Dynamics of Capillary Isoelectric Focusing in the Absence of Fluid

The simulation data provide detailed insight into the dynamics of the focusing process for the cases with the focusing column being sandwiched between...
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Anal. Chem. 2000, 72, 5493-5502

Dynamics of Capillary Isoelectric Focusing in the Absence of Fluid Flow: High-Resolution Computer Simulation and Experimental Validation with Whole Column Optical Imaging Qinglu Mao,† Janusz Pawliszyn,† and Wolfgang Thormann*,‡

Department of Chemistry, University of Waterloo, Waterloo, ON, Canada N2L 3G1, and Department of Clinical Pharmacology, University of Bern, Murtenstrasse 35, CH-3010 Bern, Switzerland

A 150-component, dynamic electrophoresis simulator was developed and applied to the description of capillary isoelectric focusing (CIEF) of amphoteric substances in quiescent solution. The simulator is shown to be capable of producing high-resolution pH 3-10 focusing data with 140 individual carrier ampholytes (20/pH unit) and at current densities that are used in CIEF, i.e., under conditions that were hitherto unaccessible by dynamic computer simulation. Having a focusing capillary of 5-cm length, the predicted focusing dynamics for amphoteric dyes obtained at a constant voltage of 1500 V (300 V/cm) are shown to qualitatively agree with data obtained by whole-column optical imaging. The simulation data provide detailed insight into the dynamics of the focusing process for the cases with the focusing column being sandwiched between 40 mM NaOH (catholyte) and 100 mM phosphoric acid (anolyte) or having the column ends only permeable for OH- and H+ at cathode and anode, respectively. Simulation data reveal that the number of sample boundaries migrating from the two ends of the column to the focusing positions is always equal to the number of sample components. The number of detectable migrating sample boundaries, however, can be lower. Whole-column optical imaging is demonstrated to be the method of choice for following the approach to equilibrium. With that detection format, transient sample peaks can be recognized and properly identified. This would also be possible with a scanning detector moving rapidly and repeatedly along the column but cannot be accomplished by a stationary detector placed at a specified location. The data presented demonstrate that the model together with imaging monitoring can be used to optimize the CIEF separation conditions. Isoelectric focusing (IEF) is a well-known high-resolution technique for separation and analysis of amphoteric biomolecules.1,2 IEF is carried out in a pH gradient that increases from * Author to whom correspondence should be addressed: (phone) ..41 31 632 3288; (fax) ..41 31 632 4997; e(-mail) [email protected]. † University of Waterloo. ‡ University of Bern. (1) Rilbe H. Ann. N. Y. Acad. Sci. 1973, 209, 11-22. 10.1021/ac000393k CCC: $19.00 Published on Web 10/05/2000

© 2000 American Chemical Society

anode to cathode. Amphoteric compounds, including proteins, migrate until they align themselves at their isoelectric positions where a dynamic equilibrium between the electrokinetic concentrating and the dispersive processes, including diffusion, is established. IEF is routinely used for characterization of biological fluids and extracts (e.g., as a first separation step in many 2D electrophoretic analyses), monitoring protein purification, evaluation of the stability or microheterogeneity of proteins, and determination of isoelectric points.2 IEF can also be employed for isolation and polishing of proteins on the milligram per hour scale.3,4 In capillary IEF (CIEF), an instrumental format of IEF, which was first reported by Hjerte´n and Zhu,5 focusing is carried out in gel-free capillaries.5-11 CIEF provides excellent resolution of proteins with the advantage that separations are carried out with on-tube solute detection. Typically, instrumentation with a single detector placed toward one column end is employed. In that configuration, CIEF performed with suppressed electroosmosis requires that after focusing the IEF zone pattern be mobilized and swept past the stationary detector.5,6,8 Alternatively, CIEF in the presence of an electroosmotic flow represents a onestep procedure in which no mobilization of the separated ampholytes is required.9,10 However, this approach has limitations associated with uneven mobilization speeds, long mobilization times for acidic proteins, and incomplete pattern detection at column locations near the capillary end.11 Other instrumental CIEF setups comprise multipoint or wholecolumn imaging detectors. First, with a rectangular capillary of 10-cm length (cross section, about 0.5 × 1 mm) and an array of 100 sensing electrodes on the bottom glass wall of the capillary, (2) Righetti, P. G. Isoelectric Focusing: Theory, Methodology and Applications; Elsevier: Amsterdam, 1983. (3) Bier, M. Electrophoresis 1998, 19, 1057-1063. (4) Thormann, W. In Protein Purification, Principles, High-Resolution Methods and Applications; Janson, J.-C., Ride´n, L., Eds.; Wiley-VCH: New York, 1998; pp 651-678. (5) Hjerte´n S.; Zhu, M. J. Chromatogr. 1985, 346, 265-270. (6) Hjerte´n, S.; Liao, J.; Yao, K. J. Chromatogr. 1987, 387, 127-138. (7) Thormann, W.; Tsai, A.; Michaud, J. P.; Mosher, R. A.; Bier, M. J. Chromatogr. 1987, 389, 75-86. (8) Rodriguez-Diaz R.; Wehr, T.; Zhu, M. Electrophoresis 1997, 18, 2134-2144. (9) Thormann, W.; Caslavska, J.; Molteni, S.; Chmelı´k, J. J. Chromatogr. 1992, 589, 321-327. (10) Mazzeo, J.; Krull, I. Anal. Chem. 1991, 63, 2852-2857. (11) Steinmann, L.; Mosher, R. A.; Thormann, W. J. Chromatogr., A 1996, 756, 219-232.

