Gradient Elution Moving Boundary Electrophoresis with Channel

Anal. Chem. 2009, 81, 7326–7335

Gradient Elution Moving Boundary Electrophoresis with Channel Current Detection David Ross* and Eugenia F. Romantseva National Institute of Standards and Technology 100 Bureau Drive, Gaithersburg, Maryland 20899 Gradient elution moving boundary electrophoresis (GEMBE) is a recently described technique for electrophoretic separations in short (1-3 cm) capillaries or microchannels. With GEMBE, the electrophoretic migration of analytes is opposed by a bulk counterflow of separation buffer through the separation channel. The counterflow velocity is varied over the course of a separation so that analytes with different electrophoretic mobilities enter the separation channel at different times and are detected as moving boundary, stepwise increases in the detector response. The resolution of a GEMBE separation is thus dependent on the rate at which the counterflow velocity is varied (rather than the length of the separation channel), and relatively high resolution separations can be performed with short microfluidic channels or capillaries. In this paper we describe an implementation of the GEMBE technique in which a very short (2.5-3.5 mm) capillary or microchannel is used as both the separation channel and a conductivity detection cell. Because the channel is so short, only a single moving boundary “step” is present in the channel at any given time, and the measured current through the channel can therefore be used to give a signal comparable to what is normally generated by more complicated detector arrangements. A theoretical description of the new technique is given along with simulation and experimental data relevant to the optimization of the method parameters such as channel length, counterflow acceleration, and applied field strength. A key theoretical prediction is that although this technique is expected to be a factor of 10 or 20 slower than conventional capillary zone electrophoresis, separation times of the order 1 s or less can still be achieved, making it applicable for ultrahigh-throughput analyses when implemented in a multiplexed format. One of the goals of research in the field of lab-on-a-chip devices is the development of complete “sample-in-answer-out” analysis systems (for recent reviews, see refs 1-10). The predominant

approach to achieve this goal has been the serial integration of individual microfluidic “unit operations” such as sample preparation, reaction, preconcentration, separation, detection, etc. into a monolithic, miniaturized device. There have been some successes based on this approach. However, the microfluidic structures used for each of the individual unit operations can be fairly complex, with multiple intersecting fluid channels, specific surface chemistry requirements, and multiple voltage and/or pressure control points. Consequently, as successive unit operations are strung together, the design, fabrication, and operation of the resulting integrated devices can become complex and expensive. The work described here is part of an effort to explore an alternative approach in which the objective is to keep the analysis system as simple as possible, while still aiming toward “samplein-answer-out” capability. Roughly speaking, the design rules for this approach are to use only very simple microfluidic structures as device elements and, whenever possible, to devise methods whereby each device element can provide the functionality of multiple unit operations, preferably simultaneously. This approach is expected to result in integrated total analysis systems that are made up of fewer and simpler device elements, making the systems more amenable to multiplexing for high-throughput applications and more robust and reliable for point-of-use applications. Examples of the kinds of methods that might be used in this approach include counterflow gradient electrofocusing techniques (electric field gradient focusing, temperature gradient focusing, etc.) that combine separation, preconcentration, and possibly even sample preparation into one operation11-14 and gradient elution moving boundary electrophoresis (GEMBE)15 in which simple, nonintersecting microfluidic channels are used for electrophoretic separations without voltage switching or injections. With GEMBE, a combination of an electric field and controlled, variable solution counterflow is used to achieve separations of multiple analyte species in short microchannels or capillaries (see Figure 1). Typically, the polarity of the applied voltage is set so that the analytes of interest are driven by electrophoresis from the sample toward the entrance to the separation channel. At the

* To whom correspondence should be addressed. (1) Crevillen, A. G.; Hervas, M.; Lopez, M. A.; Gonzalez, M. C.; Escarpa, A. Talanta 2007, 74, 342–357. (2) Roman, G. T.; Kennedy, R. T. J. Chromatogr., A 2007, 1168, 170–188. (3) Haeberle, S.; Zengerle, R. Lab Chip 2007, 7, 1094–1110. (4) Auroux, P. A.; Koc, Y.; deMello, A.; Manz, A.; Day, P. J. R. Lab Chip 2004, 4, 534–546. (5) Erickson, D.; Li, D. Q. Anal. Chim. Acta 2004, 507, 11–26. (6) Myers, F. B.; Lee, L. P. Lab Chip 2008, 8, 2015–2031. (7) Ohno, K.; Tachikawa, K.; Manz, A. Electrophoresis 2008, 29, 4443–4453.

(8) Horsman, K. M.; Bienvenue, J. M.; Blasier, K. R.; Landers, J. P. J. Forensic Sci. 2007, 52, 784–799. (9) Fair, R. B. Microfluid. Nanofluid. 2007, 3, 245–281. (10) Toner, M.; Irimia, D. Annu. Rev. Biomed. Eng. 2005, 7, 77–103. (11) Shackman, J. G.; Ross, D. Electrophoresis 2007, 28, 556–571. (12) Ivory, C. F. Electrophoresis 2007, 28, 15–25. (13) Ivory, C. F. Sep. Sci. Technol. 2000, 35, 1777–1793. (14) Kelly, R. T.; Woolley, A. T. J. Sep. Sci. 2005, 28, 1985–1993. (15) Shackman, J. G.; Munson, M. S.; Ross, D. Anal. Chem. 2007, 79, 565– 571.

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Analytical Chemistry, Vol. 81, No. 17, September 1, 2009

10.1021/ac901189y Not subject to U.S. Copyright. Publ. 2009 Am. Chem. Soc. Published on Web 08/10/2009

simulation and experimental results to study the optimization of the device geometry (channel length) and operational parameters (electric field and counterflow acceleration) and for comparison with conventional electrophoretic separation techniques such as capillary zone electrophoresis (CZE).

