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Anal. Chem. 1992, 6 4 , 192-199
Wave Form Fidelity in Pulsed-Field Capillary Electrophoresis D. N. Heiger,+S. M. Carson, A. S. Cohen, and B. L. Karger* Barnett Institute, Northeastern University, Boston, Massachusetts 02115
Wave form fidelity In pulsed-field caplllary electrophoresis has been examined. Depending on the condltlons of capillary operatlon, appllcatlon of a pulsed electric field was found not to yield the expected wave shape throughout the column. Thls dlstortlon was a resub of the signlfkant RC tlme constant formed from the very high solutlon resistance and the capacitance of the capillary. The capacitance ( ~ 0 . 0 pF/cm) 5 was formed between the caplllary and ground and thus dependent on the surroundings. Placing the caplllary In a UV detector cell more than doubled the column Capacitance and subsequently Increased the rise tlme as a consequence of the capacitive coupling between the caplllary and the grounded detector. The effect of wave form distortion on pulsed-field separations of DNA fragments was also Investigated. Under typical, hlgh-resistance condltlons, wave form rounding at the ground end llmlted high-frequency (lo0 Hz was not due to insufficient pulsing, but likely to the stretching and relaxation times of the DNA molecules. The 2-pA current generated by the higher conductivity buffer yielded a power of only 0.63 W/m, and significant Joule heating was thus not expected (30). While high salt concentrations are known to influence DNA structure and hence migration behavior (Z), the small amount of salt added to the buffer did not have a significant effect on DNA migration under continuous-field electrophoresis, and therefore it can be concluded that the increased peak separation was due to improved fidelity of the pulsed wave form. The sample was next injected and pulsed from the source end to evaluate the effect of the wave form distortion near the high-voltage electrode. Interestingly, both the high- and low-conductivity buffers yielded results similar to that shown in Figure 4 for the buffer with 10 mM NaCl added. That is, the best separation occurred at 100 Hz with a magnitude identical to that of the upper curve in the figure. This result indicates that higher wave form fidelity was maintained near the source end despite the rounding at the ground end. Thus, it appeared that r was not constant throughout the capillary. This implied difference in wave form at the two ends of the capillary was next examined by means of a breadboard model, which was used to simulate the pulsed wave forms within the capillary. Wave Form Simulation. As discussed above, it was of interest to determine the pulsed wave form fidelity throughout the entire column. Unfortunately, measurements of the wave form at the source end or within the capillary could not be easily made. Use of a Hall effect sensor (29), for example, which could externally measure the current within the capillary, would increase the capacitance to ground and significantly affect the measurement. Similarly, inserting a high-voltage probe (e.g., measuring small individual capillary sections in series) would be problematic since the impedance of the probe would be small relative to that of the capillary, and current would preferentially flow through the probe and not the capillary. For these reasons, a resistor and capacitor breadboard model of the capillary system was devised in order to simulate the pulsing and estimate 7 at various points within the capillary. The breadboard circuit which simulated the parasitic capacitance model is shown in Figure 5. Here, the capillary was approximated as individual 1-cm segments, each conCapillary
R3
zc2
R4
:IC3
Rs
_IC4
Ilcs
Figure 5. Breadboard model of pulsed-field capillary system. A 25-cm-long capillary is approximated by 25 individual 1-cm segments. Each segment consists of a series resistor (R), representing the solution resistance of the capillary, and a capacitor to ground (C), representing the parasitic capacitance. Values of RC correspond to those measured on the 50-, 7 5 , and 150-mmi.d. capillaries with 100 mM TBE. Measurement of current across resistor R, simulates the current exiting the capillary at the ground end (see Figure 1). The values of R and C were scaled as described in the text. Additional capacitance was added over an eight-segment zone to simulate the parasitic capacitance due to the detector. This zone could be moved to simulate any detector placement. R and C values per centimeter used in the model: 50-pm i.d. simulated with R = 5.4 k0, C = 500 pF; 75-pm i.d. simulated with R = 2.8 k 0 , C = 500 pF; 150-pm i.d. simulated with R = 3000, C = 1 nF. Detector capacitance distributed over eight segments: 360, 360, and 743 pF for the 50-, 7 5 , and 150-pm-i.d. simulations, respectively.
