Direct measurement of protein osmotic second virial cross coefficients by cross-interaction chromatography

Abstract

The importance of weak protein interactions, such as protein self-association, is widely recognized in a variety of biological and technological processes. Although protein self-association has been studied extensively, much less attention has been devoted to weak protein cross-association, mainly due to the difficulties in measuring weak interactions between different proteins in solution. Here a framework is presented for quantifying the osmotic second virial cross coefficient directly using a modified form of self-interaction chromatography called cross-interaction chromatography. A theoretical relationship is developed between the virial cross coefficient and the chromatographic retention using statistical mechanics. Measurements of bovine serum albumin (BSA)/lysozyme cross-association using cross-interaction chromatography agree well with the few osmometry measurements available in the literature. Lysozyme/α-chymotrypsinogen interactions were also measured over a wide range of solution conditions, and some counterintuitive trends were observed that may provide new insight into the molecular origins of weak protein interactions. The virial cross coefficients presented in this work may also provide insight into separation processes that are influenced by protein cross-interactions, such as crystallization, precipitation, and ultrafiltration.

Weak protein interactions, including both self- and cross-association, are central both to biological processes, such as substrate channeling and protein aggregation, and to technological processes, such as protein crystallization and precipitation. The current understanding of protein self-association relies heavily on measurements of protein osmotic second virial coefficients (B₂₂) using static light scattering (George and Wilson 1994; Rosenbaum and Zukoski 1996; Velev et al. 1998), small angle X-ray (Porschel and Damaschun 1977; Bonneté et al. 1997), and neutron (Velev et al. 1998) scattering, membrane osmometry (Vilker et al. 1981; Haynes et al. 1992), sedimentation equilibrium (Behlke and Ristau 1999), size-exclusion chromatography (Nichol et al. 1978), and, more recently, self-interaction chromatography (SIC; Patro and Przybycien 1996^; Tessier et al. 2002a^,b). Pioneering work has shown that solution environments conducive to protein crystallization and protein precipitation correlate with moderately or highly negative second virial coefficient values, respectively (George and Wilson 1994).

Although this information has been useful for understanding protein solution thermodynamics for single protein systems, the investigation of protein mixtures has been limited by a lack of information about the osmotic second virial cross coefficient (B₂₃) due to the absence of a technique that can determine protein cross-interactions directly. Methods that have been used to characterize protein cross-association are membrane osmometry (McCarty and Adams 1987; Moon et al. 2000), light scattering (Steiner 1953a), sedimentation equilibrium (Howlett and Nichol 1973; Clarke and Howlett 1979), size-exclusion chromatography (Nichol and Winzor 1964; Nichol et al. 1967; Gilbert and Kellett 1971), fluorescence depolarization (Steiner 1953b), and turbidity methods (Howell et al. 1995). An inherent limitation of these methods is that protein cross-interactions are determined indirectly for a two-protein mixture by first measuring the relevant properties of the individual components and then measuring the properties of a mixture at a known composition in the same solution environment. Also, even for a single protein solution, there are limitations of such techniques. For example, scattering and osmometry techniques require relatively large amounts of protein and time, which prevents extensive exploration of the effects of solution conditions, such as pH and ionic strength, on the virial coefficient values. Membrane osmometry is also limited by the difficulty in finding membranes that are not susceptible to protein adsorption or pore blockage, which is particularly difficult in the case of oppositely charged proteins at low ionic strength. A difficulty with static light scattering is that it is very sensitive to the presence of aggregates, which are difficult to avoid in practice, especially under solution conditions that promote attractive protein interactions. Sedimentation equilibrium experiments are often complicated by assumptions about the nature and extent of protein oligomerization.

Most of the previous studies have reported protein cross-association in terms of an association constant that is well suited to describe relatively strong protein interactions in which the population of bimolecular configurations is dominated by a single configuration. However, the virial cross coefficient is better suited than is the association constant to describe weak interactions because ensemble averaging must account for contributions due to many configurations. There have been only two studies, both by osmometry, that have measured B₂₃ values for lysozyme/ovalbumin (McCarty and Adams 1987) and lysozyme/BSA mixtures (Moon et al. 2000). The study of lysozyme/ovalbumin interactions was conducted at slightly elevated temperatures (30°–37°C) and at solution conditions (pH 5.8, 0.2 M) that promote electrostatic attraction between these oppositely charged proteins (McCarty and Adams 1987). However, scatter in those osmotic pressure data prevented the accurate determination of the virial cross coefficient; it was speculated that protein adsorption on the membrane may have been responsible (McCarty and Adams 1987). The most successful study of protein cross-interactions is for lysozyme/BSA at room temperature (25°C), although the measurements were limited to high ionic strength (1 M and 3 M), at which electrostatically driven protein adsorption is likely to be minimal, and at which the cross-interactions are expected to be relatively weak (Moon et al. 2000). Although these studies provide important preliminary insights into weak protein cross-association, they are not extensive enough to provide a framework for understanding B₂₂ patterns over a wide range of solution conditions.

Because methods are not available for the direct measurement of protein cross-interactions averaged over all pairwise configurations between two different proteins in solution, we have used a method that is based on the interaction of a protein in solution with a second protein fixed on a solid phase. When only a single protein is being studied, the method is referred to as SIC (Patro and Przybycien 1996); the protein is covalently immobilized on chromatographic particles that are packed into a column, and the same protein is passed through the column. The retention time (or volume) reflects average protein–protein interactions, which we have related to B₂₂ via statistical mechanics (Tessier et al. 2002a). We have previously shown that B₂₂ values measured by SIC for lysozyme and α-chymotrypsinogen (Tessier et al. 2002a), and BSA (Tessier et al. 2002b), are in quantitative agreement with values measured by static light scattering and membrane osmometry, without the use of adjustable parameters. Further, SIC is at least an order of magnitude more efficient than light scattering or osmometry in terms of time and protein consumption.

