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Addressable Electric Fields for Size-Fractioned
Sample Extraction in Microfluidic Devices
Rongsheng Lin,†,‡ David T. Burke,§ and Mark A. Burns*,†,|
Department of Chemical Engineering, Department of Human Genetics, Department of Biomedical Engineering, and
Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, Michigan 48109-2136
Fraction collection following electrophoresis is of major
importance for a variety of biological analyses. These
assays typically need to identify specific fractions in the
separated sample for further processing and require
extraction of one or a group of fragments. In this paper,
we have developed and characterized a technique to
generate addressable electric fields for improved extraction during electrophoresis in microfluidic devices. The
addressable electric field is achieved by applying a low
bias voltage (1-2 V) to microelectrode pairs within the
electrophoresis microchannel. Theoretical analysis shows
the purity of the extracted sample can be improved as
much as 30% over extraction without the shaped electric
fields, and nearly 100% predicted yield can be achieved.
We also describe the theoretical design of shaped electric
fields by characterizing the optimal electrode geometry,
field strength, channel configuration, and electrophoretic
migration behavior needed for efficient band extraction.
Electric field-mediated separation is of major importance for
analyzing biological samples, such as DNA and protein.1,2 Electrophoresing sample molecules through a sieving matrix allows
separation of species on the basis of size and charge and thus
provides a means to perform efficient separations on a routine
basis. Electrophoresis has been widely used for the sequencing
of genomes, DNA fingerprinting, identification of pathogens, and
numerous genetic assays used to identify diseases.3
Integrating electrophoresis with fraction collection further
extends the power of the separation technique. Commonly,
fractionated DNA populations are isolated from a slab gel by
cutting out pieces containing the bands or by redirecting the
eluting fractions into individual vials in a capillary electrophoresis
system.4 The isolated samples then can be recovered for further
* To whom correspondence should be addressed. Phone: (734) 764 4315.
Fax: (734) 763 0459. E-mail: [email protected].
†
Department of Chemical Engineering.
‡
Department of Electrical Engineering and Computer Science.
§
Department of Human Genetics.
|
Department of Biomedical Engineering.
(1) GaaI, O.; Vereczkey, L.; Medgyesi, G. Electrophoresis in the separation of
biological macromolecules; John Wiley & Sons: New York, 1980; pp 11-18.
(2) Westermeier, R. Electrophoresis in practice, 3rd ed.; Wiley-VCH: New York,
2000; pp 1-32.
(3) Andrews, A. T. Electrophoresis theory, techniques, and biochemical and clinical
applications, 2nd ed.; Oxford University Press: New York, 1986.
(4) Richwood, D.; Hames, B. D. Gel Electrophoresis of Nucleic Acids: A Practical
Approach, 2nd ed.; Oxford University Press: New York, 1990.
10.1021/ac048132o CCC: $30.25
Published on Web 00/00/0000
analysis, such as dot-blot assays.5 Capillary electrophoresis has
also been used to collect multiple fractions corresponding to
denatured DNA from mutated polymerase chain reaction (PCR)
products, and the collected fractions were reamplified by PCR and
reanalyzed by electrophoresis.6 More recently, a capillary array
electrophoresis system with multiple fraction collections was
reported for analysis of the yeast genomic DNA.7 Several other
examples of capillary-based fraction collector for DNA fragments,8-10
peptides,11 and protein12 have also been reported.
By allowing the electrophoretic separation integrated with
fraction collections on a single and compact format, microfludic
devices are poised to offer an alternative to perform biological
assays with performance comparable to the macroscale counterparts.13-15 Microfabricated systems offer more controllable transport of samples through manipulating the electric field employed
in the separation and fraction collection. Electrokinetic techniques
in which samples are introduced into the separation matrix using
an applied electric field in the order of several hundred volts per
centimeter have been widely used in microfabricated electrophoresis devices.16-27 The separated samples can be further
(5) Cohen, A. S.; Najarian, D. R.; Paulus, A.; Guttman, A.; Smith, J. A.; Karger,
B. L. Proc. Natl Acad. Sci. U. S. A. 1988, 85, 9660-9663.
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Chromatogr., A 1993, 621, 149-156.
(7) Berka, J.; Rultz-Martinez, M. C.; Hammond, R.; Minarik, M.; Foret, F.; Sosic,
Z.; Kleparnik, K.; Karger, B. L. Electrophoresis 2003, 24, 639-647.
(8) Ekstrom, P. O.; Wasserkort, R.; Minarik, M.; Foret, F.; Thilly, W. G.
BioTechniques 2000, 29, 582-589.
(9) Irie, T.; Oshida, T.; Hasegawa, H.; Matsuoka, Y.; Li, T.; Oya, Y.; Tanaka, T.;
Tsujimoto, G.; Kambara, H. Electrophoresis 2000, 21, 367-374.
(10) Magnusdottir, S.; Heller, C.; Sergot, P.; Viovy, J. L. Electrophoresis 1997,
18, 1990-1993.
(11) Boss, H. J.; Rohde, M. F.; Rush, R. S. Anal. Biochem. 1995, 231, 123-129.
