Anal. Chem. 2008, 80, 129-134
Analysis and Optimization of Nonequilibrium Capillary Electrophoresis of r-Fetoprotein Isoforms Rajiv Bharadwaj,* C. Charles Park, Irina Kazakova, Hui Xu, and John S. Paschkewitz
Microfluidics Group, Caliper Life Sciences, Mountain View, California 94043
The L3 isoform of r-fetoprotein (AFP) is a specific marker for hepatocellular carcinoma. The separation and quantitation of L3 isoform from the L1 isoform is facilitated by Lens culinaris agglutin (LCA) affinity of the L3 isoform. The affinity-based separation is characterized by nonequilibrium conditions since electrophoresis perturbs the species concentrations away from equilibrium. The design of such separations requires careful consideration of the interplay between the reaction, diffusion, and separation time scales. We performed experiments to investigate the effect of separation parameters such as LCA concentration and CE voltage on the L1-L3 separation dynamics. We also describe a comprehensive mathematical model to predict electropherograms for affinitybased separations. The model includes the effects of molecular diffusion, electromigration, nonequilibrium reaction, and detection process. Together, the results demonstrate a process by which to optimize the affinitybased separations of AFP isoforms. We also obtained the kinetic rate constants for LCA affinity (kon ) 1.6 × 103 mol-1 s-1 L, koff ) 1 × 10-3 s-1) by comparing the model predictions with experimental data. This study provides insight into the physics of affinity-based separations and can be extended to describe and optimize other nonequilibrium CE systems. R-Fetoprotein (AFP) has been used as a tumor marker of hepatocellular carcinoma (HCC).1 However, the serum AFP concentrations of patients with HCC and benign liver diseases (e.g., chronic hepatitis (CH), liver cirrhosis (LC)) and HCC are frequently overlapped.2 The discrimination between benign liver diseases and HCC is based on the differences in AFP structural heterogeneity. AFP obtained from patients with CH/LC and HCC is fucosylated and shows strong affinity for lectins,.3 The Lens culinaris agglutin (LCA)-reactive AFP (AFP-L3), is a specific marker for HCC.4,5 This marker allows for earlier diagnosis of HCC than imaging modalities3,6,7 and is useful for monitoring * To whom correspondence should be addressed. E-mail: rajiv.bharadwaj@ gmail.com. (1) Abelev, G. I. Cancer Res. 1968, 28, 1344-1350. (2) Taketa, K. Hepatology 1990, 12, 1420-1432. (3) Taketa, K.; Sekiya, C.; Namiki, M.; Akamatsu, K.; Ohta, Y.; Endo, Y.; K. K. Gasteroenterology 1990, 99, 508-518. (4) Taketa, K.; Endo, Y.; Sekiya, C.; Tanikawa, K.; Koji, T.; Taga, H.; Satomura, S.; Matsuura, S.; Kawai, T.; Hirai, H. Cancer Res. 1993, 53, 5419-5423. (5) Li, D.; Mallory, T. S. S. Clin. Chim. Acta 2001, 313, 15-24. 10.1021/ac071543v CCC: $40.75 Published on Web 11/29/2007
© 2008 American Chemical Society