SIC can be readily adapted to the direct measurement of protein cross-interactions by immobilizing one protein and passing a different protein through the column. We refer to this method as cross-interaction chromatography (CIC). In this work we determine B₂₃ values for BSA/lysozyme and α-chymotrypsinogen/lysozyme at a variety of solution conditions using CIC. We also investigate the dependence of the B₂₃ measurements on various experimental variables.

Theory

The osmotic pressure (π) of a single protein (species 2) in solution can be expanded in terms of the protein concentration in the form:

(1)

where ρ₂ is the protein number density, k is the Boltzmann constant, and T is the temperature. The osmotic second virial coefficient, which is a result of pairwise protein interactions, is related to molecular level interactions as (Zimm 1946; McQuarrie 1976)

(2)

where the potential of mean force (PMF), W₂₂, describes the interaction energy between two identical molecules, a and b, as a function of separation distance (r_ab) and angular configuration (Ω_a, Ω_b). Note that because the protein interactions are mediated by the solvent, the PMF and B₂₂ depend upon the solution conditions. The factor of ½ accounts for the double counting of interactions between identical particles in solution.

The osmotic pressure of a binary protein system (species 2 and 3) can be written in a similar form to equation 1 (Kurata 1982) as

(3)

where B₂₂ and B₃₃ are the osmotic second virial coefficients for the individual proteins, B₂₃ is the osmotic second virial cross coefficient that results from interactions between the two proteins, ρ_T is the total number density of the solutes in solution, and x₂ and x₃ are the mole fractions of the proteins. The cross coefficient can be related to molecular level interactions in a form analogous to equation 2

(4)

where W₂₃ is the PMF for the interaction between two different proteins in solution as a function of their separation distance and angular configurations.

Although the most common way to write the osmotic pressure for a binary protein mixture is as shown in equation 3 (Hirschfelder et al. 1964; Moon et al. 2000), others have written the cross term without the prefactor of two and not included the factor of ½ in the B₂₃ equation (equation 4; ^{Hill 1960}). The two forms are equivalent because the factors cancel. However, because the connection that is sought in this work between B₂₃ and the CIC measurements is through the PMF in equation 4, and not through the osmotic pressure of equation 3, the factor of ½ in equation 4 is included in the following derivation. The primary reasons for including the factor of ½ are for consistency with the B₂₃ values in the literature (Moon et al. 2000), and to maintain the same energy scaling between B₂₂ and B₂₃ (i.e., the same PMF would give the same value of the virial coefficient for both self- and cross-association).

It is convenient to split the osmotic cross coefficient shown in equation 4 into two terms,

(5)

where r_c(Ω_a, Ω_b) is the center-to-center separation distance at contact. The first term represents the excluded volume, and the second term accounts for intermolecular interactions between pairs of protein molecules at separation distances greater than r_c.

A relationship between the CIC measurements and B₂₃ is developed, as for B₂₂ (Tessier et al. 2002a), via the chromatographic retention factor:

(6)

V_r is the retention volume, or the volume required to elute a pulse of protein from a column containing immobilized protein, and V_o is the dead volume, or the volume required to elute a pulse of protein from the same column in which the free protein does not interact with the immobilized protein. A detailed explanation of how to determine V_o with the aid of an underivatized (blank) column has been reported previously (Tessier et al. 2002a), the key step being subtraction of a fraction of the excluded volume of the immobilized protein from the blank column dead volume prior to calculating the retention factor. The volume accounted for there was the molecular volume, that is, one-quarter of the excluded volume in the case of self-interaction, but the difference in accessible volumes between the blank and modified columns indicates that the allowance should be for one-half of the excluded volume, that is, twice the molecular volume in the case of self-interactions. For cross-interactions the correction is approximately the sum of the molecular volumes of the free and immobilized proteins, plus or minus a small additional correction when the larger or the smaller protein is immobilized respectively. The latter minor adjustment accounts for the fact that the measured excluded volume in the blank column includes a layer adjacent to the surface that is inaccessible to the probe protein, which is in general different in size to the immobilized protein.

The retention factor for protein free in solution interacting with a partial monolayer of immobilized protein can be written in terms of the PMF (Tessier et al. 2002a):

(7)

Here ρ_s is the surface concentration of protein in terms of the number of molecules per area, and φ is the phase ratio, or the amount of surface area per mobile phase volume. Both ρ_s and φ can be measured experimentally, and values of φ are available in the literature for a variety of commercially available chromatography particles (DePhillips and Lenhoff 2000). The factor of ½ is due to the assumption that only one half of the immobilized protein is accessible to free protein in solution. However, in some cases this assumption may not be valid due to the influence of neighboring immobilized protein molecules, as is discussed later.

The osmotic second virial cross coefficient can be related to the retention factor by combining equations 5 and 7

(8)

where B_23,HS is the excluded volume or hard sphere contribution (⅔ π[r₂ + r₃]³ for spheres, where r₂ and r₃ are the radii of the two proteins). Equation 8 provides a direct connection between the osmotic second virial cross coefficient and the retention factor in terms of parameters that are either measured or obtained from the literature.

