydrochloride and pH denaturation methods. Above pH 5, the m-values from guanidine hydrochloride denaturation of the WT and H73 variants remain significantly different, consistent with continued population of this intermediate. At pH 4.5 the m-values for the two proteins are within error the same. To assess stability at lower pH, acid denaturation was carried out. The midpoint is about 3.3 for both proteins but the transition is broader for the H73 protein, suggestive of intermediates again being populated during the unfolding of the H73 protein at this lower pH. Heme ligation by Met 80 was monitored (695 nm absorbance) during gdnHCl (pH 4.5 and 5.0) and acid denaturation, confirming, respectively, the absence and presence of intermediates. A thermodynamic analysis demonstrates that this complex pH dependence for the presence of histidine ligation induced intermediates is expected and implicates a titratable group with a pKa of approximately 6.6. The analysis also demonstrates when the pH dependences of global stability and stability of an intermediate differ significantly, population of folding intermediates as a function of pH will show novel behavior.     

Characterization of the free energy spectrum of peptostreptococcal protein L

BACKGROUND: Native state hydrogen/deuterium exchange studies on cytochrome c and RNase H revealed the presence of excited states with partially formed native structure. We set out to determine whether such excited states are populated for a very small and simple protein, the IgG-binding domain of peptostreptococcal protein L. RESULTS: Hydrogen/deuterium exchange data on protein L in 0-1.2 M guanidine fit well to a simple model in which the only contributions to exchange are denaturant-independent local fluctuations and global unfolding. A substantial discrepancy emerged between unfolding free energy estimates from hydrogen/deuterium exchange and linear extrapolation of earlier guanidine denaturation experiments. A better determined estimate of the free energy of unfolding obtained by global analysis of a series of thermal denaturation experiments in the presence of 0-3 M guanidine was in good agreement with the estimate from hydrogen/deuterium exchange. CONCLUSIONS: For protein L under native conditions, there do not appear to be partially folded states with free energies intermediate between that of the folded and unfolded states. The linear extrapolation method significantly underestimates the free energy of folding of protein L due to deviations from linearity in the dependence of the free energy on the denaturant concentration.     

Calorimetric investigation of proton linkage by monitoring both the enthalpy and association constant of binding: application to the interaction of the Src SH2 domain with a high-affinity tyrosyl phosphopeptide

The binding of Src homology 2 (SH2) domains to tyrosyl phosphopeptides depends on electrostatic interactions between the phosphotyrosine and its binding site. To probe the role of these interactions, we have used isothermal titration calorimetry to study the pH dependence of the binding of the SH2 domain of the Src kinase to a high-affinity tyrosyl phosphopeptide. Two independent approaches were employed. In a first series of experiments that focused on determining the peptide's association constant between pH 5.0 and 9.0, two ionizable groups were characterized. One group, with free and bound pKas of 6.2 and 4.4, respectively, could be identified as the phosphate in the phosphotyrosine while the other group, with free and bound pKas of 8.2 and 8.5, respectively, could be only tentatively assigned to a cysteine in the phosphotyrosine binding pocket. Further information on the linkage between peptide binding and protonation of the phosphotyrosine was obtained from a second series of experiments, which focused on determining the peptide binding enthalpy at low values of pH in several buffers with different ionization enthalpies. These data provided free and bound pKa values for the phosphotyrosine identical to those derived from the first series of experiments, and hence demonstrated for the first time that the two approaches provide identical information regarding proton linkage. In addition, the second series of experiments also determined the intrinsic enthalpy of binding of both the protonated and deprotonated phosphate forms of the peptide. These two sets of experiments provided a complete energetic profile of the linkage between phosphate ionization and peptide binding. From this profile, it was determined that the PO32- form of the peptide binds 2.3 kcal mol-1 more favorably than the PO3H1- form due entirely to a more favorable entropy of binding.     

pH titration of native and unfolded beta-trypsin: evaluation of the delta delta G0 titration and the carboxyl pK values

The stabilizing free energy of beta-trypsin was determined by hydrogen ion titration. In the pH range from 3.0 to 7.0, the change in free energy difference for the stabilization of the native protein relative to the unfolded one (delta delta G0 titration) was 9.51 +/- 0.06 kcal/mol. An isoelectric point of 10.0 was determined, allowing us to calculate the Tanford and Kirkwood electrostatic factor w. This factor presented a nonlinear behavior and indicated more than one type of titratable carboxyl groups in beta-trypsin. In fact, one class of carboxyl group with a pK = 3.91 +/- 0.01 and another one with a pK = 4.63 +/- 0.03 were also found by hydrogen ion titration of the protein in the folded state.     