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the temporal behavior of the electric field along the focusing column was monitored.7,12 Registration of transient and steadystate electric field distributions lead to the elucidation of the focusing dynamics of simple systems,13,14 electric field distributions across focused protein zones,7 and characterization of different carrier ampholyte mixtures.15 More recently, to overcome the drawbacks of single-point detection, instrumentation with optical whole-column imaging, including approaches based upon pulling the separation capillary through the detection window of a UV absorbance detector,16 spatial scanning laser fluorescence detection with the capillary mounted on a precision translational stage that moves the capillary through the probe beam,17 and real-time imaging without moving parts along a short (4-5 cm), internally coated capillary18-24 or microchannel,25 leads to the following of the isoelectric focusing process of amphoteric solutes. Wholecolumn imaging detection eliminates any mobilization of the focused zone pattern, provides fast analyses (∼5 min for each sample), and avoids the disadvantages associated with the mobilization process, such as distortion of pH gradient and loss in resolution. More importantly, real-time whole-column optical imaging offers a direct way in visualizing the focusing behavior of proteins or other amphoteric compounds and provides insight into the fundamental process of IEF. For many years, dynamic computer simulation of electrophoresis in the absence of fluid flow has demonstrated considerable value as a research tool.26-28 For IEF, many examples of qualitative agreement between predictions and experimental results have confirmed the utility of simulations for prediction of separation dynamics, focusing behavior of amphoteric sample components, and pH gradient formation and stability.13,14,29-32 Models featuring imposed buffer flow33 and in situ calculated electroosmosis11,34 have also been developed and applied to CIEF in the presence of up to 15 amphoteric carrier components and up to 3 proteins. Furthermore, Shimao developed a simulator for IEF of proteins in the (12) Thormann, W.; Twitty, G.; Tsai, A.; Bier, M. In Electrophoresis ’84; Neuhoff, V., Ed.; Verlag Chemie, Weinheim, 1984; pp 114-117. (13) Thormann, W.; Mosher, R. A.; Bier, M. J. Chromatogr. 1986, 351, 17-29. (14) Mosher, R. A.; Thormann, W.; Bier, M. J. Chromatogr. 1988, 436, 191204. (15) Thormann, W.; Egen, N. B.; Mosher, R. A.; Bier, M. J. Biochem. Biophys. Methods 1985, 11, 287-293. (16) Wang, T.; Hartwick, R. A. Anal. Chem. 1992, 64, 1745-1747. (17) Beale, S. C.; Sudmeier, S. J. Anal. Chem. 1995, 67, 3367-3371. (18) Wu, J.; Pawliszyn, J. Anal. Chem. 1992, 64, 224-227. (19) Wu, J.; Pawliszyn, J. Anal. Chem. 1992, 64, 2934-2941. (20) Wu, J.; Pawliszyn, J. Anal. Chem. 1994, 66, 867-873. (21) Wu, J.; Pawliszyn, J. Analyst 1995, 120, 1567-1571. (22) Wu, J.; Pawliszyn, J. Anal. Chem. 1995, 67, 2010-2014. (23) Wu, J.; Li, S.; Watson, A. J. Chromatogr., A 1998, 817, 163-171. (24) Mao, Q.; Pawliszyn, J. J. Biochem. Biophys. Methods 1999, 39, 93-110. (25) Mao, Q.; Pawliszyn, J. Analyst 1999, 124, 637-641. (26) Bier, M.; Palusinski, O. A.; Mosher, R. A.; Saville, D. A. Science 1983, 219, 1281-1287. (27) Thormann, W.; Mosher, R. A. Adv. Electrophor. 1988, 2, 45-108. (28) Mosher, R. A.; Saville, D. A.; Thormann, W. The Dynamics of Electrophoresis; VCH Publishers: Weinheim, 1992. (29) Mosher, R. A.; Thormann, W.; Bier, M. J. Chromatogr. 1986, 351, 31-38. (30) Mosher, R. A.; Dewey, D.; Thormann, W.; Saville, D. A.; Bier, M. Anal. Chem. 1989, 61, 362-366. (31) Mosher, R. A.; Thormann, W.; Kuhn, R.; Wagner, H. J. Chromatogr. 1989, 478, 39-49. (32) Mosher, R. A.; Thormann, W. Electrophoresis 1990, 11, 717-723. (33) Thormann, W.; Molteni, S.; Stoffel, E.; Mosher, R. A.; Chmelı´k, J. Anal. Methods Instrum.1993, 1, 177-184. (34) Thormann, W.; Zhang, C.-X.; Caslavska, J.; Gebauer, P.; Mosher, R. A. Anal. Chem. 1998, 70, 549-562.

