Protein Science (1995), 4:2138-2148. Cambridge University Press. Printed in the USA.
`Copyright © 1995 The Protein Society
`
`Denaturant m values and heat capacity changes:
`Relation to changes in accessible surface
`areas of protein unfolding
`
`JEFFREY K. MYERS, C. NICK PACE, AND J. MARTIN SCHOLTZ
`Department of Biochemistry and Biophysics, Department of Medical Biochemistry and Genetics, and
`Center for Macromolecular Design, Texas A&M University, College Station, Texas 77843
`
`(RECEIVED May 15, 1995; AccEPTED July 13, 1995)
`
`Abstract
`
`Denaturant m values, the dependence of the free energy of unfolding on denaturant concentration, have been col(cid:173)
`lected 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 toR = 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 (~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 mech(cid:173)
`anism, the amount of surface exposed to solvent upon unfolding is a main structural determinant for both m
`values and ~CP.
`
`Keywords: denaturation; guanidine hydrochloride; heat capacity changes; m values; protein folding; protein sta(cid:173)
`bility; solvent-accessible surface area; urea
`
`It has been known for many years that proteins can be unfolded
`in aqueous solution by high concentrations of certain reagents
`such as guanidine hydrochloride or urea. Denaturation with
`these chemicals is one of the primary ways of measuring the con(cid:173)
`formational stability of proteins and comparing the stabilities
`of mutant proteins. The use of these two denaturants is ex(cid:173)
`tremely widespread (Pace, 1986), even though the exact nature
`of the molecular interaction of denaturant molecules with pro(cid:173)
`tein surfaces is not well understood. It is known from solubil(cid:173)
`ity and transfer experiments with model compounds that the
`interaction of urea and Gdn HCl with the constituent groups of
`proteins is more favorable than the interaction of those groups
`with water (Tanford, 1970). These denaturants alter the equi-
`
`Reprint requests to: C. Nick Pace or J. Martin Scholtz, Department
`of Medical Biochemistry and Genetics, Texas A&M University, College
`Station, Texas 77843-1114; e-mail: pace@biovax.tamu.edu or jm-scholtz
`@tamu.edu.
`Abbreviations: Gdn HCl, guanidine hydrochloride; LEM, linear ex(cid:173)
`trapolation method; SPDS, solvent perturbation difference spectros(cid:173)
`copy; .:lASA, change in solvent-accessible surface area; .:lASAnp•
`.:lASApol• the nonpolar and polar contributions to .:lASA; .:lCp, dena(cid:173)
`turation heat capacity changes; DSC, differential scanning calorimetry;
`RNase, ribonuclease.
`
`librium between the native (folded) and denatured (unfolded)
`states of the protein:
`
`p,. u.
`
`The starting point for analysis of the free energy of the unfold(cid:173)
`ing reaction is:
`
`~G =- RT1n(UIF),
`
`(I)
`
`where F is the concentration of protein in the folded or native
`conformation, and U is the concentration of protein in the un(cid:173)
`folded or denatured state at a particular denaturant concen(cid:173)
`tration. The relative concentrations of F and U can be easily
`determined from studies where spectral probes are used to mon(cid:173)
`itor the conformational state of the protein (see Pace, 1986).
`Naturally, Equation 1 only works if the protein molecules are
`in either one of two conformational states (a two-state unfold(cid:173)
`ing reaction), which seems to be true for most small, globular
`proteins. If a three-state unfolding reaction is involved, or if the
`transition involves dimers or higher order species, an expression
`similar to Equation 1 can be used to determine ~G for the tran(cid:173)
`sition in question (see the Materials and methods for the dimer
`
`2138
`
`CSL EXHIBIT 1033
`CSL v. Shire
`
`Page 1 of 11
`
`

`

`Denaturant m values and heat capacity changes
`
`2139
`
`case). The free energy of unfolding so obtained is plotted against
`denaturant concentration in the transition region, and the free
`energy of unfolding in the absence of denaturant, .6GH2°, is
`determined by extrapolating back to zero denaturant concentra(cid:173)
`tion using one of several extrapolation procedures.
`The interaction of denaturants like urea or Gdn HCI with pro(cid:173)
`teins shows a dependence of the free energy of unfolding on the
`molar concentration of denaturant that appears to be linear, at
`least at moderate to high denaturant concentrations where the
`transition typically occurs. This has led to the widespread use
`of the linear extrapolation method to estimate the conforma(cid:173)
`tional stability of the protein in the absence of denaturant. Ap(cid:173)
`plication of this method gives two parameters, the free energy
`of unfolding at zero denaturant concentration (the intercept,
`.6GH20) and the dependence of free energy on denaturant con(cid:173)
`centration (the slope, which has been given the symbol m by
`Greene & Pace [I974)):
`
`.6G = .aGH20 - m [denaturant].