(12) Guttman, A.; Cohen, A. S.; Paulus, A.; Karger, B. L.; Rodriguez, H.; Hancock,
W. S. In Electrophoresis ′88; Shafer-Nielsen, C., Ed.; VCH Publishers: New
York, 1998; p 51.
(13) Ugaz, V. M.; Elms, R. D.; Lo, R. C.; Shaikh, F. A.; Burns, M. A. Philos. Trans.
R. Soc. London Ser. A 2004, 362 (1818), 1105-1129.
(14) Kan, C.; Fredlake, C. P.; Doherty, E. A. S.; Barron, A. E. Electrophoresis
2004, 25, 3564-3588.
(15) Paegel, B. M.; Blazej, R. G.; Mathies, R. A. Curr. Opin. Biotechnol. 2003,
14 (1), 42-50.
(16) Emrich, C. A.; Tian, H. J., Medintz I. L., Mathies, R. A. Anal. Chem. 2002,
74, 5076-5083.
(17) Vazquez, M.; McKinley, G.; Mitnik, L.; Desmarais, S.; Matsudaira, P.; Ehrlich,
D. Anal. Chem. 2002, 74, 1952-1961.
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Matsudaira, P.; Ehrlich, D. Electrophoresis 2002, 23, 719-726.
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(20) Fu, L. M.; Yang, R. J.; Lee, G. B. Anal. Chem. 2003, 75, 1905-1910.
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Analytical Chemistry A
© xxxx American Chemical Society
PAGE EST: 9.8
collected by directing the desired sample zones to the corresponding wells. The addition of a cross-channel allowed the
potentials to be reconfigured so that a precise collection of spatially
close consecutive bands could be facilitated.28 More controllable
transport of analyte was achieved in a three-dimensional fluidic
network by employing nuclear track-etched polycarbonate membranes.29 More recently, on-chip electrodes have been employed
in the microchannels to extract one or a group of DNA fragments
of interest during the separation.30
In addition to performing on-chip fraction collection by electrokinetic manipulation, a new concept with quantitative wholecolumn fraction collection has been developed.31 The CD-like
platform uses centrifugal force to move the liquid in the microchannels. The serpentine shape of the separation channel can
create segments for fraction collection at each turn. The centrifugal
force then can drive the separated fractions simultaneously into
individual turns. By allowing whole-column fraction collection, this
concept offers a new method to increase the collection efficiency
in a parallel manner.
We present a technique for generating addressable electric
fields to improve extraction performance. Applying finite potentials
onto the shaping electrodes modulates the electric field in the
vicinity of the extraction region. Using experiments and computational simulations, we show that localized addressable electric
fields with tunable control of the shape can be easily constructed.
Next, we demonstrate the theoretical study of utilizing shaped
electric fields to achieve high-purity extraction. The electric field
can be easily and precisely manipulated by adjusting the magnitude of the applied voltage, the electrode positions, or both. This
technique is evaluated in terms of the purity of the extracted band,
and details on designing such a system are discussed.
MATERIALS AND METHODS
Modeling and Simulation. The time-dependent concentration
field is governed by32-34
∂C
+ (µ ‚E
B ‚∇)C ) D∇2C
∂t
(1)
Here C is the concentration of the sample and D is the dispersion
coefficient. The use of dispersion coefficient is more accurate in
predicting band migration since diffusional band broadening alone
(22) Zhang, C. X.; Manz, A. Anal. Chem. 2001, 73, 2656-2662.
(23) Jacobson, S. C.; Hergenroder, R.; Moore, A. W.; Ramsey, J. M. Anal. Chem.
1994, 66, 4127-4132.
(24) Effenhauser, C. S. Anal. Methods Instrum. 1993, 1, 172-176.
(25) Koutny, L. B.; Schmalzing, D.; Taylor, T. A.; Fuchs, M. Anal. Chem. 1996,
68, 18-22.
(26) Effenhauser, C. S.; Manz, A.; Widmer, H. M. Anal. Chem. 1993, 65, 26372642.
(27) Fu, L. M.; Yang, R. J.; Lee, G. B.; Liu, H. H. Anal. Chem. 2002, 74, 50845091.
(28) Khandurina, J.; Chovan, T.; Guttman, A. Anal. Chem. 2002, 74, 1737-1740.
(29) Kuo, T.-C.; Cannon, D. M.; Chen, Y.; Tulock, J. J.; Shannon, M. A.; Sweedler,
J. V.; Bohn, P. W. Anal. Chem. 2003, 75, 1861-1867.
(30) Lin, R. S.; Burke, D. T.; Burns M. A. J. Chromatogr., A 2003, 1010, 255268.
(31) Speˇsˇny´, M.; Foret, F. Electrophoresis 2003, 24, 3745-3747.
(32) Fu, L. M., Yang, R. J.; Lee, G. B. Anal. Chem. 2003, 75, 1905-1910.
(33) Tsai, C. H.; Yang, R. J.; Tai., C. H.; Fu, L. M. Electrophoresis 2005, 26,
674-686.
(34) Radko, S. P.; Weiss, G. H.; Chrambach, A. J. Chromatogr., A 1997, 781,
277-286.
B
Analytical Chemistry
B is the electric
underestimates the observed band broadening.35 E
field and µ is the apparent mobility of the band, a combination of
electrophoretic and electroosmostic mobility.
