Investigations into the Thermodynamics of Polypeptide Interaction

Anal. Chem. 1999, 71, 4874-4885

Investigations into the Thermodynamics of Polypeptide Interaction with Nonpolar Ligands Milton T. W. Hearn* and Guoling Zhao†

Centre for Bioprocess Technology, Department of Biochemistry and Molecular Biology, Monash University, Clayton 3168, Victoria, Australia

In this paper, we describe a general procedure to evaluate the thermodynamics of the interaction between polypeptides and hydrophobic ligands in the presence of aquoorganic solvent mixtures. These studies address experimental requirements for the determination of the linear free energy relationships, derivation of partition coefficients or other extrathermodynamic parameters such as contact areas, or assessment of the conformational changes that may occur when polypeptides or proteins interact with immobilized nonpolar ligands. Not unexpectedly from thermodynamic arguments, the trends and magnitudes of free energy parameters, such as the enthalpy of association, as previously derived in many studies from gradient elution reversed-phase high-performance liquid chromatographic (RP-HPLC) measurements are often different from the data for the same parameters derived from equilibrium binding or microcalorimetric determinations. To reconcile these divergencies and to more closely examine the thermodynamic basis of the interaction of polypeptides with nonpolar ligands, the dependency of the logarithmic capacity factor, ln k′, on temperature, T, for several polypeptides (bombesin, β-endorphin, glucagon) have been investigated using a n-butylsilica and acetonitrile-water or methanol-water mixtures of defined solvent compositions. With low-pH, acetonitrile-water mixtures, the van’t Hoff plots, i.e., the plots of ln k′ versus 1/T, were nonlinear over the range of T ) 278-358 K, although within a narrow temperature range, e.g., from T ) 278-308 K, the experimental data for these polypeptides could be approximated by a linear relationship. This nonclassical van’t Hoff behavior was associated with interactive processes that involved temperature-dependent enthalpic, entropic, and heat capacity changes. In contrast, with low-pH, methanol-water mixtures, the van’t Hoff plots showed dependencies that were essentially linear over the range of T ) 278-358 K. The slopes of the van’t Hoff plots with acetonitrile-water and methanolwater mixtures at a defined T value and solvent composition were significantly larger than those found for the corresponding experiments carried out under gradient elution RP-HPLC conditions. From these plots of ln k′ versus 1/T, the changes in the apparent enthalpy of q ) and the apparent entropy of asassociation (∆Hassoc q sociation (∆Sassoc) for the interaction of these polypep4874 Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

tides with the solvated n-butyl ligands at different T and solvent compositions have been determined. For these q q and ∆Sassoc exhibited linear polypeptides, both ∆Hassoc dependencies on the volume fraction, φ, of the organic solvent over a narrow range of T, but the slopes of these plots were dependent on the T range examined. The dependencies of the slope term, S, and the intercept term, ln ko, derived from the plots of ln k′ versus φ as a function of T, have also been investigated. A new relationship q q and ∆Sassoc as a function linking the S values with ∆Hassoc of T and φ has been derived and validated. In addition, q q the relationship between S, ∆Hassoc , ∆Sassoc , the apparent q change in heat capacity, ∆Cassoc, and the accessible surface area, ∆Atot, of these polypeptides has been examined, thus providing a linkage of these thermodynamic and extrathermodynamic parameters to the partition coefficient, P, and the molecular properties of these polypeptides. The results confirm that entropy-enthalpy compensation effects participate in the interaction of polypeptides with hydrophobic ligands. This investigation has confirmed that the use of solvent-water mixtures of defined composition, rather than the more convenient practice of using gradient elution methods, is essential if thermodynamically consistent values of the binding affinities and partition coefficients are to be quantitatively derived. Similar considerations apply to the derivation of extrathermodynamic parameters associated with the conformational transitions of polypeptides (or proteins) when they interact with nonpolar n-alkyl ligands. This study thus provides a general approach to evaluate the interaction thermodynamics of polypeptides or proteins in these and similar lipophilic systems. Over the past two decades, gradient elution reversed-phase high-performance liquid chromatography (RP-HPLC) with nalkylsilica sorbents has found wide application in protein and peptide chemistry.1,2 As a versatile technique, RP-HPLC can be used to achieve high-resolution separation of complex mixtures * To whom correspondence should be addressed: (fax) Int + 61 + 3 + 99055882; (e-mail) [email protected]. † Present address: Department of Chemistry, Dalian University of Technology, Dalian 116012, China. (1) Hearn, M. T. W. In Protein Purification; Janson, J. C., Ryden, L., Eds.; VCH Press: New York, 1998; pp 239-282. (2) Aguilar, M. I.; Hearn, M. T. W. Methods Enzymol. 1996, 270, 1-25. 10.1021/ac990028x CCC: $18.00

© 1999 American Chemical Society Published on Web 09/28/1999

of peptides and proteins, as well as to analytically provide insight into the structures of these molecules. Due to their structural complexity and size, polypeptides and proteins typically exhibit very pronounced dependencies of their logarithmic capacity factors, ln k′s, on the volume fraction, φ, of the displacing solvent under isocratic (i.e., fixed solvent composition) RP-HPLC conditions. Consequently, gradient elution conditions have invariably been employed in most studies. Various investigations have also been reported3-9 whereby the conformational characteristics, membrane binding properties, or lipid partition coefficients of antimicrobial or hormonal polypeptides and proteins have been correlated with data obtained from gradient elution RP-HPLC retention data. In these gradient elution RP-HPLC studies, a number of assumptions have been made; e.g., the interaction between the polypeptide (or protein)-nonpolar n-alkyl chains has reached equilibrium or that the change in heat capacity due to the interaction is zero, and thus the changes in enthalpy and entropy are independent of T. Empirical models1,10-13 have then been used to evaluate the processes that occur when polypeptides or proteins interact with nonpolar n-alkyl chains, chemically immobilized onto a support material, with similar approaches adapted to other types of immobilized lipophilic systems. In their simplest manifestations, these empirical approaches provide a predictive framework for selecting conditions to facilitate optimization of gradient elution RP-HPLC separations. Increasingly, the same empirical approaches have been employed to quantify the extent of conformational changes or other secondary chemical equilibrium processes that occur when polypeptides or proteins interact with lipophilic environments under different experimental conditions. The use of gradient elution conditions introduces a complication, however, as far as the interpretation of the experimental data in terms of their thermodynamic significance, since these interactions between the polypeptides (or proteins) and the hydrocarbonaceous ligands are not measured under conditions of constant solvent composition or the other requirements of the Gibbs-Helmholtz relationship. When polypeptides are separated by RP-HPLC methods under conditions of constant solvent composition, the dependence of ln k′ on the volume fraction, φ, of the organic solvent in a water(3) Hodges, R. S.; Semchuk, P. D.; Taneja, A. K.; Kay, C. M.; Parker J. M. R.; Mant, C. T. Pept. Res. 1988, 1, 19-30. (4) Steer, D. L.; Thompson, P. E.; Blondelle, S. E.; Houghten, R. A.; Aguilar, M. I. J. Pept. Res. 1998, 51, 401-412. (5) Blondelle, S. E.; Houghten, R. A. Biochemistry 1992, 31, 12688-12694. (6) Kiyota, T.; Lee, S.; Sugihara, G. Biochemistry 1996, 35, 13196-13204. (7) Oroszlan, P.; Wicar, S.; Wu, S.-L.; Hancock, W. S.; Karger, B. L. Anal. Chem. 1992, 64, 1623-1631. (8) Beyermann, M.; Fechner, K.; Furkert, J.; Krause, E.; Bienert, M. J. Med. Chem. 1996, 39, 3324-3330. (9) Mant, C. T.; Hodges, R. S. In High Performance Liquid Chromatography of Peptides and Proteins: Separation, Analysis and Conformation; Mant, C. T., Hodges, R. S., Eds.; CRC Press: Boca Raton, FL, 1991; pp 589-658. (10) Aguilar, M. I.; Hearn, M. T. W. In HPLC of Peptides, Proteins and Polynucleotides; Hearn, M. T. W., Ed.; VCH Publ.: New York, 1991; pp 247275. (11) Hearn, M. T. W.; Aguilar, M. I. In Modern Physical Methods in Biochemistry; Neuberger, A., van Deenen, L. L. M., Eds.; Elsevier Sci. Publ.: Amsterdam, 1988; pp 107-142. (12) Melander W. R.; Corradini, D.; Horvath, Cs. J. Chromatogr. 1984, 317, 6785. (13) Snyder, L. R. In HPLC-Advances and Perspectives; Horva´th, Cs., Ed.; Academic Press: New York, 1980; pp 207-316.

solvent mixture can be represented1,2,14 by the empirical relationship

ln k′ ) ln ko - Sφ + S′φ2 - S′′φ3 + ...

