Thermodynamic cycles as probes of structure in unfolded proteins

Loop Entropy and Cytochrome c Stability

The loop entropy model proposes that loop closure in a protein becomes entropically more costly as the length of the loop increases. A model protein, cytochrome c, is composed of four loops connecting five helices surrounding a heme-containing core. To test the loop entropy model a series of mutant proteins are constructed with (Gly)n or (Thr)n segments (n = 4-20) inserted between Gly23 and Gly24 of omega loop A of a pseudo wild-type reference protein. Scanning calorimetry shows that protein stability decreases as n increases in the (Gly)n or (Thr)n segment. The dependence of stability on loop length is analyzed with the loop entropy model. Fitting to the model gives a quantitative description of stability differences for the mutant proteins, but with a smaller power-dependence of the probability of loop closure (c-value) than expected from polymer theory. A possible explanation for the discrepancy is that thermodynamically unfavorable loop entropy is partially offset by interactions between the inserted homopolymer and flanking heteropolymer portions of the unfolded protein. The interactions may involve molecular crowding that favors coalescence of the heteropolymer at the insert site and thus closure of the homopolymer loops, possibly as an aspect of the folding code. This may allow use of loop insert mutants to assess the strength of the heteropolymer-encoded folding signals that facilitate loop closure at the insert site.

Classical force field parameters for the heme prosthetic group of cytochrome c

Accurate force fields are essential for describing biological systems in a molecular dynamics simulation. To analyze the docking of the small redox protein cytochrome c (cyt c) requires simulation parameters for the heme in both the reduced and oxidized states. This work presents parameters for the partial charges and geometries for the heme in both redox states with ligands appropriate to cyt c. The parameters are based on both protein X-ray structures and ab initio density functional theory (DFT) geometry optimizations at the B3LYP/6-31G* level. The simulations with the new parameter set reproduce the geometries of the X-ray structures and the interaction energies between water and heme prosthetic group obtained from B3LYP/6-31G* calculations. The parameter set developed here will provide new insights into docking processes of heme containing redox proteins.

Effects of pH on protein association: modification of the proton-linkage model and experimental verification of the modified model in the case of cytochrome c and plastocyanin

Effects of pH on protein association are not well understood. To understand them better, we combine kinetic experiments, calculations of electrostatic properties, and a new theoretical treatment of pH effects. The familiar proton-linkage model, when used to analyze the dependence of the association constant K on pH, reveals little about the individual proteins. We modified this model to allow determination not only of the numbers of the H+ ions involved in the association but also of the pK(a) values, in both the separate and the associated proteins, of the side chains that are responsible for the dependence of K on pH. Some of these side chains have very similar pK(a) values, and we treat them as a group having a composite pK(a) value. Use of these composite pK(a) values greatly reduces the number of parameters and allows meaningful interpretation of the experimental results. We experimentally determined the variation of K in the interval 5.4 < or = pH < or = 9.0 for four diprotein complexes, those that the wild-type cytochrome c forms with the wild-type plastocyanin and its mutants Asp42Asn, Glu59Gln, and Glu60Gln. The excellent fittings of the experimental results to the modified model verified this model and revealed some unexpected and important properties of these prototypical redox metalloproteins. Protein association causes a decrease in the pK(a) values of the acidic side chains and an increase in the pK(a) values of the basic side chains. Upon association, three carboxylic side chains in wild-type plastocyanin each release a H+ ion. These side chains in free plastocyanin have an anomalously high composite pK(a) value, approximately 6.3. Upon association, five or six side chains in cytochrome c, likely those of lysine, each take up a H+ ion. Some of these side chains have anomalously low pK(a) values, less than 7.0. The unusual pK(a) values of the residues in the recognition patches of plastocyanin and cytochrome c may be significant for the biological functions of these proteins. Although each mutation in plastocyanin markedly, and differently, changed the dependence of K on pH, the model consistently gave excellent fittings. They showed decreased numbers of H+ ions released or taken up upon protein association and altered composite pK(a) values of the relevant side chains. Comparisons of the fitted composite pK(a) values with the theoretically calculated pK(a) values for plastocyanin indicated that Glu59 and Asp61 in the wild-type plastocyanin each release a H+ ion upon association with cytochrome c. Information of this kind cannot readily be obtained by spectroscopic methods. Our modification of the proton-linkage model is a general one, applicable also to ligands other than H+ ion and to processes other than association.