Results

Cross-interaction chromatography

BSA and lysozyme

CIC measurements were conducted for BSA/lysozyme interactions as a function of pH, ionic strength, and salt type. The resulting B₂₃ values for p-lysozyme (the notation p-protein denotes the immobilized protein) and BSA are shown in Figure 1 ▶ as a function of ammonium sulfate ionic strength at pH 4.5 and 7.0. All the values lie in a fairly narrow range between −1.5 and 1.0 × 10⁻⁴ mole-mL/g², but the trends are statistically significant given that the average standard deviation based on replication is <0.1 × 10⁻⁴ mole-mL/g². The two proteins are oppositely charged at pH 7.0, and the B₂₃ values are negative (attractive) at low ionic strength. As the ionic strength is increased, the B₂₃ values become positive (repulsive) and increase in magnitude up to 1 M ionic strength, but are slightly less positive at 3 M ionic strength. At pH 4.5, at which both proteins are positively charged, the B₂₃ values are positive at low ionic strength, and become more positive as the ionic strength is increased up to 1 M ionic strength. There is a crossover in the B₂₃ values at ~0.3 M at which the interactions at pH 4.5 become more attractive than at pH 7.0. Above 2 M ionic strength, the B₂₃ values are more sensitive to the ionic strength at pH 4.5 than at pH 7.0, and the virial coefficients become negative at high ionic strength.

Figure 1.

BSA/lysozyme osmotic second virial cross coefficients measured in the presence of ammonium sulfate by cross-interaction chromatography at pH 4.5 (open squares) and pH 7.0 (open triangles), and by membrane osmometry (Moon et al. 2000) at pH 4.5 (filled squares) and pH 7.0 (filled triangles). The cross-interaction chromatography experiments were conducted with lysozyme immobilized. The osmometry cross coefficient value at pH 4.5 was estimated by interpolation.

Membrane osmometry measurements of B₂₃ obtained for BSA and lysozyme are shown in Figure 1 ▶ at pH 4.5 and 7.0 as filled symbols (Moon et al. 2000). The B₂₃ values at pH 7.0 measured by membrane osmometry display the same trend as those measured by CIC (decreasing B₂₃ values as ionic strength is increased). The pH trend observed by osmometry is also consistent with the CIC measurements (increasing B₂₃ values as pH is increased). The average difference between the three B₂₃ values measured by osmometry and CIC is 0.5 × 10⁻⁴ mole-mL/g², which is consistent with the agreement observed previously for virial coefficients measured by SIC and static light scattering (Tessier et al. 2002a,b).

Virial cross coefficients were also measured for p-lysozyme and BSA in the presence of sodium chloride at pH 4.5 and 7.0; the results are shown in Figure 2 ▶, along with the corresponding results measured in the presence of ammonium sulfate. Overall, the B₂₃ values measured in the presence of sodium chloride and ammonium sulfate show similar trends. At low ionic strength and pH 7.0, the B₂₃ values measured in both salts are negative (attractive), whereas the values are positive (repulsive) at high ionic strength (>1 M). At pH 4.5, the B₂₃ values are positive at low ionic strength, and negative at high ionic strength. Importantly, BSA/lysozyme B₂₃ values are more negative at high ionic strength (>0.5 M) at pH 4.5 for sodium chloride than for ammonium sulfate, whereas the opposite is true at pH 7.0. The standard deviation of the B₂₃ values measured in the presence of sodium chloride was <0.1 mole-mL/g².

Figure 2.

BSA/lysozyme osmotic second virial cross coefficients measured by cross-interaction chromatography in the presence of sodium chloride at pH 4.5 (open squares) and pH 7.0 (open triangles), and in the presence of ammonium sulfate at pH 4.5 (filled squares) and pH 7.0 (filled triangles). The cross-interaction chromatography experiments were conducted with lysozyme immobilized.

α-Chymotrypsinogen and lysozyme

Virial cross coefficients for p-chymotrypsinogen and lysozyme were measured at pH 4.0 and 7.0 in the presence of sodium chloride and ammonium sulfate (Fig. 3 ▶). All of the B₂₃ values between 0.15 and 0.8 M ionic strength at both pH values are negative, indicating attractive protein interactions over a wide range of solution conditions. The B₂₃ values at pH 4.0 become more negative as the salt concentration is increased, although the change is more dramatic for the sodium chloride values. In contrast, the B₂₃ values measured at pH 7.0 in the presence of both sodium chloride and ammonium sulfate become less negative as the ionic strength is increased, and those measured in sodium chloride are more attractive than those measured in ammonium sulfate. The B₂₃ values measured in the presence of sodium chloride become independent of pH at 0.6 M ionic strength, whereas the corresponding B₂₃ values in ammonium sulfate remain pH dependent up to at least 0.8 M ionic strength. The average standard deviation of the lysozyme/α-chymotrypsinogen B₂₃ measurements was <0.3 mole-mL/g2.

Figure 3.

α-Chymotrypsinogen/lysozyme osmotic second virial cross coefficients measured by cross-interaction chromatography in the presence of sodium chloride at pH 4.0 (open squares) and pH 7.0 (open triangles), and in the presence of ammonium sulfate at pH 4.0 (filled squares) and pH 7.0 (filled triangles). The cross-interaction chromatography experiments were conducted with α-chymotrypsinogen immobilized.