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Figure 1. Schematic representation of (A) overall instrumental setup used for imaged CIEF where the valve is in sample loading position and (B) side and top views of the capillary cartridge employed for focusing.

presence of 20 carrier ampholytes.35 CIEF and most IEF separations are carried out with commercial products containing hundreds of carrier ampholytes (examples: Ampholine, Pharmalyte, Servalyte, and Biolyte2). These compounds are added to the sample and establish upon current flow the pH gradient necessary for focusing of the solutes of interest. Thus far, no dynamic computer program has been created that can handle a large amount of carrier substances. The purposes of the work described in this paper were (i) the design of a transient computer model for real-power focusing of up to 150 components, (ii) elucidation of the dynamics of low molecular mass ampholytes in highresolution CIEF in absence of flow, and (iii) validation of simulation data with those monitored using on-line optical wholecolumn imaging with the iCE280 imaged CIEF system. The overall schematic representation of that instrument is depicted in Figure 1. EXPERIMENTAL SECTION Chemical, Reagents, and Samples. All chemicals were of analytical-reagent grade, and solutions were prepared using deionized and distilled water. Methylcellulose (4000 cP for a 2% solution) was purchased from Aldrich (Milwaukee, WI). BioMark synthetic low molecular mass pI makers (substituted aminomethylphenols36-38) were purchased from Bio-Rad (Missisauga, (35) Shimao, K. Jpn. J. Electrophoresis 1994, 38, 221-225. (36) Sˇ lais, K.; Friedl, Z. J. Chromatogr., A 1994, 661, 249-256. (37) Sˇ lais, K.; Friedl, Z. J. Chromatogr., A 1995, 695, 113-122. (38) Caslavska, J.; Molteni, S.; Chmelı´k, J.; Sˇ lais, K.; Matulı´k, F.; Thormann, W. J. Chromatogr., A 1994, 680, 549-559.

Table 1. Physicochemical Input Parameters Used for Simulation compound

pKa1

pKa2

mobility (× 10-8 m2/V‚s)

initial concnb (µM)

ref

pI 8.6 dye pI 7.4 dye pI 6.6 dye pI 6.4 dye pI 5.3 dye phosphoric acida Na+ H+ OH-

7.68 5.94 5.08 4.68 3.70 2.00

9.52 8.86 8.12 8.12 6.90

3.0 3.0 3.0 3.0 3.0 3.67 5.19 36.27 19.87

9.82 13.93 18.18 13.93 16.18 100000 40000

36, 37 36, 37 36, 37 36, 37 36, 37 34 34 34 34

a Phosphoric acid was treated as a monovalent weak acid as it was employed in a low-pH environment only. b For all five dyes, the concentrations correspond to 5 µg/mL.

ON, Canada). Carrier ampholytes (Pharmalytes, pH 3-10) were from Sigma (St. Louis, MO). Samples for CIEF were prepared by mixing pI makers (final concentration: 5 µg/mL each) with carrier ampholytes (3.2% w/v) and methylcellulose (0.35% w/v). CIEF Apparatus. The experiments were performed using the iCE280 imaged CIEF system (Convergent Bioscience, Ltd, Toronto, ON, Canada). A schematic representation of the setup is shown in Figure 1 and a more detailed description of the instrument is given in ref 23. The detector was operated in the absorption mode at 280 nm. The custom-made fused-silica capillary (i.d. 100 µm, o.d. 170 µm) used was 5 cm long and internally coated with a fluorocarbon (µSIL-DNA, Product No. 199-2602, J & W Scientific, Folsom, CA). The external polyimide coating of the capillary was removed after the internal coating process. The separation capillary was assembled in a cartridge format.22 The capillary cartridge is connected with an eight-port, two-position valve for sample introduction. The loop volume is 2.5 µL. A syringe pump (model A-90, Razel Scientific Instruments, Stamford, CT) was used to deliver the washing solution. A U-glass tube was used as waste collector for balance to avoid hydrodynamic shifting. Sample injection, focusing, and imaging are fully controlled by a PC. CIEF Procedure. The detailed procedure has been described elsewhere.23 To substantially reduce the electroosmotic flow (EOF), the capillary was conditioned with 0.35% methylcellulose solution for 20 min prior to the first focusing. To match this treatment, all sample solutions and electrolytes also contained 0.35% methylcellulose. To perform imaged CIEF, the left and right electrolyte reservoirs were first filled with anolyte (100 mM H3PO4) and catholyte (40 mM NaOH), respectively. Samples were injected into the 2.5-µL fixed loop of the valve and then delivered into the separation capillary by a microsyringe pump. After the sample solution inside the capillary was stabilized for 20 s, a constant voltage of 1.5 kV was applied. The focusing time was set at any desired time and the process was monitored in a realtime mode using the imaging detection system with data registration every 20 s or longer. Electrophoresis Model. The previously described generalized, transient PC-based electrophoresis model11,33,34 was extended to handle up to 150 components (including a maximum of 4 proteins) and up to 6000 segments along the focusing column. In the interest of clarity, the major points of the model are briefly reviewed. The model is one-dimensional and based upon the principles of electroneutrality and conservation of mass and