(1)

Often, the dependency of ln k′ on φ has been approximated to a first-order relationship whereby S′ and S′′ are assumed to be zero. When such approximations prevail, the value of ln ko becomes the y-axis intercept value when φ f 0 and S becomes the slope (∂ ln k′/∂φ) of the plot at a defined φ value, respectively. Hitherto, when partition coefficient P values of polypeptides in nonpolar ligand systems have been measured under gradient elution conditions, the interacting species have been assumed to be conformationally invariant; the gradient derived S, S′, S′′, ... values independent of T; and the logarithmic partition coefficient (ln P) assumed to be linearly proportional to the logarithmic median capacity factor (ln kh′). Over a narrow range of φ values, i.e., when ∆φ e 0.2, with water-rich eluents relatively good linear correlations between ln P and ln kh′ or ln kh′ and φ have been observed in a number of previous studies1,15-18 for small peptides, i.e., with amino acid sequences corresponding to 2-10 amino acid residues, with r2 typically g 0.95. With larger polypeptides, the dependencies of ln k′ (and ln k′) on φ, however, tend to follow curvilinear relationships,1,10,11,16 particularly over wider ranges of solvent concentrations, such as 0.01 e ∆φ g 0.85, with acetonitrile-water systems. Various investigators4,5,7,8,15,17,19-22 have also suggested that variations in the median ln k′ value measured by gradient elution RP-HPLC procedures, and thus variations in the gradient derived S and ln ko values, following changes in T are evidence of conformational changes that polypeptides or proteins undergo during their interaction with nonpolar ligand(s). Analysis of the corresponding van’t Hoff plots, i.e., the ln k′ versus 1/T plots for the interaction of polypeptides (or proteins) with a nonpolar ligand, measured under isocratic conditions with solvent-water mixtures of defined composition provides an avenue to examine whether such conclusions and assumptions based on gradient elution RPHPLC procedures are valid. Evaluation of these ln k′ versus 1/T plots also provides an opportunity to determine the magnitude of changes in the respective enthalpic and entropic terms, as well as the overall changes in Gibbs free energy of association q q (∆Gassoc ) and heat capacity (∆Cassoc ), when these biomolecules interact with lipophilic environments as T and φ are changed. (14) Schoenmakers, P. J.; Billiet, H. A. H.; de Galan, L. D. J. Chromatogr. 1979, 185, 179-190. (15) Hancock, W. S.; Chloupek, R. S.; Kirkland, J. J.; Snyder, L. R. J. Chromatogr. 1994, 686, 31-43. (16) Hearn, M. T. W. In Theory and Practice of Biochromatography; Vijayalakshmi, M. A., Ed.; Harwood Academic Publishers: Lausanne, Switzerland, in press. (17) Purcell, A. W.; Aguilar, M. I.; Wettenhall, R. E. H.; Hearn, M. T. W. Pept. Res. 1995, 8, 160-170. (18) Horva´th, Cs.; Melander, W. R.; Molna´r, I. J. Chromatogr. 1976, 125, 129156. (19) Krause, E.; Beyermann, M.; Dathe, M.; Rothemund, S.; Biernet, M. Anal. Chem. 1995, 67, 252-258. (20) Lazoura, E.; Maidonis, I.; Bayer, E.; Hearn, M. T. W.; Aguilar, M. I. Biophys. J. 1997, 72, 238-246. (21) Rothemund, S.; Krause, E.; Beyermann, M.; Dathe, M.; Engelhardt H.; Bienert, M. J. Chromatogr., A 1995, 689, 219-226. (22) Blondelle, S. E.; Ostresh, J. M.; Houghten, R. A.; Perez-Paya, E. Biophys. J. 1995, 68, 351-359.

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The dependency of ln k′ on T can be expressed by

ln k′ )

q q ∆Sassoc -∆Hassoc + + ln Φ RT R

(2)

q q where ∆Hassoc and ∆Sassoc are the apparent changes in enthalpy and entropy associated with the interactive process respectively, R is the universal gas constant, T is the absolute temperature (K), and Φ is the phase ratio of the system. For the n-butylsilica system employed in this study, the Φ value at 298 K was calculated with a sodium nitrate solution to be ∼0.67 by the breakthrough volume method.13 When classical van’t Hoff behavior occurs, linear plots q of ln k′ versus 1/T are anticipated, while ∆Cassoc ) 0 and is invariant with T. Such polypeptide-nonpolar ligand interactions can be described in terms of isothermic processes.16 When the interactions of polypeptides with nonpolar ligands follow either q homothermic or heterothermic processes,16 i.e., when ∆Cassoc * 0 and is a function of T, then nonclassical curvilinear van’t Hoff plots are anticipated and the ln k′ versus 1/T plot is predicted to follow a quadratic form.12,16,23,24 Under such conditions, the dependency of ln k′ on 1/T can be expressed as

ln k′ ) b(0) +

b(1)

+

b(2)

+ ln Φ

(3)

q ∆Hassoc ) -R(b(1) + (2b(2)/T))

(4)

q ∆Sassoc ) R(b(0) - (b(2)/T2))

(5)

q ∆Cassoc ) (2Rb(2)/T2)

(6)

T

T2

with

while

and

where the coefficients b(0), b(1), and b(2) can be evaluated from the ln k′ versus 1/T plots using least-squares regression procedures. Currently, there is a paucity of data available on the thermodynamic behavior of polypeptides when they interact with n-alkyl ligands or other types of immobilized lipophilic ligands under nearequilibrium binding conditions. This situation has prompted the present investigation into the nature of the relationship of ln k′ on 1/T for polypeptides when they interact with nonpolar ligands in the presence of solvent-water mixtures of defined compositions. In this study, we have examined the thermodynamics of interaction of three polypeptides, bombesin, β-endorphin, and glucagon, in a lipophilic environment using a n-butylsilica system with acetonitrile-water and methanol-water mixtures of different solvent percentages and at different T. This investigation has permitted the respective enthalpy and entropy changes to be assessed. In addition, a theoretical relationship linking S with (23) Vailaya, A.; Horvath Cs. Ind. Eng. Chem. Res. 1996, 35, 2964-2982. (24) Boysen, R. I.; Wang, Y.; Keah, H. H.; Hearn, M. T. W. J. Biophys. Chem. 1998, 77, 79-97.

4876


q q and ∆Sassoc , and thus to extrathermodynamic terms such ∆Hassoc as accessible surface area, ∆Atot, has been derived to account for the dependency of S on T and the molecular properties of these molecules. The validity of this relationship was then experimentally examined.