Denatured state thermodynamics: residual structure, chain stiffness and scaling factors

A set of nine variants of yeast iso-1-cytochrome c with zero or one surface histidine have been engineered such that the N-terminal amino group is acetylated in vivo. N-terminal acetylation has been confirmed by mass spectral analysis of intact and proteolytically digested protein. The histidine-heme loop-forming equilibrium, under denaturing conditions (3 M guanidine hydrochloride), has been measured by pH titration providing an observed pK(a), pK(a)(obs), for each variant. N-terminal acetylation prevents the N-terminal amino group-heme binding equilibrium from interfering with measurements of histidine-heme affinity. Significant deviation is observed from the linear dependence of pK(a)(obs) on the log of the number of monomers in the loop formed, expected for a random coil denatured state. The maximum histidine-heme affinity occurs for a loop size of 37 monomers. For loop sizes of 37-83 monomers, histidine-heme pK(a)(obs) values are consistent with a scaling factor of -4.2+/-0.3. This value is much larger than the scaling factor of -1.5 for a freely jointed random coil, which is commonly used to represent the conformational properties of protein denatured states. For loop sizes of nine to 22 monomers, chain stiffness is likely responsible for the decreases in histidine-heme affinity relative to a loop size of 37. The results are discussed in terms of residual structure and sequence composition effects on the conformational properties of the denatured states of proteins.

A study of the influence of the hydrophobic core residues of yeast iso-2-cytochrome c on phosphate binding: a probe of the hydrophobic core-surface charge interactions

To gain insight into the role of hydrophobic core-surface charge interactions in stabilizing cytochrome c, we investigated the influence of hydrophobic core residues on phosphate binding by mutating residues in yeast iso-2-cytochrome c to those corresponding to iso-l-cytochrome c in various combinations. Heat transition of ultraviolet CD was followed as a function of pH in the presence and absence of phosphate. Thermodynamic parameters were deduced. It was found that the I20V/V43A/M98L mutation in the hydrophobic core, whose locations are remote from the putative phosphate sites, modulates phosphate interactions. The modulation is pH dependent. The I20V/ M98L and V43A mutation effects are nonadditive. The results lead to a model analogous to that of Tsao, Evans, and Wennerstrom, where a domain associated with the ordered hydrophobic core is sensitive to the fields generated by the surface charges. Such an explanation would be in accord with the observed difference in thermal stability between iso-2 and horse cytochromes c.

Aromatic ring-flipping in supercooled water: implications for NMR-based structural biology of proteins