charge. Isothermal conditions are assumed, and relationships between the concentrations of the various species of a component are described by equilibrium constants. The model employed here properly handles proteins, biprotic ampholytes, and monovalent weak and strong acids and bases. Component fluxes are computed on the basis of electromigration and diffusion. Electrophoretic mobilities of the components are considered to be independent of the ionic strength and temperature but may vary as function of pH. For the weak and amphoteric components, the model employs pH-dependent effective mobilities that are calculated from the input values and the degree of dissociation. Initial conditions that must be specified include (i) initial distribution, pK and input mobility for each component, (ii) magnitude and duration of constant-current density or constant voltage, and (iii) column length as well as its segmentation and the species permeabilities (boundary conditions) at the ends of the separation space. The program outputs concentration, pH, and conductivity distributions and allows the presentation of these data either as profiles along the column at specified time intervals or as temporal data that would be produced by a detector at a specified column location, i.e., segment number. Furthermore, it outputs the current density as function of time. Computer Simulations. The program was executed on Pentium computers running at 233, 300, or 600 MHz. The component’s input data used for simulation are summarized in Table 1. For the dyes, ∆pK values were estimated according to the data of Sˇ lais and Friedl,36,37 and if not stated otherwise, input mobility values were taken as 3 × 10-8 m2/V‚s. For making plots, simulation data were imported into SigmaPlot Scientific Graphing Software windows version 2.01 (Jandel Scientific, Corte Madera, CA). Focusing in the presence of 140 carrier ampholytes was simulated. If not stated otherwise, a 5-cm focusing space divided into 1000 segments of equal length, uniform initial distribution of all components, and a constant voltage of 1500 V were employed. A total of 140 hypothetical biprotic carrier ampholytes were used to establish a pH gradient between anode and cathode. Their pI values uniformly span the range 3.0-9.95 (∆pI ) 0.05). Unless otherwise stated, for each ampholyte, ∆pK was 2, the ionic mobility was 3 × 10-8 m2/V‚s, and the initial concentrations were 0.160, 0.250, or 0.625 mM. RESULTS AND DISCUSSION Dynamics of the Focusing Process. As a continuation of previous work,11,13,14,26-34 IEF with 140 hypothetical ampholytes Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

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Figure 2. Computer-simulated dynamics of various column properties during focusing of 140 carrier components (0.16 mM each) and 3 dyes between 100 mM phosphoric acid (anolyte) and 40 mM NaOH (catholyte). Distributions of (A) pH, (B) conductivity, and (C) electrode solutions after 0, 0.5, 1.0, 1.5, 2.0, 4.0, 6.0, and 12 min of application of a constant 1500 V are depicted. The focusing column is between 0 and 5 cm. In all three panels, the cathode is to the right. The arrows mark the direction of the boundary migration with successive lines produced at increasing time points. The data presented in panel D represent the temporal behavior of the current density (solid line) in comparison to that predicted for the case without the electrode solutions (broken line).

as carrier components was investigated using the newly developed simulation model. It is known that the average molecular mass of pH 3-10 Pharmalytes is ∼900.2 Thus, a z% carrier ampholyte solution corresponds to a total carrier concentration in millimolar of 10z/900. The data presented in Figures 2 and 3 are those obtained for focusing of three small molecular mass amphoteric dyes with pI’s of 6.6, 7.4, and 8.6, respectively, in the pH 3-10 gradient produced by 140 carrier compounds (2% carrier ampholyte solution, 0.16 mM of each compound). Initially the sample was uniformly distributed inside the whole focusing column of 5-cm length (0 e x e 5 cm) and electrode compartments were filled with 40 mM NaOH (catholyte, x > 5 cm) and 100 mM phosphoric acid (anolyte; ,x < 0 cm). The entire electrophoresis column length employed for simulation was 12.5 cm, the number of segments was 2500, and the constant voltage applied was 1500 V. In that configuration, most of the potential drop is across the 5496