Chromatographic considerations

BSA and lysozyme

CIC measurements were conducted to determine the sensitivity of the retention of the free protein to key experimental parameters, specifically the injection concentration and which protein was immobilized. As seen in Figure 4 ▶, the retention factor was much larger when BSA rather than lysozyme was immobilized at 0.2 M ionic strength. Notably, the retention factor remained a strong function of the injection concentration when BSA was immobilized, whereas it was approximately independent of the injection concentration above 15 mg/mL when lysozyme was immobilized. The retention factor at 1 M ionic strength (ammonium sulfate) was independent of the injection concentration above 15 mg/mL when either BSA or lysozyme was immobilized. However, the B₂₃ values differed measurably; at an injection concentration of 20 mg/mL and an ionic strength of 1 M (ammonium sulfate) at pH 7.0, the B₂₃ value was −6.7 × 10⁻⁴ mole-mL/g² when BSA was immobilized and 0.6 × 10⁻⁴ mole-mL/g² when lysozyme was immobilized. Also, the value of B₂₃ was not dependent on pH when BSA was immobilized. All B₂₃ values for BSA/lysozyme mixtures reported in Figures 1 ▶ and 2 ▶ were measured by using an injection concentration of 20 mg/mL of BSA. Finally, the average standard deviation of the retention factors in Figure 3 ▶ measured with immobilized BSA at 0.2 M ionic strength was 0.03 mole-mL/g² and for the other three cases was <0.01 mole-mL/g².

Figure 4.

The dependence of the injection concentration on the retention factor at pH 7.0 for immobilized BSA interacting with lysozyme at 0.2 M (filled squares) and 1 M (open squares) ionic strength, and for immobilized lysozyme interacting with BSA at 0.2 M (filled triangles) and 1 M (open triangles) ionic strength. The electrolytes used were sodium chloride at 0.2 M, and ammonium sulfate at 1 M, ionic strength.

α-Chymotrypsinogen and lysozyme

The dependence of the chromatographic retention on the injection concentration and which protein was immobilized was investigated at pH 7.0 at two ammonium sulfate ionic strength values (0.2 and 2 M); the results are summarized in Figure 5 ▶. It can be seen that the retention factor becomes roughly independent of the injection concentration at ~25 mg/mL at both ionic strengths. At 0.2 M ionic strength and when α-chymotrypsinogen is the free protein, the retention factor remains weakly dependent on the injection concentration. This ionic strength and pH correspond to the condition at which the α-chymotrypsinogen interactions are most attractive (Velev et al. 1998), and the reduction in the retention factor as the injection concentration is increased >25 mg/mL may be due to aggregation. The experiments with lysozyme immobilized were conducted at an injection concentration of 20 mg/mL of α-chymotrypsinogen, and the experiments in which α-chymotrypsinogen was immobilized were conducted at an injection concentration of 25 mg/mL of lysozyme. The average standard deviation of the retention factors in Figure 5 ▶ was 0.01.

Figure 5.

The dependence of the injection concentration on the retention factor at pH 7.0 for immobilized α-chymotrypsinogen interacting with lysozyme at 0.2 M (filled squares) and 2 M (filled triangles) ionic strength, and for immobilized lysozyme interacting with α-chymotrypsinogen at 0.2 M (open squares) and 2 M (open triangles) ionic strength. The electrolyte used was ammonium sulfate.

Virial cross coefficient values for lysozyme and α-chymotrypsinogen obtained in the presence of ammonium sulfate at pH 4.0 and 7.0 are shown in Figure 6 ▶ as a function of which protein is immobilized and the surface coverage. The average difference between the B₂₃ values is 0.8 × 10⁻⁴ mole-mL/g² for the lysozyme particles with a higher immobilization density. The average difference between the B₂₃ values at pH 7.0 for p-lysozyme and α-chymotrypsinogen measured at different immobilization densities was 0.9 × 10⁻⁴ mole-mL/g².

Figure 6.

The effect of interchanging the immobilized protein and the surface coverage on the virial cross coefficients for immobilized α-chymotrypsinogen (14.6 mg/mL) interacting with lysozyme at pH 4.0 (open squares) and pH 7.0 (open triangles), immobilized lysozyme (16.1 mg/mL) interacting with α-chymotrypsinogen at pH 4.0 (filled squares) and pH 7.0 (filled triangles), and immobilized lysozyme (10.8 mg/mL) interacting with α-chymotrypsinogen at pH 7.0 (filled circles). The electrolyte used was ammonium sulfate.

Discussion

Virial cross coefficient behavior

This study represents the first time that protein osmotic second virial cross coefficients have been measured directly, that is, without the need to characterize the properties of the individual components in addition to those of the mixtures. The results reported in this work are the most extensive set of such data available, and provide a basis to begin to understand weak protein cross-association. The measurements for p-lysozyme and BSA cross-association in ammonium sulfate solutions compare reasonably well with the B₂₃ values available in the literature, suggesting that CIC is capable of quantifying protein cross-association. However, due to the limited data for protein B₂₃ values in the literature, the absolute values of the cross coefficients measured for lysozyme and α-chymotrypsinogen could not be verified.

