Influence of Pressure on the Retention and Separation of Insulin

Anal. Chem. 2003, 75, 3999-4009

Influence of Pressure on the Retention and Separation of Insulin Variants under Linear Conditions Xiaoda Liu,†,‡ Dongmei Zhou,† Pawel Szabelski,§ and Georges Guiochon*,†

Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600 and Division of Chemical and Analytical Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, and Department of Theoretical Chemistry, Maria Curie-Sklodowska University, pl. M.C.-Sklodowskiej 3, 20-031 Lublin, Poland

The effect of pressure on the retention behavior of insulin variants in RPLC on a YMC-ODS C18 column was investigated under linear conditions. The retention factors of these variants increase nearly 2-fold when the average column pressure is increased from 55 to 250 bar while their separation factors remain nearly unchanged. This effect is explained by a change of the partial molar volume of the insulin variants associated with their adsorption that decreases from -99 to -80 mL/mol for mobile-phase concentrations of acetonitrile increasing from 29 to 33% (v/v). This volume change is much larger than the one observed with low molecular weight compounds. For the same pressure variation, the average number Z of acetonitrile molecules displaced from the protein and the stationary phase upon adsorption increases from 22 to 23.3. The pressure-induced relative increase of the term b[S]/[D0]Z (which corresponds to the initial slope of the adsorption isotherm) is approximately twice as large for Lispro than for porcine insulin. Because the binding constant of insulin decreases with increasing pressure, this suggests that the number of binding sites on the stationary phase increases even faster. Finally, it was observed that the column efficiency at flow rates higher than 0.6 mL/min increases slightly with increasing pressure. It is suggested that these observations are also valid for other proteins analyzed in RPLC. The study of the effects of pressure in chemistry, molecular biophysics, enzymology, and biology has attracted considerable attention for a long time.1-3 Pressure and temperature are the two fundamental thermodynamic parameters that define the state of a substance. However, while the variations of temperature affect * Corresponding author. Tel: +1-865-974-0733. Fax: + 1-865-974-2667, Email: [email protected]. † The University of Tennessee and Oak Ridge National Laboratory. ‡ Present address: Beijing Institute of Transfusion Medicine, Beijing 100850, China. § Maria Curie-Sklodowska University. (1) The effects of pressure on organisms; Symposia of the Society for Experimental Biology XXVI; Academic Press Inc.: New York, 1972. (2) Heremans, K. In High-Pressure Chemistry, Biochemistry and Materials Science; Winter, R., Jonas, J. Eds.; Kluwer Academic Publishers: Dordrecht, 1993. (3) Markly, J. L., Northrop, D. B., Royer, C. A., Eds. High-Pressure Effects in Molecular Biophysics and Enzymology; Oxford University Press: New York, 1996. 10.1021/ac0205964 CCC: $25.00 Published on Web 07/16/2003

© 2003 American Chemical Society

both the internal energy and the volume of a chemical system, those of pressure affect only its volume, without affecting its kinetic energy. From measurements made under different pressures, one can derive the changes in the partial molar volume of solutes that are associated with various equilibria. In recent years, the study of the effect of pressure on proteins has attracted great interest.4-7 It provides new insights into protein folding, its dynamics, and the structure of proteins.8-20 High pressures can also induce the denaturation of proteins, a phenomenon that begins at pressures above 1000-3000 bar and becomes prominent at higher pressures.6,9,12 Due to the action of pressure on the forces governing interand intramolecular interactions, the use of high pressures in the development of adsorption methods for the purification of bioactive molecules is of interest.21 For example, it is used in the separation of antigens from their corresponding antibodies and in the development of new affinity matrixes.21 Le Chatelier’s principle states that, at equilibrium, a system tends to minimize the effect of any external factor by which it is perturbed. So, if a positive association volume is observed in a given physical environment, pressure-induced dissociation will take place and can be used if needed. In HPLC, pressure is conventionally considered as the source of the force that drives the mobile-phase stream, but it is not thought of as an important parameter that may affect solute (4) Gross, M.; Jaenicke, R. Eur. J. Biochem. 1994, 221, 617. (5) Balny, C.; Masson, P.; Heremans, K. Biochim. Biophys. Acta 2002, 1595, 3. (6) Hayashi, R. Biochim. Biophys. Acta 2002, 1595, 397. (7) Chalikian, T. V.; Breslauer, K. Curr. Opin. Struct. Biol. 1998, 8, 657. (8) St. John, R. J.; Carpenter, J. F.; Randolphin, T. W. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 13029. (9) Prehoda, K. E.; Mooberry, E. S.; Markley, J. L. Biochemistry 1998, 37, 5785. (10) Chalikian, T. V.; Breslauer, K. J. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 1012. (11) Mozhaev, V. V.; Heremans, K.; Frank, J.; Masson, P.; Balny, C. Proteins: Struct., Funct., Genet. 1996, 24, 81. (12) Kunugi, S.; Tanaka, N. Biochim. Biophys. Acta 2002, 1595, 329. (13) Paci, E.; Marchi, M. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 11609. (14) Kharakoz, D. P. Biophys. J. 2000, 79, 511. (15) Dadarlat, V. M.; Post, C. B. J. Phys. Chem. B 2001, 105, 715. (16) Payne, V. A. P.; Matubayasi, N.; Murphy, L. R.; Levy, R. M. J. Phys. Chem. 1997, 101, 2054. (17) Chalikian, T. V.; Breslauer, K. J. Biopolymers 1996, 39, 619. (18) Paci, E.; Velikson, B. Biopolymers 1997, 41, 785. (19) Gavish, B.; Hardy, C. J. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 750. (20) Heremans, K.; Smeller, L. Biochim. Biophys. Acta 1998, 1386, 353. (21) Lemay, P. Biochim. Biophys. Acta 2002, 1595, 357.

