Article pubs.acs.org/ac
Instrument and Method to Determine the Electrophoretic Mobility of Nanoparticles and Proteins by Combining Electrical and Flow FieldFlow Fractionation Christoph Johann,*,† Stephan Elsenberg,‡ Horst Schuch,‡ and Ulrich Rösch‡ †
Wyatt Technology Europe GmbH, Hochstrasse 18, DE-56307 Dernbach, Germany Superon GmbH, Hochstrasse 12, DE-56307 Dernbach, Germany
‡
S Supporting Information *
ABSTRACT: A new FFF method is presented which combines asymmetrical flow-FFF (AF4) and electrical FFF (ElFFF) in one channel to electrical asymmetrical flow-FFF (EAF4) to overcome the restrictions of pure ElFFF. It allows for measuring electrophoretic mobility (μ) as a function of size. The method provides an absolute value and does not require calibration. Results of μ for two particle standards are in good agreement with values determined by phase analysis light scattering (PALS). There is no requirement for low ionic strength carriers with EAF4. This overcomes one of the main limitations of ElFFF, making it feasible to measure proteins under physiological conditions. EAF4 has the capability to determine μ for individual populations which are resolved into separate peaks. This is demonstrated for a mixture of three polystyrene latex particles with different sizes as well as for the monomer and dimer of BSA and an antibody. The experimental setup consists of an AF4 channel with added electrodes; one is placed beneath the frit at the bottom wall and the other covers the inside of the upper channel plate. This design minimizes contamination from the electrolysis reactions by keeping the particles distant from the electrodes. In addition the applied voltage range is low (1.5−5 V), which reduces the quantity of gaseous electrolysis products below a threshold that interferes with the laminar flow profile or detector signals. Besides measuring μ, the method can be useful to improve the separation between sample components compared to pure flow-FFF. For two proteins (BSA and a monoclonal antibody), enhanced resolution of the monomer and dimer is achieved by applying an electric field.
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avoided, but restrictions to extremely low ionic strength and minute sample load still persisted.7 These aforementioned studies focused on establishing ElFFF as a separation tool, not to determine μ. In 1986 Giddings proposed another mode of ElFFF which was called cyclical electric field-flow fractionation (CyElFFF)8 and has been developed by Gale and coworkers.9−11 CyElFFF has been shown to separate particles in suspension according to their charge and also to determine electrophoretic mobility. Published results look promising, but so far the method still can only be used in DI water or under extremely low ionic strength (micromolar). Size and mobility cannot be measured simultaneously, which is required to calculate the surface charge. In the concept of EAF4, introduced in this work, the electric field strength and therefore the quantity of electrolysis products can be kept low. Retention of sample components is mainly caused by the flow force field. A
harge is an important physical property of nanoparticles and macromolecules such as proteins. Stability of the suspension and the interaction of particles and macromolecules are influenced and driven by charge. Charge and zeta potential are derived from the measured electrophoretic mobility μ.1 One established method to measure μ is phase analysis light scattering (PALS),2 which is easy to use and has good sensitivity. However, PALS cannot measure the distribution of charge as a function of size and it has limitations for sample preparations with low scattering intensity. Electric field flow fractionation (ElFFF) is known since more than 40 years.3 It can, in principle, determine the electrophoretic mobility μ from measured retention time if the diffusion coefficient or hydrodynamic size is known. Severe limitations of the applicability4 have prevented a more widespread use. The main problem when using carrier solutions with higher ionic strengths is the resulting weak electric field strength that in itself is not sufficient for suitable retention. Using a stretched membrane construction, low efficiency and recovery problems for protein samples were reported,5 which could not be significantly improved using graphite electrodes.6 Focusing on latex particles instead of proteins, recovery problems could be © 2015 American Chemical Society
Received: December 18, 2014 Accepted: March 19, 2015 Published: March 19, 2015 4292
DOI: 10.1021/ac504712n Anal. Chem. 2015, 87, 4292−4298
Article
Analytical Chemistry minor shift in retention time caused by the electric field is sufficient to calculate the electrophoretic mobility.
