REVIEW
Comparative Study of Analytical Techniques for Determining Protein Charge DANA I. FILOTI,1 STEVEN J. SHIRE,2 SANDEEP YADAV,3 THOMAS M. LAUE1 1
CAMIS, University of New Hampshire, St. Durham, New Hampshire Late Stage Pharmaceutical and Device Development, Genentech, Inc., South San Francisco, California 3 Late Stage Pharmaceutical and Device Development, Genentech, Inc., South San Francisco, California 2
Received 16 February 2015; revised 22 March 2015; accepted 24 March 2015 Published online 24 April 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.24454 ABSTRACT: As interest in high-concentration protein formulations has increased, it has become apparent that routine, accurate protein charge measurements are necessary. There are several techniques for charge measurement, and a comparison of the methods is needed. The ¨ electrophoretic mobility, effective charge, and Debye–Huckel–Henry charge have been determined for bovine serum albumin, and human serum albumin. Three different electrophoretic methods were used to measure the electrophoretic mobility: capillary electrophoresis, electrophoretic light scattering, and membrane confined electrophoresis. In addition, the effective charge was measured directly using steady-state electrophoresis. Measurements made at different NaCl concentrations, pH, and temperatures allow comparison with previous charge estimates based on electrophoresis, Donnan equilibrium, and pH titration. Similar charge estimates are obtained by all of the methods. The strengths and limitations of each technique are discussed, as are some general considerations about protein charge and C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 104:2123–2131, 2015 charge determination. Keywords: colloid; solubility; electrophoresis; proteins; protein formulation; protein charge
INTRODUCTION
BACKGROUND
Many therapeutic proteins, especially at high concentration, may be prone to phase separation (aggregates, gels, and emulsions) and high viscosity. These unfavorable solution behaviors, which pose challenges for manufacturing, drug safety, and drug delivery, are a reflection of the colloidal properties of proteins.1 Protein colloidal properties are controlled by proximity energies, which are principally electrostatic in origin. Charge–charge repulsion is the only long-range proximity energy that maintains protein solubility and that can overcome the attractive forces that lead to high viscosities. Therefore, it is important to have routine ways to measure protein charge. Presented here is a comparison of measurements of the electrophoretic mobility, :, net effective charge, zeff , and the Debye– ¨ Huckel–Henry charge, zDHH , for bovine serum albumin (BSA) and human serum albumin (HSA) made under identical solvent conditions using three different types of electrophoretic instruments, capillary electrophoresis (CE), electrophoretic light scattering (ELS), and membrane-confined electrophoresis (MCE). These results are compared with proton titration data,2 Donnan equilibrium measurements,3 and previous CE measurements,4 as well as theoretical charge estimates computed from amino acid composition and from X-ray structure. The results are discussed with respect to how the charge estimates compare made using the different methods. The assumptions made for each method and strengths and weaknesses of each electrophoretic method are also discussed.
Because there is renewed interest in making protein charge measurements, and the fact that many protein scientists may not have much experience with charge or with charge determination by electrophoresis, some background information may be useful.
Correspondence to: Thomas M. Laue (Telephone: +603-862-2459; Fax: +603862-4013; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 104, 2123–2131 (2015) C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association
Macromolecular Charge Molecular charge is a fundamental property that directly influences protein structure, stability, solubility, and interactions with other macromolecules.5–7 Rooted in the primary structure, the charge on a protein is a system property as it is affected by the solvent composition, pH, dielectric constant, and temperature. The actual protein charge may differ substantially from the charge calculated by summing up the charge on each of its ionizable groups, as these calculations only account for H+ binding and it is known that proteins may bind other ions, particularly anions.2,8–10 Two types of ion binding are recognized, site bound and territorially bound. Site-bound ions are coordinated with the protein structure by specific bonds. These ions are fixed spatially and may be visible in an X-ray or nuclear magnetic resonance (NMR) structure. What is not depicted in an X-ray or NMR structure, but is important to protein net charge, are the territorially bound ions. These ions are not bound to a specific site. Instead, they are confined to regions of high-charge density on the protein surface in a manner similar to the “condensed ions” on a polyelectrolyte. The relevant parameter for what constitutes a high-charge density is the Bjerrum length, which is the distance separating two like-sign charges resulting in a potential energy in their vicinity comparable to the thermal energy, kB T, where kB is the Boltzmann constant and T is the absolute temperature. In physiological solutions, Bjerrum length ˚ Conversely, if two charges are closer together than is 2–3 A.