Alternative models for describing the acid unfolding of the apomyoglobin folding intermediate

The acid-induced unfolding of the pH 4 intermediate of apomyoglobin (I) is described by either of two models: (1) a Monod-Wyman-Changeux-based model (MWC) where salt bridges perturb the pKa values of specific ionizable side chains, causing unfolding of I as these salt bridges are broken at low pH, and (2) the Linderstrom-Lang smeared charge model (L-L), which attributes acid unfolding of I to charge repulsion caused by the accumulation of positive charge on the surface of the protein. Both models fit earlier acid unfolding data well, but they make differing predictions about the effects of electrostatic mutants, which have been made and tested. Deletions of positive charge within I are found to stabilize I, but disruptions of potential salt bridges have little effect. These results show that the acid unfolding of I (I<-->U) is largely caused by generalized charge effects rather than by the loss of specific salt bridges. Acid unfolding of the native form, which is caused largely by a single histidine with a severely depressed pKa, is a sensitive indicator of changes in stability produced by mutations. In contrast, the I <--> U transition is caused by a number of groups with smaller pKa perturbations and both models predict that the pH midpoint of the I right harpoon over left harpoon U transition is an insensitive indicator of stability. This result reconciles previous conflicting results, in urea and acid unfolding studies of hydrophobic contact mutants, by showing that changes in the stability of I are poorly detected by acid unfolding.     

Hydrogen exchange in ribonuclease A and ribonuclease S: evidence for residual structure in the unfolded state under native conditions

Two-dimensional NMR spectroscopy has been used to monitor the exchange of backbone amide protons in ribonuclease A (RNase A) and its subtilisin-cleaved form, ribonuclease S (RNase S). Exchange measurements at two different pH values (5.4 and 6.0) show that the exchange process occurs according to the conditions of the EX2 limit. Differential scanning calorimetry measurements have been carried out in 2H2O under conditions analogous to those used in the NMR experiments in order to determine the values of DeltaCp, DeltaHu and Tm, corresponding to the thermal denaturation of both proteins. For the amide protons of a large number of residues in RNase A, the free energies at 25 degreesC for exchange competent unfolding processes are much lower than the calorimetric denaturation free energies, thus showing that exchange occurs through local fluctuations in the native state. For 20 other protons, the cleavage reaction had approximately the same effect on the exchange rate constants than on the equilibrium constant for unfolding, indicating that those protons exchange by global unfolding. There is a good agreement between the residues to which these protons belong and those involved in the putative folding nucleation site identified by quench-flow NMR studies. The unfolding free energies of the slowest exchanging protons, DeltaGex, as evaluated from exchange data, are much larger than the calorimetric free energies of unfolding, DeltaGu. Given the agreement between DeltaDeltaGex(A-S), the difference in free energy from exchange for a given proton of the two proteins, and DeltaDeltaGu(A-S), the difference in the calorimetric free energy of the two proteins, the discrepancy indicates that the intrinsic exchange rates in the unfolded state of those protons cannot be approximated by those measured in short unstructured peptides and, consequently, exchange for those protons in RNase A and S must occur through a rather structured denatured state.     

