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Bilinear electric field gradient focusing
Journal of Chromatography A, 1216 (2009) 6532–6538
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Bilinear electric field gradient focusing Xuefei Sun a , Dan Li a , Adam T. Woolley a , Paul B. Farnsworth a , H. Dennis Tolley b , Karl F. Warnick c , Milton L. Lee a,∗ a
Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA Department of Statistics, Brigham Young University, Provo, UT 84602, USA c Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA b
a r t i c l e
i n f o
Article history: Received 7 April 2009 Received in revised form 13 July 2009 Accepted 27 July 2009 Available online 6 August 2009 Keywords: Electric field gradient focusing Bilinear gradient Proteins Focusing
a b s t r a c t Electric field gradient focusing (EFGF) uses an electric field gradient and a hydrodynamic counter flow to simultaneously separate and focus charged analytes in a channel. Previously, most EFGF devices were designed to form a linear field gradient in the channel. However, the peak capacity obtained using a linear gradient is not much better than what can be obtained using conventional CE. Dynamic improvement of peak capacity in EFGF can be achieved by using a nonlinear gradient. Numerical simulation results indicate that the peak capacity in a 4-cm long channel can be increased from 20 to 150 when changing from a linear to convex bilinear gradient. To demonstrate the increased capacity experimentally, an EFGF device with convex bilinear gradient was fabricated from poly(ethylene glycol) (PEG)-functionalized acrylic copolymers. The desired gradient profile was confirmed by measuring the focusing positions of a standard protein for different counter flow rates at constant voltage. Dynamically controlled elution of analytes was demonstrated using a monolith-filled bilinear EFGF channel. By increasing the flow rate, stacked proteins that were ordered but not resolved after focusing in the steep gradient segment were moved into the shallow gradient segment, where the analyte peak resolution increased significantly. In this way, the nonlinear field gradient was used to realize a dynamic increase in the peak capacity of the EFGF method. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Electric field gradient focusing (EFGF) depends on an electric field gradient and an opposing hydrodynamic flow to separate and focus charged analytes at their equilibrium positions [1–6]. This technique can concentrate analytes as they are separated. Unlike traditional separation techniques, such as chromatography and electrophoresis, sample injection in EFGF has much less influence on the separated band profiles. Moreover, EFGF is not affected by protein aggregation and precipitation that often occur in isoelectric focusing (IEF). It is possible to selectively retain or elute target analytes in EFGF by manipulating the applied electric field or hydrodynamic flow. To date, samples that have been tested using EFGF include proteins, peptides, amino acids, dyes and other small molecules. Analytes have been concentrated up to 10 000-fold using EFGF. One challenging issue in EFGF is creating the desired electric field gradient along the separation channel. Several methods have been developed to establish the electric field gradient, including the use of a changing cross-sectional area containing conduc-
∗ Corresponding author. Tel.: +1 8014222135; fax: +1 8014220157. E-mail address: milton [email protected] (M.L. Lee). 0021-9673/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2009.07.050
tive buffer or polymer membrane surrounding the separation channel [1,7–14], a buffer conductivity gradient in the channel generated with assistance of a dialysis membrane [15–18], the use of a computer-controlled multi-electrode array along the channel for dynamic field gradient focusing [19–24], and a temperature gradient along the channel filled with a buffer that has a temperature-dependent conductivity [25–32]. Among the approaches mentioned above to generate an electric field gradient, the changing cross-sectional area method is relatively simple to implement. Typically, a dialysis membrane or conductive hydrogel was employed to isolate the separation channel from the changing cross-sectional area. Koegler and Ivory [1,7] first fabricated a preparative-scale EFGF device by placing a dialysis membrane in a conically shaped poly(methyl methacrylate) (PMMA) cylinder. Humble et al. [8] fabricated an analytical scale EFGF device by embedding a separation channel in an ionically conductive and planar horn-shaped hydrogel. Kelly et al. [9] miniaturized a similar device in a PMMA microchip, while Liu et al. [10] fabricated a micro-EFGF device by isolating the separation channel and changing cross-sectional area with a buffer-filled ionpermeable membrane positioned on a weir structure. Recently, we have fabricated the complete EFGF device from poly(ethylene glycol) (PEG) functionalized copolymers, including the substrate and conductive hydrogel, which are resistant to protein adsorption and
X. Sun et al. / J. Chromatogr. A 1216 (2009) 6532–6538
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Here, u is the counter hydrodynamic flow velocity. is the electrophoretic mobility of the analyte. E(x, t) is the electric field strength at point x and time t. If the column has negligible adsorption, then the coefficient of dispersion is given by DT = DM + DF
(3)
where DM is the molecular diffusivity of the analyte and DF is the Taylor dispersion due to laminar flow in the channel. The flow dispersion can be approximated for circular unpacked columns as [35]: DF =
Fig. 1. Electric field gradient profiles studied for EFGF. (1) Linear, (2) convex, and (3) bilinear.
