Changes of Protein Folding Pathways by Circular Permutation
2008; Elsevier BV; Volume: 283; Issue: 41 Linguagem: Inglês
10.1074/jbc.m801776200
ISSN1083-351X
AutoresEllinor Haglund, Magnus Lindberg, Mikael Oliveberg,
Tópico(s)Protein Structure and Dynamics
ResumoThe evolved properties of proteins are not limited to structure and stability but also include their propensity to undergo local conformational changes. The latter, dynamic property is related to structural cooperativity and is controlled by the folding-energy landscape. Here we demonstrate that the structural cooperativity of the ribosomal protein S6 is optimized by geometric overlap of two competing folding nuclei: they both include the central β-strand 1. In this way, folding of one nucleus catalyzes the formation of the other, contributing to make the folding transition more concerted overall. The experimental evidence is provided by an extended set of circular permutations of S6 that allows quantitative analysis of pathway plasticity at the level of individual side chains. Because similar overlap between competing nuclei also has been discerned in other proteins, we hypothesize that the coupling of several small nuclei into extended "supernuclei" represents a general principle for propagating folding cooperativity across large structural distances. The evolved properties of proteins are not limited to structure and stability but also include their propensity to undergo local conformational changes. The latter, dynamic property is related to structural cooperativity and is controlled by the folding-energy landscape. Here we demonstrate that the structural cooperativity of the ribosomal protein S6 is optimized by geometric overlap of two competing folding nuclei: they both include the central β-strand 1. In this way, folding of one nucleus catalyzes the formation of the other, contributing to make the folding transition more concerted overall. The experimental evidence is provided by an extended set of circular permutations of S6 that allows quantitative analysis of pathway plasticity at the level of individual side chains. Because similar overlap between competing nuclei also has been discerned in other proteins, we hypothesize that the coupling of several small nuclei into extended "supernuclei" represents a general principle for propagating folding cooperativity across large structural distances. Proteins are highly evolved molecules that are selected and optimized by the functional requirements of the cell. The optimization, however, works not only on the native structures but also involves their physical properties (1Oliveberg M. Wolynes P.G. Q. Rev. Biophys. 2005; 38: 245-288Crossref PubMed Scopus (242) Google Scholar). A well known example is protein stability, i.e. the equilibrium between folded states and the denatured counterparts, that needs to be maintained within certain limits to assure functionality and yet allow degradation. Protein sequences are moreover tuned to resist aggregation and erroneous interactions with other biomolecules. In part such tuning is achieved by electrostatic repulsion (2Chiti F. Calamai M. Taddei N. Stefani M. Ramponi G. Dobson C.M. Proc. Natl. Acad. Sci. U. S. A. 2002; 99: 16419-16426Crossref PubMed Scopus (252) Google Scholar, 3Sandelin E. Nordlund A. Andersen P.M. Marklund S.S. Oliveberg M. J. Biol. Chem. 2007; 282: 21230-21236Abstract Full Text Full Text PDF PubMed Scopus (58) Google Scholar) and negative design, i.e. side chains in the form of gatekeepers that specifically reduce sequence stickiness (4Otzen D.E. Kristensen O. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 9907-9912Crossref PubMed Scopus (173) Google Scholar) or otherwise obstruct unwanted interactions between or within proteins (4Otzen D.E. Kristensen O. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 9907-9912Crossref PubMed Scopus (173) Google Scholar, 5Richardson J.S. Richardson D.C. Proc. Natl. Acad. Sci. U. S. A. 2002; 99: 2754-2759Crossref PubMed Scopus (662) Google Scholar, 6Thirumalai D. Klimov D.K. Dima R.I. Curr. Opin. Struct. Biol. 2003; 13: 146-159Crossref PubMed Scopus (292) Google Scholar, 7Matysiak S. Clementi C. J. Mol. Biol. 2006; 363: 297-308Crossref PubMed Scopus (49) Google Scholar, 8Stoycheva A.D. Brooks III, C.L. Onuchic J.N. J. Mol. Biol. 2004; 340: 571-585Crossref PubMed Scopus (24) Google Scholar). At a more generic level, protein aggregation seems also to be prevented by the folding potential itself. The factors that govern structural specificity disfavor automatically non-native contacts between molecules and bias the proteins to aggregate by native-like interactions (4Otzen D.E. Kristensen O. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 9907-9912Crossref PubMed Scopus (173) Google Scholar, 9Silow M. Tan Y.J. Fersht A.R. Oliveberg M. Biochemistry. 1999; 38: 13006-13012Crossref PubMed Scopus (71) Google Scholar, 10Yang S. Cho S.S. Levy Y. Cheung M.S. Levine H. Wolynes P.G. Onuchic J.N. Proc. Natl. Acad. Sci. U. S. A. 2004; 101: 13786-13791Crossref PubMed Scopus (153) Google Scholar). The archetypical example of such aggregates is the domain swap (11Guo Z. Eisenberg D. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 8042-8047Crossref PubMed Scopus (79) Google Scholar, 12Bennett M.J. Choe S. Eisenberg D. Proc. Natl. Acad. Sci. U. S. A. 1994; 91: 3127-3131Crossref PubMed Scopus (460) Google Scholar). A seemingly different type of aggregation is the ordered assembly into fibrils driven by sequence signatures that allow linear propagation of non-native β-structure (13Fandrich M. Fletcher M.A. Dobson C.M. Nature. 2001; 410: 165-166Crossref PubMed Scopus (735) Google Scholar). In either case, aggregation relies on the exposure of amino acid segments that are normally hidden within the native structure, for example by local unfolding. There is growing evidence that proteins suppress such detrimental unfolding events by increasing the unfolding cooperativity (14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar, 15Dumoulin M. Canet D. Last A.M. Pardon E. Archer D.B. Muylder-mans S. Wyns L. Matagne A. Robinson C.V. Redfield C. Dobson C.M. J. Mol. Biol. 2005; 346: 773-788Crossref PubMed Scopus (96) Google Scholar, 16Nordlund A. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 10218-10223Crossref PubMed Scopus (85) Google Scholar). It is interesting to note that, unlike native structure and stability, cooperativity is a property that is primarily determined by the folding-energy landscape (14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar). The principle can be illustrated as follows. If the folding-energy landscape allows only one folding route, thermal motions of the native state would repeatedly lead to excursions along the same unfolding trajectory. Such narrow sampling of the conformational space could make the affected parts of the protein loose and susceptible to local unfolding by even modest fluctuations (14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar). If in contrast the energy landscape is tuned to have a broad, diffuse folding progression there is no preferred way of unfolding the protein: each microscopic unfolding attempt involves different parts of the structure (17Plotkin S.S. Onuchic J.N. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 6509-6514Crossref PubMed Scopus (93) Google Scholar). In effect, this uniform probability of unfolding will produce a native structure that is relatively "rigid" because the simultaneous occupancy of partly unfolded states that are matched for aggregation is minimized. From experimental studies of small two-state proteins it is apparent that most natural proteins belong to the latter category (18Jackson S.E. Fold. Des. 1998; 3: R81-R91Abstract Full Text Full Text PDF PubMed Scopus (847) Google Scholar). Folding seems optimized for high cooperativity manifested in transition-state structures, i.e. folding nuclei, that resemble diffuse versions of the native structures (14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar). Consistent with the idea that the diffuse transition-state structure is a biological adaptation, it can readily be changed by circular permutation into polarized, less cooperative counterparts where half of the protein is fully structured and the other half is disordered (19Lindberg M.O. Haglund E. Hubner I.A. Shakhnovich E.I. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 4083-4088Crossref PubMed Scopus (56) Google Scholar, 20Lindberg M.O. Oliveberg M. Curr. Opin. Struct. Biol. 2007; 17: 21-29Crossref PubMed Scopus (106) Google Scholar). Also the transition-state structure responds readily to extensive changes in the side-chain contacts as observed in comparative studies of sequence-divergent homologs (21Zarrine-Afsar A. Larson S.M. Davidson A.R. Curr. Opin. Struct. Biol. 2005; 15: 42-49Crossref PubMed Scopus (87) Google Scholar, 23Lappalainen I. Hurley M.G. Clarke J. J. Mol. Biol. 2008; 375: 547-559Crossref PubMed Scopus (47) Google Scholar). Even so, the factors governing folding cooperativity are yet poorly understood, and cooperativity is also the molecular trait of naturally evolved proteins that is most difficult to reproduce in silico and by de novo design. One possibility is that cooperativity is achieved by balancing long sequence separation between interacting residues with strong contacts. Such equalization of the folding probability across the protein structure has been seen to promote diffuse nuclei in both computational (17Plotkin S.S. Onuchic J.N. Proc. Natl. Acad. Sci. U. S. A. 2000; 97: 6509-6514Crossref PubMed Scopus (93) Google Scholar, 24Matysiak S. Clementi C. J. Mol. Biol. 2004; 343: 235-248Crossref PubMed Scopus (58) Google Scholar, 25Wu L. Zhang J. Wang J. Li W.F. Wang W. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2007; 75: 031914Crossref PubMed Scopus (9) Google Scholar) and experimental studies (14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar). Consistently circular permutations of S6 and SH3 show that the contribution of individual side chains to the folding nucleus is directly related to changes in sequence separation of the interacting side chains, implicating that chain entropy is indeed a responsive factor for tuning the folding trajectory. But there is more to it. The plasticity of the S6 folding reaction seems restrained to two competing pathways corresponding to nucleation in either half of the protein structure (19Lindberg M.O. Haglund E. Hubner I.A. Shakhnovich E.I. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 4083-4088Crossref PubMed Scopus (56) Google Scholar, 20Lindberg M.O. Oliveberg M. Curr. Opin. Struct. Biol. 2007; 17: 21-29Crossref PubMed Scopus (106) Google Scholar). It is further apparent that the competing nuclei of S6 are to some degree overlapping, providing a clue to how the folding cooperativity can be extended from one part of the structure to another (20Lindberg M.O. Oliveberg M. Curr. Opin. Struct. Biol. 2007; 17: 21-29Crossref PubMed Scopus (106) Google Scholar): strand 1 (β1) in the center of the β-sheet is part of both nuclei (see Fig. 1). To shed further