Effect of the extra n-terminal methionine residue on the stability and folding of recombinant alpha-lactalbumin expressed in Escherichia coli

The structure, stability, and unfolding-refolding kinetics of Escherichia coli-expressed recombinant goat alpha-lactalbumin were studied by circular dichroism spectroscopy, X-ray crystallography, and stopped-flow measurements, and the results were compared with those of the authentic protein prepared from goat milk. The electric properties of the two proteins were also studied by gel electrophoresis and ion-exchange chromatography. Although the overall structures of the authentic and recombinant proteins are the same, the extra methionine residue at the N terminus of the recombinant protein remarkably affects the native-state stability and the electric properties. The native state of the recombinant protein was 3.5 kcal/mol less stable than the authentic protein, and the recombinant protein was more negatively charged than the authentic one. The recombinant protein unfolded 5.7 times faster than the authentic one, although there were no significant differences in the refolding rates of the two proteins. The destabilization of the recombinant protein can be fully interpreted in terms of the increased unfolding rate of the protein, indicating that the N-terminal region remains unorganized in the transition state of refolding, and hence is not involved in the folding initiation site of the protein. A comparison of the X-ray structures of recombinant alpha-lactalbumin determined here with that of the authentic protein shows that the structural differences between the proteins are confined to the N-terminal region. Theoretical considerations for the differences in the conformational and solvation free energies between the proteins show that the destabilization of the recombinant protein is primarily due to excess conformational entropy of the N-terminal methionine residue in the unfolded state, and also due to less exposure of hydrophobic surface on unfolding. The results suggest that when the N-terminal region of a protein has a rigid structure, expression of the protein by E. coli, which adds the extra methionine residue, destabilizes the native state through a conformational entropy effect. It also shows that differences in the electrostatic interactions of the N-terminal amino group with the side-chain atoms of Thr38, Asp37, and Asp83 bring about a difference in the pKa value of the N-terminal amino group between the proteins, resulting in a greater negative net charge of the recombinant protein at neutral pH.     

Stability and oligosaccharide binding of the N1 cellulose-binding domain of Cellulomonas fimi endoglucanase CenC

Differential scanning calorimetry has been used to study the thermal stability and oligosaccharide-binding thermodynamics of the N-terminal cellulose-binding domain of Cellulomonas fimi beta-1,4-glucanase CenC (CBDN1). CBDN1 has a relatively low maximum stability (delta Gmax = 33 kJ/mol = 216 J/residue at 1 degree C and pH 6.1) compared to other small single-domain globular proteins. The unfolding is fully reversible between pH 5.5 and 9 and in accordance with the two-state equilibrium model between pH 5.5 and 11. When the single disulfide bond in CBDN1 is reduced, the protein remains unfolded at all conditions, as judged by NMR spectroscopy. This indicates that the intramolecular cross-link makes a major contribution to the stability of CBDN1. The measured heat capacity change of unfolding (delta Cp = 7.5 kJ mol-1 K-1) agrees well with that calculated from the predicted changes in the solvent accessible nonpolar and polar surface areas upon unfolding. Extrapolation of the specific enthalpy and entropy of unfolding to their respective convergence temperature indicates that per residue unfolding energies for CBDN1, an isolated domain, are in accordance with those found by Privalov (1) for many single-domain globular proteins. DSC thermograms of the unfolding of CBDN1 in the presence of various concentrations of cellopentaose were fit to a thermodynamic model describing the linkage between protein-ligand binding and protein unfolding. A global two-dimensional minimization routine is used to regress the binding enthalpy, binding constant, and unfolding thermodynamics for the CBDN1-cellopentaose system. Extrapolated binding constants are in quantitative agreement with those determined by isothermal titration calorimetry at 35 degrees C.     

A partially folded intermediate during tubulin unfolding: its detection and spectroscopic characterization

The unfolding reaction of the dimeric protein tubulin, isolated from goat brain, was studied using fluorescence and circular dichroism techniques. The unfolding of the tubulin dimer was found to be a two-step process at pH 7. The first step leads to the formation of an intermediate conformation, stable at around 1-2 M urea, followed by a second step that was due to unfolding of the intermediate state. At pH 3, the urea-induced biphasic unfolding profiles obtained at pH 7 became a one-step process indicating that a stable intermediate was also formed at this pH. The intermediate at pH 3 was more stable toward urea denaturation than that at pH 7. The intermediate state has about 60% secondary structure, partially exposed aromatic residues, and less tertiary structure as compared to the native states. Also, hydrophobic surfaces were more exposed in the intermediate than in the native or unfolded states. These results indicate that the intermediate state observed during tubulin unfolding is not only distinct from both the native and unfolded forms but also possesses some properties characteristic of a molten globule.     