suppress electroosmotic flow. The hydrogel was again shaped to form a linear electric field gradient and was covalently bound to the substrate. A protein compatible monolith was incorporated in the channel to reduce flow dispersion and, therefore, narrow the focused bands [11]. So far, only a linear gradient (line 1 in Fig. 1) has been reported in EFGF devices based on changing cross-sectional area. According to the fundamental theory of EFGF, resolution and peak capacity in EFGF with a linear gradient cannot be improved simultaneously, because bandwidth and resolution are both inversely proportional to the square root of the field gradient [3]. However, theoretical work indicates that the peak capacity could be improved using an EFGF device with nonlinear (convex) gradient (curve 2 in Fig. 1), such as can be approximated with a bilinear gradient (curve 3 in Fig. 1) [3,4]. All analytes would first be focused in the steeper gradient section to form narrow stacked bands. Then they would be sequentially moved into the shallower gradient section and be resolved by manipulating the counter flow rate or applied voltage. This dynamic improvement of peak capacity is important for further development of the EFGF technique. An ineffective EFGF device with a nonlinear gradient was constructed using a buffer conductivity gradient [16]. This device provided a very steep gradient section followed by a very shallow section. Unfortunately, the first steep segment was too short to significantly improve peak capacity. In this work, we simulated and compared the separation performance of linear and bilinear gradient EFGF devices. An EFGF device with bilinear electric field gradient (curve 3 in Fig. 1) was fabricated from PEG-functionalized copolymers. A monolith was synthesized in the EFGF channel, and the separation and focusing of proteins in the channel were investigated. 2. Experimental 2.1. Simulation A numerical model for electric field gradient focusing is based on the one-dimensional flux equation for the analyte concentration at point x and time t, which can be written as [33,34]:
∂c(x, t) ∂ ∂c(x, t) ∂ DT = − [v(x, t)c(x, t)] + ∂t ∂x ∂x ∂x
(1)
where c(x, t) is the analyte concentration at point x and time t, DT is the coefficient of dispersion of the analyte, and v(x, t) is the velocity of the analyte, which is expressed as
v(x, t) = u + E(x, t)
(2)
u2 rc2 48DM
(4)
where rc is the radius of the column. If the channel is packed with beads or a polymer monolith, rc becomes an effective hydraulic radius. For materials with moderate porosity, rc = 2Vp /Sp , where Vp and Sp are the volume and surface area of the pore space, respectively. The one-dimensional diffusion equation (1) was solved numerically using the method of finite differences. The differential equation was discretized using central difference approximations for the second derivative terms and averaged forward differences for the first derivative terms. The time step (dt) and the spatial step (dx) were set to be 0.004 s and 0.003 cm, respectively. The time and spatial discretization step sizes were chosen to be small enough to ensure accuracy of the solution. The relative values of the time and spatial steps also had to be such that the numerical solution was stable. An additional length of capillary with a constant electric field was included at the end of the column to model the elution of analytes from the separation channel. The simulation was initialized at time zero with a wide Gaussian distribution for each analyte. The finite difference algorithm was implemented using the general purpose numerical programming software package, Matlab (Mathworks, Natick, MA, USA). For an EFGF separation device, there are several effects that are neglected in this simple model and that could perturb the separation process. These include background electrolyte conductivity changes, electroosmotic flow, analyte adsorption, pH variations, and the influence of high analyte concentration on the conductivity and the electric field in the separation channel. Despite these complicating factors, good agreement between simulated results and experimental measurements has been observed [13]. 2.2. Materials and reagents Poly(ethylene glycol) diacrylate (PEGDA, MW ∼258), poly(ethylene glycol) methyl ether methacrylate (PEGMEMA, MW∼1100), methyl methacrylate (MMA, 99%), 2-hydroxyethyl methacrylate (HEMA, 99%+), and 2,2 -dimethoxy-2-phenylacetophenone (DMPA) were purchased from Aldrich (Milwaukee, WI, USA). Ethoxylated trimethylolpropane triacrylate (SR 9035) was obtained from Sartomer (Warrington, PA, USA). Anhydrous methanol was purchased from Mallinckrodt Chemicals (Phillipsburg, NJ, USA). Anhydrous ethyl ether was purchased from Fisher Scientific (Fair Lawn, NJ, USA). Fluorescein isothiocyanate (FITC) was purchased from Invitrogen (Carlsbad, CA, USA). Potassium chloride (KCl) and potassium phosphate monobasic (KH2 PO4 ) were purchased from EM Science (Gibbstown, NJ, USA). Potassium phosphate dibasic (anhydrous) (K2 HPO4 ) was purchased from Mallinckrodt Specialty Chemicals (Paris, KY, USA). Dimethyl sulfoxide (DMSO) and -lactoglobulin A were ordered from Sigma (St. Louis, MO, USA). R-phycoerythrin (R-PE) was obtained from Polysciences (Warrington, PA, USA). Recombinant, enhanced green fluorescent protein was purchased from Clontech (Palo Alto, CA, USA). All chemicals were used as received without further purification. Deionized water (18.2 M cm) was prepared using a Milli-Q UF Plus water purification system (Millipore, Billerica, MA, USA).
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Carbonate buffer (10 mM, pH 9.2) and phosphate buffer (5 mM, pH 8.0) containing KCl (5 mM) were filtered using 0.2-m syringe filters (Pall, East Hills, NY, USA) before being used. Precleaned microscope slides with dimensions of 70 mm × 50 mm × 1 mm and 70 mm × 25 mm × 1 mm were obtained from Fisher Scientific (Pittsburgh, PA, USA) and Hardy Diagnostics (Santa Maria, CA, USA), respectively.
solved in absolute DMSO to form a concentration of 6 mM. Then 600 L protein solution was thoroughly mixed with 40 L FITC solution and placed in the dark for 2 days at room temperature. After completion of labeling, the protein solution was stored at 4 ◦ C. Before use, the FITC-labeled protein sample was diluted with the running buffer. 2.4. Fabrication of EFGF devices
2.3. Preparation of FITC-labeled ˇ-lactoglobulin A The procedure of labeling -lactoglobulin A was reported previously [11]. In brief, 1 mg/mL -lactoglobulin A solution was prepared in filtered 10 mM carbonate buffer (pH 9.2). FITC was dis-
All EFGF devices were fabricated using a previously reported casting method [11]. A prepolymerized top slab plate (65 mm × 25/50 mm × 1.5 mm) containing two reservoirs and a bottom plate (65 mm × 25/50 mm × 2.5 mm) containing a planar
Fig. 2. Simulation results for two EFGF devices. (A) Linear EFGF device: channel length = 4 cm, counter flow velocity = 0.01 cm/s, applied voltage = 5000 V, coefficient of dispersion = 1.6 × 10−5 cm2 /s, and resolution between adjacent peaks = 1 when reaching static focusing. (B) Bilinear EFGF device: channel length = 4 cm, counter flow velocity = 0.01 cm/s, applied voltage was alternated during operation as indicated. [Top left: initial focusing phase using the first field gradient segment; top middle: the voltage is dropped to bring the first peak into the second field gradient segment; top right to bottom middle: the single peak consisting two proteins with close electrophoretic mobilities (6% difference) begins to resolve; bottom right: the voltage is dropped further and the first protein (1a) elutes].
X. Sun et al. / J. Chromatogr. A 1216 (2009) 6532–6538
horn-shaped cavity were first fabricated using a monomer solution containing PEGDA (85%), PEGMEMA (12%), MMA (3%) and DMPA (0.1% of the total monomer weight). The concave planar horn shape of the cavity could be easily designed to generate the desired electric field gradient, such as linear and bilinear. Two fused-silica capillaries (150 m I.D.) were threaded with a nickel wire (120 m diameter, MWS Wire Industries, Westlake Village, CA, USA) and mounted as inlet and outlet capillaries on the top of the bottom plate containing the cavity, followed by placing the cover plate with two reservoirs on top. The assembly was chemically bonded together by exposure to UV radiation (8 mW/cm2 , EC-5000 Dymax UV curing system). After bonding, a hydrogel monomer solution containing SR 9035 (85%), DMPA (0.5% of the monomer weight) and phosphate buffer (5 mM, pH 8.0) containing 5 mM KCl (15%) was introduced into the planar horn-shaped cavity through the reservoir at the wide end of the cavity and photopolymerized under UV light. Finally, the nickel wire was pulled out of the fused silica capillaries, leaving a small channel through the hydrogel.
