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which would give the smallest RMSE for test sets. As in the %@phenolcase I found that training set RMSE values steadily increased as the number of competitive layer PE's decreased. However, in contrast to the 20-phenol case I found that the test set RMSE values also increased steadily as the number of competitive layer PES decreased. The best training and test set RMSEs occurred for the 42-PE networks. Table V contains a summary of test set results of leaveone-out calculations for the 42-PE networks. While the RMSE values are larger than those from regression equations they are generally quite good. With the exception of a few phenols (most notably numbers 9, 33, 41, and 42) the errors are of reasonable magnitude. Once again the RMSE+ values are smaller than the RMSE- values.
IV. SUMMARY AND CONCLUSIONS In this paper I have attempted to predict Kovats indices of two sets of substituted phenols from nonempirical structural descriptors using counter-propagation neural networks. For the 20-phenol data set, using networks containing one hidden layer PE for each phenol, I was able to achieve very small RMSE values (ranging from 6.0 to 16.3) for training sets and relatively good RMSE values (ranging from 77.5 to 207.3) for test sets. The network training and test set results are significantly better than corresponding linear regression results. We were able to improve on these one PE per phenol results by using networks containing fewer hidden layer PE's than there were phenols. This attempts to force the network to recognize statistical trends of the entire data set, rather than focusing on each input vector of the data set individually. For SE-30 the smallest RMSE values were obtained for networks containing 17 PE's in the hidden layer; the training set had an RMSE of 8.7 while the test set had an RMSE of 64.1. A network containg 10 hidden layer PE's performed nearly as well on the test sets giving an RMSE of 68.0, although the training set performance was worse having an RMSE of 70.3. For both OV-225 and NGA, networks containing 10 hidden layer PE's gave the best results. The test set RMSE values were 154.6 and 161.1 for OV-225 and NGA, respectively, while the training set RMSE values were 158.7 and 159.1, respectively. These 10-PE test set results are considerably better than both the regression results and the network results which utilized one hidden layer P E for each phenol. The corre-
sponding training set results are worse than the one hidden P E per phenol case. These training set RMSE values are, however, nearly equal to those for test sets, perhaps indicating that these networks are more robust and that they are more successful in learning statistical trends of the data. For the 43-phenol data set, using networks containing one hidden layer P E for each phenol, I was able to achieve very small RMSE values (ranging from 14.3 to 16.1) for training sets and relatively good RMSE values (ranging from 118.7 to 121.4) for test sets. The network training results are significantly better than corresponding linear regression results although the test set results are worse. I was unable to improve on these one PE per phenol results by using networks containing fewer hidden layer PES than there were phenols. Training set RMSE values steadily increased as the number of hidden layer PES decreased. However, I found that the test set RMSE values also steadily increased as the number of hidden layer PES decreased. The best training and test set RMSEs occurred for the one P E per phenol networks.
