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Protein Matrix and Dielectric Effect in Cytochromec

2001; Elsevier BV; Volume: 276; Issue: 31 Linguagem: Inglês

10.1074/jbc.m103348200

1083-351X

Christian Blouin, Carmichael J. A. Wallace,

Electrochemical sensors and biosensors

The effect of the protein matrix on the standard potential of a buried redox center has been investigated by using a selection of mutants and chemical derivatives in Saccharomyces cerevisiae cytochrome c isoform 1. Assuming only local structural perturbation and no alteration of the iron-ligation chemistry, ΔE m0′ can be regarded as a measure of the difference in polypeptide solvation of the heme charge, which reflects the dielectric properties of the protein. The evaluation of an apparent dielectric constant (U exp/U theo) yields variable, and sometimes even negative, values ifU exp = ΔG 0redox. However, some consistent result are observed if U exp = ΔH 0redox, with a measured εΔΔHredox = 19 ± 6. The variability is thus attributed to an entropic factor (εΔΔSredox) that is investigated using a series of substitutions of Asn52 and/or Tyr67. In double mutants Y67F/N52I Y67F/N52V, where most of the hydrogen bond network in the heme crevice is eliminated, ΔS redox compares to the wild type. This indicates that a fully consistent hydrogen bond network has a similar polarizability as an apolar matrix. We therefore argue that the variability in net dielectric susceptibility arises from conformational polarizability, a factor that is not a function of atomic properties and coordinates and is therefore hard to predict using conventional physical relationships. The effect of the protein matrix on the standard potential of a buried redox center has been investigated by using a selection of mutants and chemical derivatives in Saccharomyces cerevisiae cytochrome c isoform 1. Assuming only local structural perturbation and no alteration of the iron-ligation chemistry, ΔE m0′ can be regarded as a measure of the difference in polypeptide solvation of the heme charge, which reflects the dielectric properties of the protein. The evaluation of an apparent dielectric constant (U exp/U theo) yields variable, and sometimes even negative, values ifU exp = ΔG 0redox. However, some consistent result are observed if U exp = ΔH 0redox, with a measured εΔΔHredox = 19 ± 6. The variability is thus attributed to an entropic factor (εΔΔSredox) that is investigated using a series of substitutions of Asn52 and/or Tyr67. In double mutants Y67F/N52I Y67F/N52V, where most of the hydrogen bond network in the heme crevice is eliminated, ΔS redox compares to the wild type. This indicates that a fully consistent hydrogen bond network has a similar polarizability as an apolar matrix. We therefore argue that the variability in net dielectric susceptibility arises from conformational polarizability, a factor that is not a function of atomic properties and coordinates and is therefore hard to predict using conventional physical relationships. carboxyamidomethyl-methionine sulfonium ion water molecule There is still much to learn about the factors determining theE m0′ of redox-active proteins. Determinants of E m0′ such as local structural effects (1Springs S.T. Bass S.E. McLendon G.L. Biochemistry. 2000; 39: 6075-6082Crossref PubMed Scopus (41) Google Scholar) as well as the electrostatic landscape of the polypeptide (2Moore G.R. FEBS Lett. 1983; 161: 171-175Crossref PubMed Scopus (116) Google Scholar) (including the protein's own charges (3Churg A.K Warshel A. Biochemistry. 1986; 25: 1675-1681Crossref PubMed Scopus (231) Google Scholar, 4Moore G.R. Pettigrew G.W. Pitt R.C. Williams R.J.P. Biochim. Biophys. Acta. 1980; 590: 261-271Crossref PubMed Scopus (115) Google Scholar), dipolar matrix (5Simonson T. Perahia D. Brünger A.T. Biophys. J. 1991; 59: 670-690Abstract Full Text PDF PubMed Scopus (90) Google Scholar, 6Simonson T. Perahia D. Proc. Natl. Acad. Sci. U. S. A. 1995; 92: 1082-1086Crossref PubMed Scopus (204) Google Scholar), and surrounding solvent molecules (7Edholm O. Nordlander P. Chen W. Ohlsson P.I. Smith M.L. Paul J. Biochem. Biophys. Res. Commun. 