`
`(2)
`
`There are other methods that have been used to extract stabil(cid:173)
`ity parameters from denaturation data, two of which derive
`from Tanford. Although this paper will concentrate on the pa(cid:173)
`rameter m from the LEM, these other methods deserve mention
`here as well, because all three of these alternative methods pre(cid:173)
`dict an upward curvature in the dependence of .6G on denatur(cid:173)
`ant resulting in a larger estimate of .6GH20 than determined by
`the LEM.
`The denaturant binding model (Aune & Tanford, 1968) as(cid:173)
`sumes a discrete number of binding sites on the protein molecule
`for denaturant. The protein unfolds with increasing denaturant
`concentration because more binding sites are exposed in the un(cid:173)
`folded form than in the folded form. If the sites are equivalent
`and noninteracting, then
`
`(3)
`
`where .6n is the difference in the number of binding sites between
`U and F, k is the equilibrium binding constant (assumed equiv(cid:173)
`alent for all sites), and a is the activity of denaturant. In this
`method, the parameters .6GH20 and .6n are somewhat sensitive
`to the choice of k (Pace, I986). Binding constants for the de(cid:173)
`naturation of proteins and peptide helices and from the study
`of denaturant interaction with model compounds are not in ex(cid:173)
`act agreement, so the proper binding constants to use for urea
`and Gdn HCI are not clear (Pace, I 986; Makhatadze & Privalov,
`I 992; Scholtz et al., I995, and references therein). Evidence for
`specific binding of denaturant molecules to protein is not very
`strong in any case. The very weak binding of denaturant leads
`to thermodynamic inconsistencies when a stoichiometric bind(cid:173)
`ing model is applied (Schellman, I 987).
`Another method by Tan ford (I 970) makes use of model com(cid:173)
`pound data on the solubility or transfer of amino acid analogs
`from water to aqueous urea or Gdn HCI solutions. By utilizing
`the following thermodynamic cycle:
`
`FH20 <-----+ UH 20
`AGtr,f t
`
`Fden <-----+ Uden
`AG
`
`one finds .6G- .6GH20 = .6G1,,u- .6G1r.J· The difference be(cid:173)
`tween .6G,,,u and .6Gtr.f depends only on the groups exposed to
`solvent upon unfolding. If we let rx; represent the average frac(cid:173)
`tional change in exposure of groups of type i, then
`
`(4)
`
`where n; is the total number of groups in the protein and
`Og1,,; is the free energy of transfer of one group from water
`to denaturant as determined from model compound data. For
`simplicity, the right side of Equation 4 is usually changed to
`.6rx l:; n;Dg1,,; where .6rx represents the average change in expo(cid:173)
`sure of all protein groups (Pace, I 986). Thus, the equation takes
`the final form:
`
`(5)
`
`This analysis generates .1G H2o and .6rx, which represent the
`conformational stability of the protein in the absence of dena(cid:173)
`turant and the average change in accessibility of the protein
`groups upon denaturation, respectively.
`A variation on this method was employed by Staniforth et al.
`(I 993), in which the free energies of transfer from water to de(cid:173)
`naturant solution of model compounds were introduced into the
`analysis as follows:
`
`where n is the number of internal side chains exposed during
`unfolding, and .6Gsm and Kden are empirical constants repre(cid:173)
`senting the transfer behavior of internal side chains from water
`to denaturant, calculated from solubility data for model com(cid:173)
`pounds and the composition of the protein being studied.
`These three physical models require additional parameters
`representing the binding behavior of denaturant or the transfer
`behavior of protein groups into denaturant, as opposed to the
`empirical LEM, which has only two parameters. In any case,
`whether the binding model, Tanford's method, or the method
`of Staniforth et al. is used to analyze denaturation data, two key
`parameters are obtained: (I) the free energy of unfolding in the
`absence of denaturant, and (2) a parameter .6n, .6cx, or n, which
`is proportional to the amount of protein becoming exposed to
`solvent upon unfolding. In an analogous way, the LEM gives
`two parameters: the free energy of unfolding in the absence of
`denaturant and them value. Consequently, we might expect m
`to be proportional to the amount of protein becoming exposed
`to solvent when the protein unfolds.
`According to Schellman (1978), who first gave a theoretical,
`thermodynamic treatment of the interaction of denaturant mol(cid:173)
`ecules with proteins, them value should be proportional to the
`surface area of protein exposed to solvent upon unfolding. A
`similar conclusion was reached by Alonso and Dill (199I) with
`their statistical thermodynamic model for the action of solvents
`on protein stability. To our knowledge, no one has attempted
`to correlate experimental m values with changes in accessible sur(cid:173)
`face area upon unfolding, which are readily calculated from
`crystal structures using well-known methods (e.g., Lee & Rich-
`
`Page 2 of 11
`
`

`

`2140
`
`J.K. Myers et at.