REFERENCES (1) Kaliszan, Roman. Quantntltive Structure-Chromatcgraphk Retention Relatbnshlps; Wlley: New York, 1987. (2) Elrod, D. W.; Magglora, G. M.; Trenary. R. G. J . Chem. Inf. Comput. Sci. 1000. 30, 477. (3) Aoyama, T.; Suzukl, Y.; Ichikawa, H. J . Med. Chem. 1000, 33, 2583. (4) Maren, A., Harston, C., Pap. R., Eds. Handbook of Neural Computing Appllcarbns; Academic Press: San Dlego, 1990; Chapter 3. (5) Rumelhart, D. E., McClelland, J. L., Eds. Parallel DlsMbuted Processing; MIT Press: Cambridge, MA, 1987. (6) McCielland, J. L.; Rumelhart, D. E. Expbratbns in Parallel Distrlbuted Processirg; MIT Press: Cambridge, MA, 1988. (7) Slmpson, P. K. Artificial Neural Systems; Pergamon Press: New Ywk, 1990. (8) Caudill. M.; Butler, C. Naturally Intelligent Systems; MIT Press: Cambridge. MA, 1990. (9) Kllmasauskas. C. C.; Guhrer, J. P. NeuralWorks" Networks I and I I ; Neuralware, Inc.: Pittsburgh, PA, 1988. (10) HechtNielsen, R. Proceedlngs of the Instnote of ElecMcaland Electronics Engineers Fhst Intematbnal Conference on Neural Networks ; IEEE: New York. 1987; Vol. 2, pp 19-32. Hecht-Nlelsen, R. Appi. Opt. 1987, 2 6 . 4979. Hecht-Nielsen, R. Neural Netwoks 1988, 1 , 131. (1 1) Kohonen, T. In PToceedings of the 2nd Scandlnavian Conference on Image Analysis; Ob, E., Slmula, O., Eds.; Espo: Suomen Hahmontunnlstustvtklmuksen Seuro. 1981. (12) Kallszan, R.; Holtje, H A . J . Chromatogr. 1082, 234, 303. (13) Gorman, P. R.; Sejnowski, T. J. Neural Networks 1088, 1 , 75. (14) Toussaint, G. T. IEEE Trans. Inf. Theory 1074, I T - 2 0 , 472.
RECENEDfor review July 8,1991. Accepted November 6,1991.
pH Gradient Capillary Zone Electrophoresis Using a Solvent Program Delivery System Takao Tsuda Department of Applied Chemistry, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466,Japan
An apparatus is proposed that Is applicable to a general gradient In caplllary zone electrophoresls. I t conslsts of a program delivery system and a *In system. from the so'vent program The -la system is consistentb passed both for the ca@liary column, the volume Of which is lust 0.2 mL. The average PH along the capillary column IS estlmated from the Current. A Period of 1-6 mln 1s necessary to go from the PH In the column to the PH in the reservoir. The effects of gradient curve selectlon, gradlent duration period, and exchange Of medla at both reservoirs are discussed. Typlcai examples of pH gradlent are demonstrated.
INTRODUCTION A dynamic gradient of running medium in capillary zone electrophoresis and micellar electrokinetic capillary chromatography will extend the scope of its separation power, as did pH gradient in liquid chromatography. There will be many modes in dynamic gradient, such as pH, concentration of salt, aqueous-organic medium, and thermal gradients. In capillary zone electrophoresis, separation is based on the mobility of a solute. Therefore, any gradient mode, which affects the mobility, is useful. There are not many works concerning the dynamics of gradients of medium in capillary zone electrophoresis and micellar electrokinetic capillary chromatogra-
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Figure 1. Schematic diagram of the program gradient system for capillary electrophoresis: (1) solvent program delivery system; (2) three-way connector; (3) rotary injector; (4, 4' and 4") fused-silica capillary tubing (100 pm i.d.; lengths 0.7, 1.3, and 2 m, respectively); (5) interface for split injection; (6) capillary column; (7) three-way polyethylene connector (2 mm i.d.) used as reservoir; (8) electrode; (9) power supply; (10) 1OkQ resistance; (1 1) recording of current; (12) UV detector. phy.'* SustiEek et al.3used a modifying electrolyte. It was continuously poured dropwise from the upward pump outlet into the reservoir of the inlet side of the capillary column by using a pump, following the generation of the pH gradient. The pump outlet was separated from the reservoir to avoid contact with the high voltage. Using this simple device, they demonstrate the effect of pH gradient from pH 3.5 to pH 2.2 for the separation of a mixture of purine and pyrimidine derivatives. Balchunas and Sepaniak4 used a stepwise direct addition of 2-propanol to the reservoir of the inlet side of the capillary column in micellar electrokinetic chromatography. To avoid injury to the operator, they interrupted the applied voltage during the addition process of 2-propanol.4 BoEek et al.1~2~6 generated pH gradient by feeding the capillary with two different suitable ionic species from two separate electrode chambers via a three-way joint by simultaneous electromigration. In the present work, a new general gradient system is described that is applied for any gradient mode. This new system is based on the analogous method that has been adopted in liquid chromatography.
