Anal. Chem. 2000, 72, 5714-5717
Determination of Effective Protein Charge by Capillary Electrophoresis: Effects of Charge Regulation in the Analysis of Charge Ladders Manoj K. Menon and Andrew L. Zydney*
Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716
Protein charge ladders are an effective tool for measuring protein charge and studying electrostatic interactions. However, previous analyses have neglected the effects of charge regulation, the alteration in the extent of amino acid ionization associated with differences between the pH at the protein surface and in the bulk solution. Experimental data were obtained with charge ladders constructed from bovine carbonic anhydrase. The protein charge for each element in the ladder was calculated from the protein electrophoretic mobility as measured by capillary electrophoresis using the hindrance factor for a hard sphere with equivalent hydrodynamic radius. The protein charge was also evaluated theoretically from the amino acid sequence by assuming a Boltzmann distribution in the hydrogen ion concentration. The calculations were in excellent agreement with the data, demonstrating the importance of charge regulation on the net protein charge. These results have important implications for the use of charge ladders to evaluate effective protein charge in solution. Protein charge ladders are an effective tool for calculating protein charge1,2 and evaluating the effects of electrostatic interactions on biomolecular recognition,3 ligand binding,4 and membrane transport.5 The basic principle is to produce a series of chemical derivatives of a given protein by blocking one or more of the protein’s charge groups.1,6 Several different chemistries have been developed, with the simplest being acylation of lysine using acetic anhydride:
The acylated lysines can no longer be protonated; thus, the modified protein will have one less positively charged group than * Corresponding author: (phone) 302-831-2399; (fax) 302-831-1048; (e-mail)
[email protected]. (1) Gao, J.; Whitesides, G. M. Anal. Chem. 1997, 69, 575-580. (2) Gao, J.; Gomez, F. A.; Harter, R.; Whitesides, G. M. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 12027-12030.
5714 Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
the native protein (under conditions where lysine would be in the form NH3+). Similarly, treatment with 4-sulfophenyl isothiocyanate2 converts the NH3+ into a negatively charged SO3-:
In this case, the modified protein will have a charge two units lower than the unmodified protein due to the conversion of a positively charged group into the negative sulfonic acid. Since most proteins have a significant number of lysine groups, these reactions generate a series of protein derivatives with differing charge, i.e., a “charge ladder”. The concentration and electrophoretic mobility of each element in this ladder can then be analyzed by capillary electrophoresis. Since the electrophoretic mobility is directly proportional to the protein charge, data for the mobilities of the different elements in the charge ladder can be used to evaluate the effective charge of the unmodified protein (Zo). The final expression developed by Gao et al. is1,2
∆Zn ) Zo(µn/µo - 1)
(1)
where ∆Zn is the charge difference between the nth element and the unmodified protein and µn and µo are the electrophoretic mobilities of the nth element and the unmodified protein, respectively. When the charge ladder is formed by acylation of the lysine residues, ∆Zn is assumed to be n, while ∆Zn is assumed to be 2n for the charge ladder generated using 4-sulfophenyl isothiocyanate. The electrophoretic mobilities are evaluated from the time of emergence for peak n and the time of emergence of an electrically neutral marker (typically mesityl oxide). The charge on the unmodified protein is then evaluated directly from the slope of a plot of ∆Zn versus µn/µo - 1. One of the implicit assumptions in using eq 1 to evaluate the effective charge of the unmodified protein is that ∆Zn is exactly equal to the number of charge units blocked or modified in (3) Carbeck, J. D.; Colton, I. J.; Gao, J.; Whitesides, G. M. Acc. Chem. Res. 1998, 31, 343-350. (4) Gao, J.; Mammen, M.; Whitesides, G. M. Science 1996, 272, 535-537. (5) Menon, M. K.; Zydney, A. L. J. Membr. Sci., in press. (6) Colton, I. J.; Anderson, J. R.; Gao, J.; Chapman, R. G.; Isaacs, L.; Whitesides, G. M. J. Am. Chem. Soc. 1997, 119, 12701-12709. 10.1021/ac000752b CCC: $19.00
© 2000 American Chemical Society Published on Web 10/21/2000
