J. Phys. Chem. 1982, 86,3866-3870
3866
mechanism IV 72-1 =
kzintexp( -
$)I
[Ac-] + [=A1:OH2+]
KA + [Ac-] KA + [H+] + [Ac-]
\
.
.,I:OH]
lH+] KA + [H+] + [Ac-]
)(
[Ac-]
K1-' + [H+] + [=Al:OH]
+ [=Al:OH] KA + [H+] + [Ac-]
KA + [H' KA + [H'] + [Ac-]
mechanism V: [HAC]+ [sA1--0]
[=A1:OH2+] + [Ac-]
)/(
1
[=Al:OH] + [HAC] + KAKl [=AkOH2+] + [Ac-]
))
+ k-2
(B4)
Surfactant-Polyelectrolyte Interactlons. 1. Blndlng of Dodecyltrlmethylammonium Ions by Sodium Dextran Sulfate and Sodium Poly(styrenesulfonate) in Aqueous Solution in the Presence of Sodlum Chkride KatumRu Hayakawa' and Jan C. 1.Kwak' Department of Chemistfy, Dalhousie University, &/ifax, Nova Scotia, B3H A13 (Received: Februaty 16, 1982; In Final Form: June 4, 19821
Isotherms for the binding of dodecyltrimethylammonium (DTA') ions by sodium dextran sulfate (NaDxS) and sodium poly(styrenesulfonate)(NaF'S) in the presence of added NaCl are reported. The binding isotherms were determined by using a potentiometric technique based on surfactant ion selective solid-state electrodes. The solid membranes used in the electrodes consist of poly(viny1chloride) (PVC) plasticized by bis(2-ethylhexyl) phosphate with a DTA-dodecyl sulfate carrier complex. The electrodes exhibit Nernstian response for DTA+ down to concentrations as low as 1 X mol kg-* even in the presence of a large excess of NaC1, allowing for sensitive and accurate free surfactant ion determinations. The binding of DTA+ to both polyanions is shown to be highly cooperative. The cooperativity parameter from the Zimm-Bragg theory may be estimated at 650 f 100 and 200 f 100 for the NaDxS and NaPS cases, respectively, and is independent of the NaCl concentration in both cases. The binding constant K of DTA+ to an isolated site on the polyanion is considerably larger in the PS-DTA system than in the DxS-DTA system, presumably because of differences in the hydrophobic/ hydrophilic properties of the two polymers. K is found to decrease strongly with increasing NaCl concentration; this decrease is similar in magnitude to the decrease in the critical micelle concentration (cmc) of dodecyltrimethylammonium bromide (DTAI3r)with increasing total counterion concentrationin the presence of added NaC1. Introduction The interaction between dissolved surfactants and polymers or colloidal particles is of interest in areas as diverse as polymer solubilization,lJ conformational change in bi0polymers,3-~and mineral flotation and flocculation, including coal flotation6,' and clay flocculation.g10 In the specific case of the binding of ionic surfactants by dissolved polymers, adsorption isotherms exhibiting a marked degree of cooperativity have been This behavior is similar to what is observed in the binding of dyes like acridine orange and proflavine by linear biopolymers.15J6 Surfactants may, in fact, be more suitable for such binding studies because they do not dimerize or associate below the critical micelle concentration (cmc), their hydropho'Permanent address: Department of Chemistry, Kagoshima University, Kagoshima, Japan.