treatment responses and disease recurrence.8,9 Previously, affinity electrophoresis10 and affinity chromatography11 techniques have been used to separate AFP isoforms. The affinity-based separations involve noncovalent interaction between the target (e.g., AFP-L3) and the ligand (e.g., LCA). The interaction between the two biomolecules can be conceptualized in terms of a reversible reaction, L + T T C.12 The key feature of affinity-based separations is that the reaction is perturbed away from equilibrium as the separation proceeds. In general, the ligand, target, and the complex have different electrophoretic mobilities, and upon application of electric field, the three species separate. Consequently, the reaction conversion changes dynamically along the separation length. The nonequilibrium nature of the separation allows measurement of the kinetic coefficients. Krylov and co-workers have developed a host of kinetic affinity methodsformeasuringbindingparametersofcomplexformation.12-17 The general area of research is termed “kinetic CE”, and a recent review article17 summarizes the advances in this field. The design of nonequilibrium affinity-based separations is not as well developed as the standard CE systems. The nonequilibrium conditions require careful control of the reaction time in the separation channel to obtain adequate reaction conversion. In the present study, we investigate the dynamics of LCA affinity-based electrophoretic separation of AFP isoforms. We present an experimental parametric study of AFP separations to explore the effects of LCA concentration and CE potential on separation resolution, peak shapes, and AFP-L3 recovery. We have also developed a mathematical model to predict the separation per(6) Sato, Y.; Nakata, K.; Kato, Y.; Shima, M.; Ishii, N.; Koji, T.; Taketa, K.; Endo, Y.; Nagataki, S. N. Engl. J. Med. 1993, 328, 1802-1806. (7) Shiraki, K.; Takase, K.; Tameda, Y.; Hamada, M.; Kosaka, Y.; Nakano, T. Hepatology 1995, 22, 802-807. (8) Yamashita, F.; Tanaka, M.; Satomura, S.; Tanikawa, K. Eur. J. Gastroenterol. Hepatol. 1995, 7, 627-633. (9) Hayashi, K.; Kumada, T.; Nakano, S.; Takeda, I.; Sugiyama, K.; Kiriyama, S.; Sone, Y.; Miyata, A.; Shimizu, H.; Satomura, S. Am. J. Gastroenterol. 1999, 94, 3028-3033. (10) Shimizu, K.; Taniichi, T.; Satomura, S.; Matsuura, S.; Taga, H. K. T. Clin. Chim. Acta 1993, 214, 3-15. (11) Katoh, H.; Nakamura, K.; Tanaka, T.; Satomura, S.; Matsuura, S. Anal. Chem. 1998, 70, 2110-2114. (12) Okhonin, V.; Krylova, S. M.; Krylov, S. N. Anal. Chem. 2004, 76, 15071512. (13) Berezovski, M.; Krylov, S. N. Analyst 2003, 128, 571-575. (14) Okhonin, V.; Petrov, A. P.; Berezovski, M.; Krylov, S. N. Anal. Chem. 2006, 78, 4803-4810. (15) Krylov, S. N. Electrophoresis 2007, 28, 69-88. (16) Krylov, S. N.; Berezovski, M. Analyst 2003, 128, 571-575. (17) Krylov, S. N. Electrophoresis 2007, 28, 69-88.
Analytical Chemistry, Vol. 80, No. 1, January 1, 2008 129
between L3 isoform and LCA kon
L3 - + LCA {\ } L3-LCAk off
Figure 1. Immuncomplexes of L1 and L3 isoforms of R-fetoprotein. The L3 isoform has a fucose residue that enables affinity to LCA. The coupling of LCA decreases the electrophoretic mobility of L3 complex and enables separation of L1 and L3 isoforms.