The externally applied electric field is given by
E
B ) -∇φ
(2)
where φ is the electrical potential. For electrophoresis in microchannels, we assume steady electric field, uniform fluid density,
and uniformly charged solid surface. For typical conditions (1.0×
Tris-Borate-EDTA buffer, TBE) used in the electrophoresis, the
Debye length is estimated on the order of 10 nm and therefore is
much smaller compared to any channel dimension (several tens
of micrometers). Under these restrictions, the electric field
potential outside the Debye layer is governed by the Laplace
equation:36
∇2φ ) 0
(3)
The es 1-3 were solved simultaneously in a geometry of crosschannel configuration in order to obtain the band migration and
electric field distribution. Two-dimensional simulations were
performed using Femlab software, a commercial finite element
package (COMSOL Inc. Burlington, MA). As the channel width
and length is much larger than the depth, 2-D simulations offer
sufficient information to probe the feature of the transport process
without requiring considerable amounts of computation time. The
voltages at the two reservoirs were chosen to match the electric
field strength in the experiments, and the two cross-channel
potentials were allowed to float. The externally applied electric
field was subject to insulating boundary conditions on dielectic
microchannel walls; i.e., ∂φ/∂n ) 0. A condition of zero mass flux
was applied to the microchannel walls. Other parameters used in
the simulations were based on the values measured in the
experiment: D ) 10-11 m2/s, µ ) 10-9 m2 s-1 V-1. The initial
concentration of the band (C (t ) 0)) was Guassian distribution
with σ2 ) 500 µm2 unless specified individually.
Device Construction. Detailed fabrication protocols for hybrid
glass-silicon devices have been published elsewhere.30 Briefly,
the silicon wafer was spin-coated with a positive photoresist
(Microposit SC 1827, Marlborough, MA) and patterned with the
microelectrodes. After the pattern was developed (MF-319 developer; Shipley Co., Marlborough, MA), a 300-Å thick titanium metal
layer followed by a 1000-Å platinum layer was deposited on this
wafer by electron beam evaporation. The photoresist and the
overlying metal layers were lifted off using acetone, leaving only
the microelectrodes. Fabrication of channels in the glass wafer
used a wet etching process. First, metal layers of 600-Å chromium
followed by 4000-Å gold were deposited on a borofloat glass wafer
(500 µm thick, 100-mm diameter). A positive photoresist (Microposit SC 1827; Shipley) was spin-coated, patterned, and developed.
The metal layers were etched in a commercial gold etchant (Gold
Etchant TFA, Transene Co.) and chromium etchant (CR-14,
Cyantek Corp., Fremont, CA), respectively, leaving glass exposed
in the locations where the channel network was to be etched. The
(35) Ugaz, V. M.; Burke, D. T.; Mastrangelo, C. H.; Burns, M. A. Electrophoresis
2002, 23, 2777-2787.
(36) Griffiths, S. K.; Nilson, R. H. Anal. Chem. 2000, 72, 5473-5482.
Figure 1. (a) Schematic drawings (top view) depicting the microchannel layout for separation and extraction. X denotes the location of the
cross-channel. (b) Simulated image showing band expansion under the normal electric field. (c) Simulated image showing the carryover as the
target band is extracted under the normal electric field: main channel 1500 µm × 300 µm; side channel 300 µm × 1500 µm. Vseparation )
Vextraction ) 4 V.
accessible glass was then etched in a freshly prepared solution
of hydrofluoric acid (49% HF, CMOS grade; J.T. Baker). The rate
of etching was 7.0 µm/min, and the etch depth was measured
using a stylus surface profilometer. After etching to the desired
depth, the metal layers were removed using the corresponding
etchants, and the wafer was rinsed in DI water, air-dried, and ovendried at 100 °C for 20 min. The finished microchannel is 30-40
µm deep, and the width is on the order of 300 µm, depending on
the design layout. After individual devices on the substrate wafers
were diced, holes (300-µm diameter) were drilled in the glass
substrate to access the microchannels using an in-house electrochemical discharge apparatus. The glass channel was then bonded
to the silicon substrate using a UV-cured optical adhesive (SK-9,
Summers Laboratories, Fort Washington, PA). Electrical connections were made by wire bonding the assembled devices to printed
circuit boards.
Electrophoresis Procedure. Double-stranded DNA separations were performed using 100-bp standard ladders (Bio-Rad
Laboratories, Hercule, CA) labeled with YOYO-1 intercalating dye
(Molecular Probes, Eugene, OR) at a ratio of 5:1 bp/dye. A 1×
TBE solution (Bio-Rad) was used as running buffer. β-Mercaptoethanol (Sigma-Aldrich, St. Louis, MO) was added to a final
concentration of 10% to reduce photobleaching.
Separations were performed using ReproGel (Amersham
Pharmacia, Kalamazoo, MI), a commercially available photopolymerized cross-linked polyacrylamide gel, which allows the gel
interface to be precisely positioned inside the electrophoresis
channel.37 An initial polymerization period of 3 min was used to
set the gel interface, after which the interface mask and accompanying unpolyermized solution were removed. The masked
region and reservoirs were then refilled with electrophoresis
buffer, and UV polymerization was allowed to continue for an
additional 5-10 min.