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the Bjerrum length, then a counterion will be associated with them; and if there is a patch of charge on the protein surface, sufficient counterions will bind until the average charge separation equals or exceeds the Bjerrum length. Because territorial ion localization requires a high-charge density, the extent and location of territorially bound ions is affected by a protein’s structure.10–12 Territorially bound ions are characterized by their relative insensitivity to the bulk solvent ion concentration and by their close proximity to the protein surface (i.e., they are confined within the solvation layer).10 Even though territorially bound ions may exchange freely with solvent ions, they do not dissociate from the macromolecule. Because they must move with the macroion, thereby not contributing significantly to its osmotic potential, they are an integral part of the protein’s “charge structure.” Site-bound and territorially bound ions are distinct from those ions that make up the “counterion cloud” (i.e., the Debye– ¨ Huckel cloud) that forms as the solvent response to the protein’s ¨ net charge. Instead, the Debye–Huckel cloud describes an imbalance of counterion and coion concentrations in vicinity of the protein. Importantly, the charge density distribution of the ion cloud depends on the solvent ion concentration and extends out from the protein surface several Angstroms into the surrounding solvent.5,10 In short, the counterion cloud can be considered a solvent response to the presence of the charged protein, and ¨ the counterions that make up Debye–Huckel cloud are a consequence of the protein net charge rather than being an integral part of the protein charge. Often the terms “charge” and “valence” are used interchangeably. The fundamental charge on a proton, Qp , is 1.602 × 10−19 C (coulomb, SI units). The valence of a protein, z, is the unitless ratio of its charge, Q, divided by the fundamental charge, that is, z = Q/Qp . So, a protein with a valence of +5 has a net charge of +8.1 × 10−19 C. Both the charge and the valence are signed quantities, so that a protein having a valence of −5 would carry a charge of −8.1 × 10−19 C. The experimental quantities useful for charge determination are the electrophoretic mobility, : in cm2 /V-s, (the ratio of the velocity of a molecule, in cm/s, to the electric field, in V/cm) and the effective valence, zeff = f Q: p , where f is the translational friction coefficient, determined experimentally from either sedimentation or diffusion measurement and Qp is the proton fundamental charge.13 Both : and zeff include the effects ¨ of the Debye–Huckel ion shielding and of the “electrophoretic effect,” which results from the distortion of the electric field in the vicinity of the nonconducting particle and from the transport of the ion atmosphere in the vicinity of the protein.7,14 Both ion shielding and the electrophoretic effect reduce the electrophoretic mobility. Consequently, : and zeff do not distin¨ guish between bound ions and the Debye–Huckel cloud. Two values calculated from : and zeff adjust for these effects, the ¨ zeta potential, ., and the Debye–Huckel–Henry valence zDHH . In visualizing the difference between these two descriptions of a protein’s charge properties, it is useful to consider the . potential as the electrical potential difference between the shear surface surrounding a spherical particle and the bulk solvent, where the potential difference is spread uniformly over the nonconducting particle surface, and zDHH (actually zDHH *Qp ) as the charge at the center of the spherical, nonconducting particle that gives rise to the potential difference. These two quantities adjust : for different effects. The zeta potential, .(in millivolts), corrects for the effects of the field distortion and counterion Filoti et al., JOURNAL OF PHARMACEUTICAL SCIENCES 104:2123–2131, 2015
flow through Henry’s function, H (below). Values of . potential are used widely to describe the charge on larger particles (e.g., pigments, latexes, etc.), and its derivation stems from the study of the electrophoretic behavior of macroscopic particles. 30 , takes into account The relationship between . and : = : 2DH the solution viscosity (0) and the solvent dielectric constant, D. However, the calculation of . does not take into account the ¨ effects of Debye–Huckel shielding. On the contrary, ZDHH also ¨ adjusts for the solvent shielding through the Debye–Huckel (1+kD a) D a) = :f , where k is the inapproximation,ZDHH = (1+k D H HQ p