formance. The model includes effects of molecular diffusion, electromigration, nonequilibrium reaction, and detector characteristics. Together, the results demonstrate a process by which to optimize affinity-based separations and predict trends. Finally, by comparing model predictions with experimental data, we have obtained binding rate constants for interaction of LCA with AFPL3. Our approach may be extended to optimize and characterize other affinity-based separation assays. EXPERIMENTAL SECTION We used a quartz microfluidic chip to obtain the AFP separation data. The details of the assay and the microchip are described elsewhere.18 Briefly, the AFP isoforms are isolated from the sample based on a sandwich immunoassay. There are two distinct steps in the assay. The immunoreactions are performed in the first step. The second step involves LCA-affinity-based electrophoretic separation of the immunocomplexes. In this study, we will focus only on the separation dynamics. The CE length in the microchip was 21 mm. The separation channel was 80 µm wide and had a center line depth of 25 µm. The channel cross section was approximately D-shaped, which is typical of an isotropic wet etch. A photodiode was used to obtain the fluorescence signal. The separations were performed in a Tris-chloride buffer at pH 8. The three LCA concentrations used were 4, 2, and 0.75 mg/ mL. We measured the electropherograms at four different CE voltages, 500, 800, 1350, and 1900 V. The experiments were carried out at 30 °C. THEORY The separation between the two AFP isoforms is enabled by differential affinity with LCA. In Figure 1, we schematically describe the two immunocomplexes. The first complex is formed by the LCA-nonreactive AFP (AFP-L1). The second immunocomplex is formed by the LCA-reactive AFP (AFP-L3). The L3 isoform has a R1-6 fucose residue, which facilitates the interaction of LCA molecules with the immunocomplex. In the absence of LCA, the L1 and L3 isoforms have identical electrophoretic mobility and cannot be discriminated by CE. The affinity with LCA increases the hydrodynamic drag on the L3 immunocomplex. This leads to a mobility shift between the L1 and L3 immunocomplexes and enables separation of the isoforms. In this section, we will develop a mathematical model of the L1-L3 separation process. We begin by assuming a first-order equilibrium reaction for the interaction (18) Kawabata, T.; Li, C.; Bi, X.; Kirby, C.; Shih, Y.; Bousse, L.; Wada, H. M.; Watanabe, M.; Satomura, S. microTAS, Tokyo, 2006.
130
Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
(1)
The forward reaction rate is kon, and the backward reaction rate constant is koff. The L3-LCA complex so formed will have an electrophoretic mobility different from that of the L1 isoform due to the increased drag arising from the addition of a LCA molecule to the immunoassay complex. The L1 isoform does not participate in a similar reaction, and therefore ,the L1 mobility is unchanged. This forms the basis of the separation between the two isoforms. The concentration distributions of L3 and L3-LCA are denoted by C1(x,t) and C2(x,t), respectively. LCA is assumed to be a neutral molecule since in the experiments the buffer is pH 8.0, which is close to the isoelectric point of LCA. Also, LCA in the separation channel is in large excess as compared to the L3 concentration, For example, typical concentration of LCA is ∼10 µM, whereas L3 is present at ∼100 pM. Therefore, the LCA concentration can be assumed to be constant and equal to the initial value, throughout the separation process. Further, we assume that the relevant transport mechanisms are reaction, diffusion, and electromigration. We neglect effects arising from electroosmotic flow (EOF) since a dynamic polymer coating effectively suppresses EOF in the experiments. Under these assumptions, the concentration distribution of L3 and L3-LCA complex is described by the following equations:
∂C1 ∂2C1 ∂C1 ) - z1ν1FE + D1 2 + koffC2 - konC1CLCA,0 ∂t ∂x ∂x
(2)
and
∂C2 ∂2C2 ∂C2 ) - z2ν2FE + D2 2 - koffC2 + konC1CLCA,0 ∂t ∂x ∂x
(3)
where z is valence number, ν is the electrophoretic mobility, F is the Faraday’s constant, D, is the molecular discussion coefficient, E is the separation electric field, and CLCA,0 is the initial LCA concentration. The above governing equations can be cast in a nondimensional form to enable identification of key physical parameters. We define the following dimensionless parameters
jx ) x/L;
D h ) D/Do; ht ) tL/(EoνoF);
νj ) ν/νo;
C h ) C/CLCA,0 (4)