developing the charge ladder. Although this assumption might seem intuitively obvious, the change in protein charge caused by blocking a single lysine group is considerably more complex due to the effects of charge regulation. For example, the elimination of an -NH3+ group on a negatively charged protein will increase the protein’s net negative charge, which will in turn cause an increase in the local hydrogen ion concentration at the protein surface due to the electrostatic attraction of the positively charged H+. This decreases the local pH, shifting the acid-base equilibrium for the charged amino acid residues. The net result is that the first element of the charge ladder will differ by slightly less than one electronic charge from the unmodified protein. Note that any individual protein molecule will necessarily have an integral electronic charge. The fractional change in the effective charge arises from the time and number averaging of the negatively and positively charged groups over the protein population. Charge Regulation Theory. The effects of charge regulation on protein charge can be evaluated theoretically as follows. The acid-base equilibrium for a charged carboxylic acid residue can be expressed as7,8
Kia )
[R - COO-][H+] [R - COOH]
(2)
where Kia is the intrinsic dissociation constant. Similar equations can be written for the other ionizable amino acids. The H+ concentration in eq 2 is the local concentration at the surface of the protein, which is evaluated in terms of the bulk concentration assuming a Boltzmann distribution:8 +
H+ ) Hbulk exp(-(eψs/kT))
(3)
where e is the electronic charge (1.602 × 10-19 C) and ψs is the electrostatic potential at the protein surface. Equations 2 and 3 can be combined to give an expression for the number of dissociated groups of type i in terms of the bulk H+ concentration:
ri )
niKia +
Kia + [Hbulk ] exp(-eψs/kT)
) ni
1 + 10
[pKia-pH -0.43(eψs/kT)]
(4)
where k is the Boltzmann constant (1.38 × 10-23 J/K), T is the + absolute temperature, pH ) -log[Hbulk ], pKia ) -log[Kia] , and ni is the total number of titrable species of type i. Note that the pH in the denominator of eq 4 is the bulk (measured) pH. The protein charge (Z) can be calculated by summing over all the ionizable groups, yielding
Z ) Z+ max -
∑r
i
equation for the electrostatic potential around an isolated sphere:8
ψs ) eZ/4πoa(1 + κa)
(6)
where ο is the permittivity of free space (8.85 × 10-12 C V-1 m-1), is the dielectric constant, a is the protein radius, and κ is the inverse Debye length. Calculations were performed for bovine carbonic anhydrase (BCA) using the protein radius (a ) 20.5 Å) determined from the molecular volume and the pKa values reported in the literature.1,2 MATERIALS AND METHODS Experiments were performed using charge ladders generated from bovine carbonic anhydrase II obtained from bovine erythrocytes (Worthington Biochemical, Lakewood, NJ). The BCA was acylated following the procedure described by Gao and Whitesides.1 The protein was first dissolved in deionized water obtained from a Nanopure water purification system (Barnstead, Dubuque, IA) at a concentration of 1.5 g/L. This solution was split into five equal aliquots of 50-100 mL. Each aliquot was cooled to 3-5 °C to minimize protein denaturation during the chemical modification. Solution pH was set to 12.0 by the addition of 0.1 N NaOH. The five aliquots were treated with 30, 60, 90, 120, and 150 equiv of acetic anhydride (0.1 N solution in dioxane) per mole of BCA, respectively. The solution was maintained at pH 12 for 15 min by manual addition of 0.1 N NaOH to compensate for the production of acetic acid during the reaction. The pH was then lowered to 7 by adding 0.2 N HCl to quench the reaction. The different samples were mixed to yield a charge ladder containing a significant amount of the differently charged species. The resulting solution was diafiltered with at least four diavolumes of deionized water to remove the dioxane and acetic acid using an Amicon stirred cell with a Biomax 5K polyethersulfone membrane (Millipore Corp., Bedford, MA). The electrophoretic mobility of each element in the charge ladder was evaluated using capillary electrophoresis (CE) following the procedure described by Menon and Zydney.9 CE was performed using an Isco model 3850 capillary electropherograph equipped with a dual-polarity variable high-voltage dc supply (030 kV). Negatively charged fused-silica capillaries (Supelco) with total length of 84 cm (distance to detector of 64 cm) were used in all experiments. The run buffer was 192 mM glycine with 25 mM Tris (pH 8.3, 10 mM ionic strength), and the applied field strength was 25 kV. Detection was by UV absorbance at 214 nm. Data Analysis. The electrophoretic mobility of each peak, µ (cm2 V-1 s-1), was calculated as the ratio of the electrophoretic velocity (cm/s) to the applied field strength (V/cm). The mobility is a linear function of the surface potential,ψs:8
µ ) (2ψs/3η)f1(κa)
(7)
(5)
i
+ Zmax is the maximum positive charge on the molecule, which is equal to the total number of residues that are positively charged at low pH. The electrostatic potential at the protein surface is estimated from the solution of the linearized Poisson-Boltzmann
where η is the solution viscosity. The function f1(κa) accounts for the distortion of the electric field caused by the presence of the (7) Tanford, C. Physical Chemistry of Macromolecules; John Wiley & Sons: New York, 1961. (8) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: London, 1981. (9) Menon, M. K.; Zydney, A. L. Anal. Chem. 1998, 70, 1581-1584.
Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
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Figure 1. Capillary electropherogram for the BCA charge ladder in 192 mM glycine, 25 mM Tris (pH 8.3, 10 mM ionic strength). Table 1. Ionizable Residues and pKa Values for Bovine Carbonic Anhydrase residue
ni
pKia
residue
ni
pKia
C-terminal Lys Asp Glu His (Zn2+)-H2O
1 19 11 11 1
3.2 3.5 4.5 6.2 7.0
N-terminal Ser Lys Tyr Arg
1 18 7 9
7.3 10.3 10.3 12.5
protein and can be evaluated using the expression developed by Henry:10
1 5 1 1 (κa)2 - (κa)3 - (κa)4 + (κa)5 + 16 48 96 96 κa exp(-t) 1 1 (κa)4 - (κa)6 exp(κa) ∞ dt (8) 8 96 t
f1(κa) ) 1 +
[
]
∫
Equation 7 was used to evaluate the surface potential from the measured mobility by assuming that BCA can be modeled as a hard sphere with radius of 20.5 Å. The protein charge (Z) was then calculated from eq 6 using the same value of a ) 20.5 Å. RESULTS AND ANALYSIS Figure 1 shows the capillary electropherogram of the BCA charge ladder at pH 8.3. Transport in the silica capillary under these conditions is dominated by the strong electroosmotic flow toward the negative electrode, with the negatively charged BCA migrating back toward the positive electrode. The neutral marker is thus the first peak to appear, followed by the unmodified BCA and the BCA derivatives. BCA contains 18 lysines (Table 1). Nineteen species in the charge ladder are visible, corresponding to 0-18 acylated lysine groups. The charge of each protein species was evaluated from the measured electrophoretic mobility using eqs 6-8, with the results shown as the filled circles in Figure 2. The open squares represent the values of the protein charge determined from the charge regulation theory using eqs 2-6 and the pKa values in Table 1. These pKa values were taken from Gao et al.2 by assuming that (10) Henry, D. C. Proc. R. Soc. 1931, A133, 106-129.
5716 Analytical Chemistry, Vol. 72, No. 22, November 15, 2000
Figure 2. Protein charge as a function of the number of modified lysines. Filled circles are experimental values determined directly from electrophoretic mobility. Open symbols are model calculations accounting for charge regulation. Dashed line represents the charge calculated assuming that each acylated lysine decreases the protein charge by exactly one charge unit.