verse Debye length (in cm−1 ), which depends on the temperature and the square root of the ionic strength, and a is the sum of the Stokes radii of the protein and its counterion.13 The major difference between . and ZDHH is that ZDHH adjusts zeff for ¨ the effects of the Debye–Huckel cloud, whereas . does not. In other words, zDHH describes the protein charge, including any bound ions, while excluding the effects of the solvent ion cloud. In general, zDHH is a more intuitive and useful description of the protein charge than ., and will be used in this paper. Henry’s function, which is used to correct the mobility for the electrophoretic effects, depends on the unitless product kD a (i.e., H = H(kD a), and ranges from 1.0 to 1.5 as kD a ranges from 10−4 to 104 . Our calculations use the approximation proposed by Moody et al.,15 which is accurate to within 1% over the full range. Most proteins (including BSA, HSA, and IgGs) have hydrodynamic radii less than 13 nm, so that values of kD a are less than 5 in solvents having ionic strengths greater than 1 mM. For physiological solvents, a good first approximation is that 1+kD a is approximately 3 and H is approximately 1.06, so ZDHH is roughly threefold larger than Zeff . Although ZDHH is only an approximation, its accuracy seems to be within the uncertainty of the experimental measurements of charge and model calculations.13 Charge Determination by Electrophoresis
The processes involved in electrophoresis are made complex by the coupled flow of the ions in the electric field, and the effect the coupling has on the electric field.14,16,17 However, there are four general considerations to keep in mind: (1) although a neutral protein will not move in an electric field, only neutral objects can move in the electric field. Although this may seem paradoxical, the electric field does not operate on individual particles. Rather, it operates on fluid volumes whose size is not fixed by a particle’s van der Waals edges. In fact, the edges of the volume are bounded a diffuse layer that, at physiological salt concentrations, extends a few Angstroms out from the particle’s van der Waals edge. The resulting volume has an overall net charge of zero. Net charge separation over distances greater than a few Angstroms is energetically very unfavorable, and adjustments back to a neutral condition will occur on a submicrosecond time scale.18 As a consequence, at the fields used in electrophoresis experiments, it is more accurate to consider electrophoretic motion a biased diffusion process. (2) Over short time scales, the distance moved by diffusion exceeds that moved by electrophoresis. Again, this may seem counterintuitive. However, the distance moved by electrophoresis is linearly proportional with time (i.e., doubling the time of electrophoresis doubles the distance moved) and the distance moved by diffusion is proportional to the square root of time (Fig. 1), so that at times less than a few seconds, a 5-nm pro2 diffuses further than it moves by tein having : = 1 × 10−4 cm Vs DOI 10.1002/jps.24454
REVIEW
Figure 1. The log of the average distance moved by electrophoresis (xE , dashed line) and by diffusion √ (xD , solid line) as a function of the log of time. As xE = :Et and xD = 2Dt, where D is the translational diffusion coefficient, these two lines have different slopes. Shown here are the lines for electrophoresis, assuming E = 1 v/cm and : = 1 × 10−4 cm2 /v-s, and for D = 1 × 10−7 cm2 /s. Note that the two lines cross (i.e., the average distance moved by the two process is equal) at approximately 10 s.
v electrophoresis in a 1 cm field. As a consequence, estimates of the electrophoretic mobility over short time scales will have poorer signal to noise and, therefore, poorer precision than methods that measure electrophoretic motion over longer time periods. (3) The protein itself contributes to the electric field. Although sedimentation and electrophoresis are similar in that they both are characterized by a constant ratio of the velocity of a particle to the driving field (s = v/g, where g is the gravitational field and : = v/E, where E is the electric field), the gravitational field is unaffected by the presence of the protein (because the masses are so small). However, in electrophoresis, the protein carries a portion of the electrical current, i, as well as contributing to the solution conductance, 6. Therefore, the presence of proteins can affect the field, as E = kAi .16,17 Furthermore, the fraction of the current carried by the protein, hence its velocity, will depend on the solvent’s ion concentration and composition, making the protein mobility a “constitutive” value.16 There are important, practical consequences to this fact. First, the fraction of the total current carried by the protein depends on the concentrations and mobilities of the other ions in the solvent.19 In particular, low salt concentrations will force the protein to carry a greater fraction of the charge (at a fixed field), thus making the interpretation of mobility in terms of the protein’s charge problematic. Therefore, it is important to have sufficient supporting electrolyte in the solvent to achieve accurate protein charge determinations.8 Monovalent salt concentrations of 10–20 mM are sufficient to avoid this problem for proteins having a charge magnitude less than 15–20 and at protein concentrations less than approximately 5 :M. As a