EXPERIMENTAL SECTION Apparatus. All measurements were made with an instrumental system based on a Beckman System Gold autosampler 507, a Beckman System Gold programmable solvent module 126, and a Beckman System Gold programmable detector module 116. The temperature was controlled by surrounding columns of dimensions of 250 × 4.6 mm i.d., packed with the n-butylsilica, in a thermostated water-jacketed cylinder, coupled to a Bio-Rad module 486 refrigerated recirculating bath (Bio-Rad, Richmond, CA) or ICI TCl900 HPLC oven (ICI Instruments, Dingley, Australia). Capacity factor measurements were performed with Bakerbond wide-pore n-butylsilica (J. T. Baker, Phillipsburg, NJ) of 5-µm nominal particle size and 30-nm average pore size. The density of the n-butyl ligands was 2.85 µmol/m2 as determined by elemental analysis. Chemicals and Reagents. Acetonitrile and methanol (HPLC grade) were obtained from Mallinckrodt (Paris, KY). Trifluoroacetic acid (TFA) of peptide synthesis grade was purchased from Auspep (Parkville, Australia). Water was distilled and deionized with a Milli-Q system (Millipore, Bedford, MA). N-Acetyl-L-Rphenylalanine ethyl ester and glucagon were obtained from Sigma Chemical Co. (St. Louis, MO) and were of >95% purity. Bombesin (purity >98%) was obtained from Sigma and Auspep, while β-endorphin (also of purity >95%), was obtained from Auspep and Organon (Oss, Netherlands). The authenticity of different polypeptide batches, which gave identical RP-HPLC profiles, was established by ES-MS, CZE, and N-terminal Edman microsequencing. Experimental Procedures. Bulk solvents were filtered and then degassed by sparging with nitrogen. Water-solvent mixtures containing different organic solvent volume fractions (v/v) were generated from 0.1% TFA in water (buffer A) mixed with 0.09% TFA in acetonitrile-water (65:35) (buffer B) or methanol-water (65:35) (buffer B) to the desired solvent percentages with the Beckman System Gold programmable solvent module 126. The flow rate was controlled at 1.0 mL/min throughout these studies. Peak profiles were monitored at 215 nm. The temperatures investigated were 278, 288, 298, 308, 318, 328, 338, 348, and 358 K. Peptide solutions were prepared by dissolving the solute at a concentration of 500 µg/mL in 0.1% TFA in water. Injection sizes varied between 1 and 5 µg. All data points were derived from at least duplicated experiments with the capacity factor measurements between replicates varying typically by less than 5%. Column and extracolumn dead volumes were measured independently with the noninteractive solute sodium nitrate. RESULTS Dependency of ln k′ on φ for the Polypeptide and Control Solutes. In this investigation, the capacity factors, k′s, for the polypeptides, bombesin, β-endorphin, and glucagon as well as N-acetyl-L-R-phenylalanine ethyl ester were measured at different temperatures in the presence of aquo-organic solvent mixtures containing defined concentrations of acetonitrile or methanol. The molecular weight, sequence, accessible surface area, ∆Atot (Å2),

Table 1. Molecular Weight, Sequence, Accessible Surface Area, ∆Atot (Å2), and Volume, ∆V (Å3), of N-Acetyl-L-r-phenylalanine Ethyl Ester, Bombesin, β-Endorphin, and Glucagona polypeptide

sequence

MW

∆Atot (Å2)

∆V (Å3)

N-acetyl-L-R-phenylalanine ethyl ester bombesin β-endorphin glucagon

Ac-F-ee PEQRLGNQWAVGHLM YGGFMTSEKSQTPLVTLFKNAIIKNAYKKGE HSQGTFTSDYSKYLDSRRAQDFVQWLMNT

210 1640 3740 3520

394 1550 2556 2580

267 2083 4407 4470

a The accessible surface area, ∆A 2 3 54 2/3 and ∆V tot (Å ), and volume, ∆V (Å ), were calculated according to the relationships, ∆Atot ) 11.12(MW) ) 1.27(MW), where MW is the molecular weight.

and molecular volume (Å3) of these compounds is given in Table 1. At a given T, the dependencies of the k′ values on φ for the bombesin, β-endorphin, and glucagon or N-acetyl-L-R-phenylalanine ethyl ester were evaluated in terms of eq 1. In all cases with the methanol-water mixtures, and for some cases with the acetonitrile-water mixtures, the experimental data could be fitted to a first-order dependency of ln k′ on φ, with the regression coefficients typically falling within the range of r2 ) 0.9800-0.9900. Divergences from linear dependencies were observed for the ln k′ versus φ plots obtained with acetonitrile-water mixtures of lower φ values, particularly when lower T conditions were used. In these cases, the data was fitted to the quadratic form of the dependency of ln k′ on φ (where r2 g 0.9900). Illustrative of these results are the plots of ln k′ versus φ for bombesin and N-acetyl-L-R-phenylalanine ethyl ester (Figures 1 and 2). With the polypeptides, the φ value of acetonitrile required to achieve a defined k′ value was significantly smaller than the φ value of methanol at all temperatures examined, consistent with the known differences in the relative elutropic properties of these two solvents. This behavior can be contrasted to the small differences in the φ values for acetonitrile and methanol to achieve a similar k′ value for the low-molecular-weight compound, N-acetylL-R-phenylalanine ethyl ester (cf. Figure 2). Comparison of the derived S and ln ko values of bombesin, β-endorphin, and glucagon at a specified T with the corresponding experimental data obtained from linear gradient elution measurements25,26 revealed that the gradient elution data underestimated the magnitudes of ln ko by at least 40%, while the slopes (S values) of the ln k′ versus 1/T plots differed from the corresponding slopes of the logarithm of the median capacity factor ln k′ versus 1/T plots obtained by gradient experiments by a factor of g2-fold. Illustrative of these findings are the results for β-endorphin (Table 2), where substantial deviations in the S and ln ko values derived by these two procedures are apparent. van’t Hoff Plots of N-Acetyl-L-r-phenylalanine Ethyl Ester and the Polypeptides. Panels A and B of Figure 3 show respectively the van’t Hoff plots for N-acetyl-L-R-phenylalanine ethyl ester with acetonitrile-water and methanol-water mixtures of different solvent content. In the case of the acetonitrile-water q q mixtures, divergencies in the ∆Hassoc and ∆Sassoc values calculated according to eq 2 or eqs 3-5 were apparent over all ranges q q of φ and T, although similar trends in the ∆Hassoc and ∆Sassoc (25) Purcell, A. W.; Aguilar, M. I.; Hearn, M. T. W. Anal. Chem. 1993, 65, 30383049. (26) Purcell, A. W.; Zhao, G. L.; Aguilar, M. I.; Hearn, M. T. W. J. Chromatogr., in press.

Figure 1. Plots of the logarithmic capacity factor, ln k′, versus the volume fraction of the organic solvent, φ, for bombesin using acetonitrile-water (A) or methanol-water (B) mixtures containing 0.1% TFA and n-butylsilica at temperatures from T ) 278-358 K. The plots show the experimental data and the lines of best fit according to the quadratic form of the relationship given as eq 1.

values were evident at the lower φ and T values (cf. Table 3). Because of the relatively high linear correlation observed in the plots of ln k′ versus φ for N-acetyl-L-R-phenylalanine ethyl ester q q and ∆Sassoc values with methanol-water mixtures, the ∆Hassoc were also derived from the slope and intercept of the ln k′ versus 1/T plots using eq 2. In this case, good agreement was only found q q with the corresponding ∆Hassoc and ∆Sassoc values for the interaction of N-acetyl-L-R-phenylalanine ethyl ester with the n-butyl ligands determined using eqs 3-5 at lower φ values (i.e., at φ ) 0.35) while significant divergencies were evident at higher φ values, i.e., when φ g 0.40 (cf. Table 4). As evident from Figure 4A-C, the van’t Hoff plots for bombesin, β-endorphin, and glucagon with different acetonitrilewater combinations for the range of T ) 278-358 K markedly deviated from linearity. Within a relatively well-defined range, such as T ) 278-308 K, T ) 308-328 K, or T ) 338-358 K, the experimental data could be approximated to a linear relationship Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

4877

Figure 2. Plots of the logarithmic capacity factor, ln k′, versus the volume fraction of the organic solvent, φ, for N-acetyl-L-R-phenylalanine ethyl ester using acetonitrile-water (A) or methanol-water (B) mixtures containing 0.1% TFA and n-butylsilica at temperatures T ) 278-358 K. The plots show the experimental data and the lines of best fit according to the quadratic form of the relationship given as eq 1. Table 2. Comparative S, S h , ln ko, and ln k h o Values for β-Endorphin Determined as Part of the Present Investigations and from Linear Gradient Elution Experiments1,11,24 at Different Temperatures, T ) 278-358 K temp (K)

Sa

S hb

∆Sb

ln koa

ln khob

∆ ln kob

278 288 298 308 318 328 338 348 358

29.6 27.3 27.0 26.5 26.2 25.1 25.6 29.9 31.4

22.4 15.0 19.1 16.2 14.9 19.4 14.3 11.0 8.5

7.4 12.3 8.1 10.3 11.3 5.7 11.3 18.9 22.9

8.48 7.76 7.59 7.40 7.10 6.62 6.48 7.25 7.34

6.43 4.76 5.74 4.94 4.42 5.12 3.93 3.17 2.07

2.05 3.00 1.85 2.46 2.68 1.50 2.55 4.08 5.27

av

27.6

15.6

12.0

7.34

4.51

2.83

a Derived from defined composition isocratic measurements. b Derived from linear gradient elution.