`
`Table 1. Characteristics of 45 proteins that have m values and crystal structures available A
`
`Protein name
`
`PDB
`
`# Res.
`
`# Crosslinks
`
`AASA
`
`AASAnp
`
`AASApot Gdn HCl m
`
`Urea m
`
`Ovomucoid third domain (turkey)
`lgG binding domain of protein G
`BPTI (A30, AS!)
`BPTI (V30, AS!)
`SH3 domain of q,-spectrin
`Chymotrypsin inhibitor 2
`Calbindin D9K
`Ubiquitin
`HPr (B. subtilis)
`Barstar
`Lambda repressor (N-terminal)
`Cytochrome c (tuna)
`Cytochrome c (horse heart)
`Ribonuclease Tl
`Arc repressor 8
`FK binding protein (human)
`!so-l-cytochrome c (yeast)
`Thioredoxin (£. coli)
`Barnase
`Ribonuclease A
`ROP
`Che Y (£. coli)
`Lysozyme (hen egg white)
`Lysozyme (human)
`Fatty acid binding protein (rat)
`Staphylococcal nuclease
`lnterleukin 1-13
`Apomyoglobin (horse)
`Apomyoglobin (sperm whale)c
`Metmyoglobin (horse)
`Metmyoglobin (sperm whale)
`Ribonuclease H
`Dihydrofolate reductase (£. coli)
`T4 lysozyme (T54, A97)
`Gene V protein 8
`Adenylate kinase (porcine)
`HIV-1 protease 8
`SIV protease 8
`Trp aporepressor 8
`a-Chymotrypsin
`Chymotrypsinogen A
`Tryptophan synthase, a-subunitc
`13-Lactamasec
`Pepsinogenc
`Phosphoglycerate kinase (yeast)
`
`ICHO
`lPGB
`7PTI
`lAAL
`lSHG
`2CI2
`3ICH
`!UBI
`2HPR
`!BTA
`ILMB
`5CYT
`2PCB
`9RNT
`!PAR
`IFKD
`IYCC
`2TRX
`IRNB
`9RSA
`IROP
`3CHY
`6LYZ
`ILZI
`IIFC
`2SNS
`511B
`IYMB
`5MBN
`IYMB
`5MBN
`2RN2
`4DFR
`IL63
`IBGH
`3ADK
`IHVR
`IS IV
`3WRP
`4CHA
`2CGA
`IWSY
`3BLM
`2PSG
`3PGK
`
`56
`56
`58
`58
`62
`64
`75
`76
`88
`89
`102
`103
`104
`104
`106
`107
`108
`108
`110
`124
`126
`129
`129
`130
`131
`149
`!53
`!53
`!53
`!53
`153
`155
`!59
`163
`174
`194
`198
`198
`214
`241
`245
`268
`270
`370
`415
`
`3
`0
`2
`2
`0
`0
`0
`0
`0
`0
`0
`
`2
`0
`0
`
`I
`0
`4
`0
`0
`4
`4
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`0
`5
`5
`0
`0
`3
`0
`
`3,559
`4,102
`4,288
`4,098
`4,560
`4,868
`6,162
`6,075
`7,090
`7,402
`6,944
`9,756
`9,671
`8,503
`9,232
`9,015
`9,170
`9,123
`9,507
`10,117
`10,246
`11,479
`11,406
`11,809
`12,145
`12,058
`13,971
`13,557
`13,659
`14,735
`14,811
`13,726
`13,639
`14,840
`13,512
`16,759
`18,834
`17,939
`18,245
`21,699
`21,933
`23,147
`25,012
`35,002
`36,125
`
`2,257
`2,933
`2,949
`2,986
`3,439
`3,552
`4,361
`4,538
`5,212
`5,913
`4,917
`6,732
`6,909
`5,014
`6,152
`6,624
`6,235
`6,828
`6,706
`6,819
`7,072
`8,303
`7,474
`8,067
`8,411
`8,465
`10,180
`9,909
`9,791
`10,862
`10,726
`9,615
`10,286
`10,429
`9,644
`11,924
`12,564
`13,633
`13,187
`15,714
`15,586
`17,097
`17,923
`25,607
`26,212
`
`1,302
`1,169
`1,339
`1,112
`1,121
`1,316
`1,801
`1,537
`1,878
`1,489
`2,027
`3,024
`2,761
`3,488
`3,080
`2,391
`2,935
`2,295
`2,801
`3,638
`3,174
`3,176
`3,932
`3,742
`3,734
`3,593
`3,791
`3,648
`3,868
`3,873
`4,085
`4,111
`3,353
`4,411
`3,868
`4,835
`6,270
`4,306
`5,058
`5,985
`6,347
`6,050
`7,089
`9,395
`9,913
`
`58o•
`1,800b
`1,200'
`1,500'
`1,880d
`J,890C
`
`1,750g
`
`2,400i
`2,400k
`2,8oom
`3,010"
`2,560P
`3,270'
`
`3,400"
`3,310'
`4,400Z
`3,JOOP
`2,400dd
`2,26oec
`2,330ff
`3,460hh
`4,470jj
`6,830kk
`5,58omm
`
`3,710qq
`2,600qq
`4,5ooss
`
`5,500""
`3,6ooww
`4,8ooxx
`
`4, 100"
`4,440aaa
`
`7,200ddd
`
`9, 700cec
`
`25o•
`
`590•
`620b
`