ANALYTICAL CHEMISTRY, VOL. 64, NO. 2, JANUARY 15, 1992
0
197
Figure 6. Simulated current wave forms at various regions throughout a 75-pm4.d. capillary. The upper trace shows the ideal, undistorted current wave form, and the lower trace the measured wave form. The amplitude of the measured wave forms were normalizedto the ideal wave form at low frequency, where no distortion occurred: (I) segment R2; ( I I ) segment R7; ( I II ) segment R 12; (IV) segment R20; (V) segment R24. R 1 is nearest to the source, R25 is nearest to ground. Conditions: buffer, 100 mM TBE; L = 25; detector capacitance centered at I = 15; source electrode at short end of capillary; 150-Hz input square were simulating 0-250 V/cm pulse.
sisting of a series resistor and a capacitor to ground. Electronically, this circuit is simply a low-pass filter (25). In this figure, R1 denotes the fiit centimeter segment closest to the source and R25 the 25th centimeter segment furthest from the source, i.e., at the ground end. Measurement across resistor R, represented that made a t the exit on the actual capillary. The values of the electrical components in each segment of the model corresponded to those measured from the CE system and are given in the caption of Figure 5. Because the parasitic capacitance per centimeter was quite small (0.05 pF/cm) and such low-value capacitors were unavailable, it was necessary to increase the values of the capacitors used in the model. To maintain RC constant, however, the values of the resistors were decreased proportionally. For example, 2.8-kQ resistors and 500-pF capacitors (for each centimeter) were used to simulate the 75-pm4.d. capillary, which exhibited a resistance and capacitance of 28 MO and 0.05 pF/cm, respectively. In a second version of the model, additional capacitance was included in the circuit to simulate the detector by distributing the equivalent of 2.5 pF (i.e., the detector capacitance) uniformly over an eight-segment zone. This zone approximated the distance that the capillary and detector were in close proximity. The location of the detector on the capillary could be varied simply by moving these additional capacitors to other segments.
Comparison of the model to experimental results is shown in Table I. In this table, experimental values of 7 measured at the ground end of 25cm-long capillaries are compared with those obtained from the model at &. Simulationsof the 50-, 75, and 150-pm-i.d. capillaries,with and without the detector, yielded values of 7 which were within *5% of those measured directly. With this agreement, the breadboard model was next used to provide estimates of 7 and resultant wave shape within the capillary. The oscilloscope tracings of the current wave forms at various segments for the simulation of the 75-pm4.d. capillary are shown in Figure 6. Again, the upper trace is the current wave form with no capacitive element. An input square wave of relatively moderate frequency (150 Hz,50% duty cycle) was used since it was slow enough not to distort the wave form significantly, and accurate measurements of 7 could be made. The designations R2, R7, R12, R20, and R24 simulate the wave form at 2,7,12,20, and 24 cm from the source, respectively, and the current measurementsfor the model were made across the designated resistor using the differential oscilloscope. There are a number of interesting features in the wave forms of Figure 6: (1) current overshoot near the source end (R2 and R7); (2) well-formed square waves near the center of the capillary (R12); and (3) rounding near the ground end (R20 and R24). Each of these phenomena can be explained by RC circuit analysis. In essence, the capacitor in each
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Table I. Comparison of Simulated and Actual Values of T Exiting the Capillary at the Ground End"
50-pm i.d. exptl model
rise time 7 , ms 75-pm i.d. exptl model
150-pmi.d.
exptl
model
with detector 0.94 10.05 0.96 0.52 10.03 0.52 0.12 1 0.01 0.11 without detector 0.41 f 0.02 0.42 0.22 f 0.01 0.24 0.07 10.01 0.07 a Conditions: 100 mM TBE buffer, L = 25 cm, detector (when used) placed 15 cm from ground end. See Figure 2 for resistance values of the caDillaries. Model accuracy. 1 5 % . segment must become charged before current will flow to the next segment. Initially, large currents flow at the source end, resulting in the overshoot. This overshoot was caused by the input square wave, whose front edge was composed of highfrequency sine waves which easily passed through the capacitor elements (i.e., impedance, X,, is given by X , = -[l/(2rfq (23, where f is frequency). Importantly, the overshoot will exist at any pulsing frequency when a square-wave input is employed, and the magnitude of the overshoot will be dependent on the resistance and capacitance, not on the applied voltage. Except for the overshoot, which decayed rapidly, wave form fidelity was generally much higher at the source end. Similarly, the rounding of the wave form at the ground end resulted from a delay until those capacitors closer to the source had been charged. If the input wave form was changed before all capacitors became fully charged, rounding would occur near the ground end. In the center of the capillary, a balance between overshoot and rounding resulted in fairly well formed square waves. By use of the model to simulate the capillary system, the wave forms between the source and the detector were next examined in detail. In addition, localized Joule heating due to the overshoot could be of concern at higher pulsing frequencies since thermal gradients within the capillary could lead to band broadening (31,32), sample degradation (33), or change in mesh structure of a polymer network. However, this heating effect is moderated by immersion of the first few centimeters of the capillary in the buffer reservoir. Furthermore, since the overshoot was a result of the front edge of the square wave, it could be eliminated simply by rounding the input wave form. Nonetheless, these effects must be understood in order to design and operate effectively a pulsed-field capillary electrophoresis system. Control of 7. Detector placement along the capillary was observed to affect the pulsed wave form, especially as the capillary resistance was increased. Generally, 7 between the source and detector was small (