2.5. Synthesis of a monolith in the EFGF channel A protein compatible (i.e., nonadsorptive) monolith was incorporated into the EFGF channel using a previously reported method
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[11]. Briefly, a degassed mixture containing PEGDA 258 (crosslinker, 22.5 wt%), HEMA (monomer, 7.5 wt%), methanol (porogen, 25 wt%), ethyl ether (porogen, 45 wt%) and DMPA (photoinitiator, 1% of the total monomer weight) was carefully introduced into the channel to avoid bubble generation. The device was then exposed to cold UV light for 8 min under a UV dichroic mirror (Navitar, Newport Beach, CA, USA). After polymerization, the device was then connected to an HPLC micropump (Eksigent, Dublin, CA, USA) and washed with methanol for 5 h at 0.4 L/min to remove unreacted monomers and porogens, followed by flushing with operating buffer until focusing experiments were performed.
2.6. Operation of EFGF and detection The general EFGF operating procedure was reported previously [11]. First, the sample was electrokinetically injected into the EFGF separation channel by applying a voltage across the reservoir at the low field end of the device (+) and a sample solution-filled vial at the high field end of the device (−). The amount of injected sample was controlled by the applied voltage and injection time. After injection, the sample vial was replaced by a buffer-filled vial, and a hydrodynamic flow was created using a syringe pump (Harvard Apparatus, Holliston, MA, USA) from the low field end to oppose the direction
Fig. 3. (A) Design and dimensions of a bilinear EFGF device (solid line). The dashed line indicates the extension of the right segment that provides the shallow electric filed gradient. (B) Plot of counter flow rate versus R-PE peak position in an open bilinear EFGF channel at constant voltage (500 V). (C) Focusing positions of R-PE in an open bilinear EFGF channel for different applied voltages at a constant counter flow rate (20 nL/min). (D) Designed electric field gradient and measured gradient inferred from the data in (B).
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of electrophoretic migration. After focusing, the protein bands were detected using a laser induced fluorescence (LIF) inverted microscope (488 nm) by scanning along the separation channel [11]. The fluorescence signal was detected using a photomultiplier (Hamamatsu, Bridgewater, NJ, USA) and recorded using LabView software (National Instruments, Austin, TX, USA).
3. Results and discussion 3.1. Numerical simulations of EFGF separations with linear and bilinear electric field gradients Numerical simulation results for two EFGF devices with different field gradients are shown in Fig. 2. A complex sample was introduced into the EFGF channel for focusing and separation. As noted above, several potential complicating factors were not included in the model, which could have affected the results to some extent. These included background electrolyte conductivity changes, electroosmotic flow, analyte adsorption, and pH variations. If the ionic composition of the background electrolyte were to change, the local conductivity of the buffer would also change, leading to a deviation in the electric field gradient from the designed profile. Changes in the pH would influence the electrophoretic mobility of the protein sample. Since high concentrations of the analyte cause conductivity perturbations, there is also a nonlinear coupling between the analyte distribution and the electric field in the separation channel.
In Fig. 2A, a 4-cm long separation channel was modeled with a linear electric field gradient. In the model, analyte electrophoretic mobilities were chosen so that the resolution between two adjacent peaks was equal to one. Under ideal conditions, the in-channel static peak capacity of this device was found to be 20, which is not sufficient to perform separations of complex mixtures. As has been demonstrated, theoretically, the peak capacity could be greatly improved by utilizing an EFGF device with a nonlinear field gradient. Because the resolution achievable with the EFGF technique increases as the slope of the field gradient decreases, a bilinear field gradient should significantly increase the effective peak capacity of the EFGF technique. Analyte peaks could be dynamically focused, separated, and eluted by changing the voltage or the counter flow rate to move peaks from the steep field region to the shallow field region. Fig. 2B shows numerical simulation results for a bilinear gradient device. A complex sample was focused into narrow, unresolved peaks in the steeper field gradient segment. During the initial focusing phase, unwanted proteins with low electrophoretic mobilities eluted from the separation channel. The voltage was then reduced to move the first focused peak into the second shallower field gradient segment. The single peak broadened but also resolved into two distinct analyte peaks. Finally, the voltage was dropped further to elute the first of the protein peaks (1a), while retaining the second peak (1b) in the EFGF device. In this way, closely spaced peaks which were not resolved in the steep field region were dynamically resolved in the shallower field gradient segment. The mobility
Fig. 4. Separations of three proteins in a monolith-filled bilinear EFGF channel for different counter flow rates at constant voltage (800 V). Peaks: (1) FITC--lactoglobulin A, (2) R-PE, and (3) GFP.
X. Sun et al. / J. Chromatogr. A 1216 (2009) 6532–6538
of analyte 1a was 2.0 × 10−4 cm2 /(V s) and the mobility of analyte 1b was 2.12 × 10−4 cm2 /(V s). By repeating this dynamic focusing and separation process, the predicted effective peak capacity for this device was 150 or greater, depending on the range of electrophoretic mobilities in the protein mixture and the maximum voltage that could be applied to the device. The peak capacity could be increased further by lengthening the separation channel or decreasing the slope of the shallower second segment of the field gradient, at the expense of longer analysis time. To reduce the analysis time, a sample could be analyzed by operating multiple devices in parallel, with each device covering a different, narrow mobility range, the sum of which would cover the whole mobility range.