Equilibrium unfolding of proteins monitored by electrospray ionization mass spectrometry: distinguishing two-state from multi-state transitions

The acetic acid-induced unfolding of cytochrome c (cyt c) and apomyoglobin (aMb) are studied under equilibrium conditions by electrospray ionization (ESI) mass spectrometry (MS). The folding states of the proteins in solution are monitored by the charge state distributions that they produce during ESI. A tightly folded protein shows lower charge states than the same protein in an unfolded conformation. The ESI-MS data presented in this study show that during the denaturation of cyt c, only two distinct charge state distributions are observed. These can be attributed to the native and to the acid-unfolded conformation, respectively. In the transition region where the folded and the unfolded conformation are both present in solution, these two distributions are observed simultaneously, thus giving rise to a bimodal ESI mass spectrum. These data reflect a highly cooperative (two state) folding behavior. In contrast, the acid-induced unfolding of aMb is accompanied by gradual shifts in the maxima of the observed charge state distribution. This indicates a non-cooperative unfolding behavior involving multiple protein conformations. The observations made here suggest that ESI-MS might be a general method for assessing the cooperativity of protein unfolding transitions. This study also addresses the issue of 'secondary' solvent effects for ESI-MS studies on the acid-induced unfolding of proteins. These effects influence the ESI charge state distribution without being related to conformational changes of the protein in solution and could potentially complicate the interpretation of ESI mass spectra. Data obtained for bovine pancreatic trypsin inhibitor and ubiquitin indicate that secondary solvent effects influence the observed charge state distributions only to a very minor extent between pH 8.5 and 2.5.     

Denaturant m values and heat capacity changes: relation to changes in accessible surface areas of protein unfolding

Denaturant m values, the dependence of the free energy of unfolding on denaturant concentration, have been collected for a large set of proteins. The m value correlates very strongly with the amount of protein surface exposed to solvent upon unfolding, with linear correlation coefficients of R = 0.84 for urea and R = 0.87 for guanidine hydrochloride. These correlations improve to R = 0.90 when the effect of disulfide bonds on the accessible area of the unfolded protein is included. A similar dependence on accessible surface area has been found previously for the heat capacity change (delta Cp), which is confirmed here for our set of proteins. Denaturant m values and heat capacity changes also correlate well with each other. For proteins that undergo a simple two-state unfolding mechanism, the amount of surface exposed to solvent upon unfolding is a main structural determinant for both m values and delta Cp.     

Simple test to evaluate the risk of urinary calcium stone formation

The pH dependence of the association of apo trp repressor with the series of ligands, tryptophan, tryptamine, indole propionic acid (IPA), and trans-beta-indole acrylic acid (IAA), has been studied using fluorescence titrations and isothermal titration microcalorimetry (ITC). The purpose of such a comparison of ligands and the pH dependency studies is to reveal the role played by the side-chain functional groups in the energetics of the binding of the ligands to the protein. We find that, whereas the binding of tryptamine and IPA have essentially no pH dependence between pH 6 and 10, the binding of tryptophan and IAA depends on pH. For IAA, the affinity drops between pH 6 and 10, consistent with a shift in pKa of some group on the protein from a value of pKa 7.4 to 7.9 upon binding of this ligand. The affinity of IAA also drops below pH 5, but shows saturable binding at pH 2-3, where the protein has previously been found to exist as a partially folded monomeric state. For tryptophan, the pH dependence data indicate that the equilibrium is complicated. We present a model to describe the data in which the alpha-ammonium group of tryptophan has its pKa shifted upward upon binding (i.e. preferential binding of the protonated form of this functional group) and in which the pKa of an unknown group on the protein also has its pKa increased.     