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5-cm focusing space (Figure 2B). The pH gradient was predicted to become formed within ∼1 min of current flow (panel A of Figure 2), the characteristic conductivity distribution was established within ∼1.5 min (panel B), and the carrier compounds were noted to become focused in ∼2.5 min (Figure 3A). For all carrier ampholytes, a double-peak approach to equilibrium is predicted. This is particularly well seen for components focusing in the center of the gradient (e.g., for the pI 6.45 carrier depicted in Figure 3A). Low-pH carriers were found to exhibit a strong peak migrating toward the cathode and a weak peak migrating toward the anode (e.g., pI 4.45 constituent in panel A of Figure 3). The opposite was noted to be true for high-pH carrier ampholytes (see behavior of pI 8.45 compound in Figure 3A). The current density was determined to decrease from the initial value of 1295.8 A/m2 to a value of 119.5 A/m2 at 12 min (solid line in panel D of Figure 2), with the major drop occurring within the first 2 min after power application (to 294.8 A/m2), i.e., within the time interval during which the carrier gradient is established. The small, gradual decrease of the current density observed thereafter results from the previously described stabilizing process of the zone pattern13 and the gradient decay at the edges (see below32). After focusing, carrier ampholytes were predicted to have formed overlapping focused zones of ∼18.3 mM peak concentration (∼114-fold increase in concentration compared to initial configuration; see inset in Figure 3B), whereas the dyes were found to have produced Gaussian-like zones with peak concentrations of 1.26 (69-fold increase), 1.02 (73-fold increase), and 1.17 mM (119-fold increase), respectively (Figure 3B). The peak concentration is shown to be related to ∆pKa of the ampholyte.1,2,26-28 The dye with the lowest ∆pKa (pI 8.6 dye) is correctly predicted to form the sharpest focus. The dyes are shown to be well separated from each other and to only slightly influence the steady-state distributions of the carrier compounds at their foci (marked with arrows in Figure 3B). Furthermore, prolonged electrophoresis revealed the well-known, gradual isotachophoretic decay on the cathodic side. This is nicely seen in the pH, conductivity, and anolyte/catholyte distributions shown in panels A, B, and C, respectively, of Figure 2 and the 12-min distribution of all compounds depicted in panel B of Figure 3. On the basis of the high phosphoric acid concentration employed, only a very small isotachophoretic displacement is predicted on the anodic side. For detailed explanations of these drifts refer to ref 32. The graphs presented in Figure 4A represent computerpredicted transient and steady-state dye distributions as would be seen by a dye specific array detector along the column. The data for each time point represent the sum over all three dye concentrations and thus correspond to profiles seen with optical imaging and measuring the absorbance at a wavelength that does not provide a response of the carrier components (i.e., >250 nm5,9,33,38). The three dyes are predicted to migrate from both ends and to become focused at the pI points of the individual components. For each compound, a transient ”double-peak” approach is predicted (Figure 4A) and observed (Figure 4B), a process that has been reported previously for other IEF configurations.27,28,31,39,40 The number of peaks predicted by computer simulation was found to nicely correspond to those monitored by (39) Behnke, J. N.; Dagher, S. M.; Massey, T. H.; Deal, W. C. Anal. Biochem. 1975, 69, 1-9. (40) Dishon, M.; Weiss, G. H. Anal. Biochem. 1977, 81, 1-8.

Figure 3. Computer-simulated (A) dynamics of three carrier compounds with pI’s of 4.45, 6.45, and 8.45 (profiles after 0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 min, from bottom to top, respectively, presented with a y-axis offset) and (B) distribution of all compounds after 12 min of power application for the simulation example of Figure 2. The arrows in panel B mark the locations of the dye foci, and the inset depicts a section of the focused carrier ampholytes on elongated x- and y-scales. The cathode is to the right.

Figure 4. Dynamics of (A) the computer-predicted detector response for the pI 6.6, 7.4, and 8.6 dyes of the data of Figures 2 and 3, (B) the experimental data with the same three dyes, and (C) the computer-predicted detector response of the dyes in absence of electrode solutions. The cathode is to the right. Graphs at the indicated, successive time points are presented with a y-axis offset. For further explanations refer to text.

whole-column imaging. Furthermore, the relative magnitudes of the peaks were noted to qualitatively agree as well. This is interesting as the simulation data were not corrected for differences in absorbance of the three dyes. In that context, it is particularly worth mentioning that there is nice agreement for the anodic peaks of the pI 8.6 dye, this indicating that the selected IEF conditions were realistic. The absorbance of the dyes is known to be pH dependent.37 Proper correction of simulation data with

pH-dependent absorbance indexes would require the elucidation of input data in the presence of the carrier ampholytes. As this would be a demanding task, which would not provide a quantitative agreement between simulation and experimental data, no correction for differences in absorbance was implemented. The presence of base and acid in the cathodic and anodic electrode compartments, respectively, has an impact on the stability at the edges of the pH gradient but not within the gradient (i.e., at the Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