bicity can be estimated, and interaction energies between the hydrophobic parts of the molecule can be compared (1) T. Isemura and A. Imanishi, J. Polym. Sci., 33, 337 (1958). (2) M. N. Jones, J. Colloid Interface Sci., 23, 36 (1967). (3) D. K. Sarker and P. Doty, R o c . Natl. Acad. Sci. U.S.A.,55, 981 (1966). (4) M. J. Grourke and J. H. Gibbs, Biopolymers, 5, 586 (1967). (5) I. Satake and J. T. Yang, Biochem. Biophys. Res. Commun., 54, 930 (1973). (6) V. L. Basenkova and Yu. N. Zubkova, Khim. Tuerd. Topl. (Moscow), 11, 137 (1977). (7) R. V. Przhegorlinskaya and Yu. N. Zubkova, Khim. Tuer. Topl. (Moscow), 12, 125 (1978). (8)H. S. Hanna and P. Somasundaran,J . Colloid Interface Sci., 70, 181 (1979). (9) J. P. Law, Jr., and G. W. Kunze, Soil Sci. Soc. Am. Proc., 30, 321 (1966). (10) W. F. Howler, Clays Clay Miner., 18, 97 (1970). (11) H. Arai, M. Murata, and K. Shinoda,J . Colloid Interface Sci., 37, 223 (1971).
0022-3654/82/2086-3866$01.25/00 1982 American Chemical Society
Surfactant-Polyelectrolyte Interactions
The Journal of Physical Chemistry, Vol. 86, No. 19, 1982 3887
to data obtained for micelle formation. Moreover, the chain length of the hydrophobic part of the surfactant molecule can be changed, adding an important variable to the binding studies. Recently developed surfactant selective electrode^^'-'^ have been successfully applied to the study of surfactant binding by polymer~.'~-'~a20"'The advantages of surfactant selective electrodes in binding studies include excellent sensitivity and reproducibility (normally far superior to results obtained from equilibrium dialysis experiments relying on spectrophotometric or volumetric concentration determinations), small required sample volume, and electrode tolerance including large excess of inorganic electrolyte. In this paper we use a solid-state, poly(viny1chloride) (PVC) based membrane selective for dodecyltrimethylammonium (DTA+)ions to study the binding of DTA' by the water-soluble polyions dextran sulfate (as its sodium salt, NaDxS) and poly(styrenesulfonate) (as NaPS) in the presence of NaCl in various concentrations. The binding isotherms obtained are discussed within the framework of a one-dimensional nearest-neighbor interaction mode1.12v22
Experimental Section Materials. Sodium poly(styrenesu1fonate) was kindly supplied by the Dow Chemical Co., Midland, MI (designation SC-1585, average molecular weight given as 5OOOOO). Sodium dextran sulfate (average molecular weight given as 500 OOO) was obtained from Pharmacia, Uppsala, Sweden. Purification procedures and concentration determinations of the final polyelectrolyte stock solutions are described in ref 23 and 24, respectively. Dodecyltrimethylammonium bromide (DTABr) was purchased from Sigma Chemical Co., St. Louis, MO, and purified by repeated recrystallizations from acetone. Analytical-grade sodium chloride was used without further purification. All aqueous solutions were prepared by weight from the polyelectrolytes, surfactant, and sodium chloride stock solutions in distilled and deionized water. All concentrations are given as molalities (mol/kg of HzO, m). Poly(viny1 chloride) (PVC, high molecular weight, Aldrich), bis(2ethylhexyl) phthalate (GR, Aldrich), and tetrahydrofuran (AR, BDH chemicals) were used without further purification. Potentiometry. The dodecyltrimethylammoniumcation (DTA+) selective membrane was prepared from 23 wt % PVC, 76 wt % bis(2-ethylhexyl) phthalate as plasticizer, and 0.7 wt 3'% carrier complex. The carrier complex used in this membrane was prepared by dissolving equivalent amounts of DTABr and sodium dodecyl sulfate (NaDS). NaDS was prepared from dodecyl alcohol purified by fractional distillation, through esterification with chlorosulfonic acid.25 The resulting white precipitate of DTA(12)I. Satake and J. T. Yang, Biopolymers, 15,2263 (1976). (13)I. Satake, T.Gondo, and H. Kimizuka, Bull. Chem. SOC. Jpn., 52, 361 (1979). (14)K. Shirahama, H.Yuaaa, and S. Sugimoto,Bull. Chem. SOC. Jpn., 54,375 (1981). (15)G. Schwarz, S.Klw,and W. Balthasar, Eur. J. Biochem., 12,454 (1970). (16)G. Schwarz and W. Balthasar, Eur. J. Biochem., 12,461 (1970). (17)C. Gavach and C. Bertrand, AnaI. Chim. Acta, 55, 385 (1971). (18)B. J. Birch and D. E. Clarke, Anal. Chim. Acta, 67,387 (1973). (19)S.G.Cutler, P. Meares, and D. G. Hall, J. Electroanal. Chem., 85, 145 (1977). (20)B. J. Birch, D. E. Clarke, R. S. Lee, and J. Oakes, Anal. Chim. Acta, 70,417 (1974). (21)K. Hayakawa, A. L. Ayub, and J. C. T. Kwak, 'Colloids and Surfaces", in press. (22)G. Schwarz, Eur. J. Biochem., 12, 442 (1970). (23)J. C. T.Kwak and R. C. Hayes, J. Phys. Chem., 79,265 (1975). (24)Y.M. Joshi and J. C. T. Kwak, Biophys. Chem., 8, 191 (1978).