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retention. The bulk compressibility of mobile phases is minimal for the moderate pressures used in HPLC (with column inlet pressures almost always lower than 350 bar). The mobile-phase compressibility has little direct influence on the pressure dependence of the solute retention in LC.22 However, many of the equilibria associated with the separation process have been demonstrated to be pressure-dependent, such as the ionization, adsorption, partitioning, and complexation of solutes.1,2 In the pressure range used in conventional HPLC, the pressure dependence of the physicochemical properties of solutes and solvents (such as equilibrium constants, coefficients of thermal expansion, conductance, viscosity, fluidity, etc.) is linear.3 The most direct explanation for the effect of pressure on the equilibrium constant is a change of the partial volume of 1 mol of solute associated with its passage from one phase of the system to the other. (For the sake of simplicity, the change of the partial volume of 1 mol of solute associated with its passage from one phase of the chromatographic system to the other will be called the partial molar volume change and will be noted ∆Vm.) A pressure increase may also change the stationary-phase structure, its interactions with the mobile phase, or both, affecting both the partial molar volume of the solute and its molecular interactions with the stationary phase. Note that the primary factor is the partial molar volume change. The possible influence of the pressure, the temperature, and the mobile-phase composition on the protein conformation, on its hydration and solvent shells, and on the importance of the solvation layer of the stationary phase affect the molar volumes of the protein in the two phases, hence, usually, their difference. They may explain a nonlinear dependence of the effect of the pressure on retention, not the effect itself. Several experimental studies have demonstrated that pressure can have a significant impact on solute retention.23-32 It was shown that a partial molar volume change is the most probable explanation for a pressure-induced shift of the retention factors.23,24 The possible contributions of pressure-induced changes in the solute ionization, complexation constants, or both can be eliminated by controlling the mobile-phase pH.29 Bylina and Ulanowicz30 observed the strong influence of the column pressure on the retention of insulin. Chen et al.31 investigated the retention behavior of lysozyme on a stationary phase. They found that the partial molar volume change was of the order of -100 mL/mol. Szabelski et al.32 studied the pressure/temperature dependence of the retention of insulin variants on an octyl-bonded silica and found that the partial molar volume changes of bovine insulin, porcine insulin, human insulin, and Lispro were all close to -100 mL/mol at 25 and 50 °C. (22) Martin, M.; Blu, G.; Guiochon, G. J. Chromatogr. Sci. 1973, 11, 641. (23) McGuffin, V. L.; Evans, C. E. J. Microcolumn Sep. 1991, 3, 513. (24) Guiochon, G.; Sepaniak, M. J. J. Chromatogr. 1992, 606, 148. (25) McGuffin, V. L.; Chen, S. J. Chromatogr. 1997, 762, 35. (26) McGuffin, V. L.; Chen, S. Anal. Chem. 1997, 69, 930. (27) Ringo, M. C.; Evans, C. Anal. Chem. 1997, 69, 4964. (28) Evans, C. E.; Ringo, M. C.; Ponton, L. M. In Unified Chromatography; Parcher, J. F., Chester, T. L., Eds.; ACS Symposium Series 748; American Chemicl Society: Washington, DC, 1999; p 31. (29) Evans, C. E.; Davis, J. A. Anal. Chim. Acta 1999, 397, 163. (30) Bylina, A.; Ulanowicz, M. Chem. Anal. (Warsaw) 1998, 43, 955. (31) Chen, S.; Ho, C.; Hsiao, K.; Chen, J. J. Chromatogr. 2000, 891, 207. (32) Szabelski, P.; Cavazzini, A.; Kaczmarski, K.; Liu, X.; Horn, J. V.; Guiochon, G. J. Chromatogr., A 2002, 950, 41.

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A complete and rigorous mathematical formulation of the pressure equilibrium shifts in chromatographic separations was proposed by Martire,33 with emphasis on supercritical fluid chromatography. However, the application of the unified molecular theory of chromatography to investigate the influence of pressure on the retention in HPLC is difficult. The determination of accurate estimates of all the parameters involved is beyond the scope of this work. We can derive the partial volume change of the solute from experimental data, but the contributions of the other factors involved are difficult to assess. Geng and Regnier developed the stoichiometric displacement model for protein separation in reversed-phase liquid chromatography.34 This model predicts that the retention factor is a function of the number of solvent molecules that are displaced when the solute is adsorbed from the solution onto the surface of the adsorbent. In this work, we used the thermodynamic approach and the stoichiometric displacement model to investigate the pressure dependence of the chromatographic behavior of insulin, to find an estimate of the number of binding sites on the stationary phase, to assess the dependence of these parameters on the local pressure and the solvent strength, and to study the extent to which the pressure and the solvent strength dependence of the solvation of protein molecules affect the variations of their retention factor in chromatography. This discussion focus on the chromatographic behavior of insulin variants under linear conditions. The equilibrium isotherm relates the mobile (C) and the stationary phase (q) concentrations of the solute when phase equilibrium is achieved. The two-term expansion of the isotherm at low mobile-phase concentrations is q ) aC + bC2. Chromatography is carried out under linear conditions as long as a . bC, and the isotherm practically follows linear behavior. THEORETICAL SECTION All matter is compressible. Like any other volume of any substance, the molar volume of a compound decreases when placed under increasing pressure. However, this variation is small, of the order of a few percent for a pressure increase of 250 bar, the largest applied in this work, so the influence of compressibility can be rightfully neglected, as pointed out by Martire and Boehm,33 who showed that the density of the mobile phase has little effect on retention in HPLC. However, the influence of pressure on the partial molar volume of a protein (volume that includes that of its hydration or solvation shells, or both) is not constant, as we see later. Volume Change of Solute upon Adsorption. In a chromatographic system, the solute retention is directly related to the equilibrium thermodynamics. The change in the Gibbs free energy of the equilibrium is given by

∆G ) ∆H - T∆S ) -RT lnK ) -RT ln(k/Φ)

(1)

where ∆G, ∆H, and ∆S are the differences in the molar Gibbs free energy, the molar enthalpy. and the molar entropy, respec(33) Martire, D. E.; Boehm, R. E. J. Phys. Chem. 1987, 91, 2433. (34) Geng, X.; Regnier, F. E. J. Chromatogr. 1984, 296, 15.

tively, that are associated with the passage of 1 mol of solute from the mobile to the stationary phase, R is the universal gas constant, K is the distribution constant of the solute between the two phases, k is the solute retention factor, and Φ is the phase ratio. The equilibrium of the solute between the two phases may be analyzed from the pressure and the temperature dependences of the free energy:

where Cs and Cm are the equilibrium concentrations of the protein in the stationary and the mobile phases, respectively, and K is the distribution constant of the protein between these two phases. For a chromatographic separation performed under isocratic conditions, the concentration of the organic solvent in the mobile phase remains constant. In this case, we define b as an affinity constant and rewrite eq 7 as

d(∆G) ) ∆V dP - ∆S dT

b ) bds/[D0]z ) Cs/Cm[S] ) K/[S]

(2)

where ∆V represents the change in the partial specific molar volume of the solute that is associated with the passage of 1 mol from the mobile to the stationary phase. Under constant temperature,

(∂∆G/∂P)T ) ∆V

(∂ ∂Pln k)

)-

T

(3)

∂ ln φ ∆V + RT ∂P

(

)

T

(4)

with

φ ) (1 - )/

(5)

where is the total porosity of the column. Note that the internal porosity of the column varies with increasing pressure while, barring disruption in the packed bed under high pressure, the external porosity does not. Pressure affects the solvation of the bonded alkyl chains, which are also more compressible than the bulk mobile phase. Accordingly, the phase ratio is a function of the applied pressure (see later, eq 11). Number of Solvent Molecules Displaced during Adsorption. According to the stoichiometric displacement model,34 the protein (P) and the nonpolar surface (S) of a C18-bonded stationary phase are both solvated by the mobile phase. Accordingly, the solvent molecules (D0) that are in the binding area before adsorption takes place are displaced upon adsorption of the protein, through the formation of hydrophobic interactions between P and S. The protein adsorption equilibrium process can be written