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secondary consideration, the electrophoretic mobilities of the predominant solvent ions should be matched in order to maximize the accuracy of protein charge determinations. Thus, it is best to determine protein charge in solvents containing moderate concentrations of KCl or NaCl (e.g., 100 mM).8,16,20 However, most monovalent cations and monovalent anions may be substituted so long as the ion concentration is kept in the 20– 100 mM range. Ion gradients that may form during electrophoresis may result in conductance changes that affect the i , where F is Faraday’s conZi Di ∂C electric field, E(x) = ki + Fk ∂x stant and Ci is the mass concentration of the ith species. As a consequence, protein boundary spreading during electrophoresis may contain field effects in addition to diffusion.17 (4) Both H+ and OH− have exceptionally high apparent electrophoretic mobilities (−100-fold greater than other small ions) because of their ability to conduct current by charge transfer through H2 O without requiring simultaneous mass transfer. This high ion conductance means that mobility data acquired at pH extremes must be interpreted with some caution. The expectation is that protein electrophoretic mobility will be reduced (compared with expectations) at pH less than 4 (for a cationic protein) and pH greater than 10 (for an anionic protein), because H+ or OH− conductance accounts for a high fraction of the current. This effect will be most pronounced at low-salt conditions. In order to assess the importance of H+ or OH− conductance to charge measurements, it is useful to measure the apparent charge as a function of salt concentration, then extrapolate the charge to both infinite salt [e.g., as the y-intercept of a graph of ZDHH vs. (KCl)-1 ] and zero salt [e.g., the y-intercept of ZDHH vs. (KCl)] at both low and high pH. To the authors’ knowledge, this type of systematic study has yet to be performed.
MATERIALS AND METHODS All measurements and sample dialysis were carried out in 10 mM NaCl, 10 mM Tris pH 8.1, at 25°C. Over the course of the studies, the measured conductance at 25°C was 1.75 ± 0.22 mS/cm, with individual conductance measurements having a precision of ±0.05 mS/cm. Solvent was prepared using analytical grade 10 mM NaCl, 10 mM Tris–HCl, and 10 mM Tris-base, with the solvent pH adjusted to 7.5 using 1 M NaOH or HCl. The samples characterized in this manuscript are: BSA [Sigma A-3059; lot 108H0881] and HSA [Sigma A-9511-1G; lot 093K7600]. All proteins were used without further purification. All samples were dialyzed overnight against solvent (100:1) and diluted with dialysate to 1 mg/mL prior to use. Capillary Electrophoresis Free-boundary CE was carried out using either of the P/ACETM MDQ or PA800 instruments (Beckman-Coulter, Fullerton, California). Both instruments used absorbance detection at 214 nm and a PEG-coated fused silica capillary of 50 :m I.D. a total length, LT , of 30.9 cm, with the length from injection to detector, Ld , of 25.2 cm.21 Measurements were made using both constant voltage and constant current settings. Benzyl acetate (0.2%, v/v) was used as the neutral marker to calculate the electroosmotic flow (EOF). The protocol used pressure injection of the EOF marker followed by the BSA sample (concentration 1 mg/mL) at 0.5 psi for a time length of 5 s. The constant voltage runs were conducted at 5, 9, 10, and 15 kV, whereas the Filoti et al., JOURNAL OF PHARMACEUTICAL SCIENCES 104:2123–2131, 2015
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constant current runs were conducted at currents of 6, 12, and 18 :A. These running parameters were chosen to fall within the linear range of Ohm’s Law plot generated using just solvent at 25°C. The capillaries were rinsed at 20 psi for 2 min with 0.1% NaOH followed by 4 min rinse with deionized water and a 4-min rinse with the running buffer prior to each run. Calculation of the free boundary electrophoretic mobility and its uncertainty from CE measurements was performed as described previously.19 For the 1-mg/mL BSA in 10 mM NaCl, 10 mM Tris pH 8.1, at 25°C, a bimodal peak was observed in CE. The origin of the doublet is uncertain, but may be a consequence of material bound to the BSA. This observation was not considered significant as the difference in mobility for the two peaks was within the uncertainty of the measurements (
Comparative Study of Analytical Techniques for Determining Protein Charge DANA I. FILOTI,1 STEVEN J. SHIRE,2 SANDEEP YADAV,3 THOMAS M. LAUE1 1
CAMIS, University of New Hampshire, St. Durham, New Hampshire Late Stage Pharmaceutical and Device Development, Genentech, Inc., South San Francisco, California 3 Late Stage Pharmaceutical and Device Development, Genentech, Inc., South San Francisco, California 2