`1,050i
`1,250j
`1,0901
`
`1,200"
`1,210q
`1,910'
`1,4601
`1,430v
`1,300x
`I ,940aa
`1,100'"
`
`J,600CC
`I ,290gg
`
`1,770ii
`2,380kk
`
`I ,800°"
`2,040PP
`2, 140qq
`I ,460qu
`I ,930"
`1,900"
`2,000""
`
`2,050YY
`I ,880YY
`2,900Z7
`2,070"
`2,03oaaa
`3,750bbb
`3,210ddd
`7,800fl
`
`1,360h
`1,160i
`1,460i
`
`1,730°
`1,270'
`1,600'
`
`1,370w
`J,660Y
`I ,650bb
`1,230°
`I ,89octct
`
`1,540°
`1,5801i
`
`2,320ll
`I ,890""
`
`I ,870"
`2,770°
`
`2,570vv
`
`3,020"
`
`4,6ooccc
`
`6,090°
`7,5oorrr
`
`~---- - - - - - - - - · · -
`
`A For each protein, the PDB file code, number of residues, and number of disulfides or covalent heme-protein crosslinks is shown. AASA and
`the nonpolar and polar contributions are calculated as described in the text. The last three columns give experimental m values for Gdn HCl or
`urea denaturation and the observed ACp for each protein, when available. AASA values are in A2 , m values in cal!(mol· M), and ACP in call(mol· K)
`8 Dimer.
`c Three-state mechanism.
`a Swint and Robertson, 1993; b O'Neil et al., 1995; c Hurle et al., 1990; d Viguera et al., 1994; e Jackson et al., 1993; 1 Akke and Forsen, 1990;
`g Khorasanizadeh et al., 1993; h Wintrode et al., 1994; i Scholtz, 1995; i Agashe and Udgaonkar, 1995; k Lim et al., 1992; 1 Marqusee and Sauer,
`1994; m McLendon and Smith, 1978; "Hagihara et al., 1994; 0 Privalov and Gill, 1988; P Pace et al., 1990; q Shirley et al., 1992; 'Yu et al., 1994;
`s Bowie and Sauer, 1989; 1 Egan et al., 1993; u Ramdas et al., 1986; v Bryant et al., 1985; w Cohen and Pielak, 1994; x Kelley et al., 1987; Y San(cid:173)
`toro and Bolen, 1992; zclarke and Fersht, 1993; ••Pace et al., 1992; bbGriko et al., 1994; ccGreene and Pace, 1974; ddMunson et al., 1994;
`ee Filimonov et al., 1993; rr Saito and Wada, 1983; gg Ahmad and Bigelow, 1982; hh Taniyama et al., 1992; ii Heming et al., 1992; ii Ropson et al.,
`1990; kk Shortie and Meeker, 1986; n Carra et al., 1994; mm Craig et al., 1987; "" Makhatadze et al., 1994; 00 De Young et al., 1993; PP Barrick and
`Baldwin, 1993; qq Pace, 1975; "Kelly and Holladay, 1990; ss Dabora and Marqusee, 1994; tt Perry et al., 1987; ""Zhang et al., 1993; vv Hu et al.,
`1992a; ww Liang et al., 1993; xx Tian et al., 1988; YY Grant et al., 1992; zz Gittelman and Matthews, 1990; aaa Ahmad and Bigelow, 1986; bbb Stack(cid:173)
`house et al., 1988; ccc Yutani et al., 1991; ddd Mitchinson and Pain, 1985; eee Ritco-Vonsovici et al., 1995; rrr Murphy and Freire, 1992.
`
`Page 3 of 11
`
`

`

`Denaturant m values and heat capacity changes
`
`ards, 1971; Miller et al., 1987; Lesser & Rose, 1990). Here we
`examine the relationship between m values and accessible sur(cid:173)
`face areas and in the process hope to shed light on the interaction
`of denaturants with proteins, and on certain other aspects of
`protein denaturation.
`
`Results
`
`Change in surface area upon unfolding
`
`Table 1 shows the 45 proteins, gathered from the literature, that
`have m values from denaturation experiments and also have a
`crystal structure available, along with the number of residues
`and disulfide bonds present in each protein.