-5
-4
-3
log mD
Figure 1. Response of the DTA' electrode to change in DTABr concentrations in (a) 4.80 X equivikg of H,O NaDxS solution containing 0.040 m NaCi and (b) 4.76 X equiv/kg of H20 NaPS soiutlon containing 0.041 m NaCi at 30 OC. Solid circles: calibration curve. Am,: the DTA" amount bound by polyelectrolyte. md: the corresponding equilibrium concentration.
DS complex was washed repeatedly with water followed by recrystallization from acetone. A mixture of 0.35 g of PVC, 1.15 g of bis(2-ethylhexyl) phthalate, and 10 mg of carrier complex was dissolved in about 6 mL of tetrahydrofuran by heating. The clear viscous solution was cast in a petri dish of 10-cm diameter. The solvent, tetrahydrofuran, was gradually evaporated off in air. A piece of the resulting poly(viny1 chloride) membrane was glued to the bottom of a hard PVC tube by using a tetrahydrofuran solution of PVC as an adhesive.26 The membrane potential was measured with the following cell: calomel electrodelagar, 3 m NH4Clltest solutionlPVC membranelreference solutionlagar, 3 m NHICllcalomel electrode where the reference solution was 0.001 m DTABr containing 0.01 m NaCl. A double-junction electrode was used by inserting a small glass tube with a pinhole in the upper part into the test and reference solutions. The NH4C1salt bridge was placed inside this small tube. The electromotive force (emf) of the cell was measured with a Keithley 616 digital electrometer with a stability of f O . l mV. The potential was monitored with a recorder. The plastic membrane has a superior selectivity for surfactant cations over inorganic ions as shown in ref 26 and from the results in the present paper (Figure 1). As an example of the excellent electrolyte tolerance of the electrode, Nernstian response similar to what is shown in Figure 1 is obtained from the critical micelle concentration down to 1.8 X 10" m DTABr even in the presence of 1.1m sodium chloride. All measurements were conducted a t 30 OC. ~~
(25)E.E.Dregar, Znd. Eng. Chem., 36, 610 (1944). (26)T.Maeda, M. Ikeda, M. Shibahara, T. Haruta, and I. Satake, Bull. Chem. SOC. Jpn., 54, 94 (1981).