light on how this putative coupling of cooperativity works, here we specifically investigate the behavior of the nuclei overlap. The study is based on φ-value analysis of a new, expanded set of S6 permutants that includes incisions between all six secondary structure elements. The fate of each part of the S6 structure is thus monitored and compared on six different settings of the folding-energy landscape, yielding statistics that are sufficiently exact to map out folding changes at the level of individual side chains. The results show that the majority of φ-values respond to circular permutation as predicted from changes in sequence separation. A distinct exception, however, are the φ-values in β1 that remain constant around 0.5. The insensitivity of β1 to pathway changes suggests that its side chains form an approximately equal number of interactions with each of the two S6 nuclei. One side of β1 is part the α1 nucleus, whereas the other is part of the α2 nucleus. Thus, when folding shifts between the α1 and α2 nuclei, the β1 contacts simply shift from one side to the other with little effect on the macroscopic φ-values. From a general perspective, this balanced shift of nucleating contacts around β1 provides a concrete example of how structural order can be propagated from one nucleus to the other without the accumulation of partly structured intermediates. On this basis, we conclude that folding cooperativity is a modular property that can be extended through protein structures by multiple, competing, folding nuclei that share structural overlap. Protein Engineering—All circular permutants of S6 are labeled according to the position of the incisions, and their amino acids are numbered according to the wild-type sequence, Protein Data Bank code 1RIS (26Lindahl M. Svensson L.A. Liljas A. Sedelnikova S.E. Eliseikina I.A. Fomenkova N.P. Nevskaya N. Nikonov S.V. Garber M.B. Muranova T.A. Rykonova A.I. Amons R. EMBO J. 1994; 13: 1249-1254Crossref PubMed Scopus (149) Google Scholar). The wild-type numeration was used for all point mutations in this study. The circular permutants P13-14 and P68-69 were designed and constructed as described previously (27Lindberg M.O. Tangrot J. Otzen D.E. Dolgikh D.A. Finkelstein A.V. Oliveberg M. J. Mol. Biol. 2001; 314: 891-900Crossref PubMed Scopus (52) Google Scholar), and the circular permutants P54-55, P33-34, and P81-82 were designed and constructed according to the procedures in Ref. 19Lindberg M.O. Haglund E. Hubner I.A. Shakhnovich E.I. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 4083-4088Crossref PubMed Scopus (56) Google Scholar. The genes designed for P33-34 and P81-82 were purchased from Entelechon. By these five constructs, all possible incisions between the secondary structure elements of S6 have been covered. The point mutations used for mapping out the interactions in the transition-state ensembles of the permuted proteins were chosen to cover all parts of the hydrophobic core. Protein Expression and Purification—Mutations were performed with the QuikChange site-directed mutagenesis kit (Stratagene), oligonucleotides were purchased from DNA Technology, and all mutations were confirmed by sequencing (eurofins mug operon). The mutant proteins were transformed and overexpressed in competent Escherichia coli strain BL21 or C41 DE3 and then purified by two-step precipitation followed by cation-exchange chromatography (CM-Sepharose) and gel filtration (Sephacryl S-100) as described previously (28Otzen D.E. Kristensen O. Proctor M. Oliveberg M. Biochemistry. 