P + S h PS + zD0

(6)

where z is the total number of solvent molecules that are displaced by the adsorption of one protein molecule, whether these solvents molecules were associated with the protein surface or with the surface of the stationary phase. These are the solvent molecules associated with the alkyl chains of the stationary phase and with the binding area of the protein molecule. This number is unique for each protein and is related to the presence of other mobilephase additives, such as acids. The association equilibrium constant of eq 6, bds, is defined by the equation

bds )

Cs[D0]z Cm[S]

[D0]z

)K

[S]

(7)

(8)

The retention factor of the solute can be expressed as

k ) Kφ ) BdsΦ[S]/[D0]z

(9)

Although the ligand density on the surface of the stationary phase remains constant when the pressure inside the column changes, the availability of these ligands for adsorption is related to the degree of their solvation. [S] represents the number of binding sites available for a protein molecule. The constant I ) bdsΦ[S] in eq 9 is related to the equilibrium constant for the adsorption process, the stationary-phase ligand density, and the phase ratio. We can derive the slope Z and the intercept, ln I, from the variation of the retention factor with the water concentration of the mobile phase, using the loqarithmic form of eq 9

ln k ) Z ln(1/[D0]) + ln I

(10)

Through eqs 4 and 10, we can estimate the partial molar volume change of the protein molecule and the variations of the protein adsorption constant and of the density of binding sites on the stationary phase with the pressure. EXPERIMENTAL SECTION Equipment. A HP 1100 liquid chromatography system (Agilent Technologies, Palo Alto, CA) was used for the experimental determinations. This instrument is equipped with a multisolvent delivery system, an automatic sample injector with a 100-µL loop, a diode-array detector, a high-pressure flow cell, and a computer data station. The pumping system of this instrument is extremely stable. The flow rate has a long-term reproducibility better than 0.1%. The eluent was obtained by mixing the two solvents (see below) in the desired proportions, using the properly programmed multisolvent delivery system. The stability of the composition of this solution was also better than 0.1%. Chromatographic Conditions. (1) Mobile Phase and Chemicals. The mobile phase was a solution of acetonitrile, water, and trifloroacetic acid (TFA). Acetonitrile and water were both HPLC grade solvents from Fisher Scientific (Fair Lawn, NJ). TFA was from Acros. Potassium nitrate and uracil, both from Fisher Scientific, were used as unretained compounds. The mobile phase A was an aqueous solution of 20% acetonitrile and 0.1% TFA; the mobile phase B was an aqueous solution of 40% acetonitrile and 0.1% TFA. We obtained the mobile phase required, an aqueous solution of acetonitrile at concentrations ranging from 28 to 36%, by mixing the two mobile phases in the required proportion. Porcine insulin (MW ) 5778, pI ) 6.0) and Lispro were gifts from Eli Lilly (Indianapolis, IN). These two insulin variants were at a Analytical Chemistry, Vol. 75, No. 16, August 15, 2003

4001

purity of 99%, determined through an HPLC assay. All solutions were filtered, using PTFE filters (pore size 0.2 µm) purchased from Nalgene (Rochester, NY). The insulin solutions used in the experiments were all freshly prepared. The sample concentration was ∼1 g/L; the injection volume was 5 µL. (2) Column. The column used in our experiments was a 3.9 × 150 mm YMC ODS-A column (Waters, Milford, MA, column EJ26490). The mean particle size of this stationary phase is 5 µm, with an average pore diameter of 12 nm. The particles were chemically bonded to n-octadecyl chains. For determinations made under high pressures, sections of 0.0025-in.-i.d. PEEK tubing were connected to the outlet of the detector. The use of a 45-cm-long section of this tubing leads to an increase of the outlet column pressure by ∼200 bar at a flow rate of 1 mL/min. Tubings of appropriate lengths were used to achieve the desired value of the outlet pressure. Because of the design of the pumping system, adding such a tubing section downstream of the detector leaves unchanged the mobile-phase flow rate and the pressure drop along the column. Consequently, the whole column is subjected to a higher pressures, by up to 240 bar in our experiments. The maximum inlet pressure used was ∼320 bar. (3) Precision of the Measurements. Most measurements were repeated five times, some seven. The relative standard deviation (RSD) of the measurements of the retention time of the unretained compound was always smaller than 0.2% and often ∼0.09% (RSD with n ) 5). The reproducibility of the retention times of the insulin variants was always better than 0.36% (RSD with n ) 5). The RSD of the partial molar volume change was below 2%. The RSD of the column efficiency was between 4 and 6% (for seven measurements). RESULTS AND DISCUSSION It is important to note that the effects of increasing the average column pressure that we observed and that we report here are all linear. Accordingly, the average value measured for a parameter is also the value of this parameter at the average column pressure, a simple relationship that would not exist for a more complex functional dependence (e.g., by contrast, the average retention factor for a column that is not isothermal would be markedly different from the retention factor at the average column temperature35). Chromatographic Characteristics of Insulin under Different Pressures. The major influence of the local pressure on the retention factors of the insulin variants is illustrated in Figure 1, which compares the chromatograms obtained for a mixture of Lispro and porcine insulin under two different values of the average column pressure, 56 and 238 bar, respectively. As already reported, the retention factor of the insulin variants increases nearly 2-fold for a 200 bar increase in the column average pressure.30 The experimental results show also that the half-widths of the insulin peaks increase with increasing pressure, whereas their heights decrease, as expected when retention increases. However, although the separation factors of the two variants remain practically unchanged, the resolution between porcine insulin and Lispro increases by nearly 10%, from 2.3 to 2.5, when the average pressure increases from 56 to 238 bar (Figure 1). The values of (35) Goedert, M.; Guiochon, G. Anal. Chem. 1973, 45, 1180.

4002


Figure 1. Separation of Lispro and porcine insulin at the same mobile-phase flow velocity, under two different average column pressures. Mobile phase: 0.1% TFA in acetonitrile-water (30/70).

