FACILE MICROFLUIDIC BASED METHOD TO DETERMINE
EQUILIBRIUM CONSTANTS (KD) OF REACTING BIOMOLECULES
T.M. Wynne1 and S. Pennathur1*
Department of Mechanical Engineering, University of California, Santa Barbara, USA
1
ABSTRACT
In this work, we develop a method to determine the equilibrium constant (K D) of a reacting biomolecular system
using data from an experimental microfluidic electrokinetic separation and simulation results from a COMSOL
multiphysics model. This method can be used for kinetic capillary electrophoresis injections where the electrophoretic
mobilities of 2 reacting analytes are both lower or higher than the electrophoretic mobility of their bound state, like in the
case of short complementary DNA. In this work, we use such a system to validate our model. Specifically, we present
experimental separations of 10 base long DNA for ionic strengths ranging from 10 to 60 mM in Sodium-Phosphate
buffer at pH 7.5. Our numerical model of the experiment predicts that the corresponding K D values range from 4M to
63 nM, well within experimentally published values.
KEYWORDS: Kinetic Capillary Electrophoresis, Short DNA, Dissociation Constants
INTRODUCTION
Traditional measurement techniques for equilibrium constants use bulky, time-consuming and expensive techniques
including surface plasmon resonance based tools (ie. Biacore) [1], affinity capillary electrophoresis characterization [2]
and nanopore measurements of individual DNA [3]. These methods, although changing the paradigm of the study for
both proteins and DNA interactions, still do not achieve the speed, sensitivity, and ease of use to make it a staple in all
bioanalytical laboratories. Recently, we developed a numerical model that investigates reacting biomolecules in
capillary electrophoresis based systems [4], and show that reaction parameters play a critical role in the electrophoretic
transport of reacting analytes. Here, we use the model to show a method to determine KD of 10 base DNA at varying salt
concentration. This method allows for a facile, breakthrough biomolecular analysis tool for reaction kinetics of
biomolecules.
Figure 1: Schematic of microchip capillary electrophoresis separation. Sample is loaded from north to south as shown
in part (a). Next, a plug of sample is injected into the east channel where it will separate based on difference in
electrophoretic mobility (b). Part (c) shows a typical electropherogram with 3 peaks. The first peak corresponds to
fluorescein dye tracer molecule and is used to calculate the electroosmotic velocity of the fluid. The second peak is the
excess ss primary DNA, and the third peak is the dsDNA peak which migrates at a speed between the native ds ep and ss
ep. (d) Scaled experimental electropherograms of fluorescein, tagged primary ssDNA, untagged complementary
ssDNA, and tagged dsDNA for Na-Phosphate buffer concentrations of 10, 15, 20, 30 and 60mM. The time axes is scaled
to account for longer arrival times with increased ionic strength where the electroosmotic velocity is decreased due to
lower zeta potentials
THEORY
Transport of complementary DNA species in kinetic capillary electrophoresis is governed by Equation 1, the mass
transport equation with electromigration and reaction kinetics. In this system, we have 3 analytes: the primary ssDNA
assigned to variable A, the complementary ssDNA B, and the dsDNA complex C. The association and dissociation of
the non-covalent complex C between molecules of A and B are characterized by the forward rate constant k on, and the off
rate constant koff as described by Equation 2.
978-0-9798064-6-9/µTAS 2013/$20©13CBMS-0001
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17th International Conference on Miniaturized
Systems for Chemistry and Life Sciences
27-31 October 2013, Freiburg, Germany
(1)
(2)
The reactive fluxes Ri for each species assuming a second order reaction are the following:
(3)
(4)
(5)
And in equilibrium, the dissociation constant K D is defined as:
(6)
We assume that wall effects are negligible and use a 1D model to simulate the relative electrophoretic transport of the
analytes using a Lagrangian reference set to match the assigned velocity of the complex C analyte. The injection begins
with an equilibrium plug centered at x=0 and width w0, with excess A (primary ssDNA). Relative electrophoresis of A
and B perturb the equilibrium of the system which results in dissociation of C within the equilibrium plug and
reassociation of A and B into C as they migrate away from the initial complex plug. The initial excess primary ssDNA A
separates and migrates at the assigned electrophoretic mobility and can be used as a reference for the observed
electrophoretic mobility of the complex. We quantify the observed electrophoretic mobility of the complex with a new
parameter called the weighted mobility w defined as follows:
(7)
When w equals zero, the mobility of C (dsDNA) peak is representative of the true electrophoretic mobility of the
dsDNA and occurs when KD is low. When w equals 1, the dsDNA moves at the same speed as the ssDNA peak and
occurs for high KD values where the equilibrium ratio of ssDNA to dsDNA is high.