3.2. EFGF with a bilinear (convex) electric field gradient Fig. 3A shows the design and dimensions of a convex bilinear field gradient EFGF device that was fabricated and evaluated. The left segment provided a steep gradient, while the right segment gave a shallow gradient. The membrane width required to achieve the desired electric field gradient was designed using the relationship E(x) = I/[A(x)], where I is the total current through the device, is the conductivity of the buffer, and A(x) is the cross-sectional area of the device. The designed width of the membrane was given by 1/y = x/36 + 1/18, 0 < x < 20 and 1/y = x/40 + 1/9, 20
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It is difficult to measure the electric field in the separation channel directly, but the electric field can be inferred from the locations of focused peaks over a range of flow rates or applied potentials. Fig. 3D shows the designed electric field gradient and the electric field gradient inferred from the data in Fig. 3B. The measured electric field is shallower at the high field end of the device than the designed electric field. There is an even greater discrepancy between the peak positions in Fig. 3C and the designed electric field gradient. The peaks for lower voltages should be focused further to the right of the separation channel than was measured experimentally. This may be due to focusing of buffer ions during the experimental run. Resolution of these discrepancies may require more detailed modeling of the device including the effects of buffer ion focusing or a more sophisticated procedure for measuring the electric field in the device. As mentioned above, dynamic improvement of peak capacity can be realized by increasing the counter flow rate or decreasing the applied voltage to move focused peaks from the steep segment to the shallow segment. The movement of three protein peaks in a monolith-filled bilinear EFGF channel is shown in Fig. 4. A monolith was incorporated in the EFGF channel to reduce flow dispersion, which narrowed the focused bands [11]. During an experiment, the counter flow rate was increased from 5 nL/min to 20 nL/min while the voltage was kept constant (800 V). When the counter flow rate was low, all proteins were stacked together with narrow bands in the steep segment (Fig. 4A). When the counter flow rate was increased, all proteins moved toward the high field end and the resolution increased gradually (Fig. 4B). When samples moved into the shallow segment, they were even better resolved, and minor components in the sample appeared (Fig. 4C). When the counter flow rate was increased further, the protein with the smallest electrophoretic mobility (GFP, peak 3) was eluted (Fig. 4D). Meanwhile, the resolution between the first two peaks increased from approximately 0.9 (Fig. 4A) to 3.9 (Fig. 4D). These experimental results were qualitatively consistent with the simulation results. 4. Conclusions The separation performance of EFGF for devices with both linear and bilinear (convex) electric field gradients was studied using numerical simulations. The in-channel static peak capacity in a 4-cm long linear EFGF channel was only 20. Dynamic improvement of peak capacity could be realized using EFGF devices with nonlinear electric field gradients. The dynamic peak capacity in a bilinear electric field gradient of the same length was predicted to be approximately 150. To verify the dynamic capacity improvement, we fabricated a bilinear EFGF device using the changing cross-sectional area approach. The presence of two segments with different linear gradients was experimentally confirmed. The steep field segment was near the low field end and the shallow field segment was near the high field end. When samples were focused in the steep field segment, the peaks were narrow and unresolved. After moving the analytes into the shallow field segment by increasing the counter flow rate or decreasing the voltage, the peaks became broader, but the resolution of adjacent peaks increased. With a further increase in flow rate, analytes with lower mobilities were sequentially eluted while others were retained in the device. Acknowledgement This work was financially supported by the National Institutes of Health (R01 GM064547-01A1). References [1] W.S. Koegler, C.F. Ivory, Biotechnol. Prog. 12 (1996) 822.
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[2] C.F. Ivory, Sep. Sci. Technol. 35 (2000) 1777. [3] H.D. Tolley, Q. Wang, D.A. LeFebre, M.L. Lee, Anal. Chem. 74 (2002) 4456. [4] Q. Wang, H.D. Tolley, D.A. LeFebre, M.L. Lee, Anal. Bioanal. Chem. 373 (2002) 125. [5] R.T. Kelly, A.T. Woolley, J. Sep. Sci. 28 (2005) 1985. [6] J.G. Shackman, D. Ross, Electrophoresis 28 (2007) 556. [7] W.S. Koegler, C.F. Ivory, J. Chromatogr. A 726 (1996) 229. [8] P.H. Humble, R.T. Kelly, A.T. Woolley, H.D. Tolley, M.L. Lee, Anal. Chem. 76 (2004) 5641. [9] R.T. Kelly, Y. Li, A.T. Woolley, Anal. Chem. 78 (2006) 2565. [10] J. Liu, X. Sun, P.B. Farnsworth, M.L. Lee, Anal. Chem. 78 (2006) 4654. [11] X. Sun, P.B. Farnsworth, A.T. Woolley, H.D. Tolley, K.F. Warnick, M.L. Lee, Anal. Chem. 80 (2008) 451. [12] X. Sun, P.B. Farnsworth, H.D. Tolley, K.F. Warnick, A.T. Woolley, M.L. Lee, J. Chromatogr. A 1216 (2009) 159. [13] S.-L. Lin, Y. Li, A.T. Woolley, M.L. Lee, H.D. Tolley, K.F. Warnick, Electrophoresis 29 (2008) 1058. [14] P.H. Humble, J.N. Harb, H.D. Tolley, A.T. Woolley, P.B. Farnsworth, M.L. Lee, J. Chromatogr. A 1160 (2007) 311. [15] R.D. Greenlee, C.F. Ivory, Biotechnol. Prog. 14 (1998) 300. [16] Q. Wang, S.-L. Lin, K.F. Warnick, H.D. Tolley, M.L. Lee, J. Chromatogr. A 985 (2003) 455. [17] S.-L. Lin, H.D. Tolley, M.L. Lee, Chromatographia 62 (2005) 277. [18] S.-L. Lin, Y. Li, H.D. Tolley, P.H. Humble, M.L. Lee, J. Chromatogr. A 1125 (2006) 254.
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35]
Z. Huang, C.F. Ivory, Anal. Chem. 71 (1999) 1628. D.N. Petsev, G.P. Lopez, C.F. Ivory, S.S. Sibbett, Lab Chip 5 (2005) 587. P. Myers, K.D. Bartle, J. Chromatogr. A 1044 (2004) 253. J.M. Burke, C.F. Ivory, Electrophoresis 29 (2008) 1013. P.G. Tunon, Y. Wang, P. Myers, K.D. Bartle, L. Bowhill, C.F. Ivory, R.J. Ansell, Electrophoresis 29 (2008) 457. N.I. Tracy, Z. Huang, C.F. Ivory, Biotechnol. Prog. 24 (2008) 444. D. Ross, L.E. Locascio, Anal. Chem. 74 (2002) 2556. K.M. Balss, D. Ross, H.C. Begley, K.G. Olsen, M.J. Tarlov, J. Am. Chem. Soc. 126 (2004) 13474. K.M. Balss, W.N. Vreeland, K.W. Phinney, D. Ross, Anal. Chem. 76 (2004) 7243. S.M. Kim, G.J. Sommer, M.A. Burns, E.F. Hasselbrink, Anal. Chem. 78 (2006) 8028. S.J. Hoebel, K.M. Balss, B.J. Jones, C.D. Malliaris, M.S. Munson, W.N. Vreeland, D. Ross, Anal. Chem. 78 (2006) 7186. J.G. Shackman, M.S. Munson, C.-W. Kan, D. Ross, Electrophoresis 27 (2006) 3420. J.G. Shackman, M.S. Munson, D. Ross, Anal. Bioanal. Chem. 387 (2007) 155. H. Lin, J.G. Shackman, D. Ross, Lab Chip 8 (2008) 969. J.C. Giddings, Unified Separation Science, John Wiley and Sons, Inc., New York, 1990. K.F. Warnick, S.J. Francom, P.H. Humble, R.T. Kelly, A.T. Woolley, M.L. Lee, H.D. Tolley, Electrophoresis 26 (2005) 405. G. Taylor, Proc. R. Soc. Lond. A 225 (1954) 473.