Figure 2. Phase ratio versus the average column pressure at different acetonitrile concentrations in water.

the column efficiencies for Lispro and porcine insulin varied only slightly with pressure, at 2235 ( 135 and 2560 ( 100, respectively, both RSDs being calculated for seven measurements. This indicates that the influence of the pressure on this separation is most limited under these conditions and that pressure cannot be used to optimize the analytical separation of compounds that are as closely related as the insulin variants. Partial Molar Volume Changes and Concentration of Acetonitrile. Equation 4 shows that, if the phase ratio would remain constant, the partial molar volume change could be derived directly from the plot of the logarithm of the retention factor of insulin versus the average column pressure. Actually, however, the hold-up volume of the column changes with the solvent strength and with the column pressure. Because the hold-up time, t0, increases with increasing column pressure, the phase ratio Φ decreases, which means that the total porosity of the column increases (see eq 5). Because the relationship between ln Φ and P is linear in our case, we have

ln Φ ) ln Φ0 + aP

(11)

and, from the plot of Φ versus P (see Figure 2), we can derive the slope a. Using the values of the hold-up time obtained by injecting potassium nitrate and uracil as the unretained compound, we obtained average values of a equal to -1.61 × 10-4 and -1.52

Table 1. Retention Factor and Volume Change of Insulin under Different Concentrations of Acetonitrile retention factor (k) without flow restrictor (pav ∼56 bar)

with flow restrictor (Pav ∼250 bar)

partial molar volume change [-∆V (mL/mol)]

ACN (%)

Lispro

porcine insulin

Lispro

porcine insulin

Lispro

porcine insulin

29 30 31 32 33

14.1 6.2 3 1.5 0.8

17.9 8 3.8 1.9 1

29.6 12.6 5.8 2.8 1.5

38.3 16.2 7.4 3.6 1.9

97.4 93.2 90.2 86.3 81.3

99.4 93.2 90.3 85.3 80.1

× 10-4 bar-1, respectively. It is probable that the difference between these two results is not meaningful. The corresponding contributions of the dependence of the phase ratio on the pressure to the pressure-induced variation of the partial molar volume change of insulin are -3.99 and -3.77 mL/mol, respectively (average value, 3.9 mL/mol). In a separate series of experiments made with a Chromolith Performance RP-18e monolithic column (10 × 4.6 mm, Merck, Darmstadt, Germany), we measured a partial molar volume change of insulin of -114 mL/mol, while the contribution of the dependence of the phase ratio on the pressure to the pressure-induced variation of the partial molar volume change of insulin amounts to -30 mL/mol with wateracetonitrile (68:32, v/v) as the mobile phase (not shown). Most probably, this effect originates from the compression, the desolvation, or both of the bonded layer of alkyl chains because the influence of the change of the average column pressure on its actual geometrical volume (due to the resulting change in the mechanical stress of the column tubing) is negligible. The retention factors and the partial molar volume changes of the two insulin variants measured for different acetonitrile concentrations in the mobile phase are listed in Table 1. The retention factors increased nearly 2-fold when the average column pressure increased from 56 to 250 bar. By contrast, the separation factor of the two variants remains practically constant (average value, R ) 1.27) in the ranges of acetonitrile concentration and pressure investigated. This confirms that pressure has practically no influence on the separation of the insulin variants in this chromatographic system. At acetonitrile concentrations higher than ∼33%, the retention times become close to the hold-up time, the precision of the measurements of the retention factors becomes poor, and a meaningful investigation of the dependence of the retention factor on pressure is impossible. Conversely, retention times become long at acetonitrile concentrations below 29%, the peaks are broad and short, and the precision on the retention times deteriorates. Within the range investigated, the partial molar volume change of insulin decreases markedly, by ∼20%, with increasing concentration of acetonitrile (Figure 3). Our experimental results show that, under the same average column pressure (Pav ) 133 bar), the retention factors of insulin determined at different flow rates remain almost constant, at 3.4 and 4.4 for Lispro and porcine insulin, respectively (Figure 4). Note, however, that since the partial molar volume change of insulin decreases somewhat with increasing pressure, it decreases also slowly with increasing mobile-phase flow rate when the outlet pressure is kept equal to the atmospheric pressure (Figure 5).

Figure 3. Partial molar volume change of insulin versus the acetonitrile concentration in the mobile phase. Symbols: (]) Lispro; (4) porcine insulin; unretained compound is KNO3. (/) Lispro; (0) porcine insulin; unretained compound is uracil.

Figure 4. Influence of the flow rate on the retention factor under constant average column pressure. (9) Porcine insulin; ([) Lispro; (4) average column pressure. Column EI26490.

Figure 5. Volume change of Lispro versus the mobile-phase flow rate at constant outlet pressure (atmospheric pressure).

Several investigations have shown22-32 that the pressure has a prominent influence on the retention of certain solutes. Accordingly, pressure fluctuations or changes may affect the reproducibility of experimental data. This is particularly true when retention data are measured at different temperatures but under a constant flow rate. Since the viscosity of the mobile phase is a function of the temperature, the observation is the combined result of a temperature and a pressure effect and may be difficult to interpret. Depending on the specific case studied, the partial molar volume Analytical Chemistry, Vol. 75, No. 16, August 15, 2003

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Figure 6. Relative increase of the retention factor with increasing pressure for solutes having different partial molar volume changes, assuming that ∆V is independent of the pressure.

change may be positive or negative. It is usually between 200 and -200 mL/mol. We can predict the influence of a pressure change on the retention factor of a solute at constant flow rate, constant mobile-phase composition, and constant temperature, using the following equation:

ln

()

k2 ∆V (P )- PAV,1) k1 RT AV,2

(12)

Figure 6 shows that, for a solute with ∆V ) -10 mL/mol, the influence of pressure on the retention is negligible. For a protein like insulin or lysozyme, the partial molar volume change is ∼-100 mL/mol and the retention factor increases by 120% when the average column pressure increases by 200 bar. Since the partial molar volume change associated with the transfer from one phase to the other is somewhat correlated with the absolute values of the partial molar volumes in these two phases, we should expect the effect of pressure to be more important with proteins, which have a molar volume of the order of 4-100 L/mol or more, than with conventional chemicals with molecular weights in the 100-500 range, which have molar volumes less than 500 mL/mol. Parameters Controlling the Partial Molar Volume. Thermodynamics characterizes the bulk properties of a system, i.e., the net balance of the macroscopic interaction effects. Our lack of understanding of how pressure does influence the molecular behavior in dynamic systems makes it difficult to interpret the changes observed in the partial molar volume of solutes. Yet, we can follow a conventional approach in this field and decompose the observed effect into a sum of the contributions of different factors and partition the partial molar volume into the sum of the intrinsic volumes occupied by the protein and the solvent and a contribution of the void volume of their assemblage (which is referred to below as the packing defect volume, in conformity with the literature in the field). Kauzmann36 proposed one consider the partial molar volume of a protein in solution as the sum of three contributions, those of its atoms, of its internal cavities, and the hydration volume.