The sample (S), sample waste (SW), and buffer (B) reservoirs
were filled with the fluorescent sample (Figure 1a). The waste
reservoir (W) was filled with the TBE running buffer. Samples
were loaded by applying a +70-V potential at the W reservoir and
grounding the B reservoir for ∼10 s (E ∼70 V/cm). After a sample
plug was formed near the gel interface, the rest of the sample
was removed and replaced with TBE running buffer. To perform
the separation, +30 V was applied at the W reservoir while
grounding the B reservoir. Both the S and SW reservoirs were
allowed to electrically float during separation. SC1 and SC2
reservoirs were used to collect the target sample. The shaping
voltage is applied on the shaping electrodes using a floating
voltage source. Care has to be taken to avoid bubble formation
by limiting the voltage to ∼2 V.38 Introduction of wider shaping
electrodes allows slightly higher voltages (∼3 V) to be safely
applied for several tens of seconds without bubbling. Fluorescence
from the migrating bands was detected using an Olympus SZX
12 fluorescence stereoscope with a mercury arc illumination
source and imaged using a Hamamatsu C2400-08 SIT camera
(Hamamatsu Corp., Bridgewater, NJ).
(37) Brahamasandra, S. N.; Ugaz, V. M.; Burke, D. T.; Mastrangelo, C. H.; Burns,
M. A. Electrophoresis 2001, 22, 300-311.
(38) Petrucci, R. P. General Chemistry; MacMillan: New York, 1982.
Analytical Chemistry
C
Figure 2. (a) Schematic drawings depicting the separation phase and the generation of the shaped electric field for reduction of band expansion.
Vshaping is the voltage bias applied on the shaping electrodes. Lg is the gap between the symmetric electrodes, and Lp is the distance the shaping
electrode away from the separation channel. Migration direction is from left to right. Cross-hatch area denotes the target, and 9 denotes the
neighboring bands. (b) Simulated image showing the reduction of the band expansion under a single shaped electric field. Main channel 1500
µm × 300 µm; side channel 300 µm × 1500 µm. Vseparation ) 4V. Lp ) 50 µm. Lg ) 200µm. V+⊥ ) 2.5 V, V-⊥ ) 1.5 V. (c) Schematic drawings
depicting the extraction phase and the generation of the shaped electric field to reduce the carryover from the neighboring bands. WB denotes
the full width of the target band. WCC and WMC denote the width of the cross-channel and the separation channel. Migration direction is from
down to up. (d) Simulated image showing the carryover reduction through a second shaped electric field: main channel 1500 µm × 300 µm;
side channel 300 µm × 1500 µm. The shaping electrodes (V+II and V-II) are placed 50 µm away from the extraction channel and are 200 µm
away from each other. Vextraction ) 4 V, V+II ) 2.5 V, and V-II ) 1.5 V.
Particle Imaging Setup. The flow field was observed using
1-µm Fluoresbrite plain YG microspheres (Polyscience Inc.).
These particles have an excitation peak at 441 nm and emission
peak at 486 nm. The original concentration of fluorescent microspheres was 4.55 × 1012 particles/mL and was diluted to 4.55 ×
1010 particles/mL. These particles were introduced into the
microchannel by capillary action, and the experiment began when
the flow stabilized. The imaging system consists of a Zeiss
epifluorescent microscope with illumination provided by a mercury
lamp. A Nikon 10× objective lens is used for magnification of the
images so that the field of view covered the whole cross-channel.
The images were recorded using a Hamamastu C2400 CCD
camera with 512 × 512 pixels and 12-bit readout resolution and a
DVD recorder. The correlated particle images obtained were
analyzed with a PIV interrogation code.39 In the PIV image
process, the interrogation cell overlay was given as 50%. Ensemble
(39) http://sauron.civil.eng.osaka-cu.ac.jp/∼mori/softwares/mpiv/index.php.
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Analytical Chemistry
averaging of up to 10 images consecutively captured at a rate of
30 fps was used to obtain the velocity measurements.
RESULTS AND DISCUSSION
Band Extraction and Shaped Electric Fields. The addition
of an electric field perpendicular to the separation direction is the
technique used to extract migrating bands from a microchannel.
A cross-channel is positioned perpendicular to the separation
channel in order to generate the electric field for extraction
(Figure 1a). The extraction procedure includes two stages. The
first stage involves electrophoresis of the size-fractioned sample
through a sieving matrix in the separation channel. After the target
fragment is identified from the band pattern, the separation field
is stopped and the second stage begins. The capture electrodes
in the cross-channel are energized to extract the target band out
and finally release it into the buffer reservoir.
The simulation results indicate that the impurity inherent in a
simple cross-channel configuration is unlikely to be completely
eliminated because the band expands laterally into the crosschannel as it reaches the intersection (Figure 1b). A second band
can easily expand and come into contact with the end of the first
band. In addition, the carryover from the adjacent bands occurs
as the target band in the intersection is extracted into the crosschannel (Figure 1c). Both the expansion and carryover are the
contributing sources to the impurity in this process.