EXPERIMENTAL SECTION Apparatus. A schematic diagram of the apparatus used is shown in Figure 1. The apparatus consista of three main parte, namely, a supply system for the running medium, a splibinjection system, and a separation system of capillary zone electrophoresis. The running medium is supplied from a solvent program delivery system (Model660 solvent programmer,Model M-45 and M-600A solvent delivery system, Waters Associates, Inc., Milford, MA). The specified curve number (n)for gradient solvent composition of x is given as the following equation: percent of x = I(c) + (F(c) - I(c))(t/T)" where I(c), F(c), T,and t are initial condition, final condition, sweep time and elapsed time, respectively. The solvent delivery system was orginally made for a gradient system in a conventional liquid chromatograph. The running medium is supplied from the solvent program delivery system into three-way polyethylene connectors (2 mm i.d., inner volume 0.2 mL) (7 in Figure l),which served as reservoirs. The split-injection system consisted of a rotary injector with a 5-rL loop (Model No. 7030, Rheodyne, Cotati, CA), a home-built interface, and a long fused-silicacapiUary between the interface and the rotary injector?v8 The running medium is pumped through the rotary injector and then to the interface. The sample in the loop is carried into the interface by the pressurized flow of the running medium, and a portion of the sample is injected into the capillary column due to their
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Flgure 2. Relation between pH and current. Conditions: applied voltage, 12 kV; capillary column, 100 pm i.d. and 65 cm long; medlum, 5 mM phosphate buffer. mobilities and the electroosmosis generated in the capillary column. The split-injection system for capillary electrophoresis is described in detail in a separate report? Fused-silica capillaries (Polymicro,Phoenix, Arizona) are used for the analytical column (6in Figure 1)and the connections (4, 4', and 4" in Figure 1)between the reservoir and the rotary injector and between the reservoir and the solvent delivery system. The rotary injector and three-way stainless-steel connector were grounded. pH Measurement. We use 5 mhl phosphate buffer containing 5% ethylene glycol as the running medium. As the phosphate buffer is a mixture of Na2HP04and NaH2PO4, the medium in the region of alkali pH includes more Na2HPOl than NaH2P04, and the medium in the acid region contains NaH2PO4 as a major component. As Na2HP04is more ionized than NaH2P04in aqueous solution, the medium in the alkali region is more conductive than that in the acid region. Therefore, current passed through the capillary column is a good indicator of the pH of the medium in the column. The relation between pH and current is shown in Figure 2. Using this calibration curve,one determines the average pH in the whole column. The pH of the running medium in the reservoir is measured by collecting the solution overflowing from the reservoir at the end of the analytical column. Then ita pH is measured using a pH meter (digital ionizer 501, Orion Research, Cambridge, MA). Other instruments are the same as those in refs 7 and 8. Operation. Mixtures of 5 mM disodium monohydrogen posphate (A) and 5 mM sodium dihydrogen phosphate (B)are used as the running medium. In both mediums 5% ethylene glycol is always added for decreasing the surface tension between the medium and the inner glass wall of the capillary column. The gradient modes generated by mixing different ratios of A and B are selected by the gradient curve number of Water's solvent programmer. After the analytical capillary column is filled with phosphate buffer, Water's gradient curve number 2 or 10 is selected, and the pump system is started at the initial position for conditioning the whole system. High voltage, 12 kV, is applied to the capillary column (100pm i.d., 65 cm long) for all experiments. The length between the inlet of the capillary column and detector is 50 cm. Constant current is achieved generally within 20 min. Then the sample is injected using the split-injection system without interrupting the applied voltage. A t the same time, the solvent programmer has been started at a flow rate of 0.2-0.5 mL/min.