V ) Vatoms + Vcavities + ∆Vhydration 4004


(13)

It is clear that both pressure and temperature affect the volume contribution of the internal cavities and the hydration volume, but it is difficult to obtain independent data on these quantities. Generally, three factors are thought to contribute to the molar volume change of proteins when they are compressed.37 These are as follows: (1) electrostriction of the charged and polar groups that become exposed to the solvent upon conformation changes or unfolding of the protein; (2) reduction of the packing defects under the influence of pressure; (3) volume effects of the transfer of hydrophobic groups from the protein interior to its surface, where they come into contact with water. The contribution of electrostriction to the overall volume change is thought to be small. Although proteins present highly densely packed interiors, changes in their inner void volume should provide the most important contribution to their molar volume, especially when a protein becomes unfolded. The larger the volume variation under the influence of a pressure change, the lower the pressure required for protein denaturation. Prehoda et al.9 estimated that the negative contribution arising from the complete elimination of the packing voids could be ∼10% of the total protein volume. Note that the partial molar volume change observed here is of the order of 2% of the insulin molar volume. Finally, the importance of the contribution of the third factor and even its sign remain under debate. We only know that the volume change resulting from the interactions between the aliphatic groups of the stationary phase and water molecules is actually positive. Thus, protein compressibility is largely determined by the size of their internal cavities. The negative volume change of proteins upon unfolding is assumed to arise globally from the increased interactions between the polypeptide chain and the water molecules becoming more intimate when denaturation takes place. This effect includes the electrostriction of the buried charges and the polar groups that become exposed to water upon unfolding, the hydration of the polypeptide backbone and of the amino acid side chains that were initially buried inside the protein, and the elimination of the packing defects and of the internal void volumes that disappear upon unfolding of the chain. It was shown that, for the protein Snase, the loss of internal void volume upon unfolding represents the major contributing factor to the volume change caused by protein denaturation.37 Insulin is more stable than myoglobin, the volume of which has shrunk by 0.51% (∆V/V) when it begins to denaturate under a pressure of 3500 bar. The decrease in molar volume of insulin is only 0.35% (Note that this 0.35% relative volume decrease of insulin corresponds to an absolute decrease of ∼16 mL, a value that is small compared to the partial molar volume change observed in this work.) at 14 700 bar, a pressure under which it does not denature (in a 5% D2O solution, at pH 7.0), although the partial transformation of its R-helix into a random coil begins at this pressure.3 The specific volume and the partial isothermal compressibility of insulin are 0.742 mL g-1 and 1.34 × 10 -4 MPa1-, respectively. The first hydration shell around proteins (accounting for approximately 0.3 g/g or 96 molecules of water per insulin molecule) is ordered and contributes to the partial specific volume. Transverse triple-quantum-filtered NMR analysis of porcine insulin (36) Kauzmann, W. Adv. Protein Chem. 1959, 14, 1. (37) Frye, K. J.; Royer, C. A. Protein Sci. 1998, 7, 2217.

shows, however, that the apparent number of strongly bound water molecules was only about 3-4/insulin molecule.38 X-ray diffraction of cubic insulin crystals reveals the nonrandom arrangements of the water molecules in a ring that extends over several molecular layers beyond the well-ordered hydration shell that is in direct contact with the protein surface.39 The surface region of a chemically modified silica such as those used as stationary phases in RPLC is a complex solvation layer, the properties of which depend on the length of the bonded hydrocarbon moieties, their bonding density, the amount of water adsorbed at the silica surface, and the excess concentration of the organic modifier in this layer, concentration that is higher in this region than in the bulk mobile phase.40 It was shown that the adsorption isotherm data of methanol, ethanol, propanol, and butanol on an ODS3 silica are well accounted for by a Langmuir isotherm model and that nearly the same effective chromatographic surface area is derived from the data obtained with the four alcohols.41 The most strongly adsorbed is butanol, the surface being almost completely covered for a mobile-phase concentration of ∼2% (w/v). The organic solvent modifies extensively the stationary-phase surface, affecting the magnitude of the retention of solutes. When a solute molecule moves from the mobile to the stationary phase, a rearrangement of the solvent molecules around the bonded alkyl chains takes place, resulting in a decrease of the number of molecules of organic modifier solvating the bonded layer. However, the desolvation of the part of the protein binding onto the stationary phase is thought to be the main source of the partial molar volume change. It provides also a negative contribution to ∆V. The retention behavior of insulin in RPLC depends on the balance of many factors. To a various degree, the mobile-phase composition, the proportion of organic additives, the ligand density on the stationary phase, their solvation degree, and particularly the local structure of the binding sites affect the retention of solutes. The composition of the mobile phase may have a stronger effect on a given separation than the particular bonded phase used.42 The mobile phase exerts its influence essentially through the hydrophobic and the ionic interactions between the solute and the stationary phase. Gekko et al.43 demonstrated that the free energy of transfer from water to aqueous acetonitrile is negative for most nonpolar side chains of amino acids and positive for the peptide group. The nonpolar side chains have a negative transfer energy, presumably due to their preferred hydrophobic interactions with the nonpolar part of the acetonitrile molecules. Acetonitrile is more effective than methanol for solubilizing large nonpolar groups, but the effect is opposite for small nonpolar groups. The hydrophobic bonding capacity of nonpolar side chains is weakened by the addition of acetonitrile.43 Influence of Pressure on the Numbers of Binding Sites and of Solvent Molecules Displaced upon Insulin Adsorption. Series of experiments was carried out under different average column pressure (between 55 and 250 bar) and with (38) Torres, A. M.; Grieve, S. M.; Kuchel, P. W. Biophys. Chem. 1998, 70, 231. (39) Badger, J. Biophys. J. 1993, 65, 1656. (40) Schunk, T. C.; Burke, M. F. J. Chromatogr. 1993, 656, 289. (41) Scott, R. P. W. J. Chromatogr. 1993, 656, 51. (42) Rivier, J.; McClintock, R. J. Chromatogr. 1983, 268, 112. (43) Gekko, K.; Ohmae, E.; Kameyama, K.; Takagi, T. Biochim. Biophys. Acta 1998, 1387, 195.

Figure 7. Influence of the pressure on Z and ln I. Symbols: Z, (4) Lispro; (0) porcine insulin. ln I: (]) Lispro; (/) porcine insulin.