3868
6;
10
0 5! t
Hayakawa and Kwak
The Journal of Physical Chemistty, Vol. 86, No. 79, 1982
I
a
2
-5
-4
iog mb
Flgurr 4. Blndlng Isotherms of DTABr by NaPS at 30 OC. mMa: (a) 0.021, (b) 0.041, (c) 0.082, (d) 0.176, (e) 0.444, (f) 1.12 mol kg-'. TABLE I : Binding Constant Ku and t h e Cooperative Parameter u
NaDxS iO3Ku/ (mol kg-') (mol-' k g )
NaPS
1OZ"aC1/
00 0
2
,
I
4
6
10 8
io4 mD/moi kg-'
Flguro 2. Dependence of the degree of binding @) (opencircles) and the equilibrium concentration of DTA+ ion (m,') (SOM circles) on added DTABr concentration (m,) at 30 OC. Parts a and b correspond to the condklons in Figure 1.
log
m,
f
Fwe 3. Blnding isotherms of DTABr by NaDxS at 30 O C . mw: (a) 0.006, (b) 0.010,
(C)
0.020, (d) 0.040, (e) 0.062, (f) 0.106 mol kg-'.
Results and Discussion The PVC membrane electrode shows Nernstian response for DTA+ down to about m DTABr depending on the added salt concentration, as exemplified in Figure 1. The excellent reproducibility of the emf allows us to use a plot of emf vs. log mD (mD is the DTABr molal concentration) as calibration curve. Calibration solutions with added NaCl at the same concentration as in the test solutions were used. The observed potentiometric curves for the solution mixtures under study deviate from the calibration curve because of adsorption by polyelectrolyte as shown in Figure 1,where Am is the amount of DTA+ bound to the polyions and mDfthe corresponding equilibrium molal concentration of DTA+. From the data as presented in Figure 1, the degree of binding, @,defined as the bound DTA+ concentration divided by the monomolal polyion concentration, can be calculated as a function of the added surfactant concentration and for a given added salt concentration (Figure 2). Figure 2a clearly shows that, at a given ionic strength, below a certain low concentration of DTA+ (1.5 X lo4 m in the case shown) DTA+ ions do not bind appreciably to DxS polyions, while above this concentration a major portion of the added surfactant ions bind to the polyion. The poly(styrenesu1fonate) (PS)-
0.605 0.995 1.99 3.98 6.20 10.6
36.3 24.0 14.2 8.28 6.15 4.25
1O4Ku/ (mol kg-') (mol-' kg) "aC1/
u
650 "O0
0.0206 0.0410 0.0819 0.176
0.444 1.115
u
13
8.1
200
5.4 3.0 2.0 1.6
i100
DTA+ system shows a similar behavior (Figure 2b), but binding starta at a lower DTA+ concentration. These results are conveniently represented in the form of binding isotherms (Figures 3 and 4), giving P as a function of the .free surfactant concentration at various added salt concentrations for DxS and PS. Figures 3 and 4 both exhibit the steep initial rise in @ at a given free surfactant concentration which is characteristic for cooperative binding. The fact that surfactant ions bind cooperatively to polywhere, e.g., the binding of inorganic counterions is anticooperative,n suggests that the binding of surfactant ions to polyions takes place not only because of electrostatic and/or chemical interactions between surfactant ion and polyion, but also through hydrophobic interactions between the bound surfactant ions. The Zimm-Bragg theory for the helix-coil transition, based on a nearest-neighbor interaction model,% provides a convenient formalism for a description of the cooperative binding of small ions by polyions.l%z With the assumption of nearest-neighbor interactions only between the hydrophobic parts of the bound surfactant ions, SchwarzZ2and Satake and Yang12derived the following relation for the degree of binding, 6, defined previously: 2P - 1 = (y - I)/[(I - y)2 + 4 y ~ - ' ] l / ~ y = KUmD'
(la) (1b)
where K is the binding constant between the surfactant and an isolated polyion binding site, and u is a cooperativity parameter which is determined by the hydrophobic interaction between two adjacently bound surfactants. y is equivalent to the parameter s in the Zi"-Bragg theory; Ku can be seen as the binding constant between a surfactant ion and a site adjacent to a site already occupied by a surfactant. Equation 1provides a two-parameter fit of the binding isotherms of Figures 3 and 4. The solid lines (27) J. Mattai and J. C. T.Kwak, Biochim. Biophys. Acta, 677, 303 (1981). (28) B. H.Zimm and J. K. Bragg, J. Chem. Phys., 31, 526 (1959).