Figure 1. Schematic illustration of the GEMBE separation technique. A GEMBE device is comprised of two liquid reservoirs (sample and run buffer) connected by a microfluidic channel or capillary (not shown to scale). A high voltage (HV) is applied to drive electrophoresis of the analytes from the sample toward the channel (left to right in the figure). A combination of electroosmosis and an applied pressure is used to drive bulk solution flow through the channel in the opposite direction. (A) At the beginning of a measurement, the applied pressure is high and the magnitude of the bulk flow velocity is therefore greater than the electrophoretic velocity of the analyte. The analyte (shown in gray) then remains in the sample reservoir. (B) Over the course of a measurement, the applied pressure is reduced until the magnitude of the bulk flow velocity is less than the electrophoretic velocity. At this point, the analyte will begin to flow through the channel where it can be detected as a moving boundary, resulting in a step change in the detector response.

beginning of a separation, the counterflow (driven by a combination of electroosmosis and applied pressure) is high so that none of the analytes of interest can enter the channel. Over the course of the separation, the counterflow is gradually reduced so that each analyte, in turn, will begin to flow through the channel where it is detected as a stepwise change in the detector response. The time derivative of the detector signal is then equivalent to a conventional electropherogram. The simplicity of the device used for GEMBE makes it particularly suitable for multiplexed analysis. An additional advantage of GEMBE (and other counterflow electrophoretic methods) is that the solution counterflow can be used to exclude potentially problematic matrix constituents (such as serum proteins) from entering the microfluidic system, thereby avoiding the need for channel coatings or extra sample preparation steps.16 Recently, a variation of GEMBE was described in which one device element, a short (3 mm) capillary, was used to provide the dual functionality of both electrophoretic separation and conductivity-based detection.17 Because the channel was so short, only a single moving boundary was present in the channel at any given time. Consequently, the electrophoresis current could be used as a detector signal. With this modification, the light source and optical detector typically used for detection in microfluidic separations was replaced with an electrical resistor. The simplification of the detection hardware allowed for easy and inexpensive multiplexing and the new method was demonstrated for a multiplexed (16 channel) enzyme activity assay. Here we present a detailed theoretical description of the GEMBE method with channel current detection along with (16) Munson, M. S.; Meacham, J. M.; Locascio, L. E.; Ross, D. Anal. Chem. 2008, 80, 172–178. (17) Ross, D.; Kralj, J. G. Anal. Chem. 2008, 80, 9467–9474.

THEORY The objective of this section is to construct a theoretical framework describing GEMBE with channel current detection so that its performance can be compared with more conventional techniques such as capillary zone electrophoresis (CZE). We will calculate the resolution of two closely migrating analytes, and also consider as a primary performance metric the time required to separate two closely migrating analytes with a resolution of 1. We will use the standard definition for resolution:

R)

∆t 4σ

(1)

where ∆t is the peak separation and σ is the peak standard deviation (assuming the two peaks are approximately the same width). With conventional CZE, a discrete injection is formed at the entrance to the separation channel and peaks are detected as each analyte passes the detector near the end of the separation channel. The resolution for CZE is18

RCZE )

∆µEt

(2)

4√2Dt + σ02

where ∆µ is the difference in mobility between the two analytes, E is the electric field strength, t is the separation time, D is the dispersion constant (which includes molecular diffusion as well as other sources of peak broadening such as Taylor-Aris dispersion,19 and which, for simplicity, is assumed to be the same for both analytes), and σ0 is the standard deviation of the initial injection (or the detection window). The time required to achieve unit resolution is then11

tCZE )

(

16D 1+ ∆µ2E2

1+

∆µ2E2σ02 16D2

)

(3)

GEMBE is a type of moving boundary electrophoresis, so there is no defined injection, and the analytes move through the separation channel not as peaks or “zones” but as “boundaries” between regions where a given analyte is present and regions where it is not. The boundaries move into the separation channel at the sample end and migrate through the channel where they are detected as a series of steps in the detector response. By taking the time derivative of the detector signal (or by using a gradient sensitive detector), the detector signal can be transformed into a series of peaks that can be used in the same way as the peaks of a conventional electropherogram. Moving boundary electrophoresis with constant counterflow (MBE) was the predominant form of electrophoretic analysis in (18) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298–1302. (19) Taylor, G. I. Proc. R. Soc. London 1953, 219, 186–203.


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the 1940s and 1950s.20,21 Because the boundaries move and diffuse in much the same way as the zones of CZE, the theoretical descriptions of the two are similar. However, GEMBE differs from the more conventional MBE and CZE methods in a fundamental way. In CZE and MBE, selectivity is achieved as different analytes migrate with different velocities down a long separation channel. In contrast, with GEMBE, selectivity is achieved by varying the balance between the electrophoretic velocity and the bulk solution velocity so that different analytes are allowed to enter the separation channel at different times. Consequently, the theoretical description of GEMBE is not a straightforward extension of existing theories for CZE and MBE. To simplify the calculation, we will start by considering two limiting cases: the case of negligible dispersion and the case of very large dispersion. In addition, we will not consider the case of GEMBE with a conventional detector as described in the initial paper on GEMBE15 but will restrict consideration to the specific mode of GEMBE described here in which the current through the separation channel is used as the detector signal. If dispersion is negligible, then the step width and time can be calculated by considering the motion of the center of an analyte boundary through the separation channel. In that case, the position of a boundary is equal to zero (the channel entrance) at the time when the total velocity (the sum of the electrophoretic and bulk solution velocities) is zero, and the boundary moves through the separation channel with constant acceleration (assuming a constant rate of change of the applied pressure). The acceleration will be the same for every analyte, so every analyte will take the same amount of time to traverse the channel and every analyte step will have the same width. The detector step width (approximately 4σ) will then be given approximately by