different concentrations of acetonitrile (between 29 and 33%). Two parameters, Z and ln I, can be derived from the plot of the logarithm of the retention factor of Lispro versus the logarithm of the concentration of acetonitrile under different average column pressures. Both the number Z of solvent molecules displaced upon insulin adsorption and the ordinate, ln I, increase with increasing pressure (Figure 7). The number Z increases from 22 to 23.3 when the average column pressure increases from 55 to 250 bar, and the ordinate ln I increases from 40.5 to 43.5. These values are practically the same for all insulin variants. Previous results have shown that both Z and I decrease with increasing solvent strength of the organic solvent modifier; e.g., Z decreases with increasing molar volume of the organic modifier.34 NMR and ESR measurements44,45 have shown that the solvation environment of the bonded phase depends on the microstructure of the bulk mobile phase. Ellison and Marshall predicted that the surface viscosity of the layer of acetonitrile in contact with an ODS phase was 13 times larger than that of bulk acetonitrile.46 This effect was attributed to molecular interactions taking place in the hydrocarbon layer on the ODS surface. The polarity of the bondedphase solvation layer varies with the composition of the bulk mobile phase as well as with the position of the molecule along the alkyl chain.47 Motional behavior is heterogeneous over the length of the alkyl chain ligand.48 The thickness of the layer of a monomeric C18 phase was found to be 1.7 nm, that of a polymeric C18 phase, 2.1 nm, less than the length of a fully extended C18 chain.49 Solvent effects on the ligand mobility are more profound for the methylene units located near the silica surface than for those near the end of the chain.50,51 Translational and conformational dynamics are much greater at the chain ends for both the monomeric and the polymeric bonded phases.48,52 The associations of the mobile-phase components with the stationary phase are different for stationary phases having a low or a high chain density.44,52 The effects of the chain density on (44) Marshall, D. B.; McKenna, W. P. Anal. Chem. 1984, 56, 2090. (45) Bliesner, D. M.; Sentell, K. B. Anal. Chem. 1993, 65, 1819. (46) Ellison, E. H.; Marshall, D. B. J. Phys. Chem. 1991, 95, 808. (47) Miller, C.; Dadoo, R.; Kooser, R. G.; Gorse, J. J. Chromatogr. 1988, 458, 255. (48) Sindorf, D. W.; Maciel, G. E. J. Am. Chem. Soc. 1983, 105, 1848. (49) Sander, L. C.; Glinka, C. J.; Wise, S. A. Anal. Chem. 1990, 62, 1099. (50) McNally, M. E.; Rogers, L. B. J. Chromatogr. 1985, 331, 23. (51) Zeigler, R. C.; Macial, G. E. J. Am. Chem. Soc. 1991, 113, 6349. (52) Gilpin, R. K.; Gangoda, M. E. Anal. Chem. 1984, 56, 1470.


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the formation of the solvation layer are more important for acetonitrile than for water. It was shown that the density of the ligand groups on the stationary-phase surface has a strong influence on the retention of solutes.25 On stationary phases that have a low chain density, the change in partial molar volume of benzene is independent of the temperature while on stationary phases with a high chain density it is important in relative terms (up to 20 mL/mol for a molecule having a molar volume of 110 mL).25 The stationary phase YMC-ODS A used in our work is end capped, to increase its stability, to reduce the silanol density, and to reduce peak tailing. The carbon loading is 17%, and the average pore size 120 Å. The conventional end capping gives an almost totally hydrophobic surface. If a water-rich solution is used as the mobile phase, the C18 alkyl ligands collapse and leave only a small surface area of a nonpolar surface exposed for interactions with the large molecules of insulin. Only this nonpolar surface participates in their retention. The increase of Z with increasing column pressure may indicate an increase of the solvation of the stationary phase and a decrease of the hydrophobic interactions. The partial molar volume change of insulin upon adsorption does not depend on the pressure within the range investigated. However, the molar volume of insulin, whether in solution or adsorbed, decreases with increasing pressure. The local conformation of the insulin binding site may change in the process, e.g., because of an enhancement of the preferential solvation of the hydrophobic binding sites by acetonitrile molecules. It is more likely that the increase of Z arises from the combined effect of a conformational change of the insulin binding site and an increase of the solvation of the stationary phase. More acetonitrile molecules would then be displaced from the binding area upon adsorption. Conversely, if the binding area remains the same, this would indicate a decrease of the hydrophobic interactions between insulin molecules and the stationary phase. Figure 3 shows that the partial molar volume changes of the insulin variants decrease with increasing acetonitrile concentration, but Figure 7 shows that the number of solvent molecules that are displaced from the binding area upon adsorption of insulin is constant within the range of concentrations studied. Because the C18 layer of the stationary phase is well solvated in this range, we may assume that its degree of solvation remains constant. Then, the fact that the partial molar volume changes of the insulin variants decrease with increasing acetonitrile concentration may reflect a variation of the degree of solvation of the insulin binding area. The decrease of the partial molar volume change would be caused by a decrease of the number of water molecules that reside in this hydrophobic area while the number of acetonitrile molecules in the binding area remains constant. The study of adsorption-induced conformational changes of insulin by H/D exchange mass spectrometry, which probes the global conformational properties, has shown53,54 that insulin is more strongly and more irreversibly adsorbed to a methylated, hydrophobic silica surface than to a hydrophilic silica surface in an HEPES buffer, at pH 7.0. The strong interaction of insulin with the hydrophilic surface is accompanied by a strong increase in the insulin native structural stability. The desorption process of (53) Bliesner, E. H.; Sentell, K. B. J. Chromatogr. 1993, 631, 23. (54) Buijs, J.; Vera, C. C.; Ayala, E.; Steensma, E.; Hakansson, P.; Oscarsson, S. Anal. Chem. 1999, 71, 3219.

4006


the protein from the surface is promoted by the presence of an organic solvent. In solution, ∼30 protons are immediately exchanged and another 30 protons are more slowly exchanged. If insulin is adsorbed on the methylated surface, a large increase in the rate of the exchange kinetics is observed, the amide protons being less protected from the solvent. Three mechanisms coexist for the H/D exchange in proteins: the local unfolding mechanism, the solvent penetration mechanism, and the regional melting mechanism. The pressure-induced increase of the rate of H/D exchange and the spectral changes related to the protein side chains suggest that hydrogen exchange occurs by local unfolding or by the regional melting mechanism.54 It is generally accepted that the H/D exchange rate is extremely rapid for the proteins whose skeletal and side-chain amide groups are located on the protein surface and are freely exposed to bulk water. The variation in stability of the conformation can result either from fluctuations of the conformation of local regions of the insulin molecule (socalled “subglobal” fluctuations) or from the heterogeneity of the conformational population of adsorbed insulin molecules. Our results55 show that the adsorption/desorption of insulin on an octadecyl-bonded stationary phase, in an aqueous solution of acetonitrile, is reversible. The conformations of the adsorbed insulin molecules are different when they are adsorbed on a hydrophobic alkyl-bonded silica surface or on a hydrophilic neat silica surface. It is most likely that the insulin molecules undergo some local conformation change, particularly around the binding site. The conclusions of crystallographic studies56 indicate that the conformation of insulin is flexible, dynamic, and that it depends on the crystal packing forces. The N-terminal residue of the B-chain can exist in a R-helix or an extended conformation. The C-terminal segment of the B-chain is unfolded in a denatured intermediate while its secondary structure remains intact. It is believed that, to bind to the receptor, the C-terminal residue of the B-chain must unfold and move away from the N-terminal of the A-chain, exposing part of the hydrophobic core.57 Study of the denaturation equilibrium of human insulin showed that two intermediates, at least, are present at a significant concentration.58 Inclusion of 20% ethanol increased the Gibb’s free energy of unfolding for Lispro insulin and may be attributed to a general solvent effect, but it could also be due to a selective ethanol stabilization of a conformational state. Inclusion of ethanol in solution lowers the energies of nonpolar surfaces. The folding behavior of the insulin molecule is mainly controlled by that of the B-chain.59 The B-chain residues B1B19 of insulin form a contiguous R-helical region in the R-state, whereas in the T-state, the residues B9-B19 form an R-helix. The residues B20-B23 constitute a sharp β-turn, and the residues B24-B30 adopt an extended β-strand conformation.60 It has been proposed that the flexibility in the C-terminal region of the B-chain plays a functional role. This terminal undergoes considerable conformation change upon binding to the receptor. NMR studies (55) Liu, X.; Kaczmarski, K.; Cavazzini, A.; Szabelski, P.; Zhou, D.; Guiochon, G. Biotechnol. Prog. 2002, 18, 796. (56) Zhang, Y.; Wittingham, J. L.; Turkenburg, J. P.; Dodsen, E. J.; Brange, J.; Dodsen, G. G. Acta Crystallogr. 2002, D58, 186. (57) Derewenda, U.; Derewenda, Z.;E. Dodson, J.; Dodson, G. G.; Xiao, B.; Markussen, J. J. Mol. Biol. 1991, 220, 425. (58) Millican, R. L.; Brems, D. N. Biochemistry 1994, 33, 1116. (59) Guo, Z.; Shen, L.; Feng, Y. Biochemistry 2002, 41, 1556.