Received 16 February 2015; revised 22 March 2015; accepted 24 March 2015 Published online 24 April 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.24454 ABSTRACT: As interest in high-concentration protein formulations has increased, it has become apparent that routine, accurate protein charge measurements are necessary. There are several techniques for charge measurement, and a comparison of the methods is needed. The ¨ electrophoretic mobility, effective charge, and Debye–Huckel–Henry charge have been determined for bovine serum albumin, and human serum albumin. Three different electrophoretic methods were used to measure the electrophoretic mobility: capillary electrophoresis, electrophoretic light scattering, and membrane confined electrophoresis. In addition, the effective charge was measured directly using steady-state electrophoresis. Measurements made at different NaCl concentrations, pH, and temperatures allow comparison with previous charge estimates based on electrophoresis, Donnan equilibrium, and pH titration. Similar charge estimates are obtained by all of the methods. The strengths and limitations of each technique are discussed, as are some general considerations about protein charge and C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 104:2123–2131, 2015 charge determination. Keywords: colloid; solubility; electrophoresis; proteins; protein formulation; protein charge
INTRODUCTION
BACKGROUND
Many therapeutic proteins, especially at high concentration, may be prone to phase separation (aggregates, gels, and emulsions) and high viscosity. These unfavorable solution behaviors, which pose challenges for manufacturing, drug safety, and drug delivery, are a reflection of the colloidal properties of proteins.1 Protein colloidal properties are controlled by proximity energies, which are principally electrostatic in origin. Charge–charge repulsion is the only long-range proximity energy that maintains protein solubility and that can overcome the attractive forces that lead to high viscosities. Therefore, it is important to have routine ways to measure protein charge. Presented here is a comparison of measurements of the electrophoretic mobility, :, net effective charge, zeff , and the Debye– ¨ Huckel–Henry charge, zDHH , for bovine serum albumin (BSA) and human serum albumin (HSA) made under identical solvent conditions using three different types of electrophoretic instruments, capillary electrophoresis (CE), electrophoretic light scattering (ELS), and membrane-confined electrophoresis (MCE). These results are compared with proton titration data,2 Donnan equilibrium measurements,3 and previous CE measurements,4 as well as theoretical charge estimates computed from amino acid composition and from X-ray structure. The results are discussed with respect to how the charge estimates compare made using the different methods. The assumptions made for each method and strengths and weaknesses of each electrophoretic method are also discussed.
Because there is renewed interest in making protein charge measurements, and the fact that many protein scientists may not have much experience with charge or with charge determination by electrophoresis, some background information may be useful.
Correspondence to: Thomas M. Laue (Telephone: +603-862-2459; Fax: +603862-4013; E-mail: [email protected]) Journal of Pharmaceutical Sciences, Vol. 104, 2123–2131 (2015) C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association
Macromolecular Charge Molecular charge is a fundamental property that directly influences protein structure, stability, solubility, and interactions with other macromolecules.5–7 Rooted in the primary structure, the charge on a protein is a system property as it is affected by the solvent composition, pH, dielectric constant, and temperature. The actual protein charge may differ substantially from the charge calculated by summing up the charge on each of its ionizable groups, as these calculations only account for H+ binding and it is known that proteins may bind other ions, particularly anions.2,8–10 Two types of ion binding are recognized, site bound and territorially bound. Site-bound ions are coordinated with the protein structure by specific bonds. These ions are fixed spatially and may be visible in an X-ray or nuclear magnetic resonance (NMR) structure. What is not depicted in an X-ray or NMR structure, but is important to protein net charge, are the territorially bound ions. These ions are not bound to a specific site. Instead, they are confined to regions of high-charge density on the protein surface in a manner similar to the “condensed ions” on a polyelectrolyte. The relevant parameter for what constitutes a high-charge density is the Bjerrum length, which is the distance separating two like-sign charges resulting in a potential energy in their vicinity comparable to the thermal energy, kB T, where kB is the Boltzmann constant and T is the absolute temperature. In physiological solutions, Bjerrum length ˚ Conversely, if two charges are closer together than is 2–3 A.