The results presented in this work illustrate that cross-association between proteins that are not known to interact specifically is not limited to simple electrostatic interactions. For example, the B₂₃ values for BSA and lysozyme display interesting behavior as a function of pH and ionic strength. The pH 7.0 trend as a function of ionic strength for both sodium chloride and ammonium sulfate reveals attraction at low ionic strength, which is expected based on electrostatic arguments for oppositely charged proteins, and agrees with previous observations that BSA/lysozyme mixtures appear cloudy at these conditions (Steiner 1953a). The trend of decreasing attraction as a function of increasing ionic strength up to 1 M is also qualitatively as expected based on simple electrostatic attraction. The results at pH 4.5 are not as easily explained, however, because although both proteins are positively charged, the cross interactions are less repulsive at >0.3 M ionic strength than at pH 7.0, at which the proteins are oppositely charged, indicating that forces other than electrostatic interactions are involved. The significant divergence of the two pH trends at high ionic strength (>1 M) may be due to changes in protein hydration, which is a strong function of the protonation state of the acidic amino acids (i.e., increasing pH leads to increased hydration; Kuntz et al. 1969). Because it is likely that the acidic residues are partially protonated at pH 4.5, the lower extent of hydration at low pH may lead to the greater degree of attraction observed at pH 4.5 than at pH 7.0.

There is also a dependence of the BSA/lysozyme cross-interactions on the salt type at the same pH at >0.5 M ionic strength. At pH 4.5, at which the proteins are both positively charged, cross-interactions measured in sodium chloride are more attractive than are those measured in ammonium sulfate, whereas at pH 7.0, at which the proteins are oppositely charged, the opposite is true. The former finding agrees with previous observations that positively charged proteins follow the reverse Hofmeister series (Ries-Kautt and Ducruix 1989). However, the Hofmeister series does not provide insight into the latter finding because it does not discriminate between the effectiveness of various ions in inducing attraction between two different proteins with opposite charge.

Previous qualitative studies of BSA/lysozyme cross-association using turbidity (Steiner 1953a; Howell et al. 1995) and fluorescence depolarization (Steiner 1953b) have revealed attractive interactions at low ionic strength (<0.1 M) and neutral pH, with the degree of attraction decreasing as the ionic strength was increased at low ionic strength, in agreement with the results presented in this work. Fluorescence depolarization studies have also shown that BSA/ lysozyme cross-association is less attractive at low ionic strength (0.01 M) at pH 4.5 than at pH 7.0 (Steiner 1953b), which again is in agreement with the results presented in this work.

The lysozyme/α-chymotrypsinogen system shows some surprising virial coefficient behavior, especially given the fact that both proteins are positively charged at pH 4.0 and pH 7.0. The general B₂₃ trends at pH 4.0 are as expected because the interactions become more attractive as the salt concentration is increased. The B₂₃ trends at pH 4.0 are more dramatic in sodium chloride, and the interactions are more attractive than those measured in the presence of ammonium sulfate. This finding agrees with the reverse Hofmeister series (Ries-Kautt and Ducruix 1989), a possible explanation for which is binding of sulfate ions to both positively charged proteins, resulting in a repulsive barrier to protein association. This mechanism would explain why the B₂₃ values at pH 4.0 are less negative in the presence of sulfate than in the presence of chloride, as well as why the B₂₃ values display a stronger pH dependence in the presence of sulfate.

It is also interesting that at pH 7.0 in the presence of both ammonium sulfate and sodium chloride, the B₂₃ values for lysozyme and α-chymotrypsinogen are strongly negative at low ionic strength and appear to be electrostatic in nature (i.e., increasing ionic strength reduces the degree of attraction), even though both proteins have a net positive charge. This finding is significant because it confirms the important role that the charge distributions can play in influencing the overall interaction energy between protein molecules. The results in Figure 3 ▶ are also qualitatively similar to those observed previously for α-chymotrypsinogen self-association at neutral pH and low ionic strength (Velev et al. 1998). The origin of these interactions has been modeled computationally for α-chymotrypsinogen and appears to be due to attractive electrostatic interactions present in a relatively small number of pairwise configurations that show a high level of geometric complementarity and dominate the over-all B₂₃ values (Neal et al. 1998). Similar computational analysis will be required to determine whether the structurally unrelated proteins, lysozyme and α-chymotrypsinogen, exhibit pairwise configurations that display a high degree of geometric complementarity.

The elution behavior of α-chymotrypsinogen at pH 7.0 from a column of ion-exchange particles that were partially covered with immobilized lysozyme has been studied previously in a qualitative manner, and it was found that α-chymotrypsinogen eluted later than when there was no immobilized lysozyme (Ratnayake and Regnier 1996). This suggests that lysozyme/α-chymotrypsinogen interactions are attractive at neutral pH, which agrees with the CIC results.

Chromatographic considerations

It has been observed in a previous SIC study that the elution volume for free lysozyme interacting with immobilized lysozyme at pH 7.0 and 0.8 M ionic strength is strongly dependent on the injection concentration below concentrations of 20 mg/mL (Tessier et al. 2002a). It was speculated that this dependence, which correlated with the attractiveness of the pairwise protein interactions, was due to free protein molecules interacting simultaneously with more than one immobilized protein molecule (Tessier et al. 2002a). However, it was unclear whether free molecules bridged immobilized molecules directly or whether adsorption on the bare particle surface was involved as well. The results presented here provide further insight into the origin of this behavior because direct bridging implies that smaller surface voids should promote a stronger injection concentration dependence on the retention factor, whereas the opposite is implied if surface adsorption is involved as well. It was observed that the injection concentration dependence was greater when the larger proteins (BSA and α-chymotrypsinogen) were immobilized and, therefore, when larger surface voids were present relative to when lysozyme was immobilized. Thus, these results suggest that surface adsorption is involved in the association of a free protein with multiple immobilized proteins, although this will need to be confirmed for other binary mixtures. Notably, the issue of concentration dependence is of practical importance primarily when it cannot be eliminated by increasing the injection concentration, as was observed for BSA/lysozyme interactions at low ionic strength. However, it was possible to obtain retention factors independent of injection concentration for BSA and lysozyme at high ionic strength, and α-chymotrypsinogen and lysozyme over a wide range of solution conditions.