4σ =

2La

∆µE a

∆µE √2La

(5)

(7)

which is similar to the result for CZE in the limit that the dominant contribution to the peak width is the width of the injection or the detection window (with σ0 replaced by L). To solve for the case where dispersion is dominant, we will assume that the acceleration is very small and that dispersion is very large. Then, for each value of the velocity, the distribution of analyte in the separation channel is very close to its steadystate value for that velocity. The analyte distribution can then be found by solving the one-dimensional time independent convection diffusion equation:

U

∂2C(x) ∂C(x) )D ∂x ∂x2

(8)

where x is the coordinate along the length of the channel, U is the (total) velocity of the analyte through the channel, C(x) is the analyte concentration, and D is the dispersion constant. Taking C(0) ) 1 and C(L) ) 0 as the boundary conditions, the solution to eq 8 is then

( U(x D- L) ) - 1 UL exp(- ) - 1 D

exp C(x) )

(9)

S(U) ≡

1 L

∫

L

0

(

(

C(x) dx ) 1 - exp -

UL D

))

-1

-

D UL (10)

A more correct (and significantly more complicated) form for the signal can be obtained by calculating the current through the channel, but if the change in conductivity across the analyte boundary is small relative to the background buffer conductivity, the more correct solution differs only very slightly from eq 10. The form of the signal given by eq 10 matches our expectation. The signal is approximately zero for large negative U, it is approximately 1 for large positive U, and it has the form of a rounded step centered on U ) 0. To solve for the width of the step, we calculate the values of U for which the signal is equal to 0.1 and 0.9. This gives (to a very close approximation) U ) ±10D/ L. The 10-90% step width is then converted to the 4σ width by multiplying by 1.56 (the correct ratio for a Gaussian peak or step) and dividing by the acceleration. This gives the result of

(6)

where the subscript “D ) 0” indicates the result for negligible dispersion. The minimum time required to measure two adjacent (20) Tiselius, A. Trans. Faraday Soc. 1937, 33, 0524-0530. (21) Tiselius, A.; Kabat, E. A. J. Exp. Med. 1939, 69, 119–131.

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4L ∆µE

(4)

The resolution is then

RD)0 =

tD)0 =

For simplicity, we will take as the “signal” the average concentration inside the channel:

where L is the channel length, and a is the acceleration (using the Hagen-Poiseuille equation for laminar fluid flow through a cylindrical capillary, a ) |(d2/32ηL)(∂P/∂t)|, where d is the capillary inner diameter, η is the solution viscosity, P is the applied pressure, and t is time). Although they move through the channel at the same rate, different analytes can be resolved because they enter the channel at different times. The spacing (in time) between the analyte steps is then given by the difference in the start times (the times when the total velocities are zero) of the two analytes:

∆t )

steps is approximately equal to the step separation (∆t) plus one step width (4σ). Therefore the time required for unit resolution is


4σ = 31.2

D La

(11)

Again, at this point, there would appear to be a more correct solution: taking the derivative of eq 10 and calculating the second spatial moment of the resulting peak shape (equivalent to σ2 for

a Gaussian peak). However, the integral for the second spatial moment in this case does not converge; the second spatial moment is infinite (because of the -D/UL term in eq 10). Therefore, the 10-90% step width was used to match the method used to treat the simulation data (see below). The spacing between two steps is again given by eq 5, so that the resolution is

RDf∞ =

∆µEL 31.2D

(12)

where the subscript “D f ∞” indicates the result for very large dispersion. In this case, the resolution is independent of the acceleration, which is the parameter used to adjust the separation time. So, in this limit, the time required to achieve unit resolution is not a sensible figure of merit to consider; the resolution either is greater than or less than 1, and changing the separation time will have no effect on the resolution (until the change in separation time takes the system out of the dispersion-dominated limit). Given the two limiting cases, we can attempt to stitch them together to give a single expression for the resolution and the time required for unit resolution. Since the step spacing is the same in each limit, the task is then to come up with a single expression for the step width. Note that in the low dispersion limit (eq 4), we have an expression for the step width due to the finite width of the detection window (the length of the capillary). In the opposite limit (eq 11), we have an expression for the width resulting purely from dispersion. By way of analogy with the theory for conventional CZE (though without any deeper physical reasoning or motivation), we assume that the total step width can be approximated as the square-root of the sum of the squares of the step widths from the two limiting cases:

4σ =

(31.2 LaD ) + 2La 2

(13)

The resolution is then

RGEMBE =

∆µE

√(31.2D/L)2 + 2La

(14)

The result given for CZE, eqs 2 and 3, assumes that the channel length was set to an optimal value for the desired resolution. So, for comparison, we solve eq 14 for the optimal length (maximum resolution), giving

RGEMBE =

∆µE (162.2Da)1/3

(15)

To calculate the time required to achieve a resolution of 1, we will assume again that the analysis time is equal to the step separation (∆t) plus one step width (4σ), or 2∆t at unit resolution. This gives an optimal channel length of

Loptimal =

54.1D ∆µE

and an optimized separation time of

(16)

tGEMBE =

324.4D ∆µ2E2

(17)