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the Bjerrum length, then a counterion will be associated with them; and if there is a patch of charge on the protein surface, sufficient counterions will bind until the average charge separation equals or exceeds the Bjerrum length. Because territorial ion localization requires a high-charge density, the extent and location of territorially bound ions is affected by a protein’s structure.10–12 Territorially bound ions are characterized by their relative insensitivity to the bulk solvent ion concentration and by their close proximity to the protein surface (i.e., they are confined within the solvation layer).10 Even though territorially bound ions may exchange freely with solvent ions, they do not dissociate from the macromolecule. Because they must move with the macroion, thereby not contributing significantly to its osmotic potential, they are an integral part of the protein’s “charge structure.” Site-bound and territorially bound ions are distinct from those ions that make up the “counterion cloud” (i.e., the Debye– ¨ Huckel cloud) that forms as the solvent response to the protein’s ¨ net charge. Instead, the Debye–Huckel cloud describes an imbalance of counterion and coion concentrations in vicinity of the protein. Importantly, the charge density distribution of the ion cloud depends on the solvent ion concentration and extends out from the protein surface several Angstroms into the surrounding solvent.5,10 In short, the counterion cloud can be considered a solvent response to the presence of the charged protein, and ¨ the counterions that make up Debye–Huckel cloud are a consequence of the protein net charge rather than being an integral part of the protein charge. Often the terms “charge” and “valence” are used interchangeably. The fundamental charge on a proton, Qp , is 1.602 × 10−19 C (coulomb, SI units). The valence of a protein, z, is the unitless ratio of its charge, Q, divided by the fundamental charge, that is, z = Q/Qp . So, a protein with a valence of +5 has a net charge of +8.1 × 10−19 C. Both the charge and the valence are signed quantities, so that a protein having a valence of −5 would carry a charge of −8.1 × 10−19 C. The experimental quantities useful for charge determination are the electrophoretic mobility, : in cm2 /V-s, (the ratio of the velocity of a molecule, in cm/s, to the electric field, in V/cm) and the effective valence, zeff = f Q: p , where f is the translational friction coefficient, determined experimentally from either sedimentation or diffusion measurement and Qp is the proton fundamental charge.13 Both : and zeff include the effects ¨ of the Debye–Huckel ion shielding and of the “electrophoretic effect,” which results from the distortion of the electric field in the vicinity of the nonconducting particle and from the transport of the ion atmosphere in the vicinity of the protein.7,14 Both ion shielding and the electrophoretic effect reduce the electrophoretic mobility. Consequently, : and zeff do not distin¨ guish between bound ions and the Debye–Huckel cloud. Two values calculated from : and zeff adjust for these effects, the ¨ zeta potential, ., and the Debye–Huckel–Henry valence zDHH . In visualizing the difference between these two descriptions of a protein’s charge properties, it is useful to consider the . potential as the electrical potential difference between the shear surface surrounding a spherical particle and the bulk solvent, where the potential difference is spread uniformly over the nonconducting particle surface, and zDHH (actually zDHH *Qp ) as the charge at the center of the spherical, nonconducting particle that gives rise to the potential difference. These two quantities adjust : for different effects. The zeta potential, .(in millivolts), corrects for the effects of the field distortion and counterion Filoti et al., JOURNAL OF PHARMACEUTICAL SCIENCES 104:2123–2131, 2015
flow through Henry’s function, H (below). Values of . potential are used widely to describe the charge on larger particles (e.g., pigments, latexes, etc.), and its derivation stems from the study of the electrophoretic behavior of macroscopic particles. 30 , takes into account The relationship between . and : = : 2DH the solution viscosity (0) and the solvent dielectric constant, D. However, the calculation of . does not take into account the ¨ effects of Debye–Huckel shielding. On the contrary, ZDHH also ¨ adjusts for the solvent shielding through the Debye–Huckel (1+kD a) D a) = :f , where k is the inapproximation,ZDHH = (1+k D H HQ p