2000; 268: 683-687Crossref PubMed Scopus (11) Google Scholar)) have already been identified. However, implementation of this knowledge into models does not reliably reproduce experimental observations. The standard redox potential (E m0′) reflects the thermodynamics of the equilibrium between redox states. The energetics of rearrangement between redox states will therefore reflect the ability of a system to polarize in an electrostatic field. Assuming that the nature of the iron-ligand interaction remains unchanged, the values of ΔE m0′ of mutation can be regarded as a measure of change in the polarizability, or dielectric response, to the charge of the redox center. With virtually no large redox-dependent conformational change or ligand rearrangement (8Takano T. Dickerson R.E. J. Mol. Biol. 1981; 153: 79-94Crossref PubMed Scopus (377) Google Scholar, 9Takano T. Dickerson R.E. J. Mol. Biol. 1981; 153: 95-115Crossref PubMed Scopus (352) Google Scholar, 10Berghuis A.M. Guillemette J.G. McLendon G. Sherman F. Smith M. Brayer G.D. J. Mol. Biol. 1994; 236: 786-799Crossref PubMed Scopus (115) Google Scholar, 11Banci L. Bertini I. Huber J.G. Spyroulias G.A. Turano P. J. Biol. Inorg. Chem. 1999; 4: 21-31Crossref PubMed Scopus (141) Google Scholar, 12Qi P.X. Beckmann R.A. Wand A.J. Biochemistry. 1996; 35: 12275-12286Crossref PubMed Scopus (131) Google Scholar), cytochrome c is a suitable model to investigate the contribution of individual residues to the dielectric properties of the protein. Using three positively charged carboxyamidomethyl-methionine sulfonium ion (CAMMS)1derivatives 2C. Blouin and C. J. A. Wallace, unpublished observations. (Fig.1 A) generated from a mutational methionine scan (13Woods A. Guillemette G. Parrish J. Smith M. Wallace C.J.A. J. Biol. Chem. 1996; 271: 32008-32015Abstract Full Text Full Text PDF PubMed Scopus (16) Google Scholar), a series of buried mutations at position 52 (Fig. 1 B) (14Linske-O'Connell L. Sherman F. McLendon G. Biochemistry. 1995; 34: 7094-7102Crossref PubMed Scopus (24) Google Scholar) and the point mutations Y67F, Y67F/N52I, and Y67F/N52V (15Schroeder H.R. McOdimba F.A. Guillemette J.G. Kornblatt J.A. Biochem. Cell Biol. 1997; 75: 191-197Crossref PubMed Scopus (6) Google Scholar), an attempt to rationalize ΔE m0′mut in terms of polarizability of the protein matrix is made. The measurement of redox potential was made using the method of mixtures (16Wallace C.J.A. Corradin G. Marchiori F. Borin G. Biopolymers. 1986; 25: 2121-2132Crossref PubMed Scopus (23) Google Scholar) in 50 mm potassium phosphate (pH 7.0). The redox state of the sample protein was assayed in a range of redox buffers set by the ratio of ferro/ferricyanide in solution using anE m0′ for the couple of +0.43 V. Temperature dependence of the equilibrium between the reduced and oxidized form of the cytochromec was measured in 50 mm potassium phosphate (pH 7.0) with the redox potential of the buffer set at 268 mV using a ferro/ferricyanide ratio of 500. The sample was first prepared, then degassed for 15 min, then flushed with argon and kept in an airtight quartz cuvette. The temperature sweep occurred between 16 and 30 °C with a 2 °C increment using a thermostated cuvette holder (Hewlett-Packard, Mississauga, Canada), and the 550-nm absorption band was monitored. Fully oxidized and reduced proteins, respectively, were generated by the addition of ferricyanide up to a ferro/ferricyanide ratio of 3 and then a small amount of ascorbate. Control runs evaluating the temperature dependence ofE m of the buffer indicated that it was not necessary to apply a correction for the buffer effect over the experimental range of temperature. Sample cytochromes c were prepared in 10 mm phosphate (pH 7.0) in a 1-mm quartz cuvette, and the spectra were recorded from 260 to 180 nm at 10 nm·s−1 at 25 °C. Molar ellipticity was then calculated with