Figure 8. Association constant and the number of binding sites versus the average column pressure.

Figure 9. Volume change of the solvent molecules displaced upon adsorption of insulin.

showed61 that, in a 20% acetic acid solution, insulin is monomeric and its folds are stable. Observation of large variations in the widths of the amide lines suggests an intermediate exchange among the conformational substates at equilibrium.61,62 Residues B24-B28 adopt an extended configuration in the monomer while residues B29 and B30 are largely disordered. X-ray crystallography of insulin crystals56 in the presence of 20% acetic acid showed that the C-terminal residue of the B-chain fragment B25-B30 is highly flexible, when not involved in dimer formation. The fragment B21-B25 may have multiple conformations. The isolated B-chain adopts its characteristic structure in intact insulin without the need for extensive cooperative interactions with the A-chain, and the C-terminal appears to be significantly more mobile. NMR of insulin in a 35% acetonitrile buffer showed63 that the insulin conformation seen in crystallographic studies is largely retained in solution and that the extended structure of the C-terminal region of the B-chain does not control the conformation under these conditions. It is reasonable to infer that the enhancement in solvation observed for both insulin and the stationary phase with increasing column pressure results in increased configurational reorientations of chain segments of the stationary phase and conformational substates of the C-terminal of the B-chain of insulin. These effects result in a more strongly nonpolar surface and in a higher probability for insulin adsorption, hence in an increase of the retention factor. When the average column pressure is increased from 55 to 250 bar (Figure 8), the relative increases of the term I ) bdsφ[S] were approximately 13 and 19 times for Lispro and porcine insulin, respectively. Because the value of the association constant bds is still unknown, we used eq 8 to estimate the variation of [S] with increasing average column pressure:

adsorption isotherm of insulin.64 The relative increases of the term bds[S]/[D0]Z (which corresponds to the term bqs for the Langmuir adsorption isotherm) were ∼2-fold for Lispro and porcine insulin. Because the binding constant b for insulin decreases markedly with increasing column pressure, the number of binding sites of the stationary phase must increase faster. Volumetric Characteristics of the Solvent Molecules Displaced from the Binding Site. Insulin and the stationary phase are both solvated when in equilibrium with the mobile phase. Upon insulin adsorption, a number of solvent molecules are displaced from the binding area. The partial molar volume change of these molecules going from the mobile phase to the solvated state can be estimated from the plot of ln 1/[D0]z versus the average column pressure (Figure 9). The total partial molar volume change of the solvent molecules displaced by adsorption of Lispro and porcine insulin onto the stationary phase are 231.1 and 271.9 mL/mol, respectively. This result indicates that the solvent molecules in the solvation shells are denser than those in the bulk mobile phase. Studies have also shown65-69 that the hydration shell of a nonpolar species is less dense than bulk water. The opposite is true for hydration shells around atomic ions. The static dielectric constant of the hydrophobic hydration shell of amino acids was found to be higher than that of bulk water.66 The hydrogen bonding between water molecules was found to be weaker at the interface with an organic liquid than in bulk water.67 There is a strong influence of the protein surface topography on the structure and the free energy of hydrophobic hydration. Computer simulation have shown that water molecules form clathrate-like structures around the convex patches of the surface of melittin while the hydration shell near the flat regions of its surface fluctuates between a clathrate-like and a less-ordered or even an inverted structure.68 There are small differences

[S] )

K ) K/b ) k/bΦ bds/[D0]Z

(14)

We can derive the best estimate of the constant b from the (60) Baker, E. N.; Blundell, T. L.; Cutfield, J. F.; Cutfield, S. M.; Dodson, E. J.; Dodson, G. G.; Hodgkin, D. M.; Hubbard, R. E.; Isaacs, N. W.; Reynolds, C. D.; Sakabe, K.; Sakabe, N.; Vijayan, N. M. Philos. Trans. R. Soc. London Biol. 1988, 319, 369. (61) Hua, Q. X.; Weiss, M. A. Biochemistry 1991, 30, 5505.

(62) Weiss, M. A.; Nguyen, D. T.; I Khait, K Inouye, Frank, B. H.; Beckage, M.; O’Shen, E.; Shoelson, S. E.; Karplus, M.; Neuringer, L. J. Biochemistry 1989, 28, 9855. (63) Kline, A. D.; Justice, R. M., Jr. Biochemistry 1990, 29, 2906. (64) Liu, X.; Szabelski, P.; Kaczmarski, K.; Zhou, D.; Guiochon, G. J. Chromatogr., A 2003, 988, 205. (65) Gerstein, M.; Tsai, J.; Levitt, M. J. Mol. Biol. 1995, 249, 955. (66) Suzuki, M.; Shigematsu, J.; Fukunishi, Y.; Kodama, T. J. Phys. Chem. B 1997, 101, 3839. (67) Cheng, Y.; Rossky, P. J. Nature 1998, 392, 696. (68) Scatena, L. F.; Brown, M. G.; Richmond, G. L. Science 2001, 292, 908. (69) Zhang, X.; Zhu, Y.; Granick, S. Science 2002, 295, 663.