Also, as noted earlier, the retention factor for lysozyme interacting with p-chymotrypsinogen showed a small dependence on the injection concentration even at high injection concentrations (up to 30 mg/mL), which corresponds to a condition of relatively strong protein self-association for α-chymotrypsinogen (pH 7.0, 0.2 M ionic strength; Velev et al. 1998). A disadvantage of CIC is that for the proteins, particles, and columns used in this work, relatively high injection concentrations were required to eliminate the dependence of the retention factor on the injection concentration, which is not possible at all solution conditions due to solubility limitations. It will be important in the future to reduce the required injection concentration, possibly by reducing the effective surface area in the column.

The results presented here can be internally validated by confirming whether the B₂₂ values that are obtained for a pair of proteins are independent of which protein is immobilized. Measurements of lysozyme interacting with p-BSA could only be conducted at high ionic strength (1 M) because at low ionic strength (0.2 M) the retention factor was dependent on the injection concentration, even at high injection concentrations (up to 35 mg/mL). The B₂₃ value at 1 M ionic strength and pH 7.0 depended strongly on which protein was immobilized as the difference between the two values was >7 × 10⁻⁴ mole-mL/g². It may be that BSA changed structurally upon immobilization, because it has been shown that the α-helix content of adsorbed BSA is lower than that for BSA in solution (Norde and Favier 1992). The fact that lysozyme has been shown largely to retain its structure upon immobilization (Przybycien and Wilcox 2002) may also explain why the measurements conducted with lysozyme immobilized were in reasonable agreement with the osmometry results (difference of 0.5 × 10⁻⁴ mole-mL/g²). The lack of pH dependence for the B₂₃ values at 1 M ionic strength for p-BSA and lysozyme also would suggest that the immobilized BSA may have been structurally altered, whereas the pH dependence in agreement with osmometry results found for p-lysozyme and BSA would suggest that the structure of the immobilized lysozyme had not changed significantly. These results confirm the importance of understanding the structure of immobilized proteins at interfaces if immobilized protein techniques for measuring protein interactions, such as CIC, are to be used to provide insight into protein solution thermodynamics.

The results obtained for the lysozyme/α-chymotrypsinogen system are quite similar regardless of which protein is immobilized (Fig. 6 ▶), which is consistent with the fact that α-chymotrypsinogen, like lysozyme, has been shown to be highly stable and therefore to retain its structure when immobilized (Przybycien and Wilcox 2002). These results also suggest that lysozyme and α-chymotrypsinogen are immobilized in multiple orientations, an important assumption for the use of CIC to measure B₂₃. These findings agree with observations that limited proteolysis of immobilized lysozyme and α-chymotrypsinogen yields a near random distribution of peptide fragments, suggesting that these proteins are immobilized in multiple orientations (Przybycien and Wilcox 2002).

It should also be emphasized that the absolute values of B₂₃ measured by CIC are strongly dependent on the value of the chromatographic dead volume, which must therefore be measured carefully. The dead volume is the volume required to elute the protein of interest from a column without interaction with the surface; in practice, this is done by using a column without immobilized protein at a moderate salt concentration (0.5 to 1 M) to eliminate protein-surface interactions. However, in this work it was found that the lysozyme dead volume was dependent on the salt type (chloride led to a larger dead volume than did sulfate), whereas the dead volumes of the other proteins were not dependent on the salt type. Because at these ionic strengths lysozyme is more soluble (Ries-Kautt and Ducruix 1989), and associates more weakly (Curtis et al. 1998, 2002), in sulfate than chloride, it is unlikely that the difference in the dead volume measurements was due to aggregation, but a possible explanation is that it was due to protein-surface interactions. The size of lysozyme and the dead volume measured by using ammonium sulfate correlated more closely with the dead volumes measured by using either salt and protein size for several other proteins, so that value was used here. Also, the dead volume showed little variation as a function of pH for the proteins studied in this work. Finally, the dead volume measurements were more ideal (i.e., the retention volume correlated better with the protein size) for a column of AF-formyl-650M particles that were capped with ethanolamine than for a column of AF-amino-650M particles that were functionalized with glutaraldehyde and capped with ethanolamine. The less ideal retention behavior measured by using a column of the latter particles is likely due to the increased hydrophobicity of the glutaraldehyde-rich surface.

Model uncertainties

The derivation of equation 8 was based on the assumption that one immobilized protein molecule interacts with one free protein molecule, independent of neighboring immobilized molecules. Further, it is assumed that half of the space around the immobilized protein is accessible to mobile protein molecules, as shown in Figure 7A ▶. If the immobilized protein molecules are separated by approximately their diameter, which was the case in this work on average, this assumption is reasonable, but only for conditions in which the protein interactions are short-range in nature. It has been shown that weak protein interactions at moderate to high ionic strength (>0.1 M ionic strength) persist over a length scale much less than the size of the protein (Rosenbaum and Zukoski 1996; Neal et al. 1998). Consequently, CIC cannot be used to measure protein cross-interactions quantitatively at very low ionic strengths using the theory developed in this work, which is why there are no B₂₃ values reported at <0.15 M ionic strength.