exact cytochrome concentrations measured at 410 nm (ε = 106m−1·cm−1). Molecular mechanics were performed using the package DISCOVER (MSI, San Diego, CA) using the coordinates ofSaccharomyces cerevisiae ferrocytochrome cisoform 1 (17Louie G.V. Brayer G.D. J. Mol. Biol. 1990; 214: 527-555Crossref PubMed Scopus (395) Google Scholar). A typical conformational search was run over 100 ps using explicit solvent molecules. Fig. 1 was rendered using SWISS-MODELER/POV-ray. The net dipolar moment was calculated by analyzing the average atomic position of the solvent molecules in a trajectory file. A root mean square deviation matrix was generated to identify domains of local stability to allow a sampling typically of 30–40 ps. The dipole moment of a relaxed water molecule used is 1.85 Debyes, and the length of the vectorial sum of O–H bonds calculated from the model of a relaxed water molecule is 1.278 Å. Equation 1 was then applied,d=1.851.278∑ψ=x,y,zψ¯H1−ψ0+ψ¯H2−ψ02(Eq. 1) where ΨHx refers to the averaged coordinate, on a given axis, of one of the two hydrogen atoms and Ψ0′ refers to the averaged position of the oxygen atom. The behavior of E m0′ upon altering the electrostatic landscape of cytochrome c, as in most electron transport proteins, is hardly predictable. In the classical model, an electrostatic field is attenuated by the medium by a factor known as the dielectric constant. However, at the molecular level the medium cannot be treated as a continuum of matter, and the uniform nature of this effect seems to be lost. For this reason, it is preferable to refer to an effective dielectric constant rather than a dielectric constant (18Rees D.C. J. Mol. Biol. 1980; 141: 323-326Crossref PubMed Scopus (225) Google Scholar). For appropriate biological function, the mitochondrial cytochromesc seem to have evolved toward higher values ofE m0′ (19Sober H.A. Handbook of Biochemistry: Selected Data for Molecular Biology. 2nd Ed. The Chemical Rubber Co., Cleveland, OH1970: J41-J57Google Scholar), i.e. the protein matrix has been optimized to favor the reduced state of the iron (3Churg A.K Warshel A. Biochemistry. 1986; 25: 1675-1681Crossref PubMed Scopus (231) Google Scholar). This is achieved by solvating the buried dipoles that would otherwise polarize to stabilize an extra positive charge of the ferric iron. This is the case in the heme crevice, where every dipole is part of a hydrogen bond network (20Berghuis A.M. Brayer G.D. J. Mol. Biol. 1992; 223: 959-976Crossref PubMed Scopus (377) Google Scholar). The polarity of this network intrinsically acts as a suitable dielectric environment to complement a buried yet charged heme without compromising the protein stability. However, this network as a whole has a sufficiently low dielectric character to differentially disfavor the oxidized iron. Indeed, it may be that because the structure has evolved in this direction that most mutations affecting the network lower the standard redox potential of the protein, indicating that the change favors the oxidized form of the cytochrome c (21Schejter A. Koshy T.I. Luntz T.L. Sanishvili R. Margoliash E. Biochem. J. 1994; 302: 95-101Crossref PubMed Scopus (15) Google Scholar). A series of six positively charged CAMMS derivatives was generated previously. 3C. Blouin and C. J. A. Wallace, unpublished results. The magnitude of ΔE m0′ measured in most chemical derivatives is not large enough to allow the reliable calculation of effective dielectric constants. Only four modifications incurring a ±1 formal charge change were kept for thermodynamic analysis: the mutation K55M and the CAMMS derivatives of mutants V28M, K55M, and I75M (Fig.1 A). The direct use of ΔΔG redox of derivatization to evaluate ε yielded a range of values from −90 to 130. Considering the theoretical minimum ε value of 1 and the practical maximum value of 80, it is clear that ΔE m0′ is not exclusively attributable to a change in the dielectric properties of the protein matrix (as inferred from Coulomb's law). The presence of a "negative dielectric effect" for K55M and CAMMS55 indicates that the change in E m0′ is greater than would be expected from electrostatic interaction exclusively. On the other hand, the effect of the derivatization CAMMS28 is much smaller than would have been expected from dielectric relaxation (ε = 130 ± 20, Table I). This value is in fact higher than the value of ε for the bulk solvent itself. The effect on standard redox potential thus extends beyond dipolar relaxation into a factor(s) yet to be accounted for.Table IApparent dielectric constants applying between the CAMMS probe and the redox centerModificationD (FE-X)1-aDistance from the iron atom to the site of the modification as measured in the respective molecular models.ΔE m0′ΔΔG redox1-bCalculated using ΔΔG Red = −RTΔΔE m0′.ΔΔH redox1-cMeasured using Van't-Hoff's temperature dependence of equilibria graphical method.εΔΔEm0′ 1-dRatio ΔU cal/ΔUexp. ΔU calc= (e−)2/4πɛ0 r.εΔΔH1-dRatio ΔU cal/ΔUexp. ΔU calc= (e−)2/4πɛ0 r.ÅmVkJ · M−1kJ · M−1K55M14.6+11 ± 4−1.1 ± 0.4+6 ± 1(−90)1-eΔU exp diverged in sign from theoretically expected ΔΔG red. These values have no physical meaning.16 ± 2K55M → CAMMS5516.0−18 ± 5+1.8 ± 0.5−2 ± 3(−49)1-eΔU exp diverged in sign from theoretically expected ΔΔG red. These values have no physical meaning.∼441-fApproximate value considering the large error in ΔΔH red.I75M → CAMMS7510.5+33 ± 4−3.2 ± 0.4−7 ± 241 ± 819 ± 6V28M → CAMMS288.0+12 ± 2−1.3 ± 0.2−7.1 ± 0.6130 ± 2024 ± 21-a Distance from the iron atom to the site of the modification as measured in the respective molecular models.1-b Calculated using ΔΔG Red = −RTΔΔE m0′.1-c Measured using Van't-Hoff's temperature dependence of equilibria graphical method.1-d Ratio ΔU cal/ΔUexp. ΔU calc= (e−)2/4πɛ0 r.1-e ΔU exp diverged in sign from theoretically expected ΔΔG red. These values have no physical meaning.1-f Approximate value considering the large error in ΔΔH red. Open table in a new tab If, however, one uses ΔΔH redox to calculate an effective dielectric constant, the data yields a more consistent ε value (Table I), with an average of 19 ± 6. This compares with calculated values of 25 ± 10 for the whole cytochrome c derived from molecular mechanics using the Frohlich-Kirkwood theory of microscopic dielectrics (6Simonson T. Perahia D. Proc. Natl. Acad. Sci. U. S. A. 1995; 92: 1082-1086Crossref PubMed Scopus (204) Google Scholar). Derivative CAMMS55 seems to be an exception, but the standard deviation in the measurements of ΔE m0′ is such that it is impossible to formally calculate εΔΔH. A consistent εΔΔH value suggests that the dielectric constant as defined by Coulomb's law applies to microscopic systems with a value of ∼20 for the heme and its immediate environment in cytochrome c. Or, at least, this value would apply to this system extrapolated to 0 K. This implies that, from a purely enthalpic point of view, the polypeptide relaxation with respect to the heme is consistent and independent of the position of a test charge. The dielectric susceptibility in this case could thus be referred to as dielectric constant, which is one of two possible components forming the apparent dielectric constant. Most importantly, this indicates that the great variability in apparent dielectric constants is caused by the entropy of the redox equilibrium. The CD spectra of the mutants N52A, N52S, N52T, N53V, N52H, N52Q, N52I, N52C, N52D, and N52M were checked between 180 and 260 nm for deviation from the wild-type spectrum. The signal of the amide band would be expected to be sensitive to any change in the short stretch of α-helix including position 52. Only the mutants N52D and N52C showed unusual features in this domain and were discarded from the data set. Further molecular modeling of each mutant protein for which no known structure has yet been solved was performed to probe the geometry and environment of the substituted residues. All of the modeled side chain substitutions were accommodated in the heme crevice with no backbone rearrangement. As in