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Bilinear electric field gradient focusing Xuefei Sun a , Dan Li a , Adam T. Woolley a , Paul B. Farnsworth a , H. Dennis Tolley b , Karl F. Warnick c , Milton L. Lee a,∗ a
Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA Department of Statistics, Brigham Young University, Provo, UT 84602, USA c Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA b
a r t i c l e
i n f o
Article history: Received 7 April 2009 Received in revised form 13 July 2009 Accepted 27 July 2009 Available online 6 August 2009 Keywords: Electric field gradient focusing Bilinear gradient Proteins Focusing
a b s t r a c t Electric field gradient focusing (EFGF) uses an electric field gradient and a hydrodynamic counter flow to simultaneously separate and focus charged analytes in a channel. Previously, most EFGF devices were designed to form a linear field gradient in the channel. However, the peak capacity obtained using a linear gradient is not much better than what can be obtained using conventional CE. Dynamic improvement of peak capacity in EFGF can be achieved by using a nonlinear gradient. Numerical simulation results indicate that the peak capacity in a 4-cm long channel can be increased from 20 to 150 when changing from a linear to convex bilinear gradient. To demonstrate the increased capacity experimentally, an EFGF device with convex bilinear gradient was fabricated from poly(ethylene glycol) (PEG)-functionalized acrylic copolymers. The desired gradient profile was confirmed by measuring the focusing positions of a standard protein for different counter flow rates at constant voltage. Dynamically controlled elution of analytes was demonstrated using a monolith-filled bilinear EFGF channel. By increasing the flow rate, stacked proteins that were ordered but not resolved after focusing in the steep gradient segment were moved into the shallow gradient segment, where the analyte peak resolution increased significantly. In this way, the nonlinear field gradient was used to realize a dynamic increase in the peak capacity of the EFGF method. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Electric field gradient focusing (EFGF) depends on an electric field gradient and an opposing hydrodynamic flow to separate and focus charged analytes at their equilibrium positions [1–6]. This technique can concentrate analytes as they are separated. Unlike traditional separation techniques, such as chromatography and electrophoresis, sample injection in EFGF has much less influence on the separated band profiles. Moreover, EFGF is not affected by protein aggregation and precipitation that often occur in isoelectric focusing (IEF). It is possible to selectively retain or elute target analytes in EFGF by manipulating the applied electric field or hydrodynamic flow. To date, samples that have been tested using EFGF include proteins, peptides, amino acids, dyes and other small molecules. Analytes have been concentrated up to 10 000-fold using EFGF. One challenging issue in EFGF is creating the desired electric field gradient along the separation channel. Several methods have been developed to establish the electric field gradient, including the use of a changing cross-sectional area containing conduc-
∗ Corresponding author. Tel.: +1 8014222135; fax: +1 8014220157. E-mail address: milton [email protected] (M.L. Lee). 0021-9673/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2009.07.050
tive buffer or polymer membrane surrounding the separation channel [1,7–14], a buffer conductivity gradient in the channel generated with assistance of a dialysis membrane [15–18], the use of a computer-controlled multi-electrode array along the channel for dynamic field gradient focusing [19–24], and a temperature gradient along the channel filled with a buffer that has a temperature-dependent conductivity [25–32]. Among the approaches mentioned above to generate an electric field gradient, the changing cross-sectional area method is relatively simple to implement. Typically, a dialysis membrane or conductive hydrogel was employed to isolate the separation channel from the changing cross-sectional area. Koegler and Ivory [1,7] first fabricated a preparative-scale EFGF device by placing a dialysis membrane in a conically shaped poly(methyl methacrylate) (PMMA) cylinder. Humble et al. [8] fabricated an analytical scale EFGF device by embedding a separation channel in an ionically conductive and planar horn-shaped hydrogel. Kelly et al. [9] miniaturized a similar device in a PMMA microchip, while Liu et al. [10] fabricated a micro-EFGF device by isolating the separation channel and changing cross-sectional area with a buffer-filled ionpermeable membrane positioned on a weir structure. Recently, we have fabricated the complete EFGF device from poly(ethylene glycol) (PEG) functionalized copolymers, including the substrate and conductive hydrogel, which are resistant to protein adsorption and
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Here, u is the counter hydrodynamic flow velocity. is the electrophoretic mobility of the analyte. E(x, t) is the electric field strength at point x and time t. If the column has negligible adsorption, then the coefficient of dispersion is given by DT = DM + DF
(3)
where DM is the molecular diffusivity of the analyte and DF is the Taylor dispersion due to laminar flow in the channel. The flow dispersion can be approximated for circular unpacked columns as [35]: DF =
Fig. 1. Electric field gradient profiles studied for EFGF. (1) Linear, (2) convex, and (3) bilinear.