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Flgure 4. Variations of current curves due to pH gradient at one or both reservoirs. Conditions: pH gradient, beginning from 90% 5 mM Na,HPO, (A) and 10% 5 mM NaH,PO, (B) to 10% A and 90% B; gradient curve No. 2 for 1 and 2, and No. 10 for 3 and 4; duration period of gradient, 4 min.
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In most experiments, a flow rate of 0.4 mL/min is used. The responses of a detector (UV, 254 nm) and current are recorded by two strip chart recorders. One of the recorders is used for simultaneousrecording of current and UV response.
RESULTS AND DISCUSSION Phosphate buffer contains many ions, such as OH-, HPO:-, H2P0,, Na+, and H+. Under applied voltage, they move with their mobilities, u(mob), and electroosmotic flow, u(osm), generated in the capillary column. As in this experiment positive voltage is applied at the injection side, and electroosmosis moves toward the negative electrode, that is, to the outlet of the capillary column. Reservoirs at the positive and negative electrodes are abbreviated as E, and E,, respectively. Under applied voltage, anions and cations are moving toward E, and E,, respectively. When some anions have high enough mobilities, u(mob)a, they migrate from E, and reach E pagainst the flow of electrosmosis. Their apparent velocities are -(u(mob)a - u(osm)). Most anions, which have less arbitrary mobility than u(osm), move toward E, with the velocity of (-v(mob)a + u(osm)). The mobilities of H+and OH- are 362 and 205 X cm2/(V.s),respectively, and most other ions are generally less than 70 X ~ m ~ / ( V . s When ).~ a positive electrovoltage is applied at the injection side of the capillary column, the hydrogen ions and hydroxy ions are forced into the capillary column at the column inlet and outlet, respectively. Therefore, in the initial stage of development after applied voltage, weak acidic and weak alkaline zones
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Flgure 8. Time k g for pH in the capillary column up to that of the reservoirs. I and M indicate pHs being estimated from current and measured with a pH meter, respectively. Duration period of the gradient is 1 min for b and 4 min for ail others. Gradient curve No. 10 is used for a, b, and c', and curve No. 2 for a' and c. The gradient in Figure 6A is from 100% Na,HPO, (A) to 10% A and 90% NaH2P04 (e),and in Flgure 6B from 10% A and 90% B to 100% A.
compared to the original pH in the column medium would be formed a t the inlet and outlet end parts of the capillary column, respectively. The behavior of the hydrogen ion in isotachophoresis has been discussed by BoEek et al.1° The local pH at a certain position in the capillary column is dependent on the local concentration of HP042-,H2P04-, and Na+. The "average" pH of the capillary column means pH derived from the summed phenomena in the capillary column. If we use the same concentration of phosphate buffer over the range of pH used, the current under a constant voltage is dependent on the pH, as shown in Figure 2. In acidic solution the current is lower compared to the alkaline solution due to the weak dissociation coefficients of phosphates. The current would be a good indicator of average pH along the whole capillary column, although the local pH is somehow deviated from the average pH of the capillary column. Previously,workers1+' focused on the gradient of one of the reservoirs. We examined the effect of the gradient of two
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T I M E (min) Flgure 7. Comparisons between isocratic and pH gradient electropherograms. (A) Electropherogram 0 1 is obtained by pH gradient curve No. 1 0 gradlent from 100% Na2HP0, (A) to 10% A and 90% NaH2PO4. Isocratic electropherograms a-d: the percentages of A In 5 mM phosphate buffer for a-d are 100, 90, 80, and 70%, respecthrely. Samples are the mlxture of quinlne (I), 5-bromouracil (2), dansylated L-serine (3)and dansylated L-cystelc acid (4). (B) Electropherogram 0 2 : pH gradlent from 100% NaH,P04 to 100% Na2HP0,. Isocratic electropherogram e: media 100% of 5 mM Na2HP0,. Other conditions are the same as in Flgure 7A.