Addition of electrodes in the intersection offers the ability to
adjust the electric field shape in favor of reducing the lateral
expansion (Figure 2a). By energizing the shaping electrodes with
a bias voltage (Vshaping), the bands can be confined in the separation
channel and reduce band expansion (Figure 2b). While the lateral
expansion can be minimized using shaped electric fields, there is
still carryover from the adjacent bands as the target band in the
intersection is captured into the extraction channel. The shaped
electric field can also be applied in the course of extraction to
isolate the target band from its neighbors (Figure 2c). By
activating the shaping electrodes in the separation channel with
a voltage bias (Vshaping), the shape of the electric field in the vicinity
of the intersection can be tuned to reduce the carryover. Isolation
between the target and the neighboring band is clearly demonstrated in the simulation (Figure 2d).
For the purpose of quantification, we define the yield and purity
as
∫∫
Ci dA
upper cross-channel
Yi )
M0
(4)
P1 )
∫∫
C1 dA
upper cross-channel
∫∫
upper cross-channel
C1 dA +
∫∫
C2 dA
upper cross-channel
(5)
Here Yi is the yield of the band (1 stands for the target and 2
denotes the neighboring band); Ci is the concentration of the band;
M0 is the initial band mass and can be calculated by integrating
the concentration over the entire channel area. P1 is the purity of
the target band: P1 ) Y1/(Y1 + Y2) for the case of the bands (C1,
C2) having the same initial band mass. These definitions only
consider a simple case with one neighboring band and could be
extended to other situations, such as two adjacent fragments.
Shaped electric fields greatly improve the band extraction.
Figure 3 shows the computed purity (a) and yield (b) of the target
band as a function of extraction time. The purity under shaped
electric fields can reach 96% in a very short time (40 s) after
extraction began, whereas it has a maximum value around 66%
under a normal electric field. Figure 3b compares the yield in the
case with and without shaped electric field. The yield under
shaped electric fields increases almost linearly with time at a rate
of 0.0073 s-1 after extraction began and can reach 96% in 150 s,
whereas the rate is only 0.0045 s-1 and the yield goes up to 84%
only for the case in the absence of the shaped electric field.
However, the purity starts to decrease after 40 s due to carryover
from the neighboring bands (Figure 3a single electric field).
Figure 3. (a) Computed purity as a function of time during extraction
under (I) normal electric field, (II) single shaped electric field, and
(III) double shaped electric field. (b) Computed yield as a function of
time during extraction under (I) normal electric field, (II) single shaped
electric field, and (III) double shaped electric field. The channel
geometry is the same as the one used in Figure 2. Main channel
1500 µm × 300 µm; side channel 300 µm × 1500 µm. The shaping
electrodes (V+⊥ and V-⊥) are placed 50 µm away from the separation
channel and are 200 µm away from each other. Vseparation ) 4 V, V+⊥
) 2.5 V, and V-⊥ ) 1.5 V. The other shaping electrodes (V+II and
V-II) are placed 50 µm away from the extraction channel and are
200 µm away from each other. Vextraction ) 4 V, V+II ) 2.5 V, and V-II
) 1.5 V.
Formation of another shaped electric field can minimize the
carryover. After the shaping, electrodes in the separation channel
are energized (Figure 3a double electric field), and the purity
remains almost constant once it reaches 96%.
Experimental Results. Based on the simulation, we fabricated
a silicon-glass hybrid device (1.3 cm × 0.7 cm) as shown in Figure
4a. The device contains an offset double-T for sample injection,
separation channel, and cross-channel for extraction. A close-up
micrograph of the intersection is shown in Figure 4b. Note that
there are some shadows along the edge of the microchannels,
resulting from undercut during the glass etching process. The
anisotropic nature of the process generates a channel cross section
with a trapezoid shape instead of rectangle.
Generating an addressable electric field requires the appropriate setting of potentials at each shaping electrodes. The potentials
will be redistributed after a bias voltage is applied on the shaping
electrodes. By applying Vshaping, on the shaping electrodes, the
Analytical Chemistry
E
Figure 4. (a) Photograph of a microfabricated device used for separation and extraction (b) a close-up of the intersection with the shaping
electrodes.
potential at each electrode (V+, V-) can be tuned: V+ increases
whereas V- decreases linearly with the shaping potential.
Electric Field Distribution. The shaped electric field distribution was measured using particle tracking techniques, and the
experiments agreed with the simulations. The use of microparticle
image velocimetry (PIV) enables spatially resolved measurements
of instantaneous velocity fields and, therefore, has been widely
used to characterize the pressure-driven flow or electroosmosis
flow in microchannels.40-42 In this work, we chose 1-µm negative
charged fluorescent latex microspheres to visualize the movement
under the shaped electric field. Figure 5 shows a comparison
between the flow field from the particle tracking experiment and
the corresponding electric field predictions. The velocity is
proportional to the electric field (v
b ) µ‚E
B), and the results between
the experiment and simulation are similar. We also note that the
field is more curved in the vicinity of the electrodes in the
simulation. The motion of trace particles in the third dimension in the experiment may cause the discrepancy. Nevertheless,
these results qualitatively verify the formation of shaped electric
fields.