the three Asx are all Asp and that the Glx is Glu as discussed by Gao et al.2 Zmax+ ) 41 for the unmodified BCA (11 histidine + 18 lysine + 1 N-terminal serine + 9 arginine + 1 Zn2+). Zmax+ and the number of lysine residues were both reduced by one for each succeeding member of the charge ladder. The model is in good agreement with the experimental data. Results for the higher peak numbers are not shown since the protein surface potential for these species exceeded 60 mV, which is well beyond the limit of applicability for the linearized Poisson-Boltzmann equation. The dashed line in Figure 2 is the calculated charge assuming that the acylation of each lysine causes the protein charge to change by exactly one unit. This simple model significantly overpredicts the charge difference for the higher peak numbers, which is a direct result of the effects of charge regulation. In this case, the increased negative charge causes an increase in the local pH, leading to the protonation of several histidine residues in the BCA. Figure 3 shows the calculated values of ∆Z1 ) Z1 - Z0 for BCA as a function of pH. The calculations were done using eqs 2-6 with the pKa values in Table 1. The charge on the first modified species (Z1) was evaluated by decreasing the number of lysines and Zmax+ by exactly one unit. The calculated charge difference between the first peak and the unmodified BCA at pH 8.3 (the conditions examined in Figures 1 and 2) is 0.86 compared to the expected value of 1. Thus, the value of Zo that would be evaluated from eq 1 by assuming ∆Z1 ) 1 would be 16% larger than the correct protein charge. This difference is relatively small since pH 8.3 is 2 pH units below the pKa of lysine and tyrosine and well above the pKa of histidine (the single groups with pKa of 7.0 and 7.3 have a relatively small effect on the calculations). This discrepancy increases quite dramatically at both higher and lower pH as the pH becomes closer to the pKa values of the other charged amino acids. The dashed curve in Figure 3 represents the calculated values of ∆Z1 for a model version of BCA in which only the histidine residues are taken explicitly into account. All other residues were assumed to have a fixed charge equivalent to their charge at pH 8.3. At low pH, the histidine residues are fully protonated and
assuming ∆Z1 ) 1), which is identical to the value found in Figure 3 at this pH. Even larger discrepancies between the measured and calculated charge were seen with several of the other proteins. The effective charge for each negatively charged protein evaluated from the charge ladder experiments was consistently more negative than the charge determined from the amino acid sequence, with the reverse behavior seen for positively charged proteins. This effect is a direct result of ∆Z1 being smaller than 1 and is completely consistent with the behavior predicted from the charge regulation analysis.
Figure 3. Calculated values of the charge difference between the first modified species in the charge ladder and the unmodified protein as a function of pH. Dashed curve is for a model version of BCA accounting only for the presence of the histidine residues.
have a charge of +1. Thus, the change in local pH due to blockage of a single lysine group has no significant effect on the ionization of any of the histidine residues. ∆Z1 for this model protein approaches a value of 1 under these conditions. Similarly, ∆Z1 approaches a value of 1 at high pH since the histidines are fully deprotonated (having zero net charge) under these conditions. The effects of charge regulation become significant near the pKa of histidine (pH 6.2), where the perturbation in local pH caused by elimination of a single lysine group has a significant effect on the ionization equilibrium of the histidine residues. The studies by Gao and Whitesides1 and Gao et al.2 presented data for the effective charge of several proteins, including BCA, determined from protein charge ladders analyzed at pH 8.3. Since this pH is relatively far removed from the pKa of most amino acids, the effects of charge regulation on these results should be relatively small. However, even under these conditions the effects can be significant. For example, the BCA charge determined experimentally using the protein charge ladder was reported as Zo ) -3.5 compared to the value of -3.0 calculated by Gao and Whitesides1 from the known amino acid sequence. This discrepancy would be eliminated if the calculation of the protein charge had been performed using eq 1 with ∆Z1 ) 0.86 (instead of
DISCUSSION Charge regulation can have a significant effect on protein charge because of differences in the extent of amino acid ionization associated with the difference between the local and bulk pH. This causes the charge between two adjacent elements within a protein charge ladder to differ by less than one charge unit, an effect that has been unappreciated in previous studies using the charge ladder analysis. The net result is that the charge determined using eq 1 will consistently overestimate the effective protein charge. The magnitude of this effect is related to the proximity of the pH to the pKa values of the ionizable amino acids. Although the effects of charge regulation can rigorously be taken into account only if detailed information is available on the amino acid composition and pKa values for a given protein, the current analysis can be used to determine those conditions under which these effects are likely to be significant. In particular, data obtained at pH far from the pKa of the ionizable residues will be least sensitive to charge regulation phenomena. Alternatively, the approach developed by Menon and Zydney9 can be used to evaluate the charge of both the unmodified and singly modified protein using a hard-sphere model to calculate f1(κa), with these values of Zo and Z1 providing an independent estimate of the magnitude of ∆Z1. ACKNOWLEDGMENT The authors acknowledge the financial support provided by Millipore Corp., Genentech, Inc., the National Science Foundation, and the Delaware Research Partnership program.
Received for review June 30, 2000. Accepted September 7, 2000. AC000752B
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