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Supplementary Material Purification of Singly PEGylated α-Lactalbumin Using Charged Ultrafiltration Membranes Krisada Ruanjaikaen, Andrew L. Zydney Department of Chemical Engineering, The Pennsylvania State University, University Park, PA 16802; telephone: 814-863-7113; fax: 814-865-7846; e-mail: [email protected] A.1. Membrane Surface Charge The membrane surface charge density was evaluated from streaming potential measurements following the procedure described by Burns and Zydney (2000). Typical experimental data obtained using a 1 mM Bis-Tris buffer with 10 mM NaCl at pH 7 are shown in Figure A1 for an unmodified 300 kDa UltracelTM membrane and a negatively-charged version that was charged for 24 hr. The apparent zeta potential () was evaluated from the slope of the measured streaming potential as a function of the applied pressure using the Helmholtz-Smoluchowski equation (Hunter, 1981): 0 r dE z dP where Ez is the measured voltage, (A1) is the solution conductivity, is the permittivity of free space, and r is the dielectric constant of the solution. Calculations using the data in Figure A1 gave = -3.0 ± 0.2 for the unmodified membrane and = -11.7 ± 0.2 mV for the 24-hr negatively charged membrane with the slope evaluated by linear regression. The surface charge density of the membrane pores was evaluated as (Burns and Zydney, 2000): F q p 4C 0 F 1 sinh 2 RT (A2) where C0 is the bulk ion concentration, F is Faraday’s constant, 1 is the Debye length, R is the universal gas constant, and T is the temperature. The calculated surface charge density for the membrane charged for 24 hr was qp = -2.7 mC/m2. Figure A1. Streaming potential as a function of applied transmembrane pressure for an unmodified 300 kDa UltracelTM membrane and for a negatively-charged version that was charged for 24 hr. A.2. Model Calculations Molek et al. (2010) developed a simple analytical expression for the surface charge density at the outer radius of a PEGylated protein: a 2 1 b qPEG exp PEG b aqs b 1 a (A3) where a is the radius of the protein core, b is the radius of the PEGylated protein, qs is the charge on the surface of the protein core, and and density PEG are the inverse Debye length in the bulk solution and in the PEG layer surrounding the protein: N 1 1/ 2 2 zi Ci ro kB T i1 (A4) where kB is the Boltzmann constant, T is the absolute temperature, o is the permittivity of a vacuum, r is the dielectric constant of the solution, and zi and Ci are the valence and concentration of all mobile ions, respectively. The surface charge density of the protein core was evaluated directly from the protein amino acid sequence accounting for the elimination of one or more lysine amine groups associated with the attachment of the PEG chain(s) (Molek et al., 2010). The thermodynamics of PEG-salt systems have been studied quite extensively (Willauer et al., 2002). These systems tend to phase separate due to the strong "negative" interactions between the salts and the polyethylene glycol, with the salt concentration in the PEG phase as much as seven times smaller than the salt concentration in the non-PEG phase (Willauer et al., 2002) giving PEG/ = 0.38. The effective radius of the PEGylated protein (b) was calculated using the correlation presented by Fee and Van Alstine (2004) as: b where A 2 2 R RPEG PEG 6 3A 3 (A5) 1 1 3 3 3 A 108a 3 8RPEG 1281a 6 12a 3 RPEG 2 (A6) with RPEG and a are the radii of the isolated PEG and protein, respectively. The radius of a free PEG molecule was calculated as: RPEG 0.01912 MW 0.559 (A7) where RPEG is in nm and the molecular weight (MW) is in Da (Fee and Van Alstine, 2004). The radiusof the unmodified -lactalbumin was a = 2.0 nm. The sieving coefficient of the PEGylated protein was evaluated using the theoretical expression for the partition coefficient of a charged sphere in a charged cylindrical pore originally developed by Smith and Deen (1980): E 2 S a 1 K c exp k BT (A8) where Sa is the actual sieving coefficient, defined as the ratio of the protein concentration in the filtrate solution to that in the solution immediately upstream of the membrane. The term (1-)2 describes the steric (hard-sphere) exclusion of the sphere from the region within one solute radius of the pore wall (with equal to the ratio of the solute radius to the pore radius). Kc is the hindrance factor associated with convection and E is the dimensionless electrostatic energy k BT of interaction (Smith and Deen, 1980): E kB T 2 As PEG Asp PEG p Ap 2p (A9) where As, Asp, and Ap are functions of the solution ionic strength, protein size, and pore size, and PEG and p are the dimensionless surface charge densities of the PEGylated protein and the pore, respectively. The use of Equations (A3) to (A9) to evaluate the sieving coefficient of the PEGylated protein are discussed in more detail by Molek et al. (2010). References Burns DB, Zydney AL. 2000. Buffer effects on the zeta potential of ultrafiltration membranes. J Membrane Sci 172:39–48. Fee CJ, Van Alstine JM. 2004. Prediction of the viscosity radius and the size exclusion chromatography behavior of PEGylated proteins. Bioconj Chem 15:1304-1313. Hunter RJ. 1981. Zeta Potential in Colloid Science: Principles and Applications. London: Academic Press. Molek JR, Ruanjaikaen K, Zydney AL. 2010. Effect of electrostatic interactions on transmission of PEGylated proteins through charged ultrafiltration membranes. J Membrane Sci 353:60–69. Smith FG, Deen WM. 1980. Electrostatic double-layer interactions for spherical colloids in cylindrical pores. J Colloid Interf Sci 78:444-465. Willauer HD, Huddleston JG, Rogers RD. 2002. Solute partitioning in aqueous biphasic systems composed of polyethylene glycol and salt: The partitioning of small neutral organic species. Ind Eng Chem Res 41:1892-1904.