Band Migration. The band migration without shaped electric
fields was first demonstrated experimentally using a single size
DNA fragment. A 400-base pair double-stranded DNA sample was
loaded into the gel and migrated through the intersection (Figure
6aI). As a comparison, we simulated the initial band using a
Gaussian distribution (Figure 6bI). The comparison shows a very
good agreement in terms of band shape. The simulation results
(bII) show the similar expansion of a migrating band, resulting
from cross-channel configuration to the experiment data (aII). As
the band migrates forward leaving the junction, the expanded
portions are left behind in both the experiment and simulation
(aIII,bIII).
The similar experiment and simulation was performed to
demonstrate band migration under the shaped electric field. After
the shaping electrodes are energized, the band migrates in a
(40) Meinhart, C. D.; Wereley, S. T.; Santiago, J. G. Exp. Fluids 1999, 27, 414419.
(41) Devasenathipathy, S.; Santiago, J. G. Anal. Chem. 2002, 74, 3704-3713.
(42) Devasenathipathy, S.; Santiago, J. G. Exp. Fluids 2003, 34, 504-514.
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Analytical Chemistry
Figure 5. (a) Velocity field extracted from the particle tracking
images Vshaping ) 2 V. (b) Simulation of the shaped electric field
distribution under the similar condition (Vshaping ) 2V). There is no
voltage spanning the separation channel.
confined region with limited expansion into the cross-channel
(Figure 7(aII,III). The simulation results (Figure 7bII,III) show
the similar band migration behavior, indicating that the model
can accurately describe experimental behavior. The difference on
the level of curvature between experiment and simulation is most
Figure 6. (a) Experimental snapshot of (I) the initial status of a
migrating band, (II) band migrating in the junction, and (III) band
leaving the junction. Eseparation ) 25 V/cm, (b) Simulated image of (I)
initial concentration (C(t ) 0) ) Guassian distribution with σ2 ) 500
µm2), (II) band migrating in the junction, and (III) band leaving the
junction under the simulation condition similar to the experiment:
Vseparation ) 4 V corresponding to Eseparation around 27 V/cm, Migration
direction is from left to right.
likely due to the nonuniformity of the initial band observed in
the experiment.
Designing Shaped Electric Fields. We have demonstrated
shaped electric fields both theoretically and experimentally.
However, challenges still remain in terms of designing such
electric fields that are capable of reducing band expansion and
carryover. For the purpose of reduction of band expansion, the
shaping electrodes arrangement (e.g., size and relative position
to the intersection) is of major importance. On the other hand,
the channel geometry and band migration are more crucial in
reducing carryover during band extraction.
Position and Size of the Shaping Electrodes (Lp, Lg). The shaped
electric field for reduction of band expansion is affected by several
parameters (Figure 2a). These include the distance of the shaping
electrodes away from the main separation channel (Lp), the gap
between two symmetrical electrodes (Lg), and the applied shaping
voltage (Vshaping and Vseparation). To characterize the band expansion,
we define the retained band mass as
∫∫
MR separation channel
retained band mass )
)
M0
Mo
C dA
(6)
Figure 7. (a) Experimental snapshot of (I) the initial status of a
migrating band, (II) band migrating in the junction, and (III) band
leaving the junction in the experiment Eseparation ) 25 V/cm, Vshaping
) 1 V. (b) Simulated image of (I) initial concentration (C(t ) 0) )
Guassian distribution with σ2 ) 500 µm2), (II) band migrating in the
junction, and (III) band leaving the junction under the condition similar
to the experiment: Vseparation ) 4 V corresponding to Eseparation around
27 V/cm, V+⊥ ) 2.5 V, V-⊥ ) 1.5 V. Migration direction is from left to
right.
over the entire channel area. MR is the band mass retained in the
separation channel. The retained band mass defines the percentage of the band mass remaining in the separation channel as the
band passes by the cross-channel.
The position of the shaping electrodes (Lp) has a signficant
impact on the shaping effect, whereas the gap between the
electrodes (Lg) is minor. Figure 8 shows the retained band mass
as a function of Lp under a set of different electrode gaps (Lg).
The closer to the separation channel the shaping electrodes are
placed, the less band expansion is obtained. The band migration
is not sensitive to Lg and remains essentially constant once the
position of the electrodes is fixed. These results imply that the
shape of the electrodes has little influence on the band migration
as a consequence of the minor discrepancy in the electric field
distributions.
The electrodes have a minimal distance of approximately 2030 µm away from the separation channel (Figure 8). The minimum
distance (Lpc) can be estimated by scale analysis. The time
necessary for diffusive transport (tdiff) by a distance of Lp can be
estimated using the following relationship.43
tdiff ∼ Lp2/D
(7)
The convective transport time scale, tconv, is on the order of time
Here C is the DNA concentration distribution. M0 is the initial
band mass and can be calculated by integrating the concentration
(43) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Pheomenona, 2nd ed.;
J. Wiley: New York, 2002.
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Figure 8. Retained band mass (the lowest value) as a function of
Lp at a fixed Lg ) 50 (b), 100 (1), 150 (2), and 200 µm (9). The
following parameters are used for simulations: main channel 1500
µm × 300 µm; side channel 300 µm × 1500 µm, Vseparation) 4 V, V+⊥
) 2.5 V, and V-⊥ ) 1.5 V.
required to drive the band out of the intersection by Lp distance:
tconv ∼ Lp/(µE)
(8)
As tconv must be less than tdiff, for the band being able to migrate
out of the intersection, the following condition derived using the
above equations has to be satisfied: Lp . Lpc. Here Lpc is the
minimal distance defined by the relation
Lpc ) D/(µE)
(9)
For typical values of diffusivity and mobility in experiments and
simulations (D ∼ 10-11 m2/s, µ ∼ 10-9 m2 s-1 V-1), Lpc is on the
order of 10 µm under the electric field strength of 103 V/m.