We have characterized, for the first time, motional modes of a protein dissolved in supercooled water: the flipping kinetics of phenylalanyl and tyrosinyl rings of the 6 kDa protein BPTI have been investigated by NMR at temperatures between -3 and -16.5 degrees C. At T = -15 degrees C, the ring-flipping rate constants of Tyr 23, Tyr 35, and Phe 45 are smaller than 2 s(-1), i.e., flip-broadening of aromatic NMR lines is reduced beyond detection and averaging of NOEs through ring-flipping is abolished. This allows neat detection of distinct NOE sets for the individual aromatic (1)H spins. In contrast, the rings of Phe 4, Tyr 10, Tyr 21, Phe 22, and Phe 33 are flipping rapidly on the chemical shift time scale with rate constants being in the range from approximately 10(2) to 10(5) s(-1) even at T = -15 degrees C. Line width measurements in 2D [(1)H,(1)H]-NOESY showed that flipping of the Phe 4 and Phe 33 rings is, however, slowed to an extent that the onset of associated line broadening in the fast exchange limit is registered. The reduced ring-flipping rate constant of Phe 45 in supercooled water allowed very precise determination of Eyring activation enthalpy and entropy from cross relaxation suppressed 2D [(1)H,(1)H]-exchange spectroscopy. This yielded DeltaH = 14 +/- 0.5 kcal.mol(-1) and DeltaS = -4 +/- 1 cal.mol(-1).K(-1), i.e., values close to those previously derived by Wagner and Wüthrich for the temperature range from 4 to 72 degrees C (DeltaH = 16 +/- 1 kcal.mol(-1) and DeltaS = 6 +/- 2 cal.mol(-1).K(-1)). The preservation of the so far uniquely low value for DeltaS indicates that the distribution of internal motional modes associated with the ring flip of Phe 45 is hardly affected by lowering T well below 0 degrees C. Hence, if a globular protein does not cold denature, aromatic flipping rates, and thus likely also the rates of other conformational and/or chemical exchange processes occurring in supercooled water, can be expected to be well estimated from activation parameters obtained at ambient T. This is of keen interest to predict the impact of supercooling for future studies of biological macromolecules, and shows that our approach enables one to conduct NMR-based structural biology at below 0 degrees C in an unperturbed aqueous environment. A search of the BioMagResBank indicated that the overwhelming majority of the Phe and Tyr rings (>95%) are flipping rapidly on the chemical shift time scale at ambient T, while our data for BPTI and activation parameters available for ring-flipping in Iso-2-cytochrome c reveal that in these smaller proteins a total of six out of seventeen rings ( approximately 35%) are "frozen in" at T = -15 degrees C. This suggests that a large fraction of Tyr and Phe rings in globular proteins that are flipping rapidly on the chemical shift time scale at ambient T can be effectively slowed in supercooled water. The present investigation demonstrates that supercooling of protein solutions appears to be an effective means to (i) harvest potential benefits of stalled ring-flipping for refining NMR solution structures, (ii) recruit additional aromatic rings for investigating protein dynamics, and (iii) use multiple slowly flipping rings to probe cold denaturation. The implications for NMR-based structural biology in supercooled water are addressed.

Electrochemical methods of evaluating the van't Hoff enthalpy in reactions involving biological macromolecules

We highlight conditions under which coincidence of van't Hoff and calorimetric enthalpies can be experimentally verified for reactions of biochemical interest. First, we clarify that, often, chemical equations in condensed phase do not explicitly contain information on all processes involved. Second, we underline that the accuracy of electrochemical methods is much higher than that of other non-calorimetric techniques. Electrochemical data on the binding of ethidium ion to DNA are re-examined to verify that the entropy evaluated as the temperature derivative of the free energy agrees in full with the calorimetric one. Third, we point out that unfolding or self-association enthalpies of redox proteins can be reliably obtained by electromotive force measurements, taking advantage of their linkage to redox enthalpies. Thermodynamic cycles coupling biochemical transformations to redox systems are briefly discussed.

Cytochrome c folds through a smooth funnel

A dominant feature of folding of cytochrome c is the presence of nonnative His-heme kinetic traps, which either pre-exist in the unfolded protein or are formed soon after initiation of folding. The kinetically trapped species can constitute the majority of folding species, and their breakdown limits the rate of folding to the native state. A temperature jump (T-jump) relaxation technique has been used to compare the unfolding/folding kinetics of yeast iso-2 cytochrome c and a genetically engineered double mutant that lacks His-heme kinetic traps, H33N,H39K iso-2. The results show that the thermodynamic properties of the transition states are very similar. A single relaxation time tau(obs) is observed for both proteins by absorbance changes at 287 nm, a measure of solvent exclusion from aromatic residues. At temperatures near Tm, the midpoint of the thermal unfolding transitions, tau(obs) is four to eight times faster for H33N,H39K iso-2 (tau(obs) approximately 4-10 ms) than for iso-2 (tau(obs) approximately 20-30 ms). T-jumps show that there are no kinetically unresolved (tau < 1-3 micros T-jump dead time) "burst" phases for either protein. Using a two-state model, the folding (k(f)) and unfolding (k(u)) rate constants and the thermodynamic activation parameters standard deltaGf, standard deltaGu, standard deltaHf, standard deltaHu, standard deltaSf, standard deltaSu are evaluated by fitting the data to a function describing the temperature dependence of the apparent rate constant k(obs) (= tau(obs)(-1)) = k(f) + k(u). The results show that there is a small activation enthalpy for folding, suggesting that the barrier to folding is largely entropic. In the "new view," a purely entropic kinetic barrier to folding is consistent with a smooth funnel folding landscape.