where L is the separation channel length, Eo is the separation electric field, Do is the characteristic diffusivity, and νo is the electrophoretic mobility of the L1 isoform. The valence numbers of L3, L1, and L3-LCA are assumed to be -1. The dimensionless form of eqs 2 and 3 are
∂C h1 ∂th
)
2 ∂C h1 h1 1 ∂C + + Daoff C h 2 - DaonC h1 ∂xj Pe ∂xj2
(5)
∂C h2 ∂th
) νj2
h 2 ∂2C ∂C h2 D h2 + - Daoff C h 2 + DaonC h1 ∂xj Pe ∂xj2
(6)
The dimensionless parameters governing the above set of equations are
Daon )
konCLCA,0L ; EoνoF
Daoff )
koffL ; EoνoF
Pe )
EoνoFL Do
(7)
The two Damkohler numbers, Daon and Daoff, are the ratio of the electromigration time scale and the reaction times scales. A large value of the Damkohler number is associated with fast reaction rate and slow electromigration along the channel. The Peclet number as defined is the ratio of the diffusion time scale to the electromigration time scale. The dispersive effects of molecular diffusion decrease as the Pe number increases. The set of coupled eq 5 is solved in conjunction with the following initial and boundary conditions
C h 1(th ) 0, jx) ) f (x)
|
jx)0,1
)
∂C h2 ∂xj
|
)0
(8)
hx ) 0,1
where f (x) describes the distribution of the L3 isoform at the beginning of the CE separation. In our simulations, we assume the following form for the initial distribution of L3 immunocomplex
( (h w- x) + erf(h w+ x))
f(x) ) 0.5 erf
(9)
where h and w are constants that govern the width and the slope of the initial concentration distribution. Finally, to complete the mathematical description of L1-L3 separation, we require a conservation equation for the nonreactive L1 isoform. In the presence of an electric field, L1 molecules are transported due to electromigration and diffusion alone. The resulting dimensionless concentration distribution, C h 3(xj,th), is given by
∂C h3 ∂th
)
∂C h3 D h 3 ∂2C h3 + ∂xj Pe ∂xj2
allows for finer resolution along the axial position. The following variable transformation allows the change of the reference frame
ξ ) jx - ht ;
C h 2(th ) 0, jx) ) 0 ∂C h1 ∂xj
Figure 2. Effect of LCA concentration on separation between L1 and L3 isoforms. The solid and dotted electropherograms refer to LCA concentration of 0.75 and 2 mg/mL, respectively. The separation voltage was 1350 V. The recovery of L3, peak shapes, and the separation resolution are improved by increasing the LCA concentration.
(10)
Equations 5, 6, and 10 provide the concentration distribution of the species of interest during the reaction-separation process. Note that eqs 5 and 6 are coupled via the reaction terms. Method of Solution. The set of coupled partial differential eqs 5 and 6 do not yield an analytical solution; therefore, we obtain the solution numerically using Matlab. To simplify the numerical simulations, we transform the set of partial differential equations to a coordinate system moving with the L1 immunocomplex electrophoretic mobility. In this reference frame, the L1 immunocomplex species are stationary and hence the overall domain for numerical simulation is considerably reduced, which in turn
t′ ) ht
(11)
In the experiments, the data are captured using a pointwise detector, i.e., a plot of intensity versus time. The simulations, on the other hand, provide temporal and spatial distribution of the concentration distribution. A model is required for the detection system to enable comparison of simulations and experimental electropherogram. We model the pointwise detection process as a convolution operation with a Gaussian response function for the detector. A similar approach has been used previously to design and optimize CE separations.19 The detector response function is given by
D(x) )
D′
x2π σd
(
exp -
)
(x - L)2 2σd2
(12)
where, σd2 is the variance associated with the detection system and D′ is the characteristic response of the detector. The electropherogram signal is obtained from the concentration distribution by following convolution operation:
I(t′) )
∫
∞
-∞
D(ξ)C(t′ - ξ,t′) dξ
(13)
RESULTS AND DISCUSSION In this section, we first describe the experimental results (Figure 2 and Figure 3) and then summarize the simulation results. Figure 2 shows a typical L1-L3 separation electropherogram. The first peak represents the sum of the L1 complex and the unreacted L3 complex. The second peak is the reacted L3 immunocomplex. The two electropherograms show the effect of LCA concentration on separation characteristics. At lower LCA concentration, the L3 peak shapes are highly asymmetric and the (19) Bharadwaj, R.; Santiago, J. G.; Mohammadi, B. Electrophoresis 2002, 23, 2729-2744.
Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
131
Figure 3. Experimental measurement of the (a) effect of CE voltage and (b) the LCA concentration on separation resolution and recovery of L3.
recovery of L3 is reduced. At higher LCA concentration, the L3 peak shape is more symmetrical and also the peak is higher. On the other hand, the first peak height is reduced. This indicates higher conversion of the reaction between LCA and L3 complex. In Figure 3, the resolution and AFP-L3% recovery data is presented. The AFP-L3% is calculated from the peak areas of the two complexes:
total AFP: complex 1 + complex 2 (14) AFP-L3% :
(complex 2/total AFP) × 100
The separation resolution R, is defined as
R)
1.18∆t fwhm1 + fwhm2
(15)
where ∆t is the separation between the two peaks of interest and fwhm refers to the full width at half-maximum. The effect of increasing LCA concentration is to improve separation resolution as well as the L3% recovery. However, an increase in CE voltage causes a decrease in separation resolution as well the L3% recovery. This is in contrast with conventional nonreactive CE systems where the separation resolution is expected to scale with separation voltage, V:
R ∼ Vn;
0 e n e 0.5
(16)
The bounds refer to the two limits of band broadening: the injection-width-limited case and the diffusion-limited case. Note that peak resolution can decrease due to other peak-broadening mechanisms such as surface adsorption, Joule heating, and hydrodynamic dispersion (e.g., Taylor/Taylor-Aris dispersion). 132 Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
Figure 4. (a) Model prediction of the effect of LCA concentration on separation dynamics. The x-axis represents dimensionless axial location along the separation channel. The various concentration profiles were obtained for the same separation time (t ) 1). The various parameters for these simulations were Pe ) 2.2 × 105, Daoff ) 0.06, and Daon ) 0.9, 1.9, 2.8, and 3.7, corresponding to increasing LCA concentration. (b) Model prediction of the effect of CE voltage on separation dynamics. The LCA concentration was fixed at 1 mg/ mL. The various dimensionless parameters for these simulations in order of increasing CE voltage were as follows: Pe × 10-5 ) 0.1, 2.3, 3.4, 4.5, and 5.7; Daoff ) 0.1, 0.06, 0.04, 0.03, and 0.02; Daon ) 3.8, 1.9, 1.3, 0.9, and 0.7.
The latter two effects are negligible in our system due to low current density and suppressed EOF. The surface adsorption of immunocomplexes as a possible mechanism is expected to affect the peak shapes of both complexes similarly. However, in the experiments, the L3 immunocomplex (complex 2) peak is asymmetric whereas the complex 1 peak is relatively symmetric. The aforementioned observations are not captured by nonreactive CE models but can be explained by our nonequilibrium CE model. Figure 4a describes the model predictions of the effect of LCA concentration on L1-L3 separation process. The separation voltage was kept constant in these simulations. Therefore, the separation time scale is fixed whereas the forward reaction time scale is varied by changing the LCA concentration. As the LCA concentration increases, L3-LCA peak intensity increases
Figure 5. Resolution versus CE voltage. An optimum CE voltage exists for electrophoretic separation of reactive species. At low fields, separations are diffusion dominated. At high fields, lower reaction conversion decreases mobility shift and hence the separation resolution.