Comparison with eq 3 for fully optimized CZE (with σ0 ) 0) indicates that the GEMBE technique described here is approximately a factor of 10 slower than conventional CZE when run at the same electric field strength. Note that this comparison between eq 3 for CZE and eq 17 for GEMBE is made with two assumptions: that the dispersion is the same in each case and that only two components need to be separated. With regard to the first assumption, the dispersion will generally be greater for GEMBE than for CZE because of the pressure applied to control the solution counterflow. Depending on the experimental details (capillary diameter, mobilities, etc.), however, it may or may not be significantly greater. With regard to the second assumption, the counterflow velocity using the GEMBE technique can be swept over just the range necessary to measure the analyte steps of interest, and eq 17 was derived to give the minimum time for a two-component separation. Full consideration of a multicomponent separation would depend on the details of the specific application. However, if the two components considered above are taken to be the most difficult pair of analytes in a mixture (with the smallest ∆µ), then a multicomponent GEMBE analysis will always take a longer time than the time given by eq 17. With CZE, on the other hand, the time required for a multicomponent analysis may or may not take longer than the time given in eq 3 depending on whether or not the remaining components elute before or after the most difficult pair. Therefore, the factor of 10 difference indicated by comparing eqs 3 and 17 should be considered to be a lower bound on the ratio of the GEMBE analysis time to the CZE analysis time (at equivalent field strengths). Furthermore, even for a two-component separation, the assumption that the GEMBE analysis time can be reduced to the time required to sweep the velocity just over the two analyte steps does not allow for any baseline before or after the steps, which would probably be necessary for most quantitative analyses. Inclusion of some baseline before and after the steps would increase the GEMBE analysis time by an additional factor between about 1.5 and 2. Similarly, the theoretical derivation for the analysis time with CZE does not include any allowance for baseline before and after the analyte peaks. In this case, the additional time required would be dependent on the velocity (electrophoretic plus electroosmotic) at which the peaks were swept past the detector. In most cases, this velocity is relatively fast (the peak spacing is significantly less than the elution times), and the additional time required for good baselines would be a small fraction of the time indicated by eq 3. When these other factors are taken into account, a factor of 20 or more difference in analysis time might be more realistic for practical implementations of the two techniques, even for two-component separations. SIMULATIONS Certain commercial equipment, instruments, or materials are identified in this report to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. Analytical Chemistry, Vol. 81, No. 17, September 1, 2009

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The numerical simulations were performed using a scripted finite element program, FlexPDE version 5.1.2 (PDE Solutions, Inc., Antioch, CA). Simulations were performed in two-dimensional cylindrical coordinates. The simulated geometry is shown schematically in Figure S1 in the Supporting Information. The geometry consisted of two reservoirs, 5 mm diameter and 5 mm long, connected by a capillary that was 5 µm in diameter and of variable length. The electric potential, φ, and analyte concentration, C, were solved for simultaneously using the differential equations: ∂C ) ∇(D∇C) - ∇(UC) ∂t

(18)

∇(κ∇φ) ) 0

(19)

where κ is the conductivity. The differential equations for the concentration and the electric potential were coupled through the relations: κ ) 1000 + C

(20)

U ) (µEOF + µ)∇φ

(21)

where µEOF is the electroosmotic mobility of the walls of the system. To simplify the computation, the electroosmotic mobility was taken to vary with time rather than an applied pressure. Thus the assumption of similarity between the velocity field and the electric field could be used.22 The boundary conditions used were C ) 1 and φ ) 0 on the left boundary (the bold line in Figure S1 in the Supporting Information) and C ) 0 and φ ) V on the right boundary, where V is the applied voltage. No-flux boundary conditions (natural boundary conditions set to zero) were used for both C and φ on the remaining boundaries. Simulations were run for a single analyte with physical characteristics comparable to a typical analyte molecule: mobility, µ ) -2 × 10-4 cm2/V/s, and dispersion, D ) 6 × 10-6cm2/s. Simulations were run for capillary lengths ranging from 3 µm to 1 cm (to match the range that might be possible to fabricate experimentally). The accelerations and applied voltages were also chosen to match experimentally realistic values. Accelerations ranging from 0.5 to 150 µm/s2 were simulated, and the applied voltage, V, was adjusted to give the same electric field strength in the middle of the capillary for each capillary length simulated (|∇φ| = 1667 V/cm). To establish initial conditions for the time dependent simulation, we first solved for the electric potential assuming a uniform conductivity. That result was then used as a starting point to solve for the steady-state concentration and potential (eqs 18 and 19 with ∂C/∂t ) 0) with the electroosmotic mobility set to -2 times the analyte electrophoretic mobility, µEOF ) -2µ. The steady state solutions were then used as the initial conditions for the time dependent simulations. Time dependent simulations were run for values of the acceleration ranging from 0.5 to 150 µm2/s and for capillary lengths, L, from 3 µm to 1 cm. At each time point of the simulation, the current through the capillary and the average analyte velocity in the capillary were saved. The velocity vs time data was fit with a straight line to determine the acceleration, and the current vs time data was (22) Santiago, J. G. Anal. Chem. 2001, 73, 2353–2365.