Electric Field Strength (Eshaping and Eseparation). Compared to the
voltages applied on the shaping electrodes and cross the separation channel (Vshaping and Vseparation), the shaping electric field
strength (Eshaping) is a more intuitive factor influencing the field
distribution associated with the separation field (Eseparation) in the
vicinity of the cross-channel. The shaping field strength (Eshaping)
can be calculated by Vshaping/WCC, where WCC is the width of the
cross-channel. Because the band migration is insensitive to the
electrode gap (Lg), the use of cross-channel width is more
reasonable than the electrode gap. Applied separation voltage
divided by the length is used to estimate the field strength for
separation (Eseparation).
Computational modeling shows that retained band mass
increases in a manner that scales with Eshaping/Eseparation (Figure
9). To reduce the band migration laterally into the cross-channel
(<5%), a value of the ratio of Eshaping/Eseparation greater than 1 has
to be maintained. Since the shaping field strength is proportional
to the applied voltage on the electrodes (Vshaping), higher Vshaping
generates stronger shaping fields and, therefore, allows less band
expansion. This plot also offers a basic guideline for generating a
shaped electric field by matching the Eshaping with Eseparation. An
Eshaping/Eseparation ratio of ∼1 can be achieved by adjusting the
shaping voltage (Vshaping) and the cross-channel width (WCC). The
H
Analytical Chemistry
Figure 9. Retained band mass (the lowest value) as a function of
Eshaping/Eseparation. Eshaping is the shaped electric field strength and is
calculated by Vshaping divided by the cross-channel width. Eseparation is
the electric field strength for separation and is calculated by the
voltage spanning the separation channel divided by the channel
length. The following parameters are used for simulations: main
channel 1500 µm × 300 µm; side channel 300 µm × 1500 µm.
Vseparation) 4, 6, 8, and 10 V. Vshaping ) V+⊥ - V-⊥ ) 0.5 (1), 1 (2),
1.5 (b), and 2 V (9). Lp ) 50 µm. Lg ) 200µm.
analysis indicates that a shaped electric field is achievable for
separation field strengths ranging from 20 to 200 V/cm by using
cross-channel widths from 50 to 500 µm (Vshaping ) 1 V).
Length of Channel (X). The separation length determines
how far two consecutive bands can be separated or resolved. The
bandwidth (WB) affects the yield whereas the purity is influenced
by both the bandwidth and resolution (R). Discussions centering
on these two parameters (WB and R) are essential to determine
the position of the cross-channel (X) in order to achieve a certain
purity and yield.
The bandwidth (WB) can be estimated using the following
equation for a Gaussian distribution:
WB ) 4‚xσ2inj + 2(D/µE)X
(10)
Here σ2inj is the peak variance of the injection plug. WB0 ) 4σinj is
the full width of the injection plug. D is the dispersion coefficient.
By plotting the ratio of the bandwidth (WB) over the migration
distance (X) as a function of the migration distance (X) (Figure
10a), two dominant regions can be represented using two series
of straight lines corresponding to different initial injection plug
width (WB0) and dispersion (2D/(µE)). This plot offers the
flexibility of determining the transition region between the two
dominant regions by simply finding the intersection of the two
lines (e.g.,WB0 ) 100 µm, 2D/(µE) ) 0.1 µm). The procedure is
easy to follow and is suitable for any combination of settings of
WB0 and 2D/(µE).
The bandwidth is inherently related to the resolution (R) by44
R ) 2(xn - X)/(wn + WB)
(11)
Here xn is the migration distance of the neighboring band and wn
Figure 10. (a) Ratio (WB/X) as a function of migration distance (X)
under various settings of injection plug width (WB0) and 2D/µE. The
dashed line interpolates the curve with a fixed plug width and
dispersion (WB0 ) 100 µm, 2D/µE ) 0.1 µm). (b) Resolution (R) as
a function of the ratio of bandwidth over the migration distance (WB/
X) under different selectivity settings (selectivity (S) is from 0.2 to
1.6%).
is the width of the neighboring peak at the baseline. For two
neighboring peaks (wn ) WB)
R ) S‚(WB/X)-1
Figure 11. (a) Purity as a function of R(WB/WCC) in various WCC/
WMC settings under normal electric fields. The purity is obtained 140
s after the extraction starts. The main channel is 1500 µm × 300 µm
and the cross-channel is 1500 µm long. The width of the crosschannel (WCC) and the bandwidth (WB) varies from 75 to 300 µm
simultaneously to maintain the ratio of WB/WCC equal to 1. For the
case that the ratio of WCC/WMC maintains 0.5, WB/WCC ) 0.5 (1), 1
(2), and 1.5 (b). (b) Purity as a function of R(WB/WCC) in various
WCC/WMC settings under shaped electric fields. The channel geometry
is the same as those in (a) except that extra electrodes are placed
aligning the cross-channel. The distance between electrodes are 200
µm. Vextraction ) 4 V, V+II ) 2.5 V, and V-II ) 1.5 V.