Figure 7.

A schematic diagram of the surface of a chromatography particle illustrating the influence of neighboring immobilized proteins on the interaction of an immobilized protein with a protein free in solution. The spacing of the immobilized proteins is approximately equal to the size of the immobilized protein for the values of the surface coverage used in this work. (A) The free (dark) and immobilized (light) proteins are the same size, and the free protein can access a hemisphere around the immobilized protein. (B) The larger protein is immobilized, and the smaller protein can access more than a hemisphere around the immobilized protein. (C) The smaller protein is immobilized, and the larger protein can access less than a hemisphere around the immobilized protein.

The situation shown in Figure 7B ▶ of a small free protein interacting with a large immobilized protein is different because the free protein can access more than a hemisphere around the immobilized protein. However, the increased volume that a smaller molecule can access is small and does not make a significant change to the B₂₃ values calculated by equation 8, and therefore is neglected.

Figure 7C ▶ shows the opposite situation, in which the small protein is immobilized, and the larger protein can access less than a hemisphere of volume around the immobilized protein. The assumption of a hemisphere of accessible space surrounding the immobilized protein is no longer valid and, therefore, the application of equation 7 to CIC must be reconsidered. To estimate the change in the volume relative to a hemisphere available for the free protein to interact with the immobilized protein, the proteins were considered to be spherical and placed in a hexagonal lattice arrangement. For the case of p-lysozyme interacting with BSA (the binary system with the largest size difference; Fig. 7C ▶), the reduction in volume is ~56% of that of the hemispherical region. If the factor of ½ in equation 7 that accounts for the hemisphere of space around the immobilized protein is reduced accordingly, the prefactor to the term with k′ in equation 8 would become ~1.8. This adjustment results in a change in the B₂₃ values of ~−1.8 × 10⁻⁴ mole-mL/g2. The corresponding calculation for p-lysozyme and α-chymotrypsinogen (the binary system with the smallest size difference) results in a reduction of the hemispherical volume of ~20%, a prefactor of ~1.25, and a change in the B₂₃ values of ~−1.2 × 10⁻⁴ mole-mL/g2.

It has been pointed out previously that the increase in the value of the prefactor in equation 7 is likely offset by an excluded volume contribution due to the protein shape that we have neglected (Tessier et al. 2002a). The excluded volume calculated by using the crystal structure is 1.7 times greater than the value calculated by using the molecular volume and assuming a spherical shape (Neal and Lenhoff 1995). Consistent with our previous work (Tessier et al. 2002a), we calculated the excluded volume using the spherical shape assumption. The underestimation of the excluded volume provides a positive contribution not accounted for in the value of the cross coefficients of 0.7 × 10⁻⁴ mole-mL/g² for BSA/lysozyme and 0.9 × 10⁻⁴ mole-mL/g² for α-chymotrypsinogen/lysozyme. Because the positive contribution of the excluded volume approximately offsets the negative contribution of the increased prefactor, a prefactor of one was used in equation 8. A detailed comparison of BSA/lysozyme B₂₃ values calculated by using both a prefactor of one and the calculated value is shown in Table 1, which illustrates that accounting for the various offsetting contributions makes a relatively small difference, especially when the B₂₃ values are negative. However, the influence of neighboring immobilized proteins will become more important if CIC measurements are conducted at a higher surface coverage and/or with proteins that differ in size to a greater degree than those used in this work.

Table 1.

Comparison of two methods of calculating the osmotic second virial cross coefficient for p-lysozyme and BSA as a function of ionic strength (ammonium sulfate) and pH

		B23 (10−4 mole-mL/g2)
pH	I (M)	A	B
4.5	0.2	0.0	−1.1
	1	0.2	−0.5
	2	0.1	−0.6
	2.5	−0.4	−2.0
	3	−1.4	−4.8
7	0.175	−1.3	−4.4
	0.2	−0.9	−3.5
	0.4	0.2	−0.4
	0.6	0.5	0.3
	1	0.6	0.8
	3	0.4	0.1

(A) One-half of the immobilized protein is accessible to the mobile proteins and the proteins can be approximated as spheres.

(B) Less than one-half of the immobilized protein is accessible to the mobile proteins and the proteins are nonspherical.

The results in Figure 6 ▶ for p-lysozyme and α-chymotrypsinogen at two different immobilization densities confirm that the spacing between neighboring molecules does not significantly impact the B₂₃ values for this system. The agreement between the two sets of results in Figure 6 ▶ is favorable (average difference of 0.9 × 10⁻⁴ mole-mL/g²), although the difference is statistically significant given that the standard deviation of these results is 0.1 × 10⁻⁴ mole-mL/g². These results are contrary to what would be expected based on the previous discussion regarding neighboring proteins because the B₂₃ values for p-lysozyme and α-chymotrypsinogen actually correspond to greater attraction at a higher immobilization density. Because the offset between the two trends is reduced as the salt concentration is increased, it may be that attractive multibody interactions are involved at the higher immobilization density when the interactions are longer range in nature (i.e., at lower salt concentrations). These results are also consistent with the model proposed in equation 8 because the value of the cross coefficient is approximately independent of the immobilization density, although this was not tested for BSA and lysozyme. However, it should be stressed that the lysozyme immobilization densities for both experiments were high (27% and 40%), which was found previously to be necessary to prevent significant nonspecific interactions between free proteins and the particle surface (Tessier et al. 2002a).