Figure 7. Comparison of measured electropherograms (dotted lines) and model predictions (solid lines) for various CE voltages and LCA concentrations. A single set of on and off rates were used in all the model predictions: (a) 1900 V, 2 mg/ml; (b) 1900 V, 0.75 mg/ml; (c) 1350 V, 2 mg/ml; (d) 1350 V, 0.75 mg/ml; (e) 800 V, 2 mg/ml; (f) 800 V, 0.75 mg/ml. Figure 6. Scaling of L3% recovery data and comparison with model prediction. The suggested scaling collapses experimental data onto a single curve. The reaction kinetics can be obtained by comparing the model predictions with the experimental data.
and the separation resolution is enhanced. Also, the peak shapes tend toward a Gaussian distribution. The effective electrophoretic mobility of the L3-LCA complex depends on the reaction conversion, R, and can be approximated as a linear combination of the two mobility values
νeff(x,t) ≈ R(x,t)νL3-LCA + (1 - R(x,t))νL1
(17)
Note that the reaction conversion is variable along the separation channel. This leads to nonuniform mobility of the L3-LCA complex during the separation process, causing asymmetric peak shapes. The above definition of effective mobility has been used previously to describe the effective mobility of buffer ions in equilibrium.20 In our case, equilibrium conditions are not met but the conceptual definition of effective mobility is useful for qualitative understanding of the complex physics. In a limiting case of equilibrium conditions, the separation between L1 and L3 isoforms follows the diffusion-limited dynamics. For condition away from equilibrium, low and nonuniform conversion leads to asymmetric L3-LCA peaks and poor separation resolution. In Figure 4b, we investigate the effect of CE voltage on separation dynamics. At low CE voltage, the reaction conversion (20) Mosher, R. A., Saville, D. A., Thormann, W. Dynamics of electrophoresis; VCH Publishers, Inc.: New York, 1992.
Table 1. List of Parameters parameter νL1 Do h w νL3-LCA/νL1
values 1.7 × 10-8 m2/V‚s 3 × 10-11 m2/s 80 µm 2 µm 0.96
(L3% recovery) is higher since transit time in the channel is increased. However, the peaks are broadened due to enhanced molecular diffusion. Recall that the Peclet number, Pe ) EoνoFL/ Do, quantifies the role of molecular diffusion relative to CE time. The low voltage separations are in the “diffusion-limited” regime (Pe , 1). At high CE voltage, the reaction conversion is smaller since the residence time is reduced. Similar to the case of low LCA separations (Figure 4a), the L3-LCA peaks are asymmetric and the separation proceeds in the “reaction limited” regime (Da , 1 and Pe . 1). The experimental data presented in Figure 3 fall into this regime where resolution decreases with CE voltage. These two limits suggest the existence of an optimum CE voltage for maximizing separations in reactive systems. Our mathematical model can be used to predict the optimum separation parameters. In Figure 5, we calculate separation resolution for the L1-L3 separation under various conditions. The separation resolution in the spatial domain is defined as
Rx ) 2∆x/(σ1 + σ2)
(18)
where ∆x is the spatial separation between the two peaks of Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
133
interest and σ1 and σ2 are the standard deviations of the two peaks. The data presented in Figure 5 clearly demonstrate the existence of optimum resolution as CE voltage is varied. At low voltage, diffusion dominates peak broadening and reduces resolution. As CE voltage is increased, diffusion effects are minimized. However, the reaction conversion also decreases and the mobility difference between L1 and L3-LCA becomes less pronounced. This leads to reduced separation resolution at higher CE voltages. Note that, in nonreactive CE systems, the resolution is expected to monotonically increase with voltage (Rx ∼ V-0.5). Our model can be used to rationally design affinity-based separations for optimum resolution and reaction conversion. Next, we compare the model prediction with experimental data to obtain reaction rate constants (Figure 6). As noted in the introduction, kinetic coefficients have been obtained by CE of equilibrium mixtures under various configurations. We compare experimental data and model predictions of the L3 percent recovery as a function of the ratio of LCA concentration and CE voltage. The reaction rate constants are obtained by fitting the model predictions to experimental data. The suggested scaling of the x-axis collapses the data onto a single curve. This scaling is motivated by the definition of