reservoirs at both ends of capillary column. Current curves due to the gradient at one or both reservoirs are shown in Figure 4. Curves 1 and 3 are obtained by the gradient at both reservoirs, and curvea 2 and 4 a t one reservoir at the injection side of the capillary column. The former experimental condition generates faster pH variation compared to the latter. The same phenomenon is also observed in the gradient from acid to aklali solution. Therefore, it is clear that the medium in the reservoir of the column outlet contributes to the variation of the average pH in the capillary column. Namely, some anions can migrate into the capillary column. The time lag of pH change in the column after the change of the running medium in the reservoir was also studied. Figure 5 shows the variation of current after the solvent program delivery system is switched to step 10% different runningmedium, for example from 70% to 60% of component Na2HP04in the medium. In our system the change in the mixing ratio of Na2HP04and NaH2P04in the solvent gradient system reaches the reservoir after 30-40 s. If the medium
could be carried just with electroosmotic flow, it takes about 3.2-4.0min from column inlet to detector and about 4.1-5.2 min for the total capillary column length. From Figure 5, current variation starts after 30-40 s and ends after 8-10 min in most casea. That is, current becomes nearly steady at twice the period due to electroosmotic flow only. The duration of the pH gradient contributes to the time lag for following the pH change in the reservoirs, shown in Figure 6. The ward of duration means the time period from the beginning to the end of the gradient operation. After the gradient reaches the end of the curve, the isocratic medium is followed. In Figure 6, I indicates that the pH is estimated from the current using Figure 2,and M means that the pH is obtained by measuring the running medium at the E, reservoir. The duration periods for a and b in Figure 6 with gradient curve No. 10 are 4 and 1 min, respectively. The short duration period, b, causes more rapid change on the pH in the column as compared to a One can see the difference due to the gradient curve patterns in Figure 6. As with curve 2
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the initial variation rate is very remarkable, the variation of the I-curve comes with less of a time lag compared to those with curve No. 10. It is understandable because the initial increase rate of the second component is sharper in the case of curve No. 2 compared to that in No. 10. There are some time lags between the curves of the M- and I-groups. A t the maximum about 4 min in Figure 6A is necessary for change, and 6 min in Figure 6B. For separation using the pH gradient, rapid variation of the pH gradient in the capillary column is preferred. Therefore, one must select an appropriate gradient curve number and a duration period for the pH gradient. The difference period between Figure 6A,B for changes in the curves might be due to the buffering action of the phosphate buffer used. Therefore one must be careful in selecting the medium. The medium having no buffering action is the best selection for pH gradient. But in some cases a separation problem of a complex mixture with such a medium in capillary zone electrophoresis may be encountered. The average pH estimated from current is based on the summed phenomena in the column. From average pH one can suppose the pH change along the column generated by the present method. As just the average pH in the column is known, it is better to get the local pH in the column. For further attempts a more direct way will be needed to measure the local pH. For the measurement of local zone development in isotachophoresis, Hirokawa et al." devised a scanningdetector system in which a UV detector is scanned along the column. Their device might be adapted to measurement of true pH variation in capillary zone electrophoresis. Electropherograms a-d in Figure 7 are obtained with different mixing percentage of Na2HP04in 5 mM phosphate buffer. The elution times of the four solutes are dependent on the mixing percentage. The elution order of dansylated L-serine and 5-bromouracil has been changed between 100 and 70% of Na2HP04in phosphate buffer. The elution times of all solutes become larger in acidic media compared to those in alkali media. Two electropherogramswith pH gradient are shown at G-1 and G-2 in Figure 7. As in the pH gradient electropherogram
of G-1, the elution time of dansylated L-serine is later than 5-bromouracil, and it is clear that some pH gradient is generated in the capillary column from the comparative study of electropherograms a-c and G-1. The solutes of aliphatic hydrocarbons with temperature programming in gas chromatographyare eluted generally with a regular time period between every two peaks; that is, the time period between two peaks of Cnfl and C, is always the same in a wide range (C, means the number of carbon atoms in the aliphatic hydrocarbon). The same pattern is obtained by pH gradient in capillary zone electrophoresis. One of the typical examples is shown at G-2 in Figure 7 . Although these solutes are not homologous, one can observe regular time periods between two peaks in the pH gradient electropherogram of G-2.