verse Debye length (in cm−1 ), which depends on the temperature and the square root of the ionic strength, and a is the sum of the Stokes radii of the protein and its counterion.13 The major difference between . and ZDHH is that ZDHH adjusts zeff for ¨ the effects of the Debye–Huckel cloud, whereas . does not. In other words, zDHH describes the protein charge, including any bound ions, while excluding the effects of the solvent ion cloud. In general, zDHH is a more intuitive and useful description of the protein charge than ., and will be used in this paper. Henry’s function, which is used to correct the mobility for the electrophoretic effects, depends on the unitless product kD a (i.e., H = H(kD a), and ranges from 1.0 to 1.5 as kD a ranges from 10−4 to 104 . Our calculations use the approximation proposed by Moody et al.,15 which is accurate to within 1% over the full range. Most proteins (including BSA, HSA, and IgGs) have hydrodynamic radii less than 13 nm, so that values of kD a are less than 5 in solvents having ionic strengths greater than 1 mM. For physiological solvents, a good first approximation is that 1+kD a is approximately 3 and H is approximately 1.06, so ZDHH is roughly threefold larger than Zeff . Although ZDHH is only an approximation, its accuracy seems to be within the uncertainty of the experimental measurements of charge and model calculations.13 Charge Determination by Electrophoresis
The processes involved in electrophoresis are made complex by the coupled flow of the ions in the electric field, and the effect the coupling has on the electric field.14,16,17 However, there are four general considerations to keep in mind: (1) although a neutral protein will not move in an electric field, only neutral objects can move in the electric field. Although this may seem paradoxical, the electric field does not operate on individual particles. Rather, it operates on fluid volumes whose size is not fixed by a particle’s van der Waals edges. In fact, the edges of the volume are bounded a diffuse layer that, at physiological salt concentrations, extends a few Angstroms out from the particle’s van der Waals edge. The resulting volume has an overall net charge of zero. Net charge separation over distances greater than a few Angstroms is energetically very unfavorable, and adjustments back to a neutral condition will occur on a submicrosecond time scale.18 As a consequence, at the fields used in electrophoresis experiments, it is more accurate to consider electrophoretic motion a biased diffusion process. (2) Over short time scales, the distance moved by diffusion exceeds that moved by electrophoresis. Again, this may seem counterintuitive. However, the distance moved by electrophoresis is linearly proportional with time (i.e., doubling the time of electrophoresis doubles the distance moved) and the distance moved by diffusion is proportional to the square root of time (Fig. 1), so that at times less than a few seconds, a 5-nm pro2 diffuses further than it moves by tein having : = 1 × 10−4 cm Vs DOI 10.1002/jps.24454
REVIEW
Figure 1. The log of the average distance moved by electrophoresis (xE , dashed line) and by diffusion √ (xD , solid line) as a function of the log of time. As xE = :Et and xD = 2Dt, where D is the translational diffusion coefficient, these two lines have different slopes. Shown here are the lines for electrophoresis, assuming E = 1 v/cm and : = 1 × 10−4 cm2 /v-s, and for D = 1 × 10−7 cm2 /s. Note that the two lines cross (i.e., the average distance moved by the two process is equal) at approximately 10 s.
v electrophoresis in a 1 cm field. As a consequence, estimates of the electrophoretic mobility over short time scales will have poorer signal to noise and, therefore, poorer precision than methods that measure electrophoretic motion over longer time periods. (3) The protein itself contributes to the electric field. Although sedimentation and electrophoresis are similar in that they both are characterized by a constant ratio of the velocity of a particle to the driving field (s = v/g, where g is the gravitational field and : = v/E, where E is the electric field), the gravitational field is unaffected by the presence of the protein (because the masses are so small). However, in electrophoresis, the protein carries a portion of the electrical current, i, as well as contributing to the solution conductance, 6. Therefore, the presence of proteins can affect the field, as E = kAi .16,17 Furthermore, the fraction of the current carried by the protein, hence its velocity, will depend on the solvent’s ion concentration and composition, making the protein mobility a “constitutive” value.16 There are important, practical consequences to this fact. First, the fraction of the total current carried by the protein depends on the concentrations and mobilities of the other ions in the solvent.19 In particular, low salt concentrations will force the protein to carry a greater fraction of the charge (at a fixed field), thus making the interpretation of mobility in terms of the protein’s charge problematic. Therefore, it is important to have sufficient supporting electrolyte in the solvent to achieve accurate protein charge determinations.8 Monovalent salt concentrations of 10–20 mM are sufficient to avoid this problem for proteins having a charge magnitude less than 15–20 and at protein concentrations less than approximately 5 :M. As a