1999; 38: 6499-6511Crossref PubMed Scopus (181) Google Scholar). The buffer was 50 mm Tris, pH 7.5. The identity of the purified protein was confirmed by mass spectroscopy. Kinetic Measurements—Stopped-flow measurements and curve fitting were performed on SX-18MV and PiStar instruments (Applied Photophysics, Leatherhead, UK). The excitation wavelength was 280 nm, and the emission was collected with a 305-nm-cutoff filter. Mixing was 1 + 10, and the final protein concentration was 0.8 μm. All measurements were conducted at 25 °C in 50 mm MES 3The abbreviations used are: MES, 4-morpholineethanesulfonic acid; GdmCl, guanidinium chloride; wt, wild type. at pH 6.3 (Sigma) using GdmCl as denaturant (UltraPure, Invitrogen). Chevron Analysis—To minimize the effect of chevron curvatures at low and high GdmCl concentrations, the kinetic m-values were derived from the linear regime at the bottom of the chevron plots, i.e. midpoint ± 2 m, using the standard equation, where kfH2O and kuH2O are the refolding and unfolding rate constants at [GdmCl] = 0 m, and mf and mu are the slopes of the refolding and unfolding chevron limbs, respectively. Data analysis was performed with the software KaleidaGraph 4.0 and GraphPad Prism 4.0. φ-Value Analysis—By systematically truncating side chains while measuring the effects on the folding and unfolding kinetics it is possible to map out the interaction patterns in the transition-state ensemble (30Fersht A.R. Structure and Mechanism in Protein Science: a Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman and Co., New York1999Google Scholar). In essence, mutations that slow down the refolding reaction are considered to target stabilizing contacts in its structure. The strengths of these interactions are measured by the φ-values. A φ-value of 0 indicates that the targeted side chain experiences a denatured-like environment in the transition-state ensemble, whereas a φ-value of 1 indicates that it has a fully native-like environment. Fractional values of φ are thus taken to indicate the degree of native-like interactions, i.e. φ = 0.5 indicates that the truncated side-chain moieties form half of the native contacts in the folding transition state. To reduce the effects of extrapolation errors and transition-state shifts occurring at high [GdmCl] (29Oliveberg M. Acc. Chem. Res. 1998; 31: 765-772Crossref Scopus (79) Google Scholar), the φ-values (30Fersht A.R. Structure and Mechanism in Protein Science: a Guide to Enzyme Catalysis and Protein Folding. W. H. Freeman and Co., New York1999Google Scholar) were calculated from chevron fits (Equation 1) according to Equation 2, where A = 1 m and B = 4 m, referring to the GdmCl concentrations at which the refolding and unfolding rate constants were taken. The change of φ upon circular permutation was then calculated according to Equation 3. Δϕ = ϕwild type − ϕpermutant In the cases where the transition midpoints were too low to allow precise fits of the refolding limb, i.e. midpoints <2 m GdmCl, mf was locked to the average value of the permutant in question. The current procedure for calculating the φ-values is slightly different from that in Refs. 14Lindberg M. Tangrot J. Oliveberg M. Nat. Struct. Biol. 2002; 9: 818-822PubMed Google Scholar and 19Lindberg M.O. Haglund E. Hubner I.A. Shakhnovich E.I. Oliveberg M. Proc. Natl. Acad. Sci. U. S. A. 2006; 103: 4083-4088Crossref PubMed Scopus (56) Google Scholar) and in a few cases causes small deviations from previously published data. The magnitude of these differences, however, is within the experimental errors and has no significance for the interpretation of data. Data for mutations with ΔΔG < 0.7 kcal/mol were excluded together with data where the m-value changes produced artificially high values of ΔΔG, i.e. V40A and F60A in S6wt, L19A in P33-34, and F60A in P81-82 (see Tables 1, 2, 3, 4, 5 and 6). Notably derivation of φ according to Equation 2 emphasizes mainly the structures of the early transition-state ensembles. Analysis of the later transition states needs to include the downward kinks in the unfolding limb appearing at high [GdmCl] (28Otzen D.E. Kristensen O. Proctor M. Oliveberg M. Biochemistry. 