`The change in solvent-accessible surface area upon unfolding,
`as determined by the differences in solvent accessibility of the
`native form (calculated from the crystal structure) and the un(cid:173)
`folded form (as modeled by an extended polypeptide chain) is
`given in Table 1, column 5. The nonpolar and polar contribu(cid:173)
`tion to the total ~ASA are given in columns 6 and 7. The amount
`of area buried in each protein correlates very strongly (R = 0.99)
`with the number of residues in each protein, as shown in Fig(cid:173)
`ure I. Therefore, the ~ASA of a typical, globular protein can
`be estimated fairly accurately based simply on its size. On av(cid:173)
`erage, about 30o/o of the area buried in a folded protein is polar.
`Most of this is due to the burial of peptide groups.
`
`Correlations of m values and heat capacity
`changes with ~ASA
`
`Denaturant m values for Gdn HCl and urea are given in Ta(cid:173)
`ble I, columns 8 and 9. In Figure 2A and B, the dependence of
`denaturant m values on the change in accessible surface area
`upon unfolding is shown. There is a significant linear correlation
`in both cases, with an R value of 0.87 for Gdn HCl and 0.84
`for urea. The slopes of the linear regression lines are 0.11 call
`(mol·M·A2
`) and 0.22 call(mol·M·A2) for urea and Gdn HCl,
`respectively. These represent the contribution tom per square
`
`"'
`~
`<(
`(/)
`<(
`<1
`
`35000
`
`30000
`
`25000
`
`20000 '
`15000 r-
`10000 ~
`
`5000 ~
`
`0
`
`•
`
`AASA = -907 + 93(#res) R = 0.994
`
`100
`
`200
`
`300
`
`400
`
`Number of Residues
`
`Fig. 1. Dependence of the calculated change in solvent-accessible sur(cid:173)
`face area upon unfolding on the number of residues for the 45 proteins
`given in Table I.
`
`2141
`
`•
`
`0
`
`•
`
`•
`
`0
`0
`
`m = 859 + 0_22(/'J.ASA) R = 0.87
`
`•
`
`••
`..
`• • •
`·~ •
`
`~ • 0
`.§
`ni
`~
`E
`(3
`I
`c
`"C
`(9
`
`A
`
`10000
`
`8000
`
`6000
`
`4000
`
`'""" ~~f
`
`- L
`
`0
`
`5000
`
`1 0000 15000 20000 25000 30000 35000 40000
`
`I
`
`4000 r 8
`
`~ • 0
`.§
`ni
`~
`E
`(1)
`~
`::J
`
`3000 f_
`I·
`I I
`
`2000
`
`1000
`
`•
`
`•
`
`•
`•
`
`•
`•
`
`•
`•
`m = 374 + 0_11(MSA) R = 0.84
`
`0
`
`5000
`
`10000
`
`15000
`
`20000
`
`25000
`
`Q' . 0
`
`E
`ni
`~
`"-
`0
`<1
`
`8000
`
`7000 c
`
`6000
`
`5000
`
`4000
`
`3000
`
`2000
`
`1000
`
`•
`
`•
`
`0
`
`•
`
`••
`
`•• 0
`
`t.C, = -251 + 0.19(/'J.ASA) R = 0.97
`
`5000
`
`10000 15000 20000 25000 30000 35000 40000
`
`Fig. 2. Dependence of (A) m value for Gdn HCl denaturation, (B) m
`value for urea denaturation, and (C) heat capacity change upon unfold(cid:173)
`ing on ~ASA for the 45 proteins shown in Table I. Proteins with no
`crosslinks are shown as e and those with crosslinks as 0.
`
`Angstrom of buried surface and indicate that Gdn HCl is twice
`as effective as a denaturant than is urea.
`Although not the focus of this paper, denaturation heat ca(cid:173)
`pacity changes have been shown previously to be linearly depen(cid:173)
`dent on ~ASA for several proteins (Livingstone et al., 1991;
`Spolar et al., 1992). For our set of proteins, ~CP values were also
`collected (given in Table I, column 10, values in cal/[mol·K]) and
`correlated with the ~ASA values. The strong linear correlation
`(R = 0.97) is shown in Figure 2C. The average value of ~CP per
`residue is 14.2 ± 2.5 cal/(mol· K ·residue). The values range from
`a low of9.9 cal/(mol·K·residue) for RNase A to a high of 18.1
`cal/(mol· K ·residue) for sperm whale myoglobin.
`
`Page 4 of 11
`
`

`

`2142
`
`J.K. Myers et al.