A model-independent, nonlinear extrapolation procedure for the characterization of protein folding energetics from solvent-denaturation data

We have characterized the guanidine-induced denaturation of hen egg white lysozyme within the 30-75 degrees C temperature range on the basis of equilibrium fluorescence measurements, unfolding assays, kinetic fluorescence measurements, and differential scanning calorimetry. Analysis of the guanidine denaturation profiles according to the linear extrapolation method yields values for the denaturation Gibbs energy which are about 15 kJ/mol lower than those derived from differential scanning calorimetry. Our results strongly suggest that this discrepancy is not due to deviations from the two-state denaturation mechanism. We propose a new method for the determination of denaturation Gibbs energies from solvent-denaturation data (the constant-delta G extrapolation procedure). It employs several solvent-denaturation profiles (obtained at different temperatures) to generate the protein stability curve at zero denaturant concentration within the -8 to 8 kJ/mol delta G range. The method is model-independent and provides a practical, nonlinear alternative to the commonly employed linear extrapolation procedure. The application of the constant-delta G method to our data suggests that the guanidine-concentration dependence of the denaturation Gibbs energy is approximately linear over an extended concentration range but, also, that strong deviations from linearity may occur at low guanidine concentrations. We tentatively attribute these deviations to the abrupt change of the contribution to protein stability that arises from pairwise charge-charge electrostatic interactions. This contribution may be positive, negative, or close to zero, depending on the pH value and the charge distribution on the native protein surface [Yang, A.-S., & Honig, B. (1993) J. Mol. Biol. 231, 459-474], which may help to explain why disparate effects have been found when studying protein denaturation at low guanidine concentrations. Kinetic m values for lysozyme denaturation depend on temperature, in a manner which appears consistent with Hammond behavior.     

Chemical and thermal stability of ferulic acid esterase-III from Aspergillus niger

The stability of ferulic acid esterase III (FAE-III) from Aspergillus niger was examined using chemical and thermal denaturation. Thermal denaturation was irreversible and the loss of activity was dependent on pH. At 60 degrees C and pH 6.0, the rate constant of unfolding was 0.76 10(-3)/s, and the change in free energy of irreversible inactivation, deltaG*, was 101.9 kJ/mol. Sinapic acid, a product of the reaction of methyl sinapate with FAE-III, reduced the rate of unfolding (0.66 10(-3)/s at 0.1 mM sinapic acid). Chemical denaturation was performed using guanidine hydrochloride. FAE-III was very sensitive to this denaturant, and the midpoint of unfolding was 1.38 M guanidine hydrochloride at 30 degrees C, pH 6.0. The stability of FAE-III is compared to other enzymes.     

Global analysis of the effects of temperature and denaturant on the folding and unfolding kinetics of the N-terminal domain of the protein L9

The folding and unfolding kinetics of the N-terminal domain of the ribosomal protein L9 have been measured at temperatures between 7 and 85 degrees C and between 0 and 6 M guanidine deuterium chloride. Stopped-flow fluorescence was used to measure rates below 55 degrees C and NMR lineshape analysis was used above 55 degrees C. The amplitudes and rate profiles of the stopped-flow fluorescence experiments are consistent with a two-state folding mechanism, and plots of ln(k) versus guanidine deuterium chloride concentration show the classic v-shape indicative of two-state folding. There is no roll over in the plots when the experiments are repeated in the presence of 400 mM sodium sulfate. Temperature and denaturant effects were fit simultaneously to the simple model k=D exp(-DeltaG*/RT) where DeltaG* represents the change in apparent free energy between the transition state and the folded or unfolded state and D represents the maximum possible folding speed. DeltaG* is assumed to vary linearly with denaturant concentration and the Gibbs-Helmholtz equation is used to model stability changes with temperature. Approximately 60% of the surface area buried upon folding is buried in the transition state as evidenced by changes in the heat capacity and m value between the unfolded state and the transition state. The equilibrium thermodynamic parameters, DeltaCp degrees, m and DeltaG degrees, all agree with the values calculated from the kinetic experiments, providing additional evidence that folding is two-state. The folding rates at 0 M guanidine hydrochloride show a non-Arrhenius temperature dependence typical of globular proteins. When the folding rates are examined along constant DeltaG degrees/T contours they display an Arrhenius temperature dependence with a slope of -8600 K. This indicates that for this system, the non-Arrhenius temperature dependence of folding can be accounted for by the anomalous temperature dependence of the interactions which stabilize proteins.