Damkohler number in eq 7, Daon ∝ CLCA,0/Eo. In the reaction-limited regime, the L1-L3 separation is enhanced by either increasing the LCA concentration or decreasing the CE voltage. Therefore, the ratio of the two parameters can be used to scale the separation data. The reaction rate constants determined from this procedure are kon ) 1.6 × 103 mol-1 s-1 L and koff ) 1 × 10-3 s-1. The validity of the obtained reaction rate constants can be tested by detailed comparison of the experimental and theoretical electropherograms at various LCA concentration and CE voltages. In Figure 7, we summarize the results from such a comparison. The experimental electropherograms provide fluorescence signal as a function of time. On the other hand, the simulations predict concentration of the analytes. Therefore, we have normalized the intensity of the first peak to enable the comparison between simulations and experiments. The various parameter values used in the simulations are listed in Table 1. Note that a single set of reaction rate constants (as obtained from Figure 6) was used for all of the six plots. The mobility of the L1 immunocomplex was obtained from the separation data. The measured electropherograms only provide an estimate of the effective mobility of the L3-LCA complex peak since the reaction conversion varies as the separation proceeds (see eq 17). Therefore, unlike the L1 immunocomplex mobility, the mobility of the L3-LCA complex, νL3-LCA, was used as a free parameter in the comparisons. The mobility difference between L1 and L3-LCA molecules can also be estimated by using the Stokes-Einstein model for electrophoretic mobility:
can be estimated using the molecular weight of the immunocomplex. For example, Arteca21 investigated the dependence of the radius of gyration of 107 proteins on the number of amino acid residues, n. The scaling relation was found to be
ν ) q/6πµr
Received for review July 22, 2007. Accepted September 20, 2007.
(19)
where r is the radius of gyration of the macromolecule, q is the electrical charge, and µ is the fluid viscosity. The radius of gyration
134
Analytical Chemistry, Vol. 80, No. 1, January 1, 2008
r ∼ n0.37(0.03 (n > 150)
(20)
The molecular weights of L1 and L3-LCA immunocomplexes are 385 and 434 kDa, respectively. Using eqs 19 and 20, the mobility ratio between L1 and L3-LCA, νL3-LCA/νL1, is expected to lie between 0.95 and 0.96. This compares very well with the value obtained from comparison of model predictions with the experimental data (Table 1). The favorable agreement between the model predictions and experimental data validates the kinetic constants obtained from the peak area-based approach. CONCLUSIONS The affinity-based separations show complex behavior compared to conventional nonreactive CE separations. The peak shapes and separation resolution are strongly dependent on reaction conversion. We performed an experimental parametric study focused on the variation of LCA concentration and CE voltage for LCA affinity-based separation of L1 and L3 isoforms of AFP. We found that increasing LCA concentration and decreasing CE voltage improve peak shapes, separation resolution, and L3% recovery. The interplay between reaction, diffusion, and separation time scales leads to various tradeoffs in the separation design. For example, faster CE separations inherently decrease reaction conversion. To address these effects, we have developed an experimentally validated 1D mathematical model to predict detailed dynamics of nonequilibrium affinity-based separations. The model accounts for reaction dynamics, diffusion effects, and electromigration of ionic species. We also include a description of the detection process by performing a convolution operation of the detector response function with the species concentration profile. The model quantitatively addresses tradeoffs arising from competing effects of reaction conversion and separation time. The competition between molecular diffusion and reaction conversion gives rise to a maximum in separation resolution as a function of CE voltage. We also obtained reaction kinetic constants by comparing model predictions with experimental data. Similar approach may be used to obtain kinetic coefficients for other affinity-based homogeneous separation assays under various conditions such as pH, buffer composition, ionic strength, and temperature. ACKNOWLEDGMENT We would like to thank Shinji Satomura and Gary Wada, Wako Pure Chemical Industries Ltd., as sponsors of this work.
AC071543V (21) Arteca, G. A. Phys. Rev. E 1994, 49, 2417-2428.