DOI 10.1002/jps.24454
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secondary consideration, the electrophoretic mobilities of the predominant solvent ions should be matched in order to maximize the accuracy of protein charge determinations. Thus, it is best to determine protein charge in solvents containing moderate concentrations of KCl or NaCl (e.g., 100 mM).8,16,20 However, most monovalent cations and monovalent anions may be substituted so long as the ion concentration is kept in the 20– 100 mM range. Ion gradients that may form during electrophoresis may result in conductance changes that affect the i , where F is Faraday’s conZi Di ∂C electric field, E(x) = ki + Fk ∂x stant and Ci is the mass concentration of the ith species. As a consequence, protein boundary spreading during electrophoresis may contain field effects in addition to diffusion.17 (4) Both H+ and OH− have exceptionally high apparent electrophoretic mobilities (−100-fold greater than other small ions) because of their ability to conduct current by charge transfer through H2 O without requiring simultaneous mass transfer. This high ion conductance means that mobility data acquired at pH extremes must be interpreted with some caution. The expectation is that protein electrophoretic mobility will be reduced (compared with expectations) at pH less than 4 (for a cationic protein) and pH greater than 10 (for an anionic protein), because H+ or OH− conductance accounts for a high fraction of the current. This effect will be most pronounced at low-salt conditions. In order to assess the importance of H+ or OH− conductance to charge measurements, it is useful to measure the apparent charge as a function of salt concentration, then extrapolate the charge to both infinite salt [e.g., as the y-intercept of a graph of ZDHH vs. (KCl)-1 ] and zero salt [e.g., the y-intercept of ZDHH vs. (KCl)] at both low and high pH. To the authors’ knowledge, this type of systematic study has yet to be performed.
MATERIALS AND METHODS All measurements and sample dialysis were carried out in 10 mM NaCl, 10 mM Tris pH 8.1, at 25°C. Over the course of the studies, the measured conductance at 25°C was 1.75 ± 0.22 mS/cm, with individual conductance measurements having a precision of ±0.05 mS/cm. Solvent was prepared using analytical grade 10 mM NaCl, 10 mM Tris–HCl, and 10 mM Tris-base, with the solvent pH adjusted to 7.5 using 1 M NaOH or HCl. The samples characterized in this manuscript are: BSA [Sigma A-3059; lot 108H0881] and HSA [Sigma A-9511-1G; lot 093K7600]. All proteins were used without further purification. All samples were dialyzed overnight against solvent (100:1) and diluted with dialysate to 1 mg/mL prior to use. Capillary Electrophoresis Free-boundary CE was carried out using either of the P/ACETM MDQ or PA800 instruments (Beckman-Coulter, Fullerton, California). Both instruments used absorbance detection at 214 nm and a PEG-coated fused silica capillary of 50 :m I.D. a total length, LT , of 30.9 cm, with the length from injection to detector, Ld , of 25.2 cm.21 Measurements were made using both constant voltage and constant current settings. Benzyl acetate (0.2%, v/v) was used as the neutral marker to calculate the electroosmotic flow (EOF). The protocol used pressure injection of the EOF marker followed by the BSA sample (concentration 1 mg/mL) at 0.5 psi for a time length of 5 s. The constant voltage runs were conducted at 5, 9, 10, and 15 kV, whereas the Filoti et al., JOURNAL OF PHARMACEUTICAL SCIENCES 104:2123–2131, 2015
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constant current runs were conducted at currents of 6, 12, and 18 :A. These running parameters were chosen to fall within the linear range of Ohm’s Law plot generated using just solvent at 25°C. The capillaries were rinsed at 20 psi for 2 min with 0.1% NaOH followed by 4 min rinse with deionized water and a 4-min rinse with the running buffer prior to each run. Calculation of the free boundary electrophoretic mobility and its uncertainty from CE measurements was performed as described previously.19 For the 1-mg/mL BSA in 10 mM NaCl, 10 mM Tris pH 8.1, at 25°C, a bimodal peak was observed in CE. The origin of the doublet is uncertain, but may be a consequence of material bound to the BSA. This observation was not considered significant as the difference in mobility for the two peaks was within the uncertainty of the measurements (