suppress electroosmotic flow. The hydrogel was again shaped to form a linear electric field gradient and was covalently bound to the substrate. A protein compatible monolith was incorporated in the channel to reduce flow dispersion and, therefore, narrow the focused bands [11]. So far, only a linear gradient (line 1 in Fig. 1) has been reported in EFGF devices based on changing cross-sectional area. According to the fundamental theory of EFGF, resolution and peak capacity in EFGF with a linear gradient cannot be improved simultaneously, because bandwidth and resolution are both inversely proportional to the square root of the field gradient [3]. However, theoretical work indicates that the peak capacity could be improved using an EFGF device with nonlinear (convex) gradient (curve 2 in Fig. 1), such as can be approximated with a bilinear gradient (curve 3 in Fig. 1) [3,4]. All analytes would first be focused in the steeper gradient section to form narrow stacked bands. Then they would be sequentially moved into the shallower gradient section and be resolved by manipulating the counter flow rate or applied voltage. This dynamic improvement of peak capacity is important for further development of the EFGF technique. An ineffective EFGF device with a nonlinear gradient was constructed using a buffer conductivity gradient [16]. This device provided a very steep gradient section followed by a very shallow section. Unfortunately, the first steep segment was too short to significantly improve peak capacity. In this work, we simulated and compared the separation performance of linear and bilinear gradient EFGF devices. An EFGF device with bilinear electric field gradient (curve 3 in Fig. 1) was fabricated from PEG-functionalized copolymers. A monolith was synthesized in the EFGF channel, and the separation and focusing of proteins in the channel were investigated. 2. Experimental 2.1. Simulation A numerical model for electric field gradient focusing is based on the one-dimensional flux equation for the analyte concentration at point x and time t, which can be written as [33,34]:
∂c(x, t) ∂ ∂c(x, t) ∂ DT = − [v(x, t)c(x, t)] + ∂t ∂x ∂x ∂x
(1)
where c(x, t) is the analyte concentration at point x and time t, DT is the coefficient of dispersion of the analyte, and v(x, t) is the velocity of the analyte, which is expressed as
v(x, t) = u + E(x, t)
(2)
u2 rc2 48DM
(4)
where rc is the radius of the column. If the channel is packed with beads or a polymer monolith, rc becomes an effective hydraulic radius. For materials with moderate porosity, rc = 2Vp /Sp , where Vp and Sp are the volume and surface area of the pore space, respectively. The one-dimensional diffusion equation (1) was solved numerically using the method of finite differences. The differential equation was discretized using central difference approximations for the second derivative terms and averaged forward differences for the first derivative terms. The time step (dt) and the spatial step (dx) were set to be 0.004 s and 0.003 cm, respectively. The time and spatial discretization step sizes were chosen to be small enough to ensure accuracy of the solution. The relative values of the time and spatial steps also had to be such that the numerical solution was stable. An additional length of capillary with a constant electric field was included at the end of the column to model the elution of analytes from the separation channel. The simulation was initialized at time zero with a wide Gaussian distribution for each analyte. The finite difference algorithm was implemented using the general purpose numerical programming software package, Matlab (Mathworks, Natick, MA, USA). For an EFGF separation device, there are several effects that are neglected in this simple model and that could perturb the separation process. These include background electrolyte conductivity changes, electroosmotic flow, analyte adsorption, pH variations, and the influence of high analyte concentration on the conductivity and the electric field in the separation channel. Despite these complicating factors, good agreement between simulated results and experimental measurements has been observed [13]. 2.2. Materials and reagents Poly(ethylene glycol) diacrylate (PEGDA, MW ∼258), poly(ethylene glycol) methyl ether methacrylate (PEGMEMA, MW∼1100), methyl methacrylate (MMA, 99%), 2-hydroxyethyl methacrylate (HEMA, 99%+), and 2,2 -dimethoxy-2-phenylacetophenone (DMPA) were purchased from Aldrich (Milwaukee, WI, USA). Ethoxylated trimethylolpropane triacrylate (SR 9035) was obtained from Sartomer (Warrington, PA, USA). Anhydrous methanol was purchased from Mallinckrodt Chemicals (Phillipsburg, NJ, USA). Anhydrous ethyl ether was purchased from Fisher Scientific (Fair Lawn, NJ, USA). Fluorescein isothiocyanate (FITC) was purchased from Invitrogen (Carlsbad, CA, USA). Potassium chloride (KCl) and potassium phosphate monobasic (KH2 PO4 ) were purchased from EM Science (Gibbstown, NJ, USA). Potassium phosphate dibasic (anhydrous) (K2 HPO4 ) was purchased from Mallinckrodt Specialty Chemicals (Paris, KY, USA). Dimethyl sulfoxide (DMSO) and -lactoglobulin A were ordered from Sigma (St. Louis, MO, USA). R-phycoerythrin (R-PE) was obtained from Polysciences (Warrington, PA, USA). Recombinant, enhanced green fluorescent protein was purchased from Clontech (Palo Alto, CA, USA). All chemicals were used as received without further purification. Deionized water (18.2 M cm) was prepared using a Milli-Q UF Plus water purification system (Millipore, Billerica, MA, USA).
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Carbonate buffer (10 mM, pH 9.2) and phosphate buffer (5 mM, pH 8.0) containing KCl (5 mM) were filtered using 0.2-m syringe filters (Pall, East Hills, NY, USA) before being used. Precleaned microscope slides with dimensions of 70 mm × 50 mm × 1 mm and 70 mm × 25 mm × 1 mm were obtained from Fisher Scientific (Pittsburgh, PA, USA) and Hardy Diagnostics (Santa Maria, CA, USA), respectively.
solved in absolute DMSO to form a concentration of 6 mM. Then 600 L protein solution was thoroughly mixed with 40 L FITC solution and placed in the dark for 2 days at room temperature. After completion of labeling, the protein solution was stored at 4 ◦ C. Before use, the FITC-labeled protein sample was diluted with the running buffer. 2.4. Fabrication of EFGF devices
2.3. Preparation of FITC-labeled ˇ-lactoglobulin A The procedure of labeling -lactoglobulin A was reported previously [11]. In brief, 1 mg/mL -lactoglobulin A solution was prepared in filtered 10 mM carbonate buffer (pH 9.2). FITC was dis-
All EFGF devices were fabricated using a previously reported casting method [11]. A prepolymerized top slab plate (65 mm × 25/50 mm × 1.5 mm) containing two reservoirs and a bottom plate (65 mm × 25/50 mm × 2.5 mm) containing a planar
Fig. 2. Simulation results for two EFGF devices. (A) Linear EFGF device: channel length = 4 cm, counter flow velocity = 0.01 cm/s, applied voltage = 5000 V, coefficient of dispersion = 1.6 × 10−5 cm2 /s, and resolution between adjacent peaks = 1 when reaching static focusing. (B) Bilinear EFGF device: channel length = 4 cm, counter flow velocity = 0.01 cm/s, applied voltage was alternated during operation as indicated. [Top left: initial focusing phase using the first field gradient segment; top middle: the voltage is dropped to bring the first peak into the second field gradient segment; top right to bottom middle: the single peak consisting two proteins with close electrophoretic mobilities (6% difference) begins to resolve; bottom right: the voltage is dropped further and the first protein (1a) elutes].
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horn-shaped cavity were first fabricated using a monomer solution containing PEGDA (85%), PEGMEMA (12%), MMA (3%) and DMPA (0.1% of the total monomer weight). The concave planar horn shape of the cavity could be easily designed to generate the desired electric field gradient, such as linear and bilinear. Two fused-silica capillaries (150 m I.D.) were threaded with a nickel wire (120 m diameter, MWS Wire Industries, Westlake Village, CA, USA) and mounted as inlet and outlet capillaries on the top of the bottom plate containing the cavity, followed by placing the cover plate with two reservoirs on top. The assembly was chemically bonded together by exposure to UV radiation (8 mW/cm2 , EC-5000 Dymax UV curing system). After bonding, a hydrogel monomer solution containing SR 9035 (85%), DMPA (0.5% of the monomer weight) and phosphate buffer (5 mM, pH 8.0) containing 5 mM KCl (15%) was introduced into the planar horn-shaped cavity through the reservoir at the wide end of the cavity and photopolymerized under UV light. Finally, the nickel wire was pulled out of the fused silica capillaries, leaving a small channel through the hydrogel.