Surfactant-Polyelectrolyte Interactions
in these figures are the best fits of the experimental data at lower degrees of binding to eq 1. Although both K and u can be determined this way, the strong cooperativity exhibited by the isotherms in Figures 3 and 4 makes the precise determination of u difficult, but Ku, which equals the reciprocal of the equilibrium free surfactant concentration, mDf, at 8 = 0.5, can be determined accurately. Values for Ku and for u are presented in Table I. In the case of the DxS-DTA isotherms (Figure 3) we note that eq 2 gives an excellent fit of the data for degrees of binding, 8, below approximately 0.6. The binding constant K of eq 2 is expected to be a function of the electric potential at the polyion surface. According to the condensation theory for polyelectrolyte solutions,29counterions will condense on the polyion to reduce the charge density of the polyion, t = e2/(4.rrekTb)(e is the proton charge, e is the bulk permitivity, k is B o h a n n ' s constant, T is the temperature, and b is the average linear charge separation on the polyion backbone) to an effective charge density, ten,of unity in the case of univalent counterions. Thus,the binding ("site" binding) of surfactant counterions would not affect the effective linear charge density parameter until @ reaches a value of 0.64 for dextran sulfate, based on a charge density parameter [ = 2.8 for this pol y i ~ n On . ~ ~the basis of this simple reasoning, we would expect K to be constant (at a given solution ionic strength) up to 8 = 0.64 and to decrease at higher degrees of binding. In addition, this behavior should not be ionic strength dependent. The observed isotherms are in very reasonable agreement with this predicted behavior. As was mentioned before, the precise determination of the cooperativity parameter u is difficult for these highly cooperative systems. From the data presented in Figure 3 we calculate a value of u = 650 f 100, independent of the added salt concentration (Table I); individual values calculated at the various ionic strengths vary between 500 and 800 but do not show any particular trend. This may indicate that the cooperative effect in the binding of DTA' to the dextran sulfate polyanion is due completely to the hydrophobic interaction between bound surfactant ions and not to electrostatic interactions. The fact that u is independent of the added salt concentration indicates that the variation in Ku (Table I) is due solely to the dependence of K on the ionic strength of the solution. We will come back to this observation later. The isotherms for the PS-DTA systems (Figure 4) are very different from the DxS-DTA case. We note that at a given ionic strength the sharp increase in 8 occurs at much lower surfactant concentrations in the case of PSDTA compared to DxS-DTA but that the cooperative effect is less pronounced in the PS-DTA system and is observed only at low degrees of binding. Since the charge density parameter [ for the PS polyanion equals 2.81,23 very close to t for DxS, this must indicate a difference in the binding mechanism. By applying eq 2 at low degrees of binding (up to = 0.2) only, one can obtain the values of Ku for the PS-DTA case (Table I), but the accuracy is worse than for the DsX-DTA system. The cooperativity parameter u for the PS-DTA case can be estimated at 200 f 100, again independent of ionic strength. This value is significantly lower than u for the DxS-DTA system. Although both polyelectrolytes, PS and DxS, are water soluble, poly(styrenesulfonate) may be considered to have a hydrophobic polymer backbone, and dextran sulfate a hydrophilic backbone. From the data presented in Table I we can estimate the K value for PS-DTA to be about 3.5RT higher than the value for DxS-DTA at a corre(29)G.S. Manning, Q.Reu. Biophys., 2, 179 (1978).