(12)
Here S ) ∆µ/µ is the selectivity of two neighboring bands. Figure
10b shows the predicted resolution as a function of the ratio of
bandwidth over migration distance (WB/X) under different selectivity settings. High resolution requires a small ratio of WB/X,
which can be realized either by prolonging the separation length
(X) or by narrowing the bandwidth (WB). Figure 10 offers a simple
means to estimate the separation distance (X) to achieve a certain
resolution and bandwidth needed for high purity/yield extraction.
Channel Dimensions (WCC, WMC). The simulation results show
that the purity of the isolated band is a function of resolution (R),
migrating bandwidth (WB), cross-channel width (WCC), and main
channel width (WMC). R and WB are parameters associated with
the band migration, whereas WCC and WMC are microchannel
(44) Landers, J. P. Handbook of Capillary Electrophoresis, 2nd ed.: CRC Press:
New York, 1995.
geometry related (Figure 2c). To make the design process scalable
in channel geometry, we computed purity as a function of the
multiplication of resolution and WB/WCC under various fixed
settings of WCC/WMC (Figure 11a). We found that, for a range of
WB/WCC (0.5-1.5), all the curves can collapse into one with WB/
WCC equal to 1 (Figure 11a, WCC/WMC ) 0.5). This approximation
offers a simple means to capture the essential features of the
problem and provides valuable insights into the scaling of the
system. A similar model using shaped electric fields can also be
generated (Figure 11b). Purity improvement is observed through
shaping the electric field to isolate the target band from its
neighbors. The ability to scale down offered by these two plots
makes them suitable to design the channel geometry in terms of
purity and resolution under both normal electric fields and shaped
electric fields. For instance, there is little difference in purity
between two channel dimensions (I) WB ) 100 µm, WCC ) 100
µm, and WMC ) 100 µm and (II) WB ) 300 µm, WCC ) 300 µm,
Analytical Chemistry
I
relationship can be derived:
1 e (WCC/WB) e 2R - 1
(13)
This equation suggests the minimum requirement for imposing
a shaped electric field during extraction is that the consecutive
bands have to be well resolved (R g 1). In practice, migrating
bands are not exactly rectangular but approximate a Guassian
distribution, allowing the upper and lower limits of WCC/WB to be
slightly different from the derived relationship. This analysis
indicates maintaining the ratio of WCC/WB around 1 is important
to make full use of shaped electric fields for applications requiring
both high yield and purity.
Figure 12. (a) Purity as a function of resolution in various WCC/WB
settings under the shaped electric field. (b) Yield as a function of WCC/
WB under the shaped electric field. WMC ) 300 µm. WB ) 150 µm.
WCC varies from 75 to 300 µm corresponding to the ratio of WCC/WB
from 0.5 to 2. The distance between electrodes is 200 µm. Vextraction
) 4 V, V+II ) 2.5 V, and V-II ) 1.5 V. The initial target band is in the
center of the intersection. The resolution data are calculated based
on the bandwidth and the distance the neighboring band is away from
the target band.
and WMC ) 300 µm as long as the ratio of WB:WCC:WMC remains
constant.
However, there is a tradeoff between the purity and yield. As
the cross-channel becomes narrower compared to the bandwidth,
much purer sample can be extracted. Nevertheless, the yield
decreases as a result of the narrower cross-channel (Figure 12(a)(b)). Ideally, the cross-channel width should be less than the
distance between two consecutive bands and greater than the
bandwidth in order to maintain a high yield. The following
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CONCLUSIONS
We have developed a technique using addressable electric
fields to control and minimize the contamination from the adjacent
bands and selectively extract target bands during electrophoresis.
The precise control of electrode characteristics, such as position
and size, makes microfabrication an ideal tool for the development
of such a system. In this work, we theoretically characterized
shaping electrode configurations and investigated band migration
behavior and electric field distribution under these conditions. The
use of shaping electrodes within the cross-channel resulted in
improved predicted extraction selectivity and reduced carryover
by tuning the localized electric field into the desired shape. The
principle of this method is general and versatile and should be
applicable to any system that fractionates charged molecules.
The described computational models and experiments provide
a foundation for designing more complex addressable electric
fields using multiple electrodes for on-chip sample extraction.
Future work involving fully three-dimensional simulations and
rigorous comparison with experimental results would be beneficial
to understand the role of localized shaped electric fields in a more
quantitative manner. By allowing integration with microfluidic
controls, this type of devices could add more functionalities onto
the existing µTAS systems.
ACKNOWLEDGMENT
The authors acknowledge the support of the National Institutes
of Health under the Grant NIHGRI P01-HG001984.
Received for review December 17, 2004. Accepted April
22, 2005.
AC048132O