between ln k′ and 1/T; i.e., with r2 ≈ 0.9500. For these restricted q q and ∆Sassoc values for the interaction of the T ranges, the ∆Hassoc polypeptides with the n-butyl ligands were calculated according q q to eq 2, with the corresponding values of ∆Hassoc and ∆Sassoc at the same φ values over the entire T range derived according to eqs 3-5 (Tables 5-7). The results indicate that the linear approximation implicit to eq 2 significantly overestimated the q values of ∆Hassoc at all T values, and similarly overestimated the q ∆Sassoc values at the higher T values for the acetonitrile-water mixtures. 4878 Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

Figure 3. van’t Hoff plots for N-acetyl-L-R-phenylalanine ethyl ester over the range φ ) 0.25 to φ ) 0.50 using acetonitrile-water (A) or methanol-water (B) mixtures containing 0.1% TFA and n-butylsilica at temperatures T ) 278-358 K. The plots show the experimental data and the lines of best fit according to the relationship given as eq 3. Table 3. The ∆Hqassoc and ∆Sqassoc Values Derived for N-Acetyl-L-r-phenylalanine Ethyl Ester Following Interaction with a n-Butyl-(C4)-silica Sorbent Using Acetonitrile-Water Eluentsa q ∆Hassoc (kJ/mol)

vol fractn, φ 0.25 0.35

308 K eq 2 eq 3

328 K eq 2 eq 3

q ∆Sassoc (J mol-1 K-1)

308 K eq 2 eq 3

328 K eq 2 eq 3

-3.3 -3.0 -3.3 -4.2 -8.1 -8.7 -8.1 -12.1 -2.6 -2.6 -2.6 -4.26 -10.8 -3.2 -10.8 -5.0

a Based on either the fit of the experimental data to the pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the temperature ranges T ) 278-318 and 318-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., φ ) 0.25 and φ ) 0.35) and at the same designated temperatures.

When methanol-water mixtures were employed, the shapes of the van’t Hoff plots for bombesin (and the other polypeptides) was different from those shown in Figure 4A for the acetonitrilewater combinations. Illustrative of these differences are the ln k′ versus 1/T plots for bombesin at different methanol concentrations (Figure 4D), where essentially linear relationships (i.e., r2 g 0.9900) of ln k′ versus 1/T were observed over the range of T ) 278-358 K. In comparison, the corresponding data for β-endorphin and glucagon tended to follow first-order dependencies of ln k′ versus 1/T, consistent with the observation that methanol is a better solvent for hydrogen bond interactions but a poorer inducer of secondary structure with polypeptides than acetonitrile. No maximums in the ln k′ versus 1/T plots were evident in these cases. Within the limits of accuracy of the experimental measure-

Table 4. The ∆Hqassoc and ∆Sqassoc Values Derived for N-Acetyl-L-r-phenylalanine Ethyl Ester Following Interaction with a n-Butyl-(C4)-silica Sorbent Using Methanol-Water Eluentsa q ∆Hassoc (kJ/mol)

308 K vol fractn, φ eq 2 eq 3 0.35 0.40

328 K eq 2 eq 3


308 K eq 2 eq 3

328 K eq 2 eq 3

-8.6 -8.2 -8.6 -8.7 -20.9 -20.9 -20.9 -22.6 -7.7 -14.4 -7.7 -14.4 -21.7 -33.7 -21.7 -33.7

a Based on either the fit of the experimental data to the pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the temperature ranges T ) 278-318 and 318-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., φ ) 0.35 and φ ) 0.40) and at the same designated temperatures.

Figure 4. van’t Hoff plots for (A) bombesin over the range φ ) 0.18-0.26; (B) β-endorphin over the range φ ) 0.25-0.30; (C) glucagon over the range φ ) 0.25-0.32, using acetonitrile-water mixtures containing 0.1% TFA, and (D) for bombesin over the range φ ) 0.33-0.41 using methanol-water mixtures containing 0.1% TFA, with a n-butylsilica sorbent at temperatures T ) 278-358 K. The plots show the experimental data and the lines of best fit according to the relationship given as eq 3.

ments, the ln k′ versus 1/T plots for these polypeptides with methanol-water mixtures can be interpreted in terms of classical van’t Hoff behavior. This finding also indicates that, with methanolwater elution systems, considerable caution should be taken not to overinterpret experimental data derived for the interaction of peptides with immobilized nonpolar ligands, as has occurred in a recent paper,27 where the involvement or induction of conformational effects in the peptide in the bulk solvent state or at the liquid-solid interface has been assumed in the absence of detailed (27) Mozsoltis, H.; Lee, T. T.; Wirth, H. J.; Perlmutter, P.; Aguilar, M. I. Biophys. J. 1999, 77, 1428-1444.

thermodynamic and spectroscopic analysis. Representative of this q q and ∆Sassoc data for bombesin over the behavior are the ∆Hassoc ranges of T ) 278-318 K and T ) 318-358 K (Table 8). q q The dependencies of ∆Hassoc and ∆Sassoc on φ are illustrated for glucagon with acetonitrile-water mixtures for three different T ranges (Figure 5). From these data for glucagon, as well as from the corresponding results for β-endorphin and bombesin, virial coefficients for the change in enthalpy and entropy with respect to the organic solvent volume fraction at constant T were q q derived, namely, ∂(∆Hassoc )T/∂φ and ∂(∆Sassoc )T/∂φ. Using these experimentally derived virial coefficients (Table 9), S values were then calculated according to eq 15 (loc cit) and compared to the experimentally determined S values for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester with acetonitrile-water mixtures as a function of T at different φ values (Figure 6). Good agreement was evident between the observed (filled points and solid lines) and predicted (dashed lines) values of S over the range of T values from T ) 278-358 K. q q From Tables 5-8, it can be noted that the ∆Hassoc and ∆Sassoc values for each polypeptide underwent incremental changes with increasing solvent content, irrespective of whether acetonitrile or methanol was employed. It can also be seen from Table 9 that for the lower T range, e.g., at T ) 278-308 K, the corresponding q virial coefficient ∂(∆Hassoc )T/∂φ values for the three polypeptides are positive; i.e., increasing acetonitrile concentrations lead to less q negative values of ∆Hassoc . At higher T values, e.g., at T ) 328q 358 K, slightly positive or negative ∂(∆Hassoc )T/∂φ values were observed, depending on the particular polypeptide. Over the range q T ) 278-308 K, the ∂(∆Sassoc )T/∂φ virial coefficients for these solutes were positive, but at higher T values, e.g., T ) 328-358 K, they became negative. Electrospray mass spectroscopic experiments confirmed that these polypeptides were recovered following desorption from the n-butyl ligands without chemical degradation, indicating that the variations in these thermodynamic parameters were not due to changes in primary structure. In Figure 7 are shown the plots of ln ko versus 1/T for the polypeptides and N-acetyl-L-R-phenylalanine ethyl ester determined with acetonitrile-water mixtures. As evident from these results, the slopes of the ln ko versus 1/T plots for β-endorphin and glucagon were significantly different from those observed for bombesin or N-acetyl-L-R-phenylalanine ethyl ester, indicative of strong dependencies of ∆G°o/w, and thus the partition coefq q , ∆Sassoc ficients, Ps, on T. Figure 8 shows the plots of S, ∆Hassoc or ∆C°assoc versus Atot for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester at the defined value of φ ) 0.26 and different T values. According to linear free energy considerations,1,2,16 a linear dependency between Atot and these thermodynamic and extrathermodynamic parameters is expected for these different biosolutes, provided the interaction mechanism with the solvated n-butyl ligands is common. DISCUSSION Previously, N-acetyl-L-R-phenylalanine ethyl ester as well as other low-molecular-weight peptides such as pentaphenylalanine4 had been employed in investigations related to the assessment of conformational changes of polypeptides in the presence of nonpolar ligands and water-acetonitrile gradient mixtures.20-22 q In these earlier studies, it has been assumed that the ∆Hassoc q and ∆Sassoc values for the interaction of N-acetyl-L-R-phenylAnalytical Chemistry, Vol. 71, No. 21, November 1, 1999