EXPERIMENT AND SIMULATION
We performed capillary electrophoresis separations of equilibrium mixtures of complementary 10 base long DNA in
a 1 micrometer deep glass channel (Dolomite Ltd). This equilibrium sample consists of 40 M primary strand which
contained a fluorescent tag (5’-AA GAG GAG GG-3’), 20 M complement strand (5’-CC CTC CTC TT-3’), and10 M
fluorescein dye used as a reference marker for the electroosmotic flow velocity. Figure 1 shows a schematic of the
experimental procedure and raw sample data. 10 mm from the channel intersection we detect fluorescence using an
inverted microscope (Olympus IX71, Olympus Inc) and an EMCCD camera (iXon Ultra 897, Andor Inc.). Since there is
an excess of the primary single strand DNA, we observed peaks corresponding to the arrival of primary single strand and
double strand (as well as the fluorescein peak) as shown in Figure 1. Since the dsDNA peak is in dynamic equilibrium,
the observed mobility is between the true ds ep and ss ep. The observed mobility is heavily dependent on the
equilibrium ratio of ss to ds which changes with salt concentration and temperature. Numerical simulations were
performed with commercial finite element program (COMSOL Multiphysics) using the electric currents module to solve
electric fields and transport of diluate species to solve mass transport with electromigration and reaction kinetics
described by equations 1-6.
Table 1. Experimental parameters used to match weighted mobilities to find KD values. The buffer is composed of 10mM
of Sodium Phosphate buffer at pH 7.5 and the ionic strength is increased by adding NaCl, initial plug widths vary with
ionic strength due to changes in electroosmotic velocity with a constant gating time, arrival times are also dependent on
ionic strength due to change in zeta potential. Melting temperature (Tm) is provided by integrated DNA technologies,
and describes the temperature at which the equilibrium ratio of ss to ds is 1:1.
Ionic
Initial plug Arrival
KD (Determined
Tm
w
ep,ss
ep,obs,ds
Strength
width
time
from model)
28.5 C
0.24
-3.90E-8 m2/Vs
-4.12E-8 m2/Vs
10mM
322E-6 m
23.34 s
4.0E-6M
2
32.1 C
0.14
-3.70E-8 m /Vs
-3.95E-8 m2/Vs
15mM
301E-6 m
25.47 s
1.6E-6M
2
34.6 C
0.07
-3.55E-8 m /Vs
-3.82E-8 m2/Vs
20mM
275E-6 m
33.76 s
4.0E-7M
2
37.8 C
0.03
-3.37E-8 m /Vs
-3.65E-8 m2/Vs
30mM
238E-6 m
54.36 s
6.3E-8M
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RESULTS AND DISCUSSION
Simulation results show that the observed electrophoretic mobility (and resulting weighted mobility) of the dsDNA
peak is dependent on initial concentration, plug width and K D shown in Figures 2 and 3. Using our model, one can input
the experimental system parameters into the numerical model to perform a parametric simulation over a range of KD values, determining the KD of an experiment by matching weighted mobilities between simulation and experiment. We determined KD for 4 buffer concentrations, shown in Table 1, ranging from 4M to 63nM which are in agreement with
nanopore measurements of similar length DNA [3].
Figure 2. Surface plot of weighted mobilities to show
trends of initial concentration (c0) and dissociation
constants (KD). Increasing initial concentration or
decreasing KD decreases weighted mobility.
Parametric simulations were performed with all other
parameters constant: initial plug width of 230 m,
diffusivity of 2E-11 m2/s, difference in electrophoretic
velocity of 123 m/s, and arrival time of 16 s.
Figure 3: Weighted mobility trend for initial plug width
at various initial concentrations values. Increasing the
initial plug width decreases the weighted mobility, in
other words, the observed dsDNA mobility is closer to
the true value. The initial plug width in the experiment
varies ionic strength due to changes in zeta potential.
CONCLUSION
We demonstrated a facile method to determine dissociation constant of short complementary DNA using microfluidic
injection experiments and numerical simulation. Reaction kinetics influence the observed electrophoretic mobility of the
dsDNA peak and we define a new parameter, weighted mobility w, to find agreement between parametric simulations of
KD and experimental electrophoretic mobilities. This model elucidates the dynamics of electrophoretic transport of reacting species with relative electrophoretic mobilities typically found for DNA samples. The model is not limited to this
case, all parameters can be modified to match the experiment of interest, however, the weighted mobility method is only
valid for relative electrophoretic mobilities where the complex electrophoretic mobility is not in between the other 2
analytes.
ACKNOWLEDGEMENTS
This work is supported by the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 and
W911NF-12-1-0031 from the U.S. Army Research Office. The content of the information does not necessarily reflect
the position or the policy of the Government, and no official endorsement should be inferred.
REFERENCES
1. “DNA-DNA Hybridization in Real Time Using BIAcore,” S. Wood, Microchemical Journal, 47, 330 (1993).
2. “Affinity capillary electrophoresis of DNA detection of single-nucleotide polymorphisms and point mutations
Comprehensive study for optimization of the weak affinity,” K. Sato, M. Onogushi, K. Hosokawa, M. Maeda, Journal of Chromatography A, 120 (2006).
3. “Kinetics of duplex formation for individual DNA strands within a single protein nanopore,” S. Howorka, L.
Movileanu, O. Braha, H. Bayley, PNAS, 23, 12996 (2001).
4. “Analysis of non-equilibrium species kinetics during capillary electrophoresis,” T. Wynne, S. Pennathur, Analytical
Chemistry, Submitted
CONTACT
*S. Pennathur, tel: +1-805-893-5510; [email protected]
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