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Figure 2. Schematic of double Luer lock device for GEMBE with channel current detection. The devices were made with two Luer lock fittings and a 360 µm o.d., 5 µm i.d. capillary connecting them. The capillary length was determined by the thickness of the Luer lock fittings plus spacers for lengths greater than 2.5 mm. One side of the device was connected to a manifold for voltage and pressure control, and the other side of the device was used to contain the samples for analysis.

analyzed to determine the step width. The 4σ step width was determined by taking the difference between the times at which the step was at 10% and 90% of its maximum value and multiplying that width by 1.56 as described in the Theory section above. Simulation results for resolution were calculated using the simulated 4σ step width and the theoretical expression for the step spacing given by eq 5, with ∆µ ) 2 × 10-5 cm2/V/s and E ) 1667 V/cm. EXPERIMENTAL SECTION Chemicals and Reagents. Adenosine 5′-triphosphate disodium salt hydrate (ATP), 1 mol/L magnesium chloride solution, tartaric acid, malic acid, citric acid, succinic acid, acetic acid, lactic acid, ascorbic acid, histidine, 2-(N-morpholino)ethanesulfonic acid hydrate (MES), bis(2-hydroxyethyl)amino-tris(hydroxymethyl)methane (bis-tris), and 4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid (HEPES) were obtained from Sigma Aldrich (St. Louis, MO). Kemptide with trifluoroacetate (TFA) impurity was obtained from Calbiochem (San Diego, CA). All solutions were made with water from a Barnstead (Dubuque, IA) Easypure II ultrapure water system. Device Fabrication. The construction of the devices used is shown schematically in Figure 2. Two female nylon Luer-lock caps (McMaster-Carr, Atlanta, GA) were used for each fitting. A 360 µm diameter hole was drilled through the end of each cap, and a length of fused silica capillary (5 µm inner diameter (i.d.), 360 µm outer diameter, approximately 2 cm long; Polymicro Technologies, LLC, Phoenix, AZ) was pushed through the holes. For capillary lengths greater than 2.5 mm, one or more plastic washers were used as a spacer. The assembly was glued together with a two-part epoxy (Bondit B45TH; McMaster-Carr, Atlanta, GA) and cured in an oven at 65 °C overnight. A small jewelers’ file was

then used to score the capillary near the bottom of each Luer lock fitting, and the capillary ends were broken off, leaving the desired length of capillary (2.5-5.5 mm) for each device. Instrumentation. The apparatus used here was similar to that described previously for a 16-channel array measurement,17 though for this work, a single channel manifold was used. The devices were mounted on a buffer-filled manifold as shown in Figure 2. The manifold was connected to a 20 mL polypropylene syringe (not shown in Figure 2), which acted as a buffer reservoir for application of the voltage and pressure. The head space pressure of the syringe was controlled with a precision pressure controller (series 600, Mensor, San Marcos, TX) with a range of ±68.9 kPa (±10 psi). Helium was used as the supply gas for the pressure controller. The syringe was fitted with a custom built plunger to allow access for the high voltage and pressure control. The syringe was connected to the manifold via 0.125 cm i.d. highpurity Tygon tubing, approximately 10 cm long. The manifold was machined from Delrin with an internal volume of approximately 1 mL, and the connection between the manifold and the Luerlock capillary device was made with a 1/4 in.-28 threaded polypropylene Luer-lock coupling (McMaster-Carr, Atlanta, GA). Care was taken to ensure that the entire manifold, Tygon tubing, and Luer-lock coupling were completely filled with buffer with no bubbles. Samples to be analyzed were pipetted into the top Luer lock fitting, and the ground electrode was inserted. The high voltage source was a Stanford Research Systems model PS350 (Stanford Research Systems, Inc., Sunnyvale, CA). Electrical connections to all solutions were made through highpurity platinum wires (Sigma Aldrich, St. Louis, MO). Measurements of the electrophoresis current were made using a 1 MΩ precision metal film resistor (Mouser Electronics, Inc., Mansfield, TX) in series with the capillary device and either a data acquisition device (model USB-6229 National Instruments, Austin TX) or a digital multimeter (model 34401A, Agilent, Santa Clara, CA). Electrophoresis Procedures. Between separations, during sample pipetting, and at the start of each separation, the pressure applied to the buffer reservoir head space was set to a relatively high positive value (typically +30 000 to +40 000 Pa) to prevent air bubbles from entering the capillary. Samples were prepared in the same buffer solution as used for the run buffer in each case. At the start of a separation, the high voltage was turned on and the pressure was reduced to the starting pressure value for 10 s, after which the pressure was reduced at a fixed rate until all the analytes of interest had been detected. The pressure was then increased to a high positive value and held for 10 s with the voltage on. Then the voltage was turned off until the next separation. Data Processing and Analysis. Instruments and data acquisition were controlled using LabView (National Instruments, Austin, TX) software written in house. For most experiments, electrophoresis current data was acquired at 50 Hz with the data acquisition device. For quantitative analysis of the step heights and widths, the unprocessed data was fit to a functional form consisting of the sum of a linear baseline and an error function. Nonlinear least-squares fits were performed with Mathematica (Wolfram Research Inc., Champaign, IL). Plots of the current derivative were obtained by taking a 51 point second order Savitzky-Golay derivative23 of the data followed by adjacent (23) Savitzky, A.; Golay, M. J. E. Anal. Chem. 1964, 36, 1627.

Figure 3. Example of GEMBE separation with channel current detection. Sample: 200 µmol/L each of tartaric acid (1), malic acid (2), citric acid (3), succinic acid (4), acetic acid (5), lactic acid (6), and ascorbic acid (7). Peak identities were determined by repeated measurements with single components. Separation conditions: 5 µm i.d., 2.5 mm long capillary, 8000 V/cm, acceleration ) 53 µm/s2 (150 Pa/s) from time ) 0 (60 000 Pa) to time ) 6.5 min (6000 Pa), then 18 µm/s2 (50 Pa/s) to -49 000 Pa; run buffer ) 20 mmol/L His, 100 mmol/L MES, pH 5.5. (A) Plot of electrophoresis current vs time. Each step corresponds to one of the analytes in the sample. (B) Plot of current derivative vs time.