`
`Table 2. Contribution of disulfide cross/inks to changes in accessible surface area (6ASA)
`from solvent perturbation difference spectroscopy (SPDS;a
`
`"lo Trp + Tyr accessibility
`
`# -S-S-
`
`Disulfides
`intact
`
`Disulfides
`broken
`
`Lysozyme
`RNase A
`RNase Tl
`
`4
`4
`2
`
`69
`68
`86
`
`93
`88
`95
`
`Difference
`
`ASA(unf}
`
`AASA
`
`24
`20
`9
`
`18,097
`17,001
`13,863
`
`4,343
`3,400
`1,248
`
`~ASA/
`disulfide
`
`1,086
`850
`624
`
`a Data on Trp and Tyr accessibility are from Pace et at (1992). Effects on AASA for folding are calculated as described in
`the text. ASA values are expressed in A 2 •
`
`Correlations using llASA values corrected for cross/inks
`
`It can be noticed in the plots of m against llASA that proteins
`with disulfide bonds or other crosslinks4 tend to have lower m
`values than expected based on their llASA (they fall below the
`regression line). This is expected because the presence of cross(cid:173)
`links in the unfolded state will result in a more compact unfolded
`state, thus reducing the accessibility of the unfolded polypep(cid:173)
`tide chain to solvent. Consequently, the AASA computed using
`our method would be too high relative to a protein with no cross(cid:173)
`links. To compensate for the effect of crosslinks, we employ
`three different ways to estimate the magnitude of the reduction
`in AASA per disulfide bond. In the first method, the results pro(cid:173)
`vided by measurements of the accessibility of aromatic groups
`in proteins using solvent perturbation difference spectroscopy
`have been analyzed. The presence of certain reagents will change
`the extinction coefficients of aromatic residues. Because the
`amount of this change is proportional to the accessibility of
`the aromatic group to the perturbant, one can get an idea of the
`solvent accessibility of aromatic residues using this technique.
`Table 2 shows SPDS results for three proteins, taken from Pace
`et a!. (1992), where the accessibility of the protein aromatic
`groups in three unfolded proteins is compared with and with(cid:173)
`out disulfides. Clearly, the average accessibility of the aromatic
`groups increases when the disulfides are broken. Assuming that
`this change in accessibility applies to all protein groups, then the
`change in square Angstroms is obtained by multiplying the to(cid:173)
`tal ASA of the extended chain by the percent difference. This
`total, divided by the number of disulfides, gives the average
`change in ASA of the unfolded state (and hence the change in
`AASA) per disulfide for the three proteins. The average of the
`three is about 900 A2 •
`Doig and Williams (1991) have estimated the change in
`LlASA per disulfide bond from the dependence of hydration
`np
`•
`o 2
`o 2
`free energy and ACP on crosslmks to be 590 A and 690 A , re-
`spectively. Because the fraction of total area buried that is non(cid:173)
`polar is about 0. 70, these values correspond to a change in total
`area of 850 ;\2 and 990 A2 per disulfide. These values are in
`
`4 The three cytochromes contain a covalently attached heme. group.
`For the purposes of the present analysis, we have assumed ~hat ~his cross(cid:173)
`linking can be treated in the same manner as a n.ormal d1sulf1de bond.
`This may be an oversimplification, but the paucity of data precludes a
`more detailed evaluation.
`
`good agreement with the value calculated from the SPDS results.
`The final method used to estimate the effect of crosslinks on
`4.ASA is discussed below.
`Therefore, based on the above evidence, corrections of AASA
`for the effect of disulfide crosslinks on the accessibility of the
`unfolded state were made at 900 A2 per disulfide bond and the
`m values and ACP values were correlated with the corrected
`AASA values. Linear correlation coefficients improve to 0.90
`for both urea and Gdn HCl and improve to 0.98 for ACP, as
`shown in Figure 3A, B, and C. The amount that a particular di(cid:173)
`sulfide bond reduces the accessibility of a protein in the unfolded
`state depends on several factors: the size of the loop connected
`by the crosslink, the position relative to other crosslinks, and
`the overall size of the protein. The fact that using a single value
`for all crosslinks, obviously a major simplification, improves all
`three correlations suggests that our treatment is at least a rea(cid:173)
`sonable approximation.
`
`Other correlations of interest
`
`If the mechanism of denaturation is similar for both urea and
`Gdn HCl, then the two m values should correlate with each
`other. For proteins with m values for both Gdn HCI and urea
`available, the two m values were correlated in Figure 4 (R =
`0.90), indicating that the same factors are affecting both m val(cid:173)
`ues. Because m values and llCP values both show a strong cor(cid:173)
`relation with AASA, they should correlate with each other.
`Figure 5A and B shows the relation of Gdn HCl and urea m val(cid:173)
`ues to the AC11 of the same protein; a good correlation is found
`for each.