mutant N52I (PDB entry 1CRG (10Berghuis A.M. Guillemette J.G. McLendon G. Sherman F. Smith M. Brayer G.D. J. Mol. Biol. 1994; 236: 786-799Crossref PubMed Scopus (115) Google Scholar)), the hydrophilic cavity beside the heme in mutation N52M, N52Q, and N52H did not offer sufficient space to keep the structural water molecule bound in the wild-type Asn52. In mutants with side chains smaller than that of asparagine, the ambiguity between one or two buried water molecules was addressed by measuring the stability of the buried water molecule over simulation time by calculating the dipolar moment of the molecule. As a control experiment, a simulation was run on the wild-type ferricytochrome c with the Met80 ligand replaced by Lys73. A large range of buried water molecules was present because a buried pocket was created in this simulation, which included two poorly stabilized solvent molecules (Fig.2, solid data points). The calculated net dipolar moment of a (stable) structural molecule is constant for a structure averaged for >10 ps, whereas the bulk solvent molecules decayed to no net dipolar moment as demonstrated in Fig. 2. The elimination of the amide at 52 decreased the number of dipoles competing for oxygen lone-pairs of Wat166, hence the increase in the net dipolar moment baseline for the mutants. We used as control protein N52A, for which we know that the structure has a crevice large enough to accommodate two water molecules (10Berghuis A.M. Guillemette J.G. McLendon G. Sherman F. Smith M. Brayer G.D. J. Mol. Biol. 1994; 236: 786-799Crossref PubMed Scopus (115) Google Scholar). In this structure, both of these molecules have a high net dipolar moment over the simulation time (Table II). Of the mutants N52S, N52T, and N52V, only N52S allows two water molecules to stably reside in the pocket, whereas the extra methyl in N52T forbids the presence of a second molecule (both averaged molecules attempt to share the same stabilizing groups). It is arguable that the hydrophilic nature of the crevice in mutant N52V would be insufficient to accommodate even a single water molecule. This is supported by a poor net dipolar moment for the model of this mutant.Table IINet dipolar moment of buried water molecules in models of Asn52mutant seriesModelWat1662-aThe water molecule occupying the space of the amide nitrogen of Asn52 in the wild-type structure.Wat13002-bThe second structural water molecule present in the structure of mutant N52A (1IRW,).Wat1212-cThe water molecule tethered between Arg38 and Hpr7.DebyeWild type0.921.37N52A1.271.281.37N52S1.201.351.51N52T2-dOverlapping of atoms by averaged water molecule Wat166–Wat1300.1.171.061.31N52V2-dOverlapping of atoms by averaged water molecule Wat166–Wat1300.0.780.631.632-a The water molecule occupying the space of the amide nitrogen of Asn52 in the wild-type structure.2-b The second structural water molecule present in the structure of mutant N52A (1IRW,).2-c The water molecule tethered between Arg38 and Hpr7.2-d Overlapping of atoms by averaged water molecule Wat166–Wat1300. Open table in a new tab Calculation of ε′ as performed with the CAMMS series could not be applied to mutants at position 52 because of the lack of change in formal charge. Instead, the thermodynamic breakdown ofE m0′ was performed by the independent determination of ΔΔH redox and ΔΔG 0′redox, which permitted the calculation of TΔΔS redox. ΔE m0′ values in the series of mutants involving Asn52 range from −5 mV in N52M to −47 mV in N52I. Mutations at this position have been reported to stabilize the fold of both oxidation states (21Schejter A. Koshy T.I. Luntz T.L. Sanishvili R. Margoliash E. Biochem. J. 1994; 302: 95-101Crossref PubMed Scopus (15) Google Scholar, 22Koshy T.I. Luntz T.L. Plotkin B. Schejter A. Margoliash E. Biochem. J. 1994; 299: 347-350Crossref PubMed Scopus (13) Google Scholar), with an enhanced preference for the oxidized protein (23Lett C.M. Berghuis A.M. Frey H.E. Lepock J.R. Guillemette J.G. J. Biol. Chem. 1996; 271: 29088-29093Abstract