conductivity of the solvent. Using eq 4, E is obtained from the electric current flowing through the solution and its conductivity. During the experiment the current I is kept constant and k is measured. Changes in the solvent conductivity due to electrolysis products are thus taken into account and the correct value of E is used for the determination of the electrophoretic mobility. The total drift velocity v of a sample component is the sum of the drift velocity induced by the electric field vEP and the drift velocity vc caused by the cross-flow. v = vc + vEP (5)
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METHODS Flow-FFF. In order to determine μ, a modified flow-FFF experiment is applied. In flow-FFF the retention time depends on the drift velocity of sample components toward the accumulation wall which is caused by a cross-flow permeating through the bottom wall.12−14 The particle retention time tR depends on the channel thickness w, the particle diffusion coefficient D, the cross-flow rate Fc, and the detector-flow rate Fout. If the flow rates are constant over time and retention is sufficiently high, the retention time is, in good approximation, given by12 tR =
fF ⎞ w2 ⎛ ln⎜1 + c ⎟ 6D ⎝ Fout ⎠
The drift velocity vc is given by the cross-flow rate divided by the channel area (which in our case is identical to the electrode area) vc =
(1)
f is the ratio of the channel area, downstream the focusing line to the total channel area. f can be derived by the ratio of the flow rates entering the channel during focusing. The channel thickness is determined by measuring the retention time of a sample with known diffusion coefficient using eq 1.14 Care has to be taken that the diffusion coefficient relates to the same temperature and solution conditions applied in the FFF experiment. If the flow rates are varied during elution, instead of eq 1, a mathematical discretization of the channel into finite volume elements is necessary. From element to element, the cross-flow rate and channel flow rate can have a different value but they are constant within each element. The total retention time is given by the addition of the individual retention times of all elements. This procedure15 is described in the Supporting Information. Electrical Asymmetrical Flow-FFF. The electrophoretic mobility μ is defined by v μ = EP (2) E
V IR = d d
⎛ t ln(1 + fFc )/ t ⎛ fFc ⎞⎞ Fout Fout R − ⎜1 + vEP = ⎜⎜e Ri ⎟⎟⎟ Fout ⎠⎠ Ael f ⎝ ⎝
I Ael k
(7)
Equation 7 is valid for constant flow rates Fc and Fout and sufficient high retention. Under these conditions, the evaluation of μ is independent of the channel thickness w and the particle diffusion coefficient D. However, if the condition of constant flows is not fulfilled or a calculation of the particle surface charge is intended, both w and D are required. In this case eq 1 or the implementation given in the Supporting Information is used to calculate the drift velocity corresponding to the crossflow rate plus electric field strength. The diffusion coefficient of the sample can be calculated from the measurement with no electric field applied.
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EXPERIMENTAL SECTION Chemicals. Chemicals used in this work were carboxylate modified spherical polystyrene latex particles (Otsuka Electronics, Osaka, Japan) with a diameter of 310 nm and a nominal electrophoretic mobility of (−4.05 ± 0.36) μm cm V−1 s−1 at pH 7, sulfate stabilized spherical polystyrene latex particles with diameter of (21 ± 2) nm, (46 ± 2) nm, and (102 ± 2) nm (Thermo Scientific, Waltham, MA), bovine serum albumin (Thermo Scientific, Waltham, MA), sodium phosphate dibasic, sodium phosphate monobasic, and sodium nitrate (all from Sigma-Aldrich, St. Louis, MO). The source of the humanized monoclonal antibody for therapeutic application cannot be disclosed. All experiments were performed using an ultrafiltration membrane with a molecular weight cutoff of 10 kDa and regenerated cellulose as an active layer (Millipore, Billerica, MA). All the above-mentioned uncertainties are expressed as standard deviation. The particle diameters of all spherical polystyrene latex particles were determined by dynamic light scattering specified by the manufacturer. They are therefore hydrodynamic diameters. Instruments. The experiments were performed on an Agilent 1220 HPLC system (Agilent Technologies, Santa Clara, CA), consisting of a low pressure gradient pump, an auto
(3)