Measuring denatured state energetics: deviations from random coil behavior and implications for the folding of iso-1-cytochrome c

The changes in the free energy of the denatured state of a set of yeast iso-1-cytochrome c variants with single surface histidine residues have been measured in 3 M guanidine hydrochloride. The thermodynamics of unfolding by guanidine hydrochloride is also reported. All variants have decreased stability relative to the wild-type protein. The free energy of the denatured state was determined in 3 M guanidine hydrochloride by evaluating the strength of heme-histidine ligation through determination of the pK(a) for loss of histidine binding to the heme. The data are corrected for the presence of the N-terminal amino group which also ligates to the heme under similar solution conditions. Significant deviations from random coil behavior are observed. Relative to a variant with a single histidine at position 26, residual structure of the order of -1.0 to -2.5 kcal/mol is seen for the other variants studied. The data explain the slower folding of yeast iso-1-cytochrome c relative to the horse protein. The greater number of histidines and the greater strength of ligation are expected to slow conversion of the histidine-misligated forms to the obligatory aquo-heme intermediate during the ligand exchange phase of folding. The particularly strong association of histidine residues at positions 54 and 89 may indicate regions of the protein with strong energetic propensities to collapse against the heme during early folding events, consistent with available data in the literature on early folding events for cytochrome c.

Rational design of a more stable yeast iso-1-cytochrome c

Yeast iso-1-cytochrome c is one of the least stable mitochondrial cytochromes c. We have used a coordinated approach, combining the known functional and structural properties of cytochromes c, to engineer mutations into yeast iso-1-cytochrome c with the goal of selectively increasing the stability of the protein. The two redox forms of the native protein and six different mutant forms of yeast iso-1-cytochrome c were analyzed by differential scanning calorimetry (DSC). The relative stability, expressed as the difference in the Gibb's free energy of denaturation at a given temperature between the native and mutant forms (DeltaDeltaG(Tref)), was determined for each of the proteins. In both oxidation states, the mutant proteins C102T, T69E/C102T, T96A/C102T, and T69E/T96A/C102T were more stable than the wild-type protein, respectively. The increased stability of the mutant proteins is proposed to be due to the removal of a rare surface cysteine and the stabilization of two distorted alpha-helices.

Refolding rate of stability-enhanced cytochrome c is independent of thermodynamic driving force

N52I iso-2 cytochrome c is a variant of yeast iso-2 cytochrome c in which asparagine substitutes for isoleucine 52 in an alpha helical segment composed of residues 49-56. The N52I substitution results in a significant increase in both stability and cooperativity of equilibrium unfolding, and acts as a "global suppressor" of destabilizing mutations. The equilibrium m-value for denaturant-induced unfolding of N52I iso-2 increases by 30%, a surprisingly large amount for a single residue substitution. The folding/unfolding kinetics for N52I iso-2 have been measured by stopped-flow mixing and by manual mixing, and are compared to the kinetics of folding/unfolding of wild-type protein, iso-2 cytochrome c. The results show that the observable folding rate and the guanidine hydrochloride dependence of the folding rate are the same for iso-2 and N52I iso-2, despite the greater thermodynamic stability of N52I iso-2. Thus, there is no linear free-energy relationship between mutation-induced changes in stability and observable refolding rates. However, for N52I iso-2 the unfolding rate is slower and the guanidine hydrochloride dependence of the unfolding rate is smaller than for iso-2. The differences in the denaturant dependence of the unfolding rates suggest that the N52I substitution decreases the change in the solvent accessible hydrophobic surface between the native state and the transition state. Two aspects of the results are inconsistent with a two-state folding/unfolding mechanism and imply the presence of folding intermediates: (1) observable refolding rate constants calculated from the two-state mechanism by combining equilibrium data and unfolding rate measurements deviate from the observed refolding rate constants; (2) kinetically unresolved signal changes ("burst phase") are observed for both N52I iso-2 and iso-2 refolding. The "burst phase" amplitude is larger for N52I iso-2 than for iso-2, suggesting that the intermediates formed during the "burst phase" are stabilized by the N52I substitution.