1999; 38: 6499-6511Crossref PubMed Scopus (181) Google Scholar, 29Oliveberg M. Acc. Chem. Res. 1998; 31: 765-772Crossref Scopus (79) Google Scholar) (see data in Fig. 2). Slight shifts to parallel folding pathways upon point mutation were in some cases indicated by anti-Hammond behavior but are currently not possible to account for in an accurate manner. However, the error due to such shifts is likely to be small but could contribute to under-estimating the φ-values in the α1 nucleus (see scheme in Fig. 8).TABLE 1S6wtlogkfH2OlogkuH2O β‡log KH2OΔGD-NΔΔGD-NφφelementWild type2.64−1.26−3.630.570.693.421.836.278.971.38−1.34V6A1.86−1.49−2.000.410.792.041.903.865.343.640.37−0.370.51I8A1.61−1.41aValue set to average mf because MP <2 M.−1.940.570.731.841.923.564.824.170.200.100.450.43β1L10A1.83−1.41aValue set to average mf because MP <2 M.−1.670.510.701.672.013.504.374.620.420.720.32L19A2.42−1.41−2.220.500.742.431.914.646.362.611.01−0.230.25I26A1.86−1.35−2.690.660.672.272.004.555.943.030.51−0.060.400.33α1L30A2.03−1.56−2.710.780.672.032.344.745.313.660.470.410.34V37A2.39−1.42−2.250.510.742.411.934.656.312.660.98−0.220.27V40A2.64−1.37−3.480.580.703.141.956.138.230.741.27−1.17bData excluded because ΔΔGD-N largely due to m-value changes.0.27β2L48A2.65−1.32−2.980.450.753.181.775.638.320.651.33−1.17cData excluded because ΔΔGD-N <0.70.F60A2.54−1.36−2.740.430.762.961.795.287.741.231.19−1.01bData excluded because ΔΔGD-N largely due to m-value changes.L61A2.40−1.53−2.010.550.732.122.084.405.553.420.870.200.25Y63A2.30−1.41aValue set to average mf because MP <2 M.−1.800.570.711.941.984.115.083.910.890.460.210.28β3V65A2.16−1.55−2.430.580.732.152.134.585.643.330.61−0.090.38V72A2.59−1.34−2.790.530.722.881.875.387.561.421.25−0.690.17L75A2.30−1.39−2.670.500.732.631.894.976.892.080.91−0.660.410.25α2L79A2.27−1.41aValue set to average mf because MP <2 M.−0.920.540.721.611.953.194.214.780.861.260.17V85A2.51−1.31−1.250.480.732.101.793.765.513.461.210.680.08V88A2.39−1.21−1.780.380.762.631.594.186.882.091.19−0.260.150.13β4V90A2.42−1.29−1.400.350.792.331.643.826.122.861.140.000.16a Value set to average mf because MP <2 M.b Data excluded because ΔΔGD-N largely due to m-value changes.c Data excluded because ΔΔGD-N <0.70. Open table in a new tab TABLE 2P13-14logkfH2OlogkuH2O β‡log KH2OΔGD-NΔΔGD-NsφφelementΔLΔLwPseudo wt3.01−1.17aValue set to average mf because MP <2 M.0.070.570.671.691.742.944.291.842.35V6A1.39−1.17aValue set to average mf because MP <2 M.0.110.670.640.691.841.271.762.530.222.790.79−39.49−23.90I8A1.77−1.17aValue set to average mf because MP <2 M.0.710.810.590.541.981.061.372.930.603.940.440.51β1−16.61−14.12L10A2.32−1.17aValue set to average mf because MP <2 M.1.280.660.640.571.831.041.442.851.153.900.3116.253.97L19A2.80−1.17aValue set to average mf because MP <2 M.0.580.750.611.161.922.222.951.351.633.570.159.6511.03I26A2.88−1.17aValue set to average mf because MP <2 M.0.300.820.591.301.992.583.300.991.713.560.100.12α124.8215.68L30A2.64−1.17aValue set to average mf because MP <2 M.0.831.030.530.822.201.812.092.201.474.940.133.447.93V37A2.94−1.17aValue set to average mf because MP <2 M.0.990.670.641.061.841.952.691.601.773.670.05−1.09−1.09V40A3.05−1.17aValue set to average mf because MP <2 M.−0.060.710.621.651.883.114.200.101.882.79bData excluded because ΔΔGD-N <0.70.0.05β2——L48A2.97−1.17aValue set to average mf because MP <2 M.0.090.640.651.591.812.884.050.241.802.64bData excluded because ΔΔGD-N <0.70.