`
`Nonlinear least-squares fitting of the data
`
`As mentioned above, previous studies have already noted a cor(cid:173)
`relation between llASA and heat capacity changes, llCP. By
`fitting data for the transfer of model compounds from the liq(cid:173)
`uid state to water, Spolar et al. (1992) determined an equation
`to estimate the ACP from nonpolar and polar AASA values:
`
`ACP == (0.32 0.04)(1lASAnp)- (0.14 ± 0.04)(1lASApo/).
`(7)
`
`Page 5 of 11
`
`

`

`Denaturant m values and heat capacity changes
`
`2143
`
`10000 A
`
`BODO
`
`£000
`
`4000
`
`2000
`
`E
`u
`I
`c:
`"0
`CJ
`
`8000
`
`6000
`
`4000
`
`2000
`
`•
`
`•
`
`..
`•
`• •
`•
`
`•• • •
`
`.. •
`
`Gdn HC\ m
`
`-110 + 2.3(urea m) R 0.90
`
`953 + 0.23(MSA) R = 0.90
`
`0
`
`5000
`
`1 0000
`
`15000 20000 25000 30000 35000 40000
`MSA(N)
`
`0
`
`500
`
`3000
`2500
`2000
`1500
`1 000
`urea m value (cal/moi•M)
`
`3500
`
`4000
`
`Fig. 4. Relationship between m values derived from denaturation with
`urea and Gdn HCI for proteins that had both m values available.
`
`0
`
`5000
`
`10000
`
`15000
`
`20000
`
`25000
`
`i
`
`8000
`
`7000 t c
`
`6000 [
`
`/
`
`/
`
`5000:
`'
`4000 l
`l
`/
`::::t / '
`
`y
`
`/
`
`100: ~ . ..__;_,_,ACP=·119+,0.20(AASA) R=0.98
`
`0
`
`5000
`
`1 0000
`
`15000 20000 25000 30000 35000 40000
`
`Fig. 3. Dependence of (A) m value for Gdn HCI denaturation, (B) m
`value for urea denaturation, and (C) heat capacity change upon unfold(cid:173)
`ing on LlASA for the 45 proteins in our data set, corrected for the ef(cid:173)
`fect of crosslinks by 900 A2 per crosslink (see text). Proteins with no
`crosslinks are shown as e and those with crosslinks as 0.
`
`By nonlinear fitting of data for the dissolution of solid model
`compounds, Murphy and Freire (1992) give as the best equation:
`
`f:..CP = (0.45 ± 0.02)(f:..ASA,p)
`
`(0.26 ± 0.03)(t:..ASApol>·
`
`(8)
`
`The heat capacity changes for the proteins in our set were cal(cid:173)
`culated using each of these equations and plotted versus the ob(cid:173)
`served heat capacities in Figure 6. Both methods fit the data well
`(R = 0.97), but as can be seen from the slope of the regression
`line (slope = 0. 72), Equation 8 overestimates the experimental
`
`values of t:..CP by about 250Jo. This is most likely due to the dif(cid:173)
`ferent methods of calculating t:..ASA (see Murphy & Freire,
`1992). However, the equation given by Spolar eta!. (1992) is no
`better for estimating f:..CP than simply using the equation from
`the fit in Figure 3C (R = 0.97), which uses the total t:..ASA and
`thus does not require a separation into polar and nonpolar com(cid:173)
`ponents. In addition, Equation 7 is only slightly better than sim(cid:173)
`ply multiplying the number of residues in a protein by 14 cal/
`mol· K ·res). Still more accurate is using the regression equation
`given in Figure 4C, which features t:..ASA corrected for cross-
`
`sz
`• 0
`E
`I
`
`"-
`(.)
`<1
`
`sz • 0
`
`E
`
`Q.
`(.)
`<1
`
`8000
`
`7000 A
`
`6000
`
`5000
`
`4000
`
`3000
`
`2000
`
`1000
`
`5000
`
`4000
`
`3000
`
`2000
`
`1000
`
`0
`
`0
`
`•
`
`•
`
`•
`•
`•
`~C0 = -336 + 0.66(Gdn HCI m) R =
`
`2000
`
`4000
`6000
`8000
`Gdn HCI m (cal/moi•M)
`
`10000
`
`B
`
`•
`
`•
`
`•
`
`= 117 + 1.1(urea m) R = 0.88
`
`1000
`
`3000
`2000
`urea m (cal/moi•M)
`
`4000
`
`f'ig. 5. Relationship between (A) Gdn HCI m values and (B) urea m
`values and heat capacity changes.
`
`Page 6 of 11
`
`

`

`2144
`
`8000 A
`
`~ 6000
`0
`
`E --"itt
`~ 4000
`en
`.0
`.9..
`c.
`()
`<l
`
`2000
`
`•
`
`•
`
`•
`
`•
`
`•
`
`••
`
`aCP obs=-123+0.96(aCP calc) R=0.97
`
`1000
`
`5000
`6000
`4000
`2000
`3000
`~CP (calc) (callmoi·K)
`
`7000
`
`8000
`
`8000 B
`
`~ 6000
`0
`
`E --"itt
`~ 4000
`en
`.0
`.9..