4879

Table 5. The ∆Hqassoc and ∆Sqassoc Values Derived for Bombesin Following Interaction with the n-Butyl-(C4)-silica Using Acetonitrile-Water Mixturesa q ∆Sassoc (J mol-1 K-1)

q ∆Hassoc (kJ/mol)

308 K

328 K

358 K

308 K

328 K

358 K

vol fractn, φ

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

0.18 0.20 0.22 0.24 0.26

-14.6 -12.3 -9.9 -7.6 -5.2

-10.2 -8.5 -7.5 -6.8 -6.7

-27.1 -20.9 -22.8 -20.7 -18.6

-12.7 -11.5 -10.8 -10.9 -11.5

-33.4 -33.4 -33.3 -33.2 -33.2

-15.8 -15.4 -15.2 -16.3 -17.7

-26.9 -25.6 -24.3 -23.0 -21.6

-27.5 -24.9 -24.3 -24.6 -29.1

-67.1 -66.5 -66.0 -65.5 -64.9

-35.2 -34.4 -34.9 -37.7 -44.2

-86.0 -91.9 -97.7 -104 -109

-44.4 -45.7 -47.6 -53.3 -63.2

a Based on either the fit of the experimental data to the three pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the three temperature ranges of T ) 278-308, 308-328, and 328-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., from φ ) 0.18 to φ ) 0.26) and at the same designated temperatures.

Table 6. The ∆Hqassoc and ∆Sqassoc Values Derived for β-Endorphin from the Interaction with the n-Butyl-(C4)-silica Using Acetonitrile-Water Mixturesa q ∆Sassoc (J mol-1 K-1)


308 K

328 K

358 K

308 K

328 K

358 K

vol fractn, φ

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

0.24 0.26 0.28 0.30

-22.7 -17.1 -11.5 -5.8

-8.1 -10.0 -12.4 -10.4

-42.9 -40.2 -37.4 -34.7

20.4 -22.0 -20.7 -18.5

-65.7 -67.5 -69.2 -71.0

-36.4 -37.5 -31.4 -28.9

-46.4 -38.3 -30.1 -22.0

-20.6 -28.7 -40.6 -38.6

-112 -113 -114 -116

-59.4 -66.4 -66.7 -63.9

-181 -196 -211 -226

-106 -112 -98 -94.5

a Based on either the fit of the experimental data to the three pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the three temperature ranges of T ) 278-308, 308-328, and 328-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., φ ) 0.24 to φ ) 0.30) and at the same designated temperatures.

Table 7. The ∆Hqassoc and ∆Sqassoc Values Derived for Glucagon from the Interaction with a n-Butyl-(C4)-silica Using Acetonitrile-Water Mixturesa q ∆Sassoc (J mol-1 K-1)


308 K

328 K

358 K

308 K

328 K

358 K

vol fractn, φ

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

eq 2

eq 3

0.26 0.28 0.30 0.32

-29.7 -25.4 -21.1 -16.8

-9.3 -13.6 -18.6 -14.3

-48.6 -49.2 -49.8 -50.4

-23.9 -28.0 -27.6 -21.5

-79.3 -80.5 -81.7 -82.8

-42.8 -46.4 40.5 30.7

-73.1 -67.2 -61.4 -55.5

-24.6 -42.8 -57.5 -50.4

-134 -145 -155 -165

-70.6 -88.1 -89.1 73.0

-228 -240 -252 -264

-124 -142 -127 -100

a Based on either the fit of the experimental data to the three pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the three temperature ranges of T ) 278-308, 308-328, and 328-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., φ ) 0.24 to φ ) 0.30) and at the same designated temperatures.

alanine ethyl ester or pentaphenylalanine with the nonpolar ligands were independent of T, permitting the corresponding changes in the extrathermodynamic parameters, such as the S values, of larger polypeptides to be analyzed in terms of conformational effects. As evident from Figure 3A, when acetonitrile-water mixtures of defined composition were employed, N-acetyl-L-Rphenylalanine ethyl ester manifested nonclassical van’t Hoff plots. The shape of each plot corresponded to the quadratic form16,23,24,28 of the dependency of ln k′ on 1/T, with the plots reaching a (predicted) maximum value near to 278 K. On the other hand, when methanol, a solvent that more easily forms hydrogen bonds with water molecules than acetonitrile, was used, the corresponding data (Figure 3B) for N-acetyl-L-R-phenylalanine ethyl ester over (28) Hearn, M. T. W.; Boysen, R. I.; Wang, Y.; Muraledaram, S. In Peptide Science-Present and Future; Shimonishi, Y., Ed.; Kluwer Academic Publishers b.v.: Amsterdam, 1999; pp 246-250.

4880 Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

the same ranges of φ and T exhibited ln k′ dependencies on 1/T that much more closely approximated the classical form of the van’t Hoff equation; i.e., the experimental data could be fitted to a linear relationship whereby the correlation coefficients were typically r2 g 0.9900. As such, the interaction of N-acetyl-L-R-phenylalanine ethyl ester with the n-butyl ligands in the presence of acetonitrilewater mixtures can, from a thermodynamic perspective, be characterized as a weakly heterothermic process,16,24,28 with the changes in enthalpy and entropy for the interaction temperaturedependent. With the methanol-water mixtures on the other hand, an isothermic interaction appears to prevail16,24,28 with N-acetyl-LR-phenylalanine ethyl ester. Thus, the current practice4 to use N-acetyl-L-R-phenylalanine ethyl ester, pentaphenylalanaine, and related low-molecular-weight compounds as control substances to evaluate the conformational status of polypeptides on interaction

Table 8. The ∆Hqassoc and ∆Sqassoc Values Derived for Bombesin from the Interaction with the n-Butyl-(C4)-silica Using Methanol-Water Mixturesa q ∆Hassoc (kJ/mol)

vol fractn, φ 0.35 0.40

308 K eq 2 eq 3

328 K eq 2 eq 3


308 K eq 2 eq 3

328 K eq 2 eq 3

-21.7 -12.6 -21.7 -18.9 -65.2 -37.0 -65.2 -56.8 -17.1 -17.7 -17.1 -18.8 -54.9 -57.0 -54.9 -60.1

a Based on the fit of the experimental data to either the pseudolinear regions (r2 g 0.98) of the ln k′ versus 1/T plots within the temperature ranges of T ) 278-318 and 318-358 K, according to eq 2, or alternatively determined according to eqs 3-5 at the same values of φ (i.e., φ ) 0.33 to φ ) 0.40) and at the same designated temperatures.

Figure 5. Dependence of the enthalpy change, ∆Hqassoc (A), and the entropy change, as ((∆Sqassoc/R) + ln Φ) (B) for glucagon using acetonitrile-water mixtures containing 0.1% TFA over the range φ ) 0.24-0.32 and T ) 278-308, 308-328, and 328-358 K. The filled points corresponded to the experimentally derived values; while the open circles correspond to the predicted values derived according to eqs 11-15.

with n-alkyl or other types of lipophilic ligands would now have to be questioned. Similar conclusions can be drawn from the recent observations on the interactive behavior of dansyl amino acids with reversed-phase sorbents where similar curvilinear van’t Hoff plots has been found.23 When heterothermic processes occur, the corresponding change in the heat capacity of the system is nonzero, i.e., ∆C°p * 0, and is also temperature-dependent. Under these circumstances, changes in enthalpy and entropy are both expected24,29 to become zero at critical values of T, i.e., at the critical temperatures TH when ∆H°assoc ) 0 and TS when ∆S°assoc ) 0, respectively. To q q evaluate ∆Hassoc and ∆Sassoc at a defined φ value for heterother(29) Privalov, P. L.; Gill, S. J. Adv. Protein Chem. 1988, 39, 191-234.