——F60A2.93−1.17aValue set to average mf because MP <2 M.0.300.560.681.521.732.633.870.431.762.54bData excluded because ΔΔGD-N <0.70.——L61ANDNDNDNDNDNDNDNDNDNDNDNDND−3.96−2.75Y63A2.63−1.17aValue set to average mf because MP <2 M.0.910.660.640.941.831.722.391.911.463.550.240.24β3−3.07−5.28V65A2.41−1.17aValue set to average mf because MP <2 M.0.600.900.570.872.071.812.222.071.244.200.24−11.00−6.27V72A2.94−1.17aValue set to average mf because MP <2 M.0.540.500.701.441.672.403.650.641.772.55bData excluded because ΔΔGD-N <0.70.−24.54−13.12L75A2.11−1.17aValue set to average mf because MP <2 M.−0.310.590.661.371.762.423.480.810.942.061.470.86α2−3.41−10.85L79ANDNDNDNDNDNDNDNDNDNDNDNDND−12.04−6.87V85A2.58−1.17aValue set to average mf because MP <2 M.0.560.570.671.161.742.022.961.331.412.830.47−22.22−17.24V88A2.14−1.17aValue set to average mf because MP <2 M.−0.300.680.631.321.852.453.360.930.972.410.940.68β4−24.50−30.48V90A1.91−1.17aValue set to average mf because MP <2 M.−0.130.800.591.041.972.042.631.660.743.050.61−50.68−31.47a Value set to average mf because MP <2 M.b Data excluded because ΔΔGD-N <0.70. Open table in a new tab TABLE 3P33-34logkfH2OlogkuH2Oβ‡log KH2OΔGd-nΔΔGd-nφφelementΔLΔLwPseudo wt3.06−0.92−1.130.440.683.081.364.195.762.140.63V6A2.01−0.95aValue set to average mf because MP <2 m.0.300.380.721.291.321.712.413.351.061.800.48−42.43−28.71I8A2.12−0.95aValue set to average mf because MP <2 m.0.340.440.681.291.381.782.413.351.182.090.400.37β1−29.97−29.50L10A2.46−0.95aValue set to average mf because MP <2 m.0.760.510.651.171.451.702.183.581.512.790.22−15.63−15.31L19A2.87−0.86−0.790.500.632.701.363.655.040.722.011.21bData excluded because ΔΔGd-n largely due to m-value changes.5.873.77I26A2.91−0.91−0.670.560.622.441.473.584.571.202.001.580.130.13α13.3211.61L30A2.82−0.95aValue set to average mf because MP <2 m.0.220.520.641.771.472.603.312.451.882.320.1433.9417.80V37A2.96−0.87−1.120.440.663.101.314.085.81−0.052.090.65cData excluded because ΔΔGd-n <0.70.41.3841.38V40A3.01−0.87−1.300.480.643.201.344.305.99−0.232.140.61cData excluded because ΔΔGd-n <0.70.NDβ2——L48ANDNDNDNDNDNDNDNDNDNDNDNDND——F60A3.12−1.050.070.370.742.161.423.064.031.732.081.550.06——L61A2.87−0.93−0.100.410.692.221.342.974.161.601.941.530.183.683.68Y63A2.86−0.93−0.820.510.652.561.433.674.790.971.931.210.270.19β37.363.41V65A2.70−0.88−0.010.380.702.161.262.724.031.731.821.510.27−4.75−0.53V72A2.95−0.82−0.280.440.652.571.263.234.800.962.131.470.02−24.54−11.70L75A2.61−1.04−0.480.390.732.181.423.104.081.681.581.060.570.30α22.30−9.12L79A2.31−0.95aValue set to average mf because MP <2 m.0.780.410.701.121.361.522.103.661.362.420.30−16.53−7.69V85A2.80−0.95aValue set to average mf because MP <2 m.0.460.460.671.671.402.343.122.641.862.280.15−27.26−19.76V88A2.48−0.95aValue set to average mf because MP <2 m.−0.430.480.672.041.422.903.821.941.531.470.420.39β4−24.50−31.74V90A2.30−0.95aValue set to average mf because MP <2 m.−0.500.410.702.061.362.803.851.911.351.150.60−50.68−31.47a Value set to average mf because MP <2 m.b Data excluded because ΔΔGd-n largely due to m-value changes.c Data excluded because ΔΔGd-n <0.70. Open table in a new tab TABLE 4P54-55logkfH2OlogkuH2Oβ‡log KH2OΔGd-nΔΔGd-nφφelementΔLΔLwPseudo3.30−0.95−3.400.690.584.091.646.709.362.35−0.64V6A2.44−1.20−2.360.640.652.621.834.805.983.381.250.190.57−42.43−28.71I8A2.48−1.06−2.140.720.602.591.784.625.923.441.420.740.400.39β1−29.97−29.50L10A2.94−1.12−1.260.740.602.261.864.205.164.201.821.700.18−15.63−15.31L19A3.26−0.97−2.040.650.603.261.625.297.461.902.280.560.054.583.12I26A3.01−0.91−2.890.770.543.511.685.908.031.332.100.190.230.14α13.326.23L30A3.21−1.08−1.510.580.652.841.664.726.492.872.130.800.1413.707.68V37A3.24−0.94−1.930.500.653.581.445.178.191.172.300.080.0718.0218.02V40A3.28−0.94−3.200.670.584.021.616.479.200.162.34−0.51bData excluded because ΔΔGd-n <0.70.0.07β2——L48A3.32−0.96−2.970.630.603.961.596.299.060.302.36−0.45bData excluded because ΔΔGd-n <0.70.