where d is the distance between the electrodes, R the resistance, and I the electric current. The electrodes are two plates with equal shape opposing each other. There is a potential drop close to the electrodes due to the electrolysis products and the electric double layer. The effective electric field strength which is responsible for the transport in the solution is therefore smaller compared to what would be expected from the external applied voltage.17 In order to obtain the effective electric field strength from quantities which can be measured, we convert eq 3 to E=
(6)
In the EAF4 experiment, vc is known from the applied crossflow rate Fc and v is obtained from the measured retention time. Thus, vEP can be calculated from at least two experiments measuring the retention time tRi at specific electric field strength with respect to the retention time tR without the electric field. Equation 1 can be applied to obtain
vEP is the migration or drift velocity due to the electric field in a given medium and E is the electric field strength. μ allows for deducing the particle surface charge by applying models of the particle architecture.16 The electric field strength E is proportional to the voltage drop V across the solution and is given by17 E=
Fc Ael
(4)
where Ael is the electrode area, which for the channel used in this work is identical to the membrane area, and k is the specific 4293
DOI: 10.1021/ac504712n Anal. Chem. 2015, 87, 4292−4298
Article
Analytical Chemistry
volume was 1 μL of a solution with a concentration of 10 g L−1, resulting in a total injection amount of 10 μg. The mixture of polystyrene latex particles was measured at a detector flow rate of 1 mL min−1 with a cross-flow rate of 1.6 mL min−1 during the first 9 min of elution. Then the cross-flow rate was reduced linearly within 15 min to 0.2 mL min−1 and afterward maintained constant until the end of the experiment. The injection volume was 20 μL containing 6.7 μg each of the 21 and 46 nm particle and 0.4 μg of the 102 nm particle. The BSA experiments for determining μ were performed with a detector flow of 0.5 mL min−1 and a constant cross-flow of 1.5 mL min−1. A volume of 5 μL was injected with a sample amount of 10 μg. The carrier solution was a 0.01 M sodium phosphate buffer at pH 8. The BSA experiments done to improve the separation used a detector flow rate of 1 mL min−1 in combination with 3 mL min−1 constant cross-flow rate, 20 μL injection volume containing 10 μg sample amount and 0.05 M NaNO3 as the carrier solution. The monoclonal antibody was measured at 3 mL min−1 constant cross-flow rate, 0.7 mL min−1 detector flow rate, and 10 μL injection volume containing 0.2 μg sample amount. The carrier solution was a 0.01 M sodium phosphate buffer at pH 7. For all experiments the current was applied only during the elution phase and was kept constant. It was varied between experiments from 0 mA to 6 mA in steps of 2 mA for the carboxylate modified polystyrene latex particles, from 0 mA to 8 mA in steps of 4 mA for the sulfate stabilized polystyrene latex particles and was 0 mA, 8 mA, and 12 mA for determining μ of BSA. The experiments on improving the separation process were performed at 0 mA and 10 mA.
sampler, and a variable wavelength detector. It was coupled to a Wyatt DAWN HELEOS II MALS detector, a Wyatt Eclipse AF4 (all from Wyatt Technology Corp., Santa Barbara, CA) with the center downstream injection technique, together with a custom-made EAF4 channel according to Figure 1. It is an
Figure 1. Scheme of the channel construction used for the EAF4 experiments. 1, upper plate; 2, upper electrode, here shown to be positive but it can be of either polarity; 3, channel volume with a sketch of the parabolic flow profile of the detector flow rate Fout and the cross-flow rate Fc; 4, ultrafiltration membrane with sample particles (blue dots) close to it; 5, ceramic frit; 6, bottom electrode; 7, bottom plate of the channel.
assembly of a top frame, made of aluminum with a polycarbonate inlay, a bottom block, made of PEEK, a ceramic frit, an O-ring (made of Viton), an ultrafiltration membrane (regenerated cellulose), and a spacer foil (made of biaxial oriented polyethylene terephthalate) with 350 μm thickness. The outer dimensions of the top frame were 56 mm × 22 mm × 291 mm (width × height × length) and the bottom block dimensions 56 mm × 19 mm × 291 mm. The electrodes were made of platinized stainless steel, opposing each other parallel in a symmetrical manner with a distance of 3.85 mm. One electrode was flush mounted into the polycarbonate inlay of the top frame, while the other one was integrated into the bottom part and placed below the ceramic frit. The effective membrane and electrode area was 0.003 525 m2. A custom-made software controllable high precision power supply (−50 mA to +50 mA ± 1% of set/read value