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between the compressibility of a hydration shell and that of bulk water.70 This implies that nonpolar groups and their associated water molecules are less tightly packed than the separate species. For organic solvent molecules, however, the situation is reversed. Acetonitrile is a dipolar solvent and a weak hydrogen bond acceptor.71 The behavior of water-acetonitrile mixtures is influenced by the clustering of acetonitrile molecules around polar solutes. Molecular dynamic simulations of water-acetonitrile mixtures have demonstrated that the solution composition is heterogeneous on the scale of a few molecular sizes.72 There are water-rich and acetonitrile-rich regions in the liquid. It has been suggested that, in water-rich regions, acetonitrile occupies water cavities, dissolving interstitially. In the regions between the waterrich regions and the acetonitrile-rich regions, molecules of each species are believed to be preferentially solvated by molecules of the same species. The intensity of intercomponent interactions increases from the water-rich to the water-poor regions. Experimental evidence originating from mass spectrometric studies of clusters isolated from the vacuum adiabatic expansion of liquid droplets showed73 that the dodecahedral structure was prominent for pure water. In water-acetonitrile mixtures, the water clusters were found to include acetonitrile, with compositions following H+(H2O)21(CH3CN)m, m ) 1, 2, 3... were observed as magic number clusters. X-ray diffraction and infrared spectroscopy studies of acetonitrile-water mixtures74 suggest that hydrogen bonds are formed between acetonitrile and water molecules in mixtures for which the mole fraction XACN is less than 0.8 and that both water and acetonitrile clusters coexist in mixtures in the concentration range 0.2 e XAN e 0.6. Microheterogeneity takes place in these mixture. The proportion of free acetonitrile molecules increases with increasing acetonitrile concentration in the range 0.1 e XAN e 0.7 whereas the proportion of hydrogen-bonded acetonitrile molecules decreases gradually. At high water concentrations (XACN e 0.2), acetonitrile clusters are broken and water clusters become predominant. In our case, the mobile-phase concentration of acetonitrile ranged between 28 and 36% (v/v), which corresponds to an acetonitrile mole fraction 0.117 < XACN < 0.161. Because of the complexity of the structure of acetonitrilewater solutions at the microscopic scale, it is worthwhile to study the microheterogeneity of solvent mixtures and the effect on solvation of the stationary phase and preferential solvation of the hydrophobic binding sites for a better elucidation of the influence of pressure on protein separation. Influence of Pressure on the Separation of Insulin at Different Flow Rates. A series of experiments was carried out to study the influence of flow rate and pressure on the separation of the two insulin variants. Figure 10 shows plots of the column HETP for porcine insulin versus the mobile-phase flow velocity, with and without an on-line capillary flow restriction (45 cm). In this velocity range, the HETP increases almost linearly with increasing flow velocity. Band broadening arises in part from eddy diffusion but mostly from the mass-transfer resistances.55 At flow (70) Dadarlat, V. M.; Post, C. B. J. Phys. Chem. 2001, 105, 715. (71) Karger, B. L.; Synder, L. R.; Eon, C. J. J. Chromatogr. 1976, 125, 71. (72) Ban, K.; Jinno, K. Anal. Sci. J. 2001, 17, 113. (73) Wakisaka, A.; Abdoul-Carime, H.; Yamamoto, Y.; Kiyozumi, Y. J. Chem. Soc. Faraday Trans. 1998, 94, 369. (74) Takamuku, T.; Tabata, M.; Yamaguchi, A.; Nishimoto, J.; Kumamoto, M.; Wakita, H.; Yamaguchi, T. J. Phys. Chem. B 1998, 102, 8880.

4008 Analytical Chemistry, Vol. 75, No. 16, August 15, 2003

Figure 10. Height equivalent to a theoretical plate of porcine insulin versus the interstitial velocities at two average column pressures. Column EI26490.

rates higher than 0.6 mL/min, the HETP of the column connected to a capillary restriction increases more slowly than that of the same column without restriction. Lispro exhibits the same trend (not shown). Thus, the column efficiency improves with increasing average column pressure, a surprising result since diffusion in liquids may but decrease slightly with increasing pressure. The diffusivity is inversely proportional to the solvent viscosity and [1/η][dη/dP], 1 × 10-3 bar-1. CONCLUSION In this work, we demonstrated that pressure has a strong influence on the retention behavior of the insulin variants in RPHPLC, under linear conditions. Their retention factors increase nearly 2-fold when the average column pressure is increased by 200 bar. Peak heights decrease linearly with increasing column pressure while peak widths increase linearly. The separation factors of Lispro and porcine insulin remain almost unchanged, and their resolution increases slightly. There is little gain to be expected from an increase of the average column pressure in terms of the quality of the analytical separation. Note that the effect of pressure on the retention factors is much smaller than that of the acetonitrile concentration: a pressure increase of 200 bar is approximately equivalent to a decrease of acetonitrile concentration of 1%. The influence of pressure on the retention is caused by the large partial molar volume change of adsorption, a change that is around -100 mL/mol. This partial molar volume change decreases with increasing acetonitrile concentration, from -99 to -80 mL mol -1 for acetonitrile concentrations of 29 and 33% (v/v), respectively. The hold-up volume of the column (hence its phase ratio) decreases also with increasing acetonitrile concentration and with increasing average column pressure. The number of acetonitrile molecules that are displaced from both the protein and the stationary-phase surfaces upon adsorption of the protein increases from 22 to 23.3 when the average column pressure is increased by 200 bar. Although the partial molar volume change of insulin remains constant in this process, the volume of the insulin molecule changes. It is likely that this variation arises from the combined effects of conformational changes of the insulin binding area and variations of the degree of solvation of the stationary phase, more acetonitrile molecules

being replaced in the binding area. The relative increases of the term b[S]/[D0]Z, which corresponds to the slope bqs of the adsorption isotherm, is about twice larger for Lispro than for porcine insulin when the average column pressure increases by 250 bar. Because the binding constant of insulin decreases, the number of binding sites on the stationary phase must increase even more. It is probable that the increase of the degree of solvation of insulin and of the stationary phase with increasing column pressure causes increased configurational reorientations of chain segments of the stationary phase and changes in conformational substates of the C-terminal of the B-chain of insulin. These effects result in an increased alkyl surface area available and a higher probability for insulin adsorption, hence in an increase of the column retention factor. This result is most important because an increase of the number of adsorption sites is potentially beneficial in preparative chromatography. It will result in a proportional increase of the saturation capacity. It is clear that a pressure-induced increase of the number of adsorption sites, not a change in the adsorption energy, is the major cause for the observed increase of the retention factors. The increase of the solvation of the stationary phase results in an increase of the number of insulin binding sites. The molecular origin of the mechanism of this effect remains to be identified.

Pressure may be expected to play an important role in solute retention for numerous chromatographic separations.28 For solute having a ∆V between -10 and 10 mL/mol, the influence of pressure on the retention is negligible. Only for those solutes having a large partial molar volume change does pressure have a large influence on their retention. It seems that many proteins may be found in this group. ACKNOWLEDGMENT This work was supported in part by Grant CHE-00-70548 of the National Science Foundation (USA) and by the cooperative agreement between the University of Tennessee and the Oak Ridge National Laboratory. P.S. is grateful to the Polish Foundation for Science for the Award of a Stipend for Young Scientists. Note Added after ASAP. This paper was placed on the Web before all changes had been made. The paper was reposted on July 17, 2003.

Received for review September 26, 2002. Revised manuscript received May 30, 2003. Accepted May 31, 2003. AC0205964


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Influence of Pressure on the Retention and Separation of Insulin

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