average smoothing (typically 50-200 points) using Origin software (OriginLab Corporation, Northampton, MA). For some of the slowest accelerations, data was acquired with a digital multimeter at 0.5 Hz. For quantitative analysis of the step widths, the width between the 10% and 90% points (see above) was determined using a linear interpolation function with Mathematica (Wolfram Research Inc., Champaign, IL). RESULTS Figure 3 shows an example result for GEMBE with channel current detection. For this example, a 2.5 mm long, 5 µm i.d. capillary was used (see Figure 2 for device schematic). Figure 3A is a plot of the current through the capillary as a function of time for the analysis of a sample containing a mixture of seven organic acids. For this example, the sample was pipetted into the device reservoir and a voltage of 2000 V was applied to electrophoretically pull the organic acids from the sample space through the capillary. Initially, a high positive pressure (60 000 Pa) was applied to the buffer reservoir so that the buffer counterflow velocity (driven by electroosmosis and pressure) was greater in magnitude than the electrophoretic velocity of the organic acids. Analytical Chemistry, Vol. 81, No. 17, September 1, 2009

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Consequently, the acids did not enter the capillary and the current through the capillary was determined by the background buffer composition. As the applied pressure was gradually reduced, the magnitude of the counterflow velocity eventually became less than the electrophoretic velocity of each of the acids and each acid (in order from fastest to slowest) began to move through the capillary. As the acids moved into the capillary, the conductivity of the solution in the capillary was increased and a step was measured in the current through the capillary. There are seven upward steps in Figure 3A, one for each of the organic acids in the sample, and one small downward step (at t ) 2.2 min) due to carbonate (the downward step indicates that there was a higher concentration of carbonate in the run buffer than in the sample; for some experiments it was a small upward step, indicating slightly more carbonate in the sample than in the run buffer). The time derivative of the current gives a series of peaks as shown in Figure 3B, with each peak providing the same analytical information as a conventional chromatographic peak: peak positions provide information about analyte identity, and peak areas (equivalent to step heights from Figure 3A) provide information about the concentration of each analyte. For this example, step heights increased linearly with concentration up to a step height of about 10 nA (see Figure S2 in the Supporting Information), standard deviations of repeated measurements were typically about 2.5% of the mean, and detection limits (extrapolated to a signal-to-noise of 3) were between 1.5 and 4 µmol/L. At the pH used for this analysis (5.5), acetic acid and lactic acid have a similar mobility and are therefore more difficult to resolve than the other acids. The first four acids (tartaric, malic, citric, and succinic) could be well resolved even with a fairly high counterflow acceleration, 52 or 104 µm/s2 (corresponding to a rate of pressure change of 150 or 300 Pa/s). However, a slower counterflow acceleration (17 µm/s2, corresponding to 50 Pa/s) was required to resolve the next two acids (acetic and lactic, see Figure S3 in the Supporting Information). As was shown previously for GEMBE with a conventional detection scheme, different counterflow accelerations can be used for different segments of the separation to minimize the separation time while providing the necessary resolution for the more difficult to resolve analytes. For the channel lengths that were possible with the fabrication techniques used here (2.5 mm and longer) and the range of accelerations typically used in the experiments, the theoretical prediction is that the system is always in the regime of negligible dispersion (assuming that the dispersion constant is equal to the molecular diffusion constant). Consequently, the step width is expected to be dependent only on the channel length and the counterflow acceleration, as given by eq 4. Figure 4A shows the theoretically predicted step width from eq 4 along with some simulation results and results from several experiments with different analytes. The solid black line is the theoretical prediction for a channel length of 3 mm (to compare with the simulation results), and the dashed black line is the theoretical result for a channel length of 3.5 mm (to compare with the experimental results). The simulation data is shown as the solid black squares and agrees very well with the theoretical prediction. Experimental data for a variety of electric field strengths, analytes, and buffer systems are shown as the various colored 7332


Figure 4. Comparison of theoretical predictions, simulation results, and experimental data for step width and resolution as a function of acceleration. (A) Step width vs acceleration. The solid black line is the theoretical prediction for a channel length of 3 mm. The dashed black line is the theoretical prediction for a channel length of 3.5 mm. The black squares are the simulation results for a channel length of 3 mm. The open and solid colored symbols are experimental data for a channel length of 3.5 mm. The solid colored symbols are data from separations of ATP and TFA in pH 7.1 buffer (100 mmol/L bistris, 100 mmol/L HEPES), at field strengths of 714 V/cm (orange squares), 1429 (blue diamonds), 2857 (reddish-orange triangles), and 5714 V/cm (bluish-green circles). The open symbols are data from acetic acid in pH 7.1 buffer (reddish-orange), lactic acid in pH 7.1 buffer (bluish-green), tartaric acid in pH 5.5 buffer (orange, 20 mmol/L His, 100 mmol/L MES), and succinic acid in pH 5.5 buffer (blue); and field strengths of 4286 (squares), and 5714 V/cm (triangles). (B) Resolution vs acceleration. The solid colored symbols are data from separations of ATP and TFA in pH 7.1 buffer (100 mmol/L bis-tris, 100 mmol/L HEPES), at field strengths of 714 (orange squares), 1429 (blue diamonds), 2857 (reddish-orange triangles), and 5714 V/cm (bluish-green circles). The lines are a fit to the data of the form: log(R) ) C + R log(E) + β log(a), where C, R, and β are the adjustable parameters for the fit. The resulting fit parameters are R ) 0.72 ( 0.05, β ) -0.40 ( 0.02, and C ) 1.44 ( 0.05. The stated uncertainties are the standard errors resulting from the fit to the data.