mic interactions measured over a wide T range, i.e., 278-358 K, nonlinear least-squares fitting procedures are required. Alternatively, over a limited range of T, van’t Hoff plots that exhibit slightly curvilinear characteristics have, by convention, often been approximated to pseudolinear dependencies, assuming that an q and isothermic interaction prevails with the values of ∆Hassoc q ∆Sassoc derived accordingly. As evident from Figure 3A and q q and ∆Sassoc for N-acetyl-L-R-phenylalanine ethyl Table 3, ∆Hassoc ester in acetonitrile-water mixtures showed weak dependencies q q on T at a defined φ value, with ∆Hassoc and ∆Sassoc decreasing as T was increased, but becoming less negative as φ was increased. q and In contrast with methanol-water mixtures, the ∆Hassoc q ∆Sassoc were found to be independent of T (Figure 3B). Acetonitrile-water and methanol-water systems represent the two most frequently used solvent systems in the RP-HPLC of polypeptides. These two solvents generate binary water combinations of different molecular organization.30,31 The solution chemistry characteristics of methanol-water mixtures are predominantly controlled by competitive hydrogen bonding.32 Acetonitrile, on the other hand, poorly forms hydrogen bonds33 and is organized in aggregates or loosely defined clusters in aqueous solution.34 From the above results, it is evident that the nature of the organic solvent in solvent-water mixtures of defined composition influences the van’t Hoff plot characteristics, even with relatively small compounds such as N-acetyl-L-R-phenylalanine ethyl ester. Linear van’t Hoff plots have been previously observed30-33 with low-molecularweight organic molecules, such as benzene derivatives, in the presence of acetonitrile- or methanol-water based eluents with n-alkylsilicas, suggesting that for these structurally simple comq q pounds ∆Hassoc and ∆Sassoc are essentially temperature-independent over a defined temperature range. The thermodynamic behavior of even these relatively simple organic compounds with n-alkylsilicas is however more complicated35,36 than would appear q q from such observations. For example, for ∆Hassoc , ∆Sassoc , and the phase ratio, Φ, to all be invariant of T, then the change in the heat capacity, ∆C°p, of the system must also be zero and independent of T over the entire range of T examined, with no phase transitions or changes in state occurring. When ∆C°p is nonzero and temperature dependent, then curvilinear van’t Hoff plots will arise as observed above for acetonitrile-water eluents with N-acetyl-L-R-phenylalanine ethyl ester. Previously, investigators have pointed out that phase transitions in the immobilized n-alkyl chains may cause nonlinearity in the van’t Hoff plots.31,32,35 For example, Gilpin and Squires36 found that the transition temperatures for n-octyl (C8), n-nonyl (C9), and n-decyl (C10) chains immobilized onto porous silica were 313.7 ( 0.71, 324.8 ( 2.1, and 333.1 ( 1.00 K, respectively, when pure water was used as the eluent. These differences correspond to an increase in the transition temperature of ∼10 K for each additional methylene unit in the bonded n-alkyl chain. On the basis of this empirical (30) Cole, L. A.; Dorsey, J. G.; Dill, K. A. Anal. Chem. 1992, 64, 1324-1329. (31) Jino, K.; Nagoshi, T.; Tanaka, N.; Okamoto, M.; Fetzer, J. C.; Biggs, W. R. J. Chromatogr. 1988, 436, 1-10. (32) Katz, E. D.; Lochmuller, C. H.; Scott, R. P. W. Anal. Chem. 1989, 61, 349356. (33) Johnson, B. P.; Khaledi, M. G.; Dorsey, J. G. Anal. Chem. 1986, 58, 23542365. (34) Hansen, R. L.; Harris, J. M. Anal. Chem. 1995, 67, 492-498. (35) Gilpin, R. K.; Sisco, W. R. J. Chromatogr. 1980, 194, 65-72. (36) Gilpin, R. K.; Squires, J. A. J. Chromatogr. Sci. 1981, 19, 195-201.


4881

Table 9. Virial Coefficients for the Enthalpy and Entropy Changes with Respect to Organic Solvent Concentration for Bombesin, β-Endorphin, and Glucagon for the Interaction with a n-Butyl-(C4)-silica Using Acetonitrile-Water Mixtures for the Temperature Ranges of T ) 278-308, 308-328, and 328-358 K, respectively q ∂(∆Hassoc )T/∂φ (kJ/mol)(0.01)-1

polypeptide bombesin β-endorphin glucagon

278-308 K 1.2 2.8 2.2

308-328 K 1.1 1.4 -0.30

328-358 K 3.1 × -0.87 -0.59

Figure 6. Dependence of the S values on temperature, T, for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester (N-acetyl-Fee). The dashed lines represent the calculated values according to the dependencies given by eqs 11-15, while the solid points and solid lines correspond to the experimental data. Also shown on these plots are the boundary lines corresponding to the confidence limit interval of 95%.

rule, the predicted transition temperature for the n-butyl (C4) chains of the sorbent used in this present work in the presence of aquo-organic solvent mixtures would be outside and below the investigated temperature range. Other retention studies30,32,33 as well as investigations on the molecular dynamics simulation of the n-alkylsilica surface37-39 have confirmed that the n-butyl chains have greatly reduced flexibility compared to the corresponding n-octyl or n-octadecyl chains; nevertheless the methyl headgroup of the n-butyl chain can still exhibit significant motion in water-lean mobile-phase conditions, but becomes more constrained in water-rich mobile phases. With the polypeptides examined in the present investigation, a relatively narrow isocratic range of φ values was utilized, and hence, the opportunity for significant solvational transitions and thus changes in the phase ratio of the chromatographic system were minimized. The carbon number of the bonded n-alkyl chain is not the only factor that conceptually could affect the linearity of van’t Hoff plots. According to the observations of Cole and co-workers,30 the van’t Hoff plots for benzene on a n-octadecylsilica sorbent with a bonded ligand density lower than 2.84 µmol/m2 were linear over a wide (37) Yarovsky, I.; Aguilar, M. I.; Hearn, M. T. W. Anal. Chem. 1995, 67, 21452153. (38) Klatte, S. J.; Beck, T. L. J. Phys. Chem. 1995, 99, 16024-16029. (39) Yarovsky, I.; Aguilar, M. I.; Hearn, M. T. W. J. Phys. Chem. 1997, 101, 10962-10971.

4882 Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

q ∂(∆Sassoc )T/∂φ (J mol-1 K-1)(0.01)-1

10-2

278-308 K

308-328 K

328-358 K

0.67 4.1 2.9

0.26 -0.7 -5.22

-2.9 -7.5 -6.1

Figure 7. Plots of ln ko versus 1/T for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester determined at the organic solvent volume fraction of φ ) 0.26 with an acetonitrilewater mixture containing 0.1% TFA and n-butylsilica. The plots show the experimental data and the lines of best fit according to the relationship given as eq 9, together with boundary lines corresponding to confidence limits interval of 95%.

temperature range (268-353 K) but when the bonded ligand density was g3.06 µmol/m2, nonlinear relationships were observed. In the present investigations, the n-butylsilica sorbent had a ligand density of ∼2.85 µmol/m2. Although the ligand density with n-alkysilicas will affect the thermodynamics of the system in terms of the extent of sorbent solvation and/or participation of silanophilic interactions, as is apparent from the results with N-acetyl-L-R-phenylalanine ethyl ester and the polypeptides investigated in this study, with a sorbent of defined ligand density and phase ratio, the molecular characteristics of the solute and the choice and volume fraction of the organic modifier used to form the water-rich mobile phase make dominant contributions to the thermodynamic processes that determine the shape of van’t Hoff plot. As is evident from Figure 4, the van’t Hoff plots for bombesin, β-endorphin, and glucagon using acetonitrile-water mixtures show marked deviations from linearity. As discussed elsewhere,12,16,24,28 such nonclassical van’t Hoff plots for polypeptides or proteins in the presence of nonpolar ligands reflect heterothermic interactions, whereby the changes in heat capacity and, hence, the changes in enthalpy and entropy of the system are functions of T. The results obtained with the methanol-water mixtures in contrast indicated that T does not affect these thermodynamic parameters as markedly as observed for acetonitrile-water mixtures. In the context of these studies, it is interesting to note that critical temperatures of TH ≈ 308 K and

Figure 8. Plots of the dependencies of S, ∆Hqassoc, ∆Sqassoc, and ∆C°assoc on the accessible surface area, Atot, calculated from the expression Atot ) 11.4(MW)2/3 for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester (N-acetyl-Fee) with an acetonitrile-water mixture of φ ) 0.26 for T ) 278-358 K. The solid symbols correspond to the experimental data, while the lines represent the linear regression plots of the data at specific temperatures.