The Journal of Physical Chemlsfty, Vol. 86, No. 19, 1982 3889
c I
5
3
I
\ -2
-1
log ms Flgure 5. Dependence of blnding constant Ku (DTA' ion bound to a site adjacent to a site already occupled) on NaCl concentration: (a)
NaDxS; (b) NaPS. Open squares: data from ref 14 (see text).
sponding concentration range of 0.024.1 M NaCl. In micelle formation, the hydrophobic contribution of one phenyl ring in the surfactant chain is approximately equivalent to the contribution of 3.5 methylene groupsw and thus contributes about 3.5RT per mole of phenyl groups to the free energy of micelle formation based on a contribution of 1.02kT per methylene This suggests that the increase in K for the PS-DTA system may be due mainly to the hydrophobicity of the polyion backbone, through interactions between the backbone and the hydrophobic chain of the surfactant. The lower value of u observed in this system may then be due to hydrophobic interactions between the bound surfactant ions and the polyion backbone, since such interaction would not contribute to the overall cooperative effect. A complete understanding of these effects would require a detailed microscopic model for the surfactant-surfactant and surfactant-polymer interactions. It is interesting to note that in the PS-DTA system we find Scatchard plots at high degrees of binding to be convex downward. We now turn our attention to the ionic strength dependence of the binding constant K . Figure 5 shows a plot of log Ku vs. log ms,where ms is the molal concentration of the added NaC1. Both plots show a linear relationship below 0.2 m NaC1. For comparison, we have included the recent data by Shirahama et al.14 (open squares) for the interaction between decyl sulfate and a cationic copolymer of dimethyldialkylammoniumchloride and SOz. Observed slopes (log Kullog Q,) are -0.68 f 0.02 for DxS-DTA and -0.75 f 0.01 for PS-DTA. When we would assume that the binding of a surfactant ion involves a 1:l exchange with a (possibly territorially bound) Na+ counterion, a slope of -1 would be expected at large excess of NaC1. If in addition the constant K is lowered because of a lowered electrical potential at the binding site due to the effect of the added salt, the slope may be estimated at -0.5, using Manning's theoretical treatment.32 Alternatively, Schwarz22assumed cooperative binding between dye and sodium counterions, leading to the expression K = &/(l + K,ms) (2) This expression predicts a larger curvature in the plot of log Ku vs. log msthan what is observed in Figure 5. It is (30)K. Shinoda, T. Nakagawa, B. Tanamushi, and T. Isemura, 'Colloidal Surfactants", Academic Press, New York, 1963,p 52. (31)J. Th. G.Overbeek and D. Stigter, R e d . Trau. Chim. Pays-Bas, 75, 1263 (1956). (32)G . S . Manning, J. Chem. Phys., 51, 924 (1969).
J. Phys. Chem. 1982, 86, 3870-3881
3870
of interest to note that the slopes observed in Figure 5 are comparable with the observed slopes of 4 . 6 6 for the linear relationships between log cmc and log mc (mc = total counterion concentration) for micelle formation in the presence of added NaCl.% This observation points at the similarity between micelle formation and the observed (33)From data by D. A. Haydon and F. H. Taylor at 20 OC (Philos. Trans. R. SOC.London, Ser. A , 252, 225 (1960)).
polyion-surfactant counterion cooperative binding process, even though this last cooperative effect takes place at concentrations far below the cmc of DTABr.
Acknowledgment. We thank Dr. I. Satake, Kagoshima University, Kagoahima, Japan, for his valuable cooperation. This research was supported by the Natural Sciences and Engineering Research Council of Canada and by the Dalhousie Research Development Fund.
Heat Capacltles and Volumes of Several Ollgopeptides In Urea-Water Mixtures at 25 OC. Some Impltcatlons for Protein Unfoldlng Octav Enea Labomtoke de chimbs I, Electrochlmbs et Interactbns. Unlversit6 de FDMers, 86022 Poitlers, France
and C a m d Jollcoeur D6partemnt de Chimbs, Unhwstt6 de Sherbrooke, Sherbrooke, Q&bec, Canada J1K 2R1 (Recelved: February 18, 1982; In Final F m : June 8, 1082)
(cpo)
The partial molar volumes (V")and heat capacities of the amino acids gylcine, L-alanine, and L-serine and several of their oligomers have been determined in urea-water (U-W) mixtures at 25 "C. Data for selected compounds are reported as functions of urea concentration up to 8 mol L-l, and detailed results are presented for all compounds at a common urea concentration of 7 mol L-l. The changes in Voand Cpo of the oligopeptides upon transfer from water to 7 M urea were calculated by using similar data reported earlier for these peptides in water. The total and transfer quantities are examined for additive group contributions which are discussed on the basis of current concepts describing interactions in urea-water mixtures. In particular, the analysis shows that ACpo (water 7 M urea) for a backbone glycyl group is near zero, while corresponding quantities for ionic and apolar groups are both large, respectively positive and negative. These results and data for several other model compounds indicate that the charged groups of a protein contribute significantly to changes in its partial molar heat capacity upon isothermal unfolding in urea-water mixtures. The interpretation of Cpo data in relation to thermodynamic fluctuations suggests an interesting approach to understand the various events occurring in urea-induced protein unfolding.