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foci of the dyes investigated in this work).32 Thus, in the absence of electroosmosis, the foci of the amphoteric dyes should remain stationary. This was found to be true for simulations (tested up to 30 min of power application during which a tiny cathodic drift of the pI 8.6 dye was predicted only; data not shown) and essentially also observed in the experiments. The experimental data presented in Figure 4B do reveal a small cathodic drift of all three dye foci. For this set of data it can thus be concluded that there was a small, residual electroosmotic displacement toward the cathode. This was not the case for other data sets (see below). Focusing Speed and Boundary Conditions at Column Ends. Focusing of the three dyes is predicted to be complete within ∼5 min (panel A of Figure 4), whereas the three-peak pattern was first monitored after ∼6 min (panel B). Not knowing the exact mobilities of the dyes and carrier compounds, as well as the exact composition of the commercial mixture of carrier ampholytes, this can be considered as a remarkable agreement. The boundary conditions at the column ends were found to have an impact on the focusing speed as well. With specific IEF conditions (without acid and base as anolyte and catholyte, respectively, i.e., species permeabilities at column ends are restricted to those of H+ and OH- on anodic and cathodic column ends, respectively26-28), a constant 1500 V across a 5-cm column and dye mobilities of 3 × 10-8 m2/V‚s revealed a focusing time interval of ∼4.25 min (Figure 4C). This is 0.75 min shorter than with the electrode compartments containing 40 mM NaOH and 100 mM phosphoric acid. The reason for the difference is the somewhat smaller voltage drop across the focusing column in the presence of the base and the acid, which results in a slightly different temporal behavior of the current density (Figure 2D). In this configuration, the gradient pattern becomes somewhat more compressed (compare data of Figures 3B and 5), which results in slightly higher peak concentrations of carrier and sample components. For the data presented in Figure 5, the carrier ampholyte peak concentration was found to be ∼21.2 mM, i.e., 2.9 mM (15%) higher compared to the data presented in Figure 3B, and the dye peak concentrations were predicted to be 1.52 (84-fold increase compared to initial stage), 1.23 (88-fold increase), and 1.28 mM (130-fold increase), respectively. The pH gradient formed (Figure 6A) and the focusing dynamics in terms of the transient stages formed, however, does not differ at all (Figure 4C). Thus, all further simulations were performed in the absence of the base and the acid. Furthermore, the simulation data reveal that the time interval required for focusing of the sample components is somewhat larger compared to that required for the establishment of the pH gradient (compare data of Figure 4A with those of Figures 2A,B and 3A). This difference is somewhat more pronounced than previously investigated in simpler IEF configurations.28,31,33 It is important to realize that the major current drop is associated with the formation of the carrier ampholyte gradient (Figure 2). Finally, using the IEF boundary conditions, the impacts of carrier ampholyte concentration and input dye mobility values on focusing were investigated. A change of the carrier ampholyte concentration, e.g., to 3.2% (0.25 mM of each of the 140 carrier compounds corresponding to the carrier concentration that was used experimentally), and otherwise identical conditions was found to provide the same focusing dynamics when operated at 5498 Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

Figure 5. Simulation data at a constant 1500 V (300 V/cm) for focusing of 140 carrier compounds and the pI 6.6, 7.4, and 8.6 dyes in a 5-cm column in the absence of electrode solutions. The depicted data represent the distribution of all components after 12 min with 2% carrier ampholytes. The arrows mark the locations of the dye foci, and the inset depicts a section of the focused carrier ampholytes on elongated x- and y-scales. The cathode is to the right.

the same constant voltage (data not shown) and almost identical pH gradients (Figure 6A). The current density, however, did change. It became higher as the carrier concentration was increased (Figure 6B). Use of the conditions of Figure 4C with dye mobilities of 2 × 10-8 m2/V‚s instead of 3 × 10-8 m2/V‚s revealed a focusing time interval of ∼6 min (a value that corresponds to that observed experimentally), whereas dye mobilities of 4 × 10-8 m2/V‚s lead to complete focusing within 3.5 min. In the latter case, the small transient peak of the pI 8.6 dye migrating toward the cathode was not predicted, this indicating that a mobility of 4 × 10-8 m2/V‚s is definitely too high. With a dye mobility of 2 × 10-8 m2/V‚s, the small peak of the pI 8.6 dye was a bit higher compared to that shown in Figure 4. Except for that, the transient dye peaks formed were found to be comparable in all three cases (data not shown). Thus, on the basis of all the investigations, the conclusion can be reached that the dye mobilities are between 2 × 10-8 and 3 × 10-8 m2/V‚s. In all instances with equal mobilities, the components focusing in the column center were predicted to require more time to become focused (see, e.g., data presented in Figures 3A and 4A,C). Number of Migrating Transient Sample Peaks. Figure 7 shows the full dynamic focusing process of another set of three pI markers using computer simulation (A) and the imaged CIEF instrument (B). In that example, amphoteric dyes with pI’s of 5.3, 6.4, and 7.4 (Table 1) and a carrier ampholyte concentration of 3.2% (0.25 mM of each of the 140 carrier components) were employed. As for the first example, nice agreement between simulation and experimental data was noted. The initial focusing

Figure 6. Simulation data at a constant 1500 V (300 V/cm) for focusing of 140 carrier compounds and the pI 6.6, 7.4, and 8.6 dyes in a 5-cm column in the absence of electrode solutions. (A) pH distributions at 10 min for the cases of 2, 3.2, and 8% of carrier ampholytes in comparison to that of the configuration of Figure 2 (plotted with a 1 pH unit y-axis offset). The cathode is to the right. (B) Temporal behavior of the current density for 2, 3.2, and 8% of total carrier ampholyte concentration.