symbols in Figure 4A. In this case, it looks as if the theoretical prediction is a lower bound for the step width. Much of the experimental data agree with the prediction to within a factor of 2 (a reasonable margin given the rough estimates used to derive the theory). However, for some analytes, the step width is as much as a factor of 3 greater than the prediction, indicating that there are potential sources of step broadening not accounted for by the theory given above. Note that moderate variations in the disper-

sion constant used for the prediction cannot account for the difference; since for this channel length and range of accelerations, the theory predicts that the behavior should be clearly within the negligible dispersion limit if the dispersion is due only to molecular diffusion. For example, a dispersion constant approximately 120 times greater than the molecular diffusivity would be required to bring the prediction in line with the data shown for tartaric acid at pH 5.5 and 2000 V (open orange triangles in the figure). Possible sources of excess dispersion of this magnitude include Taylor-Aris dispersion,19,24 Joule heating,25 and electrodispersion.26 Figure 4B is a plot of the experimentally measured resolution vs acceleration for separations of TFA and ATP at pH 7.1. Resolutions were calculated from some of the same data sets as shown in Figure 4A for a range of applied field strengths and accelerations. The solid lines in Figure 4B indicate the results of fitting the data to the equation: log(R) ) C + R log(E) + β log(a), where C, R, and β are the adjustable parameters for the fit. The resulting fit parameters are R ) 0.72 ± 0.05, β ) -0.40 ± 0.02, and C ) 1.44 ± 0.05, where the stated uncertainties are the standard errors resulting from the fit to the data. For comparison, the predicted results from eq 6 are R ) 1, β ) -1/2, and C ) 1.62 (∆µ ) 3500 µm2/V/s, L ) 3500 µm). The deviations from the prediction indicate that the resolution does not increase as much as predicted when the field strength is increased and/ or the acceleration is decreased. This is consistent with the previously stated conclusion that there are potentially additional sources of step broadening not accounted for in the theory. Figure 5A is a plot of the current derivative as a function of time for the separation with the fastest acceleration from Figure 4B. The separation conditions were channel length ) 3.5 mm, field strength ) 5714 V/cm, and acceleration ) 818 µm/s2 (3300 Pa/s); and the resulting resolution was 1.3. The theoretical prediction given above for minimum separation times in GEMBE assumes that the separation can be run just across the region containing the peaks of interest. For the example of Figure 5A, this would mean starting the separation just before the TFA step/peak (t ) 9 s) and stopping just after the ATP step/ peak (t ) 16 s), for a minimum separation time of 7 s. With the use of the mobility difference calculated from the step spacing (∆µ ) 3.5 × 10-5 cm2/V/s, from data at slower accelerations), the theoretical prediction for the minimum separation time, from eq 7, is also 7 s. For comparison, Figure 5B shows a similar separation run at the much slower acceleration used for a previously reported multiplexed kinase activity assay (37.2 µm/ s2, 150 Pa/s).17 In this case the resolution is significantly higher (R ) 3.3), but the minimum analysis time is also much longer (80 s). To examine the behavior at shorter channel lengths than were accessible experimentally, we used simulations of the system as discussed above. Figure 6A shows a plot of the step width as a function of channel length for several different values of the counterflow acceleration. The solid symbols are the simulation results, and the lines are the theoretical prediction from eq 13. The theoretical predictions agree quite well with the simulation results except for the shortest channel lengths simulated. How(24) Aris, R. Proc. R. Soc., Ser. A: Math. Phys. Eng. Sci. 1956, 235, 69–77. (25) Gobie, W. A.; Ivory, C. F. J. Chromatogr. 1990, 516, 191–210. (26) Hjerten, S. Electrophoresis 1990, 11, 665–690.

Figure 5. Separations of TFA (1) and ATP (2). Separation conditions: 5 µm i.d., 3.5 mm long capillary, 5714 V/cm, run buffer ) 100 mmol/L bis-tris, 100 mmol/L HEPES, pH 7.1, sample ) 200 µmol/L ATP + 2 mmol/L MgCl2 + 100 µmol/L kemptide (with TFA impurity). (A) Fast GEMBE measurement: acceleration ) 818 µm/s2 (3300 Pa/s), resolution ) 1.3, minimum separation time ≈ 7 s. (B) Slower GEMBE measurement: acceleration ) 37.2 µm/s2 (150 Pa/s), resolution ) 3.3, minimum separation time ≈ 80 s.

ever, in those cases, the channel length was comparable to or even less than the channel diameter (5 µm). So it is not surprising that the theoretical description, which assumed a one-dimensional system, was not adequate. Both the theoretical and simulation results clearly show the crossover from the dispersion dominated regime at low channel lengths and the negligible dispersion regime at longer channel lengths. Note that the step width is a minimum at this crossover point. Figure 6B shows a plot of the resolution vs channel length for the same set of accelerations used in Figure 6A. The solid symbols are the simulation results, and the lines are the theoretical predictions. The results indicate that for a given value of the counterflow acceleration, there is an optimal channel length at which the resolution is a maximum. This maximum occurs at the crossover from high dispersion to negligible dispersion. For the dispersion assumed for these results (6 × 10-6 cm2/s), the optimal channel length is typically between 0.1 and 1 mm. For channel lengths less than the optimal value, the resolution decreases linearly with the channel length and is independent of the counterflow acceleration. Analytical Chemistry, Vol. 81, No. 17, September 1, 2009

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Figure 6. Comparison of theoretical prediction and simulation results for a range of different channel lengths. The solid lines are the theoretical predictions, and the point symbols are the simulation results for accelerations of 0.5 µm2/s (black squares), 1.5 µm2/s (orange triangles pointing up), 5 µm2/s (blue circles), 15 µm2/s (reddish-orange triangles pointing down), 50 µm2/s (bluish-green diamonds), and 150 µm2/s (reddish-purple triangles pointing left). (A) Step width vs channel length and (B) resolution vs channel length.