——F60A3.17−0.94−2.780.630.603.791.575.968.670.692.23−0.26bData excluded because ΔΔGd-n <0.70.——L61A3.22−1.02−1.280.590.632.791.614.496.392.972.201.090.0813.8112.11Y63A3.24−1.04−1.420.550.652.921.594.656.672.692.190.790.100.12β320.8315.65V65A3.11−1.03−1.450.540.652.901.574.556.622.742.080.730.177.148.78V72A3.26−0.91−2.290.630.593.601.545.558.221.142.350.240.00−24.54−11.62L75A2.98−1.10−2.740.640.633.291.745.737.531.831.88−0.200.510.25α22.61−8.96L79A2.75−1.05−1.490.770.582.331.824.245.334.031.701.580.23−16.53−7.61V85A3.17−1.08−1.920.680.612.901.765.106.622.742.090.790.15−27.26−19.76V88A3.02−1.12−3.250.720.613.401.846.277.771.591.90−0.360.610.44β4−24.50−31.74V90A2.92−1.20−2.790.660.653.081.865.717.032.331.72−0.160.56−50.68−31.47a Value set to average mf because MP <2 m.b Data excluded because ΔΔGd-n <0.70. Open table in a new tab TABLE 5P68-69logkfH2OlogkuH2Oβ‡log KH2OΔGD-NΔΔGD-NφφelementΔLΔLwPseudo wt2.72−1.27−2.520.650.662.721.925.246.911.450.08V6A1.64−1.24aValue set to average mf because MP <2 m.−1.540.760.621.592.003.174.032.880.401.500.43−34.09−23.49I8A1.66−1.24aValue set to average mf because MP <2 m.−1.420.780.611.522.023.083.873.050.421.720.380.37β1−25.76−24.60L10A1.81−1.24aValue set to average mf because MP <2 m.−0.500.640.661.231.882.323.133.790.572.060.31−12.77−12.83L19A2.33−1.15−1.310.600.662.081.753.645.291.631.181.080.21−2.95−2.80I26A2.32−1.21−1.810.630.662.251.844.135.711.201.110.700.350.29α1−5.30−3.04L30A2.10−1.24aValue set to average mf because MP <2 m.−1.520.730.631.841.973.624.672.250.861.400.311.40−0.63V37A2.40−1.10−1.220.610.652.111.713.625.371.541.301.210.12−1.09−1.09V40A2.70−1.25−2.240.630.662.631.884.946.690.221.460.29bData excluded because ΔΔGD-N <0.70.0.12β2——L48A2.71−1.22−1.910.540.692.621.764.616.660.251.490.26bData excluded because ΔΔGD-N <0.70.——F60A2.68−1.26−1.800.550.702.471.814.476.280.631.420.40bData excluded because ΔΔGD-N <0.70.——L61A2.46−1.24aValue set to average mf because MP <2 m.−0.180.490.721.531.722.643.883.031.221.760.120.250.43Y63A2.35−1.24aValue set to average mf because MP <2 m.−0.700.600.671.651.843.044.202.721.111.720.170.18β31.211.01V65A2.18−1.24aValue set to average mf because MP <2 m.−0.720.570.681.601.812.904.062.860.941.580.251.360.98V72A2.58−1.19−2.210.700.632.531.904.796.410.501.390.60bData excluded because ΔΔGD-N <0.70.−2.191.55L75A2.32−1.14−1.440.730.612.001.883.755.081.831.171.500.160.14α210.590.61L79A2.33−1.24aValue set to average mf because MP <2 m.−0.270.750.621.311.992.603.333.591.102.730.12−16.53−5.62V85A2.39−1.24aValue set to average mf because MP <2 m.−0.650.670.651.601.913.044.062.861.152.020.13−27.20−19.73V88A2.33−1.28−1.730.640.672.111.924.065.361.551.050.840.350.27β4−24.50−31.72V90A2.17−1.24aValue set to average mf because MP <2 m.−1.390.630.661.911.863.564.852.070.931.110.33−50.68−31.47a Value set to average mf because MP <2 m.b Data excluded because ΔΔGD-N <0.70. Open table in a new tab TABLE 6P81-82logkfH2OlogkuH2Oβ‡log KH2OΔGD-NΔΔGD-NφφelementΔLΔLwPseudo wt2.64−1.20aValue set to average mf because MP <2 m.−1.080.700.631.971.893.725.151.441.70V6A1.63−1.20aValue set to average mf because MP <2 m.−0.110.840.590.852.041.732.222.920.433.260.39−23.93−16.41I8A1.63−1.20aValue set to average mf because MP <2 m.−0.380.820.591.002.022.012.612.540.442.910.450.39β1−17.78−18.36L10A1.98−1.20aValue set to average mf because MP <2 m.0.820.580.670.651.781.161.713.440.793.150.31−13.96−11.43L19A2.43−1.20aValue set to average mf because MP
Referência(s)