Figure 7. Dynamics of (A) the computer-predicted detector response for the pI 5.3, 6.4, and 7.4 dyes during focusing at 1500 V in a gradient produced by 140 carrier ampholytes (0.25 mM each) and (B) the corresponding experimental data with the same three dyes. The cathode is to the right. Graphs at the indicated, successive time points are presented with a y-axis offset.

stage is characterized by three, well-defined transient peaks on each side. The peak intensities and resolution are shown to increase with time, and as focusing advances, anodic and cathodic

peaks of each dye are depicted to merge to a stationary single peak. All the predicted transient states could be clearly visualized via whole-column imaging. Furthermore, focusing is predicted to Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

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Figure 8. Computer-predicted dynamics for focusing of all five dyes at a constant 1500 V (300 V/cm) in a gradient established by 140 carrier ampholytes (0.25 mM each). (A) Detector response as would be seen by imaging, (B) distributions of the five dyes (lower graphs with 0.1 mM y-axis offset for presentation purposes) and detector profile (upper graph) after 0.5 min, (C) dye distributions and detector profile after 1.5 min, and (D) pH (solid lines) and conductivity (broken lines) profiles at 0.5 and 1.5 min. The cathode is to the right.

be complete within ∼6 min (A), which compares well with the experimental focusing time of ∼6.5 min (see above). In the two examples discussed thus far, the number of visualized, transient peaks migrating in the same direction was found to correspond to the number of sample constituents. This is not surprising as focusing is based upon a transient double-peak approach to equilibrium.27,28,31,39,40 In the case of Figure 7, all three dyes were shown to produce nice peaks whereas in the example presented in Figure 4, the pI 8.6 peak migrating toward the cathode was barely detectable but clearly present. Furthermore, following the focusing of all five dyes, five transient peaks are predicted for the anodic side whereas there are only four transient peaks on the cathodic side (Figure 8A). The boundaries of pI 6.4 and 6.6 dyes arising from the cathodic column end are predicted to comigrate, which is illustrated with the data of the 0.5- and 1.5-min time points presented in panels B and C, respectively, of Figure 8. For the two time points, computer-predicted concentration distributions of all five dyes (lower graphs, depicted with a 0.1 mM y-axis shift for the sake of clarity) and their summation as would be seen by whole-column imaging (top graph) are presented. These data nicely illustrate the two-peak approach to equilibrium that is characteristic for IEF. Furthermore, for sample compounds with 5500 Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

similar pI values (see pI 6.4 and 6.6 dyes), complete resolution of the two compounds is only predicted shortly prior to reaching equilibrium. Although this example was not validated experimentally, it becomes clear that the number of sample boundaries migrating from the two ends of the column to the focusing positions is always equal to the number of sample components. The number of detectable migrating sample boundaries, however, can be lower. Furthermore, the computer-predicted 0.5-min pH and conductivity profiles presented in panel D of Figure 8 reveal that the transient dye peaks migrate along gradients of these properties. At 1.5 min, the electric field is uniform across a large portion of the column and the peaks are predicted to migrate along the pH gradient only. Advantages of Whole-Column Imaging in CIEF. With the presented examples, the advantages of using optical whole-column imaging are demonstrated. The entire focusing process can be followed in a straightforward matter. After complete equilibrium is reached, the final pattern is immediately monitored and the run can be terminated. No mobilization for detection purposes is required, thereby guaranteeing minimal run times and solute dispersion. Furthermore, the temporal behavior of the current (as a means to assess the progress of focusing) does not need to be followed. If fixed-point detectors placed toward the cathodic end (e.g., at 90 or 70% of column length), in the column center, or toward the anodic end (e.g., 30 or 10% of column length) would be employed, absorbance vs migration time electropherograms would be obtained.5-10 To register a fully resolved CIEF pattern in that mode, focusing has to be completed prior to detection and the entire zone pattern has to be swept across the point of detection. The first aspect can be accomplished via (i) partial filling of the column with sample9 or (ii) addition of a strong base to the sample which permits establishment of the focused pattern within the capillary part in front of the point of detection.8 In these configurations, CIEF patterns are typically detected with mobilization toward the cathode; i.e., the foci are registered in the order of decreasing pI values. Furthermore, not knowing whether the steady state was reached prior to detection requires the performance of a second run with, for example, a lower sample load. Otherwise, there is a definite risk that electropherograms reflecting transient focusing stages are monitored and the obtained data plots do not necessarily contain a peak for each sample compound. This is illustrated with the data presented in Figure 9 that correspond to the predicted electropherograms as would be seen by single-point detectors placed at the indicated column locations. The depicted concentration vs time responses are those obtained for the five-dye configuration of Figure 8A. The peaks detected at locations close to the column ends (10 and 90% of column length, panels A and G, respectively, of Figure 9) represent the transient peaks that migrate across the points of detection in cathodic and anodic directions, respectively. At the anodic column end, peaks are detected in the order of decreasing pI values, whereas the opposite is true on the cathodic side. In both electropherograms, the baseline before the peaks is higher compared to the baseline after the peaks. In panel A, the number of peaks monitored is equal to the number of amphoteric sample components whereas in panel G four peaks are registered only (anodically migrating peaks of pI 6.4 and 6.6 dyes are comigrating; see Figure 8B,C). Detector responses monitored at 20 (panel B