A histidine variant of yeast iso-1-cytochrome c that strongly affects the energetics of the denatured state

Iso-1-cytochrome c has been engineered to remove all histidine residues not involved in heme ligation in the native state to produce a variant designated TM. Single histidine residues were then introduced at positions 26, TM + His26, and 54, TM + His54. Since histidine residues not involved in native state heme ligation are known to replace the methionine 80 heme ligand in denatured cytochrome c, these variants were expected to affect the structure of the denatured state. Guanidine hydrochloride denaturations were performed to assess the stability of these proteins relative to the wild-type protein. The free energy difference for heme ligation in the denatured state was assessed by pH titration. The experimentally observed mutation-induced change (delta deltaG(D-state)) in the free energy of heme ligation for unfolded TM + His54 versus TM + His26 is -0.4 kcal/mol. The expected mutation-induced change in delta deltaG(D-state) calculated for a random coil unfolded state is +2 kcal/mol. Thus, unfolded TM + His54 has residual structure stabilizing its denatured state by -2.4 kcal/mol relative to TM + His26. The results imply that the denatured state can contribute significantly to mutation-induced changes in the free energy of unfolding of a protein.

The role of a conserved water molecule in the redox-dependent thermal stability of iso-1-cytochrome c

Eukaryotic cytochromes c contain a buried water molecule (Wat166) next to the heme that is associated through a network of hydrogen bonds to three invariant residues: tyrosine 67, asparagine 52, and threonine 78. Single-site mutations to two of these residues (Y67F, N52I, N52A) and the double-site mutation (Y67F/N52I) were introduced into Saccharomyces cerevisiae iso-1-cytochrome c to disrupt the hydrogen bonding network associated with Wat166. The N52I and Y67F/N52I mutations lead to a loss of Wat166 while N52A and Y67F modifications lead to the addition of a new water molecule (Wat166) at an adjacent site (Berghuis, A. M., Guillemette, J. G., McLendon, G., Sherman, F., Smith, M., and Brayer, G. D. (1994) J. Mol. Biol. 236, 786-799; Berghuis, A. M., Guillemette, J. G., Smith, M., and Brayer, G. D. (1994) J. Mol. Biol. 235, 1326-1341; Rafferty, S. P., Guillemette, J. G., Berghuis, A. M., Smith, M., Brayer, G. D., and Mauk, A. G. (1996) Biochemistry, 35, 10784-10792). We used differential scanning calorimetry (DSC) to determine the change in heat capacity (DeltaCp) and the temperature dependent enthalpy (DeltaHvH) for the thermal denaturation of both the oxidized and reduced forms of the iso-1 cytochrome c variants. The relative stabilities were expressed as the difference in the free energy of denaturation (DeltaGD) between the wild type and mutant proteins in both redox states. The disruption of the hydrogen bonding network results in increased stability for all of the mutant proteins in both redox states with the exception of the reduced Y67F variant which has approximately the same stability as the reduced wild type protein. For the oxidized proteins, DeltaGD values of 1.3, 4.1, 1.5, and 5.8 kcal/mol were determined for N52A, N52I, Y67F, and Y67F/N52I, respectively. The oxidized proteins were 8.2-11.5 kcal/mol less stable than the reduced proteins due to a redox-dependent increase in the entropy of unfolding.