TS ≈ 328 K, respectively, were obtained for these three polypeptides with acetonitrile-water mixtures, indicative of significant transitions in the organization of the molecular nature of the ternary complex involving the polypeptide-nonpolar ligandsolvent molecules at or near these temperatures. Such heterothermic processes are often associated with enthalpy-entropy compensation effects.40,41 When similar, temperature-dependent q q and ∆Sassoc occur with polypeptides or variations in ∆Hassoc proteins in bulk solution, these thermodynamic processes are frequently attributed to conformational changes due to thermal disruption of the secondary structures of these biomacromolecules.42,43 It has been previously documented by circular dichroism (CD) and two-dimensional 1H NMR studies that bombesin, β-endorphin, and glucagon can adopt a significant extent of R-helical and/or β-sheet structure in nonpolar solvent environments.44-49 Acetonitrile in the range of 15-65% (v/v) has been shown to induce or stabilize R-helical and β-sheet structures of these polypeptides,24,26,28 while methanol over similar percentage ranges tends to destabilize their secondary structures. The results from the (40) Leffler, J.; Grundwald, E. In Rates and Equilibria of Organic Reactions; WileyInterscience: New York, 1963; p 128. (41) Lumry, R.; Rajender, S. Biopolymers 1970, 9, 1125-1131. (42) Murphy, K. P.; Privalov, P. L.; Gill, S. J. Science 1990, 247, 559-561. (43) Murphy, K. P.; Gill, S. J. J. Mol. Biol. 1991, 222, 699-709. (44) Cavorta, P.; Farrugia, G.; Masotli, L.; Sarto, G.; Szabo, A. G. Biochem. Biophys. Res. Commun. 1986, 141, 99-105. (45) Carver, J. A. Eur. J. Biochem. 1987, 168, 193-199. (46) Carver, J. A.; Collins, J. G. Eur. J. Biochem. 1990, 187, 645-650. (47) Hruby, V. J. Mol. Cell. Biochem. 1982, 44, 49-64. (48) Korn, A. P.; Ottensmeyer, F. P. J. Theor. Biol. 1983, 105, 403-415. (49) Mattice, L.; Robinson. R. M. Biochem. Biophys. Res. Commun. 1981, 101, 1311-1317.

present investigation support the concept that, with methanolwater mixtures, bombesin, β-endorphin, and glucagon when bound to solvated lipophilic ligands manifest limited or no changes in their conformations from those present in the free solution state. In contrast, with the acetonitrile-water mixtures, the trends in q q and ∆Sassoc values suggest that acetonitrile and the the ∆Hassoc nonpolar n-butyl groups synergistically induce and stabilize the secondary structures, e.g., R-helical and/or β-sheet, of these polypeptides at lower T values. As indicated above, the solvents used in these experiments have different solution structures as water-rich mixtures. Comparison of the ln k′ values for bombesin at the same value of the volume fraction, φ, of these two different solvent (cf. Figure 1) revealed that this polypeptide was more prone to partition from the nonpolar ligand to a non-hydrogen-bonding solvent than a highly hydrogen-bonded solvent, and analogous results were evident for glucagon and β-endorphin. Thus, with an acetonitrilewater mixture of φ ) 0.25 at 298 K, the ln k′ value for bombesin was -1.02. For methanol-water at the same φ value, the corresponding ln k′ value was estimated to be g3.67 (a value obtained by extrapolation). The ln k′ value when φ f 0, i.e., ln ko, can be related to the incremental free energy change, ∆G°o/w, and empirically to the partition coefficient, Po, for the process of transferring the polypeptide from a pure water state to a nonpolar ligand bound state, through the expression,

ln ko ) -(∆G°o/w/RT) ) ln Po + c

(7)

where c is a constant related to the molecular properties of the polypeptide and the solvent system. Central to earlier determinations of Po values by gradient elution methods has been the assumption that ∆G°o/w and ln ko are temperature-independent. Although such behavior appears to be followed by N-acetyl-L-Rphenylalanine ethyl ester (Figure 7), clearly with bombesin, β-endorphin, or glucagon this situation does not prevail. As discussed above, gradient elution RP-HPLC procedures have been widely used over the past several years to explore conformational properties, to derive partition coefficients, and to assess other parameters related to the interaction of polypeptides and proteins with lipophilic ligands. In light of the present investigations, the significance of gradient-generated results related to partition coefficients or similar biophysical properties of polypeptides requires reexamination, particularly in circumstances where the interaction thermodynamics remain poorly understood. q The change in Gibbs free energy (∆Gassoc ) for the interaction of a polypeptide with a nonpolar ligand at a defined T and solvent composition is related to ln k′ through the dependency q ln k′ ) -∆Gassoc /RT + ln Φ

(8)

q The value of ∆Gassoc can be directly evaluated from the Gibbs-Helmhotz relationship, i.e.,

q q q ∆Gassoc ) ∆Hassoc - T∆Sassoc

(9)

As expected for a thermodynamically favorable process, the q ∆Gassoc values derived according to eqs 2, 8, and 9 were negative Analytical Chemistry, Vol. 71, No. 21, November 1, 1999

4883

for the polypeptides and N-acetyl-L-R-phenyl-alanine ethyl ester at lower T values and with the more water-rich solvent mixtures. For example, at 298 K, the process of transferring bombesin from an acetonitrile-water mixture of φ ) 0.25 to the nonpolar ligands q was associated with a Gibbs free energy change of ∆Gassoc ) -0.36 kJ/mol. When a methanol-water mixture of φ ) 0.25 was q used, the value of ∆Gassoc associated with the transfer of bombesin to the n-butyl ligands was -9.7 kJ/mol. At elevated T values, q i.e., T g 338 K and high φ values, positive values of ∆Gassoc were observed for bombesin and the other polypeptides, consistent with a limited interaction occurring with the nonpolar ligand(s) under these conditions. The results given in Tables 5-8 indicate that over the range q q of T ) 278-358 K, the magnitudes of ∆Hassoc and ∆Sassoc q changed markedly. At T values of g288 K, the values of ∆Hassoc q and ∆Sassoc for bombesin, β-endorphin, and glucagon were all negative, while at lower T values, i.e., at T ) 278 K, positive values for these thermodynamic parameters were obtained. Negative q ∆Hassoc values imply that the interaction processes involving these polypeptides and the nonpolar ligand were exothermic. q Negative ∆Sassoc values on the other hand imply that the order of the system increased as part of the polypeptide-ligand binding q q process. The ∆Hassoc and ∆Sassoc data for these polypeptidenonpolar ligand systems are thus consistent with the contribution from both conformational and solvational effects as the temperature of the system was increased between T ) 278 and 358 K. These results indicate that conformational stabilization of polypeptides occurs in the bulk solvent and in the ligand-bound state depending on the T and the solvent composition. Higher acetonitrile concentration at low T will tend to preferentially solvate these polypeptides and stabilize their secondary structures in the bulk solution state compared to the ligand-bound state, resulting q in less negative values of ∆Sassoc for the interactive process and q small negative or even positive values of ∂(∆Sassoc )T/∂φ. However, when higher T conditions but lower acetonitrile concentrations were employed, hydrophobic effects mediated by the n-butyl ligands assume a relatively greater importance in the conformational stabilization of the polypeptide in the ligand-bound state q q where again negative values of ∆Sassoc and ∂(∆Sassoc )T/∂φ were observed (Tables 5-8). Polypeptides with the propensity like bombesin, β-endorphin, or glucagon to form preferred β-sheet or R-helical secondary structures in lipophilic environments will thus more readily exhibit these conformational features when acetonitrile-water mixtures rather than methanol-water mixtures are used at low T values. Such observations are consistent with our associated investigations with diasteriomeric polypeptides24,28 and insulin variants (Hearn and Wang, unpublished results) where q the effect of temperature changes on ∂(∆Hassoc )T/∂φ as polypeptides thermally unfold has been elaborated. Since the apparent q )T/∂φ values for bombesin, glucagon, and β-endorphin ∂(∆Hassoc were markedly different over the different temperature ranges, it can be concluded that the extent of interaction of the amino acid side chains and backbone amide groups of each of these polypeptides with the organic solvent or water molecules in the mobile phase, as well as with the nonpolar stationary-phase ligands, at the lower temperatures differs as the temperature is increased due to conformational changes of these polypeptides. Arising from this process, the solvational characteristics of these 4884


polypeptides will change in terms of the hydrogen-bonding status of these biomolecules as the temperature is varied. To support these conclusions, similar RP-HPLC investigations have been conducted in this laboratory using simple organic compounds such as toluene, nitrobenzene, and phenol. Interestingly, the experimental data with these small organic compounds indicated that with increasing acetonitrile concentrations over the range of φ ) q value for toluene increased, but de0.25-0.50, the ∆Hassoc creased for phenol and remained essentially constant for nitrobenzene (Hearn and Zhao, manuscript in preparation). From eqs 2 and 3 and the general form of eq 9, an expression q q q linking S with∆Gassoc , and hence S to ∆Hassoc and ∆Sassoc , can be obtained. Thus, q ∆Gassoc ) -RT ln k′ + RT ln Φ