Full Text Full Text PDF PubMed Scopus (48) Google Scholar). Contraintuitively, the elimination of the dipole of the Asn52 side chain and its replacement by another residue induced a decrease in enthalpy of reduction. This indicates that Asn52 enthalpically favors the oxidized state over any other single mutation at this position. Thus, a mutation at position 52 would be expected to provoke an increase inE m0′. However, most are found below the isocurve ΔE m0′ = 0 (Fig.3), indicating that these mutations lead to a net decrease of E m0′. The favorable enthalpy of reduction is, in these cases, opposed by a larger unfavorable entropic cost. In mutations not involving Asn52 (I75M, V28M, Y67F, and K55M), ΔΔS redox correlates with ΔE m0′. As shown in Fig.4 A, the series of mutations at position 52 have an absolute ΔΔS redoxindependent of the net effect of a mutation onE m0′ and the nature of the substitution. In these mutants, ΔΔS redox averages to −74 ± 3 J·Mol−1·K−1 except for N52S, N52T, and N52H. The first two mutations are the only substitutions in which position 52 conserved the ability to donate a hydrogen bond to the structural water Wat166, which may explain the lesser entropic penalty. This suggests that this bond is responsible for the attributed switchlike properties of the water molecule upon oxidoreduction (10Berghuis A.M. Guillemette J.G. McLendon G. Sherman F. Smith M. Brayer G.D. J. Mol. Biol. 1994; 236: 786-799Crossref PubMed Scopus (115) Google Scholar). It is unclear as to why N52H does not group with the other mutants. The hydroxyl group at position 67 is thought to contribute to the electron-withdrawing power of Met80 (24Berghuis A.M. Guillemette J.G. Smith M. Brayer G.D. J. Mol. Biol. 1994; 235: 1326-1341Crossref PubMed Scopus (85) Google Scholar), to the binding of Wat166(17Louie G.V. Brayer G.D. J. Mol. Biol. 1990; 214: 527-555Crossref PubMed Scopus (395) Google Scholar), and to stabilizing the lysine ligands in the state IV alkaline isomer (15Schroeder H.R. McOdimba F.A. Guillemette J.G. Kornblatt J.A. Biochem. Cell Biol. 1997; 75: 191-197Crossref PubMed Scopus (6) Google Scholar). The ΔΔS redox of mutant Y67F suggests that the hydroxyl group of Tyr67 is not part of the block Asn52-Wat166 (Fig. 4 B). The enthalpy of reduction upon losing the hydroxyl group also favors the reduced state. This is possible either by affecting the electron-withdrawing power of Met80 or more generally by deleting one dipole that is able to react favorably to the fluctuations in the electrostatic charge on the heme. Again, the enthalpic effect is counteracted by a larger entropic effect, resulting in a net decrease of E m0′. The effects of the double mutations Y67F/N52I and Y67F/N52V differ radically from those of the corresponding single mutations. The enthalpy of deleting the polarity at both positions 52 and 67 actually favors the oxidized state. This may be caused by a more direct effect of the negatively charged heme propionate on the cationic iron ion because of the lack of screening by the protein matrix. Alternatively, because these double mutants fail to undergo an alkaline transition3 (10Berghuis A.M. Guillemette J.G. McLendon G. Sherman F. Smith M. Brayer G.D. J. Mol. Biol. 1994; 236: 786-799Crossref PubMed Scopus (115) Google Scholar), it is conceivable that the second heme propionate (Hpr6) is ionized in these proteins, which would clearly favor a positive charge on the heme and hence a lowerE m0′. The entropies of reduction of both double mutants indicate that the temperature-dependent component of the free energy of a fully hydrophobic heme crevice is similar to that of a wild-type fully hydrophilic cavity (Fig. 2 B). This means that the polarizability of the heme crevice is similar whether the heme crevice is made of a fully consistent hydrogen bond network or has no polarity at all. The question of whether the frequently observed enthalpy-entropy compensation is real or artifactual leaves much over which to argue. But as can be inferred from Sharp (25Sharp K. Protein Sci. 2001; 10: 661-667Crossref PubMed Scopus (365) Google Scholar), the reason why research groups overlook the "artifact explanation" is that it yields no physical rationale for discussion. Table III shows the thermodynamic values determined in this study. It is clear from these results that the enthalpy of reduction is of an opposing sign to the net change in free energy. If ΔH redox was not compensated by ΔS redox, the magnitude of ΔE m0′ would be in the order of hundreds of millivolts for the Asn52 mutant series in the opposite direction to that which is observed. Some form of compensation must therefore occur.Table IIIThermodynamics of reduction of cytochromes c determined by the Van't-Hoff methodMutationΔE m0′3-aUsing the method of the mixtures. Standard error = 3 mV (n = 3).ΔΔG red3-bCalculated using ΔΔG red = −RTΔE m0′.ΔΔH red3-cMeasured using Van't-Hoff's temperature dependence of equilibria graphical method. Average error = 1.2 kJ · Mol−1.ΔΔS red3-dCalculated using ΔΔS red0′ = ΔΔH red0′ − ΔΔG red0′. Standard error = 6 J · Mol−1 K−1.mVkJ · M−1kJ · M−1J · M−1K−1V28M−8 ± 40.8 ± 0.4−1.5 ± 0.7−8 ± 3CAMMS285 ± 4−0.5 ± 0.4−8.6 ± 0.6−27 ± 3K55M11 ± 4−1.1 ± 0.46 ± 123 ± 4CAMMS55−7 ± 40.7 ± 0.44 ± 312 ± 11I75M−29 ± 42.8 ± 0.4−5 ± 2−27 ± 8CAMMS754 ± 4−0.4 ± 0.4−12 ± 2−39 ± 8N52M−5 ± 20.5 ± 0.2−20 ± 0.4−69 ± 2N52S−8 ± 30.8 ± 0.3−9 ± 1−34 ± 4N52T−9 ± 20.9 ± 0.2−15 ± 0.3−51 ± 2N52V−20 ± 41.9 ± 0.4−20 ± 0.4−74 ± 2N52A−21 ± 32 ± 0.3−20 ± 2−70 ± 8N52H−34 ± 23.3 ± 0.2−10 ± 1−44 ± 4Y67F/N52I−30 ± 22.9 ± 0.27 ± 115 ± 4N52Q−36 ± 13.5 ± 0.1−20 ± 3−77 ± 10N52I−47 ± 74.5 ± 0.7−18 ± 1−75 ± 3Y67F/N52V−47 ± 34.5 ± 0.34.8 ± 0.51 ± 2Y67F−42 ± 14.1 ± 0.1−13 ± 0.2−57 ± 13-a Using the method of the mixtures. Standard error = 3 mV (n = 3).3-b Calculated using ΔΔG red = −RTΔE m0′.3-c Measured using Van't-Hoff's temperature dependence of equilibria graphical method. Average error = 1.2 kJ · Mol−1.3-d Calculated using ΔΔS red0′ = ΔΔH red0′ − ΔΔG red0′. Standard error = 6 J · Mol−1 K−1. Open table in a new tab Although we make no attempt to prove this point, it seems logical that preferential distribution into lower energy levels will affect the entropy of a system (26Hill T. An Introduction to Statistical Thermodynamics. Dover Books, New York1986Google Scholar). This would bind S and H to correlate in accordance with statistical thermodynamics. In the present cases the entropic penalty consistently overcomes the enthalpy regardless of the actual effect on ΔH redox. This suggests that the dynamic nature of the protein matrix weighs more heavily in the balance than the actual energy levels. If the cytochrome chas evolved toward a higher level of intramolecular neutralization of its dipolar groups to restrain its polarizability, any candidate mutation will be likely to free one or more chemical groups and therefore favor the oxidized state, which is what we observe. The sign of ΔΔH redox or even the functional relevance of a mutation to the biological activity, therefore, may have nothing to do with the effect on E m0′. This study concludes that the apparent dielectric constant (ε′) measured for microscopic systems such as cytochromec is comprised of εΔΔH and εΔΔS. The enthalpic factor, εΔΔH, showed a constant nature with a value of about 20, leaving εΔΔS as responsible for the wide variability in ε′. The polarizability of the matrix as a whole, mainly responsible for εΔΔS, refers to conformational polarizability and is therefore not a function of atomic properties or coordinates and cannot be calculated in a straightforward way. Although the network of hydrogen bonds within the protein matrix contributes enthalpically to the oxidized state, if any of its components is deleted, the loss of polarity is overcome by the concomitant conformational freedom of the polar groups left unpaired by the mutations. In dynamic systems such as proteins, the entropic penalty overcomes the enthalpy, which explains why known physical relationships perform poorly at predictingE m0′ changes.