DISCUSSION AND CONCLUSIONS The approach described here is intended to be the simplest possible electrophoretic separation and detection system, and is therefore expected to be highly suitable for multiplexed measurement applications. With this approach, much of the conventional detector hardware for each channel is replaced with a resistor, reducing the cost of a multiplexed system enormously when compared with multiplexed laser induced fluorescence (LIF)27-29 or UV absorbance30 detection systems. Although a multiplexed conventional conductivity detection system31 can be simpler and less expensive than multiplexed optical detection systems, it still requires a multiple-stage amplifier circuit for each detection channel to condition signals for input into a data acquisition device. In addition, the mode of detection described here removes many of the geometrical constraints imposed by conventional detection systems such as the requirement for optical access to channels (27) Huang, X. H. C.; Quesada, M. A.; Mathies, R. A. Anal. Chem. 1992, 64, 967–972. (28) Kambara, H.; Takahashi, S. Nature 1993, 361, 565–566. (29) Takahashi, S.; Murakami, K.; Anazawa, T.; Kambara, H. Anal. Chem. 1994, 66, 1021–1026. (30) Gong, X. Y.; Yeung, E. S. Anal. Chem. 1999, 71, 4989–4996. (31) Shadpour, H.; Hupert, M. L.; Patterson, D.; Liu, C. G.; Galloway, M.; Stryjewski, W.; Goettert, J.; Soper, S. A. Anal. Chem. 2007, 79, 870–878.

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or sensing electrodes in contact with or close proximity to channels. Consequently, a variety of different device formats can be employed. In particular, it would not be difficult to construct a multiplexed system that is compatible with current microtiter platebased high-throughput screening systems. The detection limits provided by this approach are typically in the low micromoles per liter range. This is comparable to the detection limits for CZE with UV absorbance or conductivity detection in capillary or microchip electrophoresis. Although it is much higher than typical detection limits for CZE with LIF detection, it is nevertheless adequate for a large variety of chemical and biochemical analyses. The results presented here provide the framework for method and device optimization that is necessary for future applications of the technique for high-throughput measurements. For these applications, an important question is how fast a separation can be run. Given that CZE methods have been described with millisecond32,33 or even microsecond34 separation times, can the technique described here deliver higher throughput than CZE? The theoretical indication is that for single-channel implementations, this technique is slower than conventional CZE by approximately a factor of 10 or 20 when both techniques are fully optimized and implemented with the same electric field strength. However, as noted in the first publication on this technique,17 when implemented in a multiplexed format, it could provide higher total throughput at lower cost than CZE, even at equivalent field strengths. Furthermore, because the separation channels used with this technique are much shorter than those typically used for CZE, higher field strengths can be applied with relatively modest voltages. Because the separation time is inversely proportional to the square of the field strength, this can result in a significant reduction in the separation time. In any case, for practical implementation of the technique in high-throughput applications, the important comparison is not between the GEMBE separation time and the best reported separation times for CZE but between the GEMBE separation time and the time required for the other steps of an assay (sample mixing, manipulation of microtiter plates, etc.). If the GEMBE separation can be run more quickly than the other assay steps, then it can be used without negatively impacting the total throughput of the assay. For many assays used in high-throughput screening applications, a GEMBE separation time of 1 or 2 minutes would be adequate to satisfy this requirement. The feasibility of GEMBE separation times of 1 minute or less is demonstrated by the examples shown in Figure 5. If the measurement shown in Figure 5B was optimized so that only the two peaks of interest were measured with one peak width of baseline before and after the peaks, the separation time could be shortened to approximately 2 min. However, in this case, the resolution achieved is more than adequate and the separation time can be further reduced by increasing the acceleration. Even with relatively long channels (3.5 mm), the data of Figure 5A verifies the theoretical prediction that the separation time could be reduced (32) Jacobson, S. C.; Culbertson, C. T.; Daler, J. E.; Ramsey, J. M. Anal. Chem. 1998, 70, 3476–3480. (33) Jacobson, S. C.; Hergenroder, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994, 66, 1114–1118. (34) Plenert, M. L.; Shear, J. B. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 3853– 3857.

to approximately 10 s while maintaining a resolution of at least 1. The theory and simulation results also indicate, however, that the separation time could be reduced significantly beyond that if shorter channels were used. Note that the asymmetric triangular shape of the peaks in Figure 5A is indicative that the separation is well into the negligible dispersion limit and that significant reductions in the separation time could therefore be achieved with shorter channels. Assuming a dispersion constant of 1 × 10-5 cm2/s (theoretical estimate for Taylor-Aris dispersion for ATP, see Supporting Information), the theoretically optimal channel length for the separation shown in Figure 5 is 27 µm, and the predicted separation time for unit resolution (with baseline) is less than 0.2 s. Even if the dispersion is an order of magnitude greater than that estimate (1 × 10-4 cm2/s), the optimal channel length would be 270 µm and the separation time would be less

than 2 s. If separation times of about 2 s can be achieved with this technique, implementation in a multiplexed 96-well format could then give a throughput of well over 100 000 measurements per hour, which is probably much faster than the rate at which samples could be mixed and otherwise prepared for measurement. Work is ongoing to fabricate and test channels less than 2 mm long and to determine whether separation times of order 1 s or less are possible. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review June 1, 2009. Accepted July 20, 2009. AC901189Y


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Gradient Elution Moving Boundary Electrophoresis with Channel

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