Conclusions

The goal of this investigation was to demonstrate a method of measuring protein osmotic second virial cross coefficients directly using CIC in which one protein is immobilized on a solid support. The advantage of CIC over other methodologies used previously is that it enables the direct measurement of interactions between two different proteins and eliminates the need to determine B₂₃ from the difference between solution properties of the mixture and each of the individual proteins. However, an important requirement for using CIC to measure the thermodynamic properties of proteins in solution is that the protein largely retains its solution structure when immobilized at a solid/liquid interface. Also, it should be emphasized that the larger protein should be immobilized whenever possible to simplify the interpretation of the results. Finally, the availability of this relatively large collection of protein B₂₃ data should be useful in understanding separations that involve weak protein interactions. We have demonstrated recently that the diafiltration sieving behavior of lysozyme in the presence of BSA correlates with the BSA/lysozyme B₂₃ values reported in this paper (Tessier et al. 2003), and it is expected that similar correlations can be developed for protein crystallization and precipitation involving binary protein mixtures.

Materials and methods

Materials

BSA (A-7638), chicken egg white lysozyme (L-6876), and bovine pancreatic α-chymotrypsinogen (C-4879) were obtained from Sigma-Aldrich and were used as received. Bistris (B-7535), bistris propane (B-6755), MES (M-8250), 25% glutaraldehyde (G-5882), sodium cyanoborohydride (S-8628), and ethanolamine (E-9508) were also purchased from Sigma-Aldrich. Potassium phosphate (ACS grade, P288), boric acid (ACS grade, A73), sodium hydroxide (ACS grade, S318), hydrochloric acid (ACS grade, A114), ammonium sulfate (ACS grade, A702), sodium carbonate (ACS grade, S263), and sodium chloride (ACS grade, 5271) were purchased from Fisher Scientific. Glacial acetic acid (3121) was obtained from Mallinckrodt Laboratory Chemicals. Micro-BCA assay reagents (23231BP, 23232BP, and 23234BP) were obtained from Pierce Biotechnology. AF-formyl-650M (08004) and AF-amino-650M (08002) affinity chromatography particles were purchased from Tosoh Bioscience.

Methods

The immobilization of lysozyme and α-chymotrypsinogen on AF-formyl-650M and of BSA on AF-amino-650M affinity chromatography particles has been described previously (Tessier et al. 2002a,b), so only the essential details are included below. For lysozyme and α-chymotrypsinogen, protein was dissolved in 0.1 and 1 M potassium phosphate at pH 7.5 and 8.5, respectively, and the protein was added to the AF-formyl-650M particles. Sodium cyanoborohydride was added as a reducing agent, and the reaction was allowed to proceed overnight. The unreacted protein was removed by using 200 mL reaction buffer, the remaining reactive groups were endcapped by adding the particles to 15 mL ethanol-amine along with 0.03 to 0.07 mg sodium cyanoborohydride, and the reaction was allowed to proceed for a few hours. The unreacted ethanolamine was then removed with a 1 M sodium chloride solution (pH 7.0), and the amount of protein bound to the particles was measured both by the micro-BCA method (Plant et al. 1991; Tessier et al. 2002a) and by the difference between the amounts of protein in the initial reaction solution and in the wash solutions after the reaction. A similar procedure was followed for the immobilization of BSA on AF-amino-650M particles by using glutaraldehyde as the cross-linking reagent, as has been described previously (Tessier et al. 2002b). In Table 2 the amounts of the reagents that were used to prepare the particles described in this work are reported, along with the immobilization densities. The immobilization density measured by the micro-BCA method is assumed to be more accurate because it is a direct measure of the immobilized protein and, therefore, is the value used in calculating the B₂₃ values.

Table 2.

Experimental details of the protein immobilization reactions conducted in this work

Protein	Initial protein mass (mg)	Initial protein conc. (mg/mL)	Settled particle volume (mL)	Reducing (mg) or cross-linking (mL) reagent	Mass balance (mg/mL)	Micro-BCA assay (mg/mL)
Lysozyme	67.4	6.8	3.0	95a	17.5	16.1
Lysozyme	26.7	4.0	1.8	60a	13.4	10.8
α-Chymotrypsinogen	33.6	6.7	2.0	50a	16.6	14.7
α-Chymotrypsinogen	19.5	3.9	1.7	180a	9.2	7.6
BSA	58.0	5.7	2.0	2b	21.4	16.8

The reducing and cross-linking reagents are sodium cyanoborohydride (^a) and glutaraldehyde (^b), respectively.

The particles with immobilized protein were packed into 3 × 50-mm glass columns (993301 obtained from Cobert Associates) at 5 mL/min for ~10 min. The packing procedure was considered successful if an injection of acetone into the column resulted in a sharp symmetric peak. Protein samples were prepared at injection concentrations ranging from 5 to 40 mg/mL in various solution environments, and were filtered by using 220-nm syringe filters (Fisher Scientific, SLGVR25LS) prior to use. For each B₂₃ measurement, the column was equilibrated at 0.5 mL/min for approximately four column volumes at the solution condition of interest, the flow rate was reduced to 0.13 mL/min, and 50 μL of protein solution was injected into the column. The elution peak maximum was taken as the retention volume because the peaks were typically symmetric. After the peak was eluted, the salt concentration was adjusted to ~1 M for three column volumes at 0.5 mL/min and then lowered to 5 mM for approximately three column volumes, to ready the column for reuse. All measurements were carried out at room temperature (23 ± 2°C).