-
Introduction In recent years, experimental investigations and theoretical modeling of biopolymers have provided highly detailed picturea of their structural and dynamical properties. The level of refinement achieved in these descriptions contrasts rather sharply with our current understanding of other aspects of biopolymers. For instance, a quantitative assessment of the factors which contribute to the thermodynamic stability of proteins in solution remains elusive in spite of numerous remarkable investigations (see, for example, reviews by Tanford,' Kauzmann,2 Franks and Eaglar~d,~ Brandts,' Lumry and Biltonen? and Paces). Considering the complexity of a system containing a biopolymer and its "hydration shell", however, this situation (1)C. Tanford in 'Advances in Protein Chemistry", Vol. 23, parta A and B, C. B. Afinsen, Jr., J. T. Edsall,and F. M. Richards, Eds., Academic Press, New York, 1968,p 122; ibid, Vol. 24, part C, p 2. (2) W. Kauzmann, Adu. Protein Chem., 14, 1 (1959). (3)F.Franks and D. Eagland, CRC Cn't. Reu. Biochem. 3,165(1975). (4) J. F. Brandts in "Structure and Stability of Biological Macromolecules", S. Timawheff and G. D. Fasman, Eda., Marcel Dekker, New York, 1969,Chapter 3,p 213. ( 5 ) R. Lumry and R. L. Biltonen in 'Structure and Stability of Biological Macromolecules", s. Timascheff and D. G. Fasman, Ed., Marcel Dekker, New York, 1969,Chapter 2, p 67. (6)C. N.Pace, CRC Crit. Rev. Biochem. 3, 1 (1975). 0022-3654/82/2086-3870$01.25/0
is not so surprising. The thermodynamicproperties of such systems are hardly amenable to a priori calculations and, indeed, most interpretations of the thermodynamic behavior of proteins are based on data for simpler model compounds. The latter, for example, amino acids and peptides, have obvious limitations in representing portions of protein molecules, but the model compound approach has already provided fundamental key results. Among those, the illustration of the role of hydrophobic effects on the thermodynamic stability of globular proteins stands out as an important example,lI2 and numerous recent studies (e.g., ref 7-12) further show how the thermodynamic properties of proteins can be understood from model compound investigations. A quantitative evaluation of the thermodynamicstability of native protein structures in solution essentially requires measurements of thermodynamic changes as the protein unfolds from a native state (N) into a fully solvated ran(7)J. M. Sturtevant, Proc. Natl. Acad. Sci. U.S.A.,74,2236 (1977). (8)J. Bello, J. Phys. Chem., 82,1607 (1978). (9)K.P.Prasad and J. C. Ahluwalia, Biopolymers, 19,263,273 (1980). (10)M. Y. Schrier, A. H. C. Ying, M. E. Ross, and E. F. Schrier, J. Phys. Chem., 81,674 (1977). (11)S. Lapanje, J. Skerjanc, S. Glavnik, and S. Zibret, J . Chem. Thermodyn., 10,425 (1978). (12)M. Roseman and W. P. Jencks, J. Am. Chem. Soc., 97,631(1975).
0 1982 American Chemical Soclety