2.5. Synthesis of a monolith in the EFGF channel A protein compatible (i.e., nonadsorptive) monolith was incorporated into the EFGF channel using a previously reported method
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[11]. Briefly, a degassed mixture containing PEGDA 258 (crosslinker, 22.5 wt%), HEMA (monomer, 7.5 wt%), methanol (porogen, 25 wt%), ethyl ether (porogen, 45 wt%) and DMPA (photoinitiator, 1% of the total monomer weight) was carefully introduced into the channel to avoid bubble generation. The device was then exposed to cold UV light for 8 min under a UV dichroic mirror (Navitar, Newport Beach, CA, USA). After polymerization, the device was then connected to an HPLC micropump (Eksigent, Dublin, CA, USA) and washed with methanol for 5 h at 0.4 L/min to remove unreacted monomers and porogens, followed by flushing with operating buffer until focusing experiments were performed.
2.6. Operation of EFGF and detection The general EFGF operating procedure was reported previously [11]. First, the sample was electrokinetically injected into the EFGF separation channel by applying a voltage across the reservoir at the low field end of the device (+) and a sample solution-filled vial at the high field end of the device (−). The amount of injected sample was controlled by the applied voltage and injection time. After injection, the sample vial was replaced by a buffer-filled vial, and a hydrodynamic flow was created using a syringe pump (Harvard Apparatus, Holliston, MA, USA) from the low field end to oppose the direction
Fig. 3. (A) Design and dimensions of a bilinear EFGF device (solid line). The dashed line indicates the extension of the right segment that provides the shallow electric filed gradient. (B) Plot of counter flow rate versus R-PE peak position in an open bilinear EFGF channel at constant voltage (500 V). (C) Focusing positions of R-PE in an open bilinear EFGF channel for different applied voltages at a constant counter flow rate (20 nL/min). (D) Designed electric field gradient and measured gradient inferred from the data in (B).
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of electrophoretic migration. After focusing, the protein bands were detected using a laser induced fluorescence (LIF) inverted microscope (488 nm) by scanning along the separation channel [11]. The fluorescence signal was detected using a photomultiplier (Hamamatsu, Bridgewater, NJ, USA) and recorded using LabView software (National Instruments, Austin, TX, USA).
3. Results and discussion 3.1. Numerical simulations of EFGF separations with linear and bilinear electric field gradients Numerical simulation results for two EFGF devices with different field gradients are shown in Fig. 2. A complex sample was introduced into the EFGF channel for focusing and separation. As noted above, several potential complicating factors were not included in the model, which could have affected the results to some extent. These included background electrolyte conductivity changes, electroosmotic flow, analyte adsorption, and pH variations. If the ionic composition of the background electrolyte were to change, the local conductivity of the buffer would also change, leading to a deviation in the electric field gradient from the designed profile. Changes in the pH would influence the electrophoretic mobility of the protein sample. Since high concentrations of the analyte cause conductivity perturbations, there is also a nonlinear coupling between the analyte distribution and the electric field in the separation channel.
In Fig. 2A, a 4-cm long separation channel was modeled with a linear electric field gradient. In the model, analyte electrophoretic mobilities were chosen so that the resolution between two adjacent peaks was equal to one. Under ideal conditions, the in-channel static peak capacity of this device was found to be 20, which is not sufficient to perform separations of complex mixtures. As has been demonstrated, theoretically, the peak capacity could be greatly improved by utilizing an EFGF device with a nonlinear field gradient. Because the resolution achievable with the EFGF technique increases as the slope of the field gradient decreases, a bilinear field gradient should significantly increase the effective peak capacity of the EFGF technique. Analyte peaks could be dynamically focused, separated, and eluted by changing the voltage or the counter flow rate to move peaks from the steep field region to the shallow field region. Fig. 2B shows numerical simulation results for a bilinear gradient device. A complex sample was focused into narrow, unresolved peaks in the steeper field gradient segment. During the initial focusing phase, unwanted proteins with low electrophoretic mobilities eluted from the separation channel. The voltage was then reduced to move the first focused peak into the second shallower field gradient segment. The single peak broadened but also resolved into two distinct analyte peaks. Finally, the voltage was dropped further to elute the first of the protein peaks (1a), while retaining the second peak (1b) in the EFGF device. In this way, closely spaced peaks which were not resolved in the steep field region were dynamically resolved in the shallower field gradient segment. The mobility
Fig. 4. Separations of three proteins in a monolith-filled bilinear EFGF channel for different counter flow rates at constant voltage (800 V). Peaks: (1) FITC--lactoglobulin A, (2) R-PE, and (3) GFP.
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of analyte 1a was 2.0 × 10−4 cm2 /(V s) and the mobility of analyte 1b was 2.12 × 10−4 cm2 /(V s). By repeating this dynamic focusing and separation process, the predicted effective peak capacity for this device was 150 or greater, depending on the range of electrophoretic mobilities in the protein mixture and the maximum voltage that could be applied to the device. The peak capacity could be increased further by lengthening the separation channel or decreasing the slope of the shallower second segment of the field gradient, at the expense of longer analysis time. To reduce the analysis time, a sample could be analyzed by operating multiple devices in parallel, with each device covering a different, narrow mobility range, the sum of which would cover the whole mobility range.