ACKNOWLEDGMENT I thank deeply Richard N. Zare and Kinio Doi for their very helpful discussions and John B. St. John for his technical assistance. Part of this paper was presented at the 15th International Symposium on Column Liquid Chromatography, June 3-7, 1991, Basel. REFERENCES BoEek. P.; Deml. M.; Pospkhal, J.; Sudor, J. J. Chromatogr. 1989, 470, 309-312. Pospichal, J.; Deml, M.; Gebauer, P.; BoEek, P. J. Chromatcgr. 1889, 470. 43-55. SustBEek, V.; Foret, F.; BoEek, P. J. Chromatogr. 1989, 480, 271-276. Balchunas, A. T.; Sepaniak, M. Anal. Chem. 1988. 6 0 , 617-621. Foret, F.; Fanall, S.; BoEek, P. J. Chromatogr. 1990, 516, 219-222. Sudor, J.; Stransky, Z.; Pospkhal, J.; Deml, M.; BoEek, P. Nectrophoresis 1989, 10, 802-605. Tsuda, T.; Sweedler. J. V.; Zare, R. N. Anal. Chem. 1990, 62, 2149-2 152. Tsuda, T.; Zare, R. N. J. Chromatcgr. submitted for publication. Everaerts, E. M.; Beckers, J. L.; Verheggen, Th. P. E. M. Isotachophoresis ; Journal of Chromatography Library; Elservler: Amsterdam, 1976; Vol. 6. BoEek, P.; Gebauer, P.; Deml, M. J. Chromatcgr. 1981, 219, 21-28. Hirokawa, T.; Yokota, Y.; Kiso, Y. J. Chromatogr. 1991, 538, 403411; 545, 267-261.
RECEIVED for review August 1,1991. Accepted November 13, 1991.
Effects of Analyte Velocity Modulation on the Electroosmotic Flow in Capillary Electrophoresis Tshenge Demana, Urmi Guhathakurta, and Michael D. Morris* University of Michigan, Department of Chemistry, Ann Arbor, Michigan 48109-1055 Modulation of the electroosmotlc flow In capillary zone electrophoresls by modulatlon of the drlvlng voltage gives rlse to a flow proflle that changes between lamlnar and flat profiles. The changlng flow profile Induces a radial movement of Sample specles to and from the capillary surface. The Induced sample concentration gradlent can be monitored by carefully problng the capillary surface. The resuitlng slgnal Is a derlvative of the normal-shaped peak. Derlvatlve-shaped peaks can be observed wlth catlons, but not with anlons. Anions are unable to approach the doublelayer reglon and therefore are unaffected by the modulatlon process.
INTRODUCTION Modern capillary electrophoresis (CE), introduced first in 1979 by Mikkers' and then Jorgenson? is a powerful analytical
technique for the separation of charged specie^.^-^ The advantages of short analysis times, high resolution, and low buffer and sample consumption continue to generate great interest in the application of CE to bioseparati~ns.~-~ Capillaries of less than 100 pm i.d. are used in order to eliminate convection. The tiny column volumes are ideal for the separation of nanoliter samples. However, the ultrasmd samples pose a severe challenge to detector d e ~ i g n . ~ The nanoliter samples of capillary electrophoresis make the concentrationdetection limits of most detectors relatively high. Laser fluorometry1°and perhaps on-line voltammetry'l are the major exceptions. However few compounds fluoresce12 or are electrochemically active without prior derivatization. Thus, it is worthwhile to consider improving the performance of CE detectors which are not operating at fundamental shot noise limits. Analyte velocity modulation13J4was developed
0003-2700/92/0364-0390$03.00/00 1992 American Chemical Society