`c.
`()
`<l
`
`2000
`
`•
`
`•
`
`•
`
`•
`
`•
`
`••
`••
`
`aCP obs=-96+0.72(aCP calc) R=0.97
`
`1 000
`
`2000
`
`3000
`4000
`5000
`6000
`7000
`~CP (calc) (cal/moi·K)
`
`8000
`
`9000 1 0000
`
`Fig. 6. Comparison of observed heat capacity changes given in Ta(cid:173)
`ble I and heat capacity changes calculated using the equations given by
`(A) Spolar et al. (1992) and (8) Murphy and Freire (1992).
`
`links (R = 0.98). Nonlinear least-squares fitting of our data to
`equations in the form given provides:
`
`!::.CP = (0.28 ± 0.12)(!::.ASAnp)- (0.09 ± 0.30)(!::.ASApol),
`
`(9)
`
`which is within error of the values of Spolar et al. It gives a fit
`of the experimental data that is not significantly better, how(cid:173)
`ever (R = 0.97).
`For denaturant m values, nonlinear least-squares fitting was
`used to try to separate the contribution to m of nonpolar and
`polar surface:
`
`Gdn HCl m = (0.18 ± 0.35)(!::.ASAnp)
`+ (0.50 ± 0.87)(!::.ASApall
`
`Urea m = (0.15 ± O.l2)(!::.ASAnp)
`+ (0.08 ± 0.29)(!::.ASApal).
`
`(10)
`
`(11)
`
`J.K. Myers et a/.
`
`It appears from this that both denaturants interact favorably
`with both nonpolar and polar surfaces, but for Gdn HCl, the
`interaction with polar surfaces is more favorable than with non(cid:173)
`polar surfaces. This may be expected because Gdn HCl is ionic.
`The opposite appears to be true with urea, although the contri(cid:173)
`butions are closer in value. Note that the separation into polar
`and nonpolar components of m or !::.CP is difficult due to the
`high correlation of polar !::.ASA with nonpolar t::.ASA, result(cid:173)
`ing in large errors in the fitted parameters. The large errors in
`the respective fits hinder unequivocal interpretation .
`Fits of them values and !::.CP 'staking into account cross links
`gives the following:
`
`Gdn HCl m = (0.28 ± 0.03)
`
`x [!::.ASA- (792 ± 780)(# crosslinks)]
`
`(12)
`
`Urea m = (0.14 ± 0.01)
`x [!::.ASA- (995 ± 570)(# crosslinks)]
`
`(13)
`
`t::.CP = (0.19 ± 0.01)
`x [!::.ASA -
`
`(864 ± 370)(# crosslinks)]. (14)
`
`The disulfide bond corrections that maximize the fits are all close
`to the 900 A2 value calculated above.
`
`Discussion
`
`The correlations between m values and !::.ASA are good, but the
`variations in m values for proteins close in !::.ASA are quite large
`in some cases. We have addressed one possible cause, the effect
`of crosslinks on the ASA of the unfolded state, and the plots
`featuring the corrected D.ASA show improved correlation for
`Gdn HCl and urea m values and D.CP. But there are several
`other possible contributing factors.
`One major consideration in any experimental measure of
`t::.GH 20 is the possibility of deviation from a two-state unfold(cid:173)
`ing mechanism. Deviation from a two-state mechanism should
`lower them value (Pace, 1986). Some of the proteins in our set
`have been analyzed using a three-state model, but most have
`been analyzed using a two-state assumption. For only a few has
`the two-state model been confirmed experimentally. The most
`rigorous way of confirming the lack of intermediates present at
`equilibrium during thermal unfolding is to use differential scan(cid:173)
`ning calorimetry. The calorimetric enthalpy can be compared
`to the van't Hoff enthalpy, which is calculated from the data
`with the two-state assumption. If these two enthalpies agree, it
`is good evidence for a lack of appreciable amounts of intermedi(cid:173)
`ate species. But this is only good for thermal unfolding. There
`is always the possibility that intermediates are present in unfold(cid:173)
`ing by denaturants and not in thermal unfolding and there is no
`rigorous way of confirming a two-state denaturant unfolding
`mechanism. The best approach is to monitor denaturation by
`multiple spectral probes; CD, UV difference spectroscopy, flu(cid:173)
`orescence, and NMR have been used for this purpose. The co(cid:173)
`incidence of the unfolding curves is consistent with a two-state
`mechanism. For those proteins without such confirmation, a low
`m value may mean more than two equilibrium states. The vari(cid:173)
`able amount of intermediates present at equilibrium is one ex(cid:173)
`planation of the chang