3.2. EFGF with a bilinear (convex) electric field gradient Fig. 3A shows the design and dimensions of a convex bilinear field gradient EFGF device that was fabricated and evaluated. The left segment provided a steep gradient, while the right segment gave a shallow gradient. The membrane width required to achieve the desired electric field gradient was designed using the relationship E(x) = I/[A(x)], where I is the total current through the device, is the conductivity of the buffer, and A(x) is the cross-sectional area of the device. The designed width of the membrane was given by 1/y = x/36 + 1/18, 0 < x < 20 and 1/y = x/40 + 1/9, 20
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It is difficult to measure the electric field in the separation channel directly, but the electric field can be inferred from the locations of focused peaks over a range of flow rates or applied potentials. Fig. 3D shows the designed electric field gradient and the electric field gradient inferred from the data in Fig. 3B. The measured electric field is shallower at the high field end of the device than the designed electric field. There is an even greater discrepancy between the peak positions in Fig. 3C and the designed electric field gradient. The peaks for lower voltages should be focused further to the right of the separation channel than was measured experimentally. This may be due to focusing of buffer ions during the experimental run. Resolution of these discrepancies may require more detailed modeling of the device including the effects of buffer ion focusing or a more sophisticated procedure for measuring the electric field in the device. As mentioned above, dynamic improvement of peak capacity can be realized by increasing the counter flow rate or decreasing the applied voltage to move focused peaks from the steep segment to the shallow segment. The movement of three protein peaks in a monolith-filled bilinear EFGF channel is shown in Fig. 4. A monolith was incorporated in the EFGF channel to reduce flow dispersion, which narrowed the focused bands [11]. During an experiment, the counter flow rate was increased from 5 nL/min to 20 nL/min while the voltage was kept constant (800 V). When the counter flow rate was low, all proteins were stacked together with narrow bands in the steep segment (Fig. 4A). When the counter flow rate was increased, all proteins moved toward the high field end and the resolution increased gradually (Fig. 4B). When samples moved into the shallow segment, they were even better resolved, and minor components in the sample appeared (Fig. 4C). When the counter flow rate was increased further, the protein with the smallest electrophoretic mobility (GFP, peak 3) was eluted (Fig. 4D). Meanwhile, the resolution between the first two peaks increased from approximately 0.9 (Fig. 4A) to 3.9 (Fig. 4D). These experimental results were qualitatively consistent with the simulation results. 4. Conclusions The separation performance of EFGF for devices with both linear and bilinear (convex) electric field gradients was studied using numerical simulations. The in-channel static peak capacity in a 4-cm long linear EFGF channel was only 20. Dynamic improvement of peak capacity could be realized using EFGF devices with nonlinear electric field gradients. The dynamic peak capacity in a bilinear electric field gradient of the same length was predicted to be approximately 150. To verify the dynamic capacity improvement, we fabricated a bilinear EFGF device using the changing cross-sectional area approach. The presence of two segments with different linear gradients was experimentally confirmed. The steep field segment was near the low field end and the shallow field segment was near the high field end. When samples were focused in the steep field segment, the peaks were narrow and unresolved. After moving the analytes into the shallow field segment by increasing the counter flow rate or decreasing the voltage, the peaks became broader, but the resolution of adjacent peaks increased. With a further increase in flow rate, analytes with lower mobilities were sequentially eluted while others were retained in the device. Acknowledgement This work was financially supported by the National Institutes of Health (R01 GM064547-01A1). References [1] W.S. Koegler, C.F. Ivory, Biotechnol. Prog. 12 (1996) 822.
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[2] C.F. Ivory, Sep. Sci. Technol. 35 (2000) 1777. [3] H.D. Tolley, Q. Wang, D.A. LeFebre, M.L. Lee, Anal. Chem. 74 (2002) 4456. [4] Q. Wang, H.D. Tolley, D.A. LeFebre, M.L. Lee, Anal. Bioanal. Chem. 373 (2002) 125. [5] R.T. Kelly, A.T. Woolley, J. Sep. Sci. 28 (2005) 1985. [6] J.G. Shackman, D. Ross, Electrophoresis 28 (2007) 556. [7] W.S. Koegler, C.F. Ivory, J. Chromatogr. A 726 (1996) 229. [8] P.H. Humble, R.T. Kelly, A.T. Woolley, H.D. Tolley, M.L. Lee, Anal. Chem. 76 (2004) 5641. [9] R.T. Kelly, Y. Li, A.T. Woolley, Anal. Chem. 78 (2006) 2565. [10] J. Liu, X. Sun, P.B. Farnsworth, M.L. Lee, Anal. Chem. 78 (2006) 4654. [11] X. Sun, P.B. Farnsworth, A.T. Woolley, H.D. Tolley, K.F. Warnick, M.L. Lee, Anal. Chem. 80 (2008) 451. [12] X. Sun, P.B. Farnsworth, H.D. Tolley, K.F. Warnick, A.T. Woolley, M.L. Lee, J. Chromatogr. A 1216 (2009) 159. [13] S.-L. Lin, Y. Li, A.T. Woolley, M.L. Lee, H.D. Tolley, K.F. Warnick, Electrophoresis 29 (2008) 1058. [14] P.H. Humble, J.N. Harb, H.D. Tolley, A.T. Woolley, P.B. Farnsworth, M.L. Lee, J. Chromatogr. A 1160 (2007) 311. [15] R.D. Greenlee, C.F. Ivory, Biotechnol. Prog. 14 (1998) 300. [16] Q. Wang, S.-L. Lin, K.F. Warnick, H.D. Tolley, M.L. Lee, J. Chromatogr. A 985 (2003) 455. [17] S.-L. Lin, H.D. Tolley, M.L. Lee, Chromatographia 62 (2005) 277. [18] S.-L. Lin, Y. Li, H.D. Tolley, P.H. Humble, M.L. Lee, J. Chromatogr. A 1125 (2006) 254.
[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35]
Z. Huang, C.F. Ivory, Anal. Chem. 71 (1999) 1628. D.N. Petsev, G.P. Lopez, C.F. Ivory, S.S. Sibbett, Lab Chip 5 (2005) 587. P. Myers, K.D. Bartle, J. Chromatogr. A 1044 (2004) 253. J.M. Burke, C.F. Ivory, Electrophoresis 29 (2008) 1013. P.G. Tunon, Y. Wang, P. Myers, K.D. Bartle, L. Bowhill, C.F. Ivory, R.J. Ansell, Electrophoresis 29 (2008) 457. N.I. Tracy, Z. Huang, C.F. Ivory, Biotechnol. Prog. 24 (2008) 444. D. Ross, L.E. Locascio, Anal. Chem. 74 (2002) 2556. K.M. Balss, D. Ross, H.C. Begley, K.G. Olsen, M.J. Tarlov, J. Am. Chem. Soc. 126 (2004) 13474. K.M. Balss, W.N. Vreeland, K.W. Phinney, D. Ross, Anal. Chem. 76 (2004) 7243. S.M. Kim, G.J. Sommer, M.A. Burns, E.F. Hasselbrink, Anal. Chem. 78 (2006) 8028. S.J. Hoebel, K.M. Balss, B.J. Jones, C.D. Malliaris, M.S. Munson, W.N. Vreeland, D. Ross, Anal. Chem. 78 (2006) 7186. J.G. Shackman, M.S. Munson, C.-W. Kan, D. Ross, Electrophoresis 27 (2006) 3420. J.G. Shackman, M.S. Munson, D. Ross, Anal. Bioanal. Chem. 387 (2007) 155. H. Lin, J.G. Shackman, D. Ross, Lab Chip 8 (2008) 969. J.C. Giddings, Unified Separation Science, John Wiley and Sons, Inc., New York, 1990. K.F. Warnick, S.J. Francom, P.H. Humble, R.T. Kelly, A.T. Woolley, M.L. Lee, H.D. Tolley, Electrophoresis 26 (2005) 405. G. Taylor, Proc. R. Soc. Lond. A 225 (1954) 473.