(10)

Differentiation of eq 10 with respect to φ yields q ∂(∆Gassoc ∂(ln k′)T )T ) -RT ∂φ ∂φ

(11)

Substitution of eq 2 into eq 11 gives

∂(ln k′)T/∂φ ) -S

(12)

q )T/∂φ ) RTS ∂(∆Gassoc

(13)

Following substitution of eqs 11-13 into eq 8, we have q q q ∂(∆Sassoc )T ∂(∆Hassoc )T )T ∂(∆Gassoc ) -T ∂φ ∂φ ∂φ

(14)

and hence q

S)

q

q

∂(∆Sassoc)T 1 ∂(∆Hassoc)T 1 ∂(∆Sassoc)T -T RT ∂φ R ∂φ ∂φ

(15)

By using eq 15 and the experimentally obtained values of the q q virial coefficients ∂(∆Hassoc )T/∂φ and ∂(∆Sassoc )T/∂φ listed in Table 9, comparisons were made between the predicted and the experimentally determined S values for bombesin, β-endorphin, glucagon, and N-acetyl-L-R-phenylalanine ethyl ester with acetonitrile-water eluents as a function of T at different φ values. These results (Figure 6) demonstrated that as the molecular weight of the polypeptide was increased, the S values also increased. The S versus T curves for bombesin, β-endorphin, and glucagon followed U-shaped dependencies. Larger S values are evident at lower and higher T values, suggesting that under these conditions these polypeptides generate on association with the nonpolar ligands greater hydrophobic contact areas, presumably due to the involvement of R-helical or β-sheet states at low T and more q unfolded states at high T. Moreover, when the ∆Hassoc and q ∆Sassoc values for bombesin were compared to the corresponding values for β-endorphin or glucagon at the same eluent composition (i.e., at φ ) 0.26), it was evident that with these higher molecular weight polypeptides, the magnitudes of the

q q ∆Hassoc and ∆Sassoc changes were also larger. This behavior is consistent with the larger polypeptides having greater total surface areas, Atots, and potentially having larger hydrophobic areas, ∆Ahyds, in contact with the nonpolar ligands. This finding is in accord with the known linkage12,16,50-53 between these enthalpic and entropic terms and the extrathermodynamic molecular parameters, such as the hydrophobic surface area, ∆Ahyd. Previously, we proposed10,16,17 that the S value of a polypeptide can be related to both the hydrophobic contact area, ∆Ahyd, and the cavity factor, κe, through the relationship

S ) a∆Ahyd + bκe + c

(16)

where a, b, and c are constants related to the molecular properties of the polypeptide. The term κe is a solvophobic parameter10,11,16,18 related to the ratio in energy required for the formation of a cavity with surface area equal to the accessible surface area, Atot, of the polypeptide and the energy required to extend the planar surface of the liquid by the same area. Since ∆Ahyd is an extrathermodynamic parameter proportional to Atot and reflects a group molecular property of the polypeptide at the nonpolar ligand interface, a q q nexus should thus exist between S, ∆Hassoc , ∆Sassoc , and ∆C°assoc and these extrathermodynamic molecular properties at defined φ and T values. q q From the plots (Figure 8) of S, ∆Hassoc , ∆Sassoc , or ∆C°assoc versus Atot for bombesin, β-endorphin, glucagon, and N-acetyl-LR-phenylalanine ethyl ester, it is apparent that the molecular weight per se is not the sole determinant. From CD investigations,26,49 β-endorphin is known to assume ∼21% R-helical and ∼31% β-sheet content in low-pH acetonitrile-water combinations encompassing the range of 0.25 < φ < 0.35, but 56% β-sheet content and no R-helical structure in neat water systems. In the case of glucagon,26,48 the R-helical and β-sheet content is about 23 and 21%, respectively, in similar acetonitrile-water combinations, with 65% β-sheet content and no R-helical structure in neat water systems. In contrast, bombesin exhibits26,44-46 a very small R-helical content (∼5%) but ∼60% β-sheet content in acetonitrilewater combinations. In this context, it can also be noted that the q q magnitude of the changes in the values of S, ∆Hassoc , ∆Sassoc , or ∆C°assoc for bombesin as T was increased were much smaller than those observed for β-endorphin or glucagon. In the present investigations, the mole fractions of the acetonitrile used for the (50) Dill, K. A. Biochemistry 1990, 29, 7133-7155. (51) Lee, B. Proc. Natl. Acad. Sci. U.S.A. 1991, 88, 5154-5158. (52) Murphy, K. P.; Freire, E. Adv. Protein Chem. 1992, 43, 313-361. (53) Richards, F. M. Annu. Rev. Biophys. Bioeng. 1977, 6, 151-176. (54) Creighton, T. E. In Proteins, Structure and Molecular Properties; W. H. Freeman & Co.: New York, 1984; pp 240-245.

derivation of the ln k′ versus 1/T plots were selected to correspond to the concentration values known from CD measurements to induce polypeptide secondary structures. The scatter evident in Figure 8, particular with the data for bombesin, may reflect the differences between the conformational states of these polypeptides under these conditions. Results from our earlier CD studies24,26 as well as from these polypeptide-ligand binding measurements collectively suggest that the extent of conformational stabilization that occurs with different polypeptides in the bulk aquo-organic solvent milieu and/or at the interface with the nonpolar ligands plays a significant role in determining the magnitude of the changes in these thermodynamic and extrathermodynamic parameters at different T and φ values. Transitions from random coil to R-helical or β-sheet structures induced by the lipophilic environment of the nonpolar ligands will be associated with greater changes in the total interaction energy and the order of the system when conformationally more promiscuous polypeptides are transferred from a bulk solvent state to a ligandbound state, such as occurs with, for example, glucagon. As evident from these results as T was increased, β-endorphin and glucagon, and to a lesser extent bombesin, showed compensatory effects in terms of their enthalpic and entropic changes. q As discussed elsewhere,16,27 these dependencies of ∆Hassoc and q ∆Sassoc for bombesin, β-endorphin, or glucagon on T and φ are similar to entropy-enthalpy compensation effects previously noted16,27,40-43 with other middle-molecular-weight polypeptides and proteins in solution and in the bound states. Finally, the dependency of the S values of these polypeptides on these thermodynamic parameters and T underscores the curvilinear behavior observed in the ln k′ versus φ plots, not only of bombesin, β-endorphin, or glucagon but for many other polypeptides and proteins when acetonitrile-water eluents are employed with RPHPLC sorbents of different n-alkyl chain length. Since analogous experiments can be contemplated for salt-mediated hydrophobic interaction systems with proteins and polypeptides, the approach described in this paper should be of generic application for studies on the thermodynamic basis of the binding behavior of polypeptides and proteins in lipophilic environments where the hydrophobic effect constitute the dominant mechanism of interaction. ACKNOWLEDGMENT These investigations were supported by the Australian Research Council, the Bilateral Program of the Australian Academy of Science and the Academia Sinica, and the Centre for Bioprocess Technology Special Research Grant program. Received for review January 13, 1999. Accepted July 21, 1999. AC990028X


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Investigations into the Thermodynamics of Polypeptide Interaction

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