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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

 dP
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  aqs
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 
ro kB T i1

(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
 1281a 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
radiusof 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.