Figure 9. Computer-predicted detector responses for the five-dye example of Figure 8 with a single detector placed at (A) 10, (B) 20, (C) 30, (D) 50, (E) 70, (F) 80, and (G) 90% of column length.

of Figure 9) and 30% (panel C) of column length are similar to that obtained at 10% (panel A). The further away the detector is placed from the anodic column end, however, the higher the peaks become. Furthermore, at 30%, the pI 5.3 dye peak migrates very slowly across the point of detection (refer to Figure 8A) and is thus recorded as a very broad peak. The same relationships are true for the cathodic side, except that the anodically migrating pI 8.6 dye peak is not reaching the detectors placed at or before 80% of column length. Without having the data of Figure 8, patterns registered at (panel D) or close to the center of the column are difficult to relate to the sample. The advantage of having whole-column imaging in CIEF is further illustrated with a look at literature data, e.g., at those presented in ref 41. There is great similarity between the simulated time-based electropherograms of Figure 9 and the experimental data of Figures 4 and 5 in the paper of Hofmann et al.; e.g., the (41) Hofmann, O.; Che, D.; Cruickshank, K. A.; Mu ¨ ller, U. R. Anal. Chem. 1999, 71, 678-686.

data shown in their Figure 4 were obtained at 92.9% of column length and the pattern resembles that of Figure 9G in both the signal format and the reversed detection order of the substances in comparison to that characteristic for most CIEF approaches. This can explain why Hofmann et al. inferred an incorrect conclusion on the migration order. It is believed that EOF in this system has been highly suppressed by glycerol, used at the high concentration of 40%, and that Hofmann et al. detected transient stages and not the final steady-state IEF zone pattern. With wholecolumn optical imaging, the focusing process could have been followed conclusively and much needed information on the behavior of the sample in their setup would have been obtained. CONCLUSIONS This paper reports the first high-resolution, dynamic pH 3-10 IEF simulation data produced by 140 carrier ampholytes (20/pH unit) and the first ”real power” IEF simulation data, i.e., data at a current density that is used in CIEF. The impact of the boundary conditions at the column ends on focusing (large electrode Analytical Chemistry, Vol. 72, No. 21, November 1, 2000

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reservoirs containing 40 mM NaOH (catholyte) and 100 mM phosphoric acid (anolyte) vs transport restricted to that of OHand H+ on cathodic and anodic sides, respectively) is also discussed. In this paper, major emphasis is focused on the elucidation of the behavior of amphoteric dye samples with pI values between 5.3 and 8.6. The predicted focusing dynamics are shown to qualitatively agree well with data obtained by wholecolumn optical imaging. The simulation data reveal that the number of sample boundaries migrating from the two ends of the column to the focusing positions is always equal to the number of sample components. Due to comigration and/or insufficient transient peak formation, however, the number of detectable migrating sample boundaries can be lower. Whole-column optical imaging is the method of choice for following the approach to complete separation. After the equilibrium is reached, the final pattern can be monitored precisely and quickly. No mobilization for detection purposes is required, and the temporal behavior of the current does not need to be followed. Simulation is shown to provide detailed insight into the focusing process and the responses obtained with single-point detectors and whole-column imaging. Input data for each sample and carrier component can be chosen freely and are thus not restricted to those used by other

models, including the steady-state model of Almgren which was established to predict focusing around neutrality.42 Thus, after having established the validity with the data presented here, the new model will be employed for the elucidation of the fundamental focusing characteristics at pH extremes and will comprise an invaluable tool to the practitioner who is faced with phenomena that cannot be explained by simple models. From a practical point of view, simulations performed on the power level of experiments (>100 V/cm) are currently too slow to cut the time and cost of optimization procedures; e.g., using a PC running at 600 MHz, simulations with 150 compounds and 300 V/cm as described in this paper do require up to 10 h CPU time. With the availability of faster computers, however, CIEF simulations will become a more efficient way to do experiments on the computer.

(42) Almgren, M. Chem. Scr. 1971, 1, 69-75.

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ACKNOWLEDGMENT The authors thank Dr. Jiaqi Wu and Arthur Watson, Convergent Bioscience, Ltd., for their help. This work was partly sponsored by the Swiss National Science Foundation and the National Science and Engineering Research Council of Canada. Received for review April 6, 2000. Accepted August 22, 2000.