Extraction of Mass Spectra and Chromatographic Profiles from

In this study, an adaptive immune algorithm (AIA) was proposed, in which the ... The proposed AIA approach was used to resolve the overlapping GC/MS s...
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Anal. Chem. 2004, 76, 5143-5148

Extraction of Mass Spectra and Chromatographic Profiles from Overlapping GC/MS Signal with Background Xueguang Shao,* Guoqing Wang, Sufang Wang, and Qingde Su

Department of Chemistry, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China

An adaptive immune algorithm (AIA) was proposed for resolution of the overlapping GC/MS signal with background. By using AIA, the chromatographic profiles corresponding to the independent components (ICs) in the overlapping signal are calculated with the mass spectra extracted by means of independent component analysis (ICA). The number of the ICs in the overlapping signal is determined by the difference between the reconstructed and the original data. Both simulated and experimental data are investigated with the proposed AIA approach. It was found that the mass spectra and chromatographic profiles of the components in an overlapping multicomponent GC/MS signal can be accurately resolved with the existence of background, and the results are better than that by using an interactive self-modeling mixture analysis (SIMPLISMA) method. The AIA approach may be a promising tool for the resolution of overlapping GC/MS signal. With the increasing applications of GC/MS to complex mixture analysis and component identification in various areas, it has become an important task to isolate and identify the components in overlapping chromatographic peaks. For complex samples, incomplete GC separation is unavoidable. If the GC is in tandem with a mass spectrometric detector (MSD), the detected mass spectra are the combinations of more than one component. The detected signal may be generated by the inseparable components under the GC conditions, the column bleed background, the GC septum, etc.1,2 To resolve the overlapping chromatographic data, a number of methods have been proposed, such as chemical factor analysis (CFA),2-7 interactive self-modeling mixture analysis method (SIMPLISMA),8,9 wavelet transform (WT)-based techniques,10-12 * To whom correspondence should be addressed. Tel.: +86-551-3606160. Fax: +86-551-3601592. E-mail: [email protected]. (1) Davis, J. M.; Giddings, J. C. Anal. Chem. 1983, 55, 418-424. (2) Gemperline, P. J. J. Chem. Inf. Comput. Sci. 1984, 24, 206-212. (3) Maeder, M. Anal. Chem. 1987, 59, 527-530. (4) Schostack, K. J.; Malinowski, E. R. Chemom. Intell. Lab. Syst. 1993, 20, 173-182. (5) Manne, R.; Shen, H.; Liang, Y. Chemom. Intell. Lab. Syst. 1999, 45, 171176. (6) Kvalheim, O. M.; Liang, Y. Z. Anal. Chem. 1992, 64, 936-946. (7) Shao, X. G.; Cai, W. S. J. Chemom. 1998, 12, 85-93. (8) Windig, W. Chemom. Intell. Lab. Syst. 1997, 36, 3-16. (9) Sa´nchez, F. C.; Massart, D. L. Anal. Chim. Acta 1994, 298, 331-339. 10.1021/ac035521u CCC: $27.50 Published on Web 07/23/2004

© 2004 American Chemical Society

and immune algorithm (IA).13-16 Besides the resolution of the chromatographic profiles, the spectral information can be extracted from the overlapping spectral signal by using CFA and SIMPLISMA methods. However, it is often not easy to interpret the relationship between the statistic results and the physical meaning of the mixtures in CFA. For the SIMPLISMA method, the pure variable may not really exist, and in some cases, determination of pure variables maybe interfered by the backgrounds. Other curve-fitting techniques,17 e.g., the Fourier selfdeconvolution method, Fourier derivation method, and maximum likelihood restoration (MLR) method, are also able to resolve overlapping spectra, but these techniques need optimization of the parameters in the models, which is generally a difficulty task. The WT-based techniques and IA have a strong ability for resolution of the seriously overlapping analytical signal, but the standard information (spectral or concentration information obtained from the measurement of the reference substances or theoretical simulations) must be provided. In resolution of the overlapping HPLC signal, the standard information can be obtained from measurement of the reference substances or theoretical simulations. However, it is very difficult to obtain the standard information in the GC separation of a real complex sample. Therefore, it is very important to retrieve the standard information directly from the measured overlapping signal. As a newly developed statistical approach, independent component analysis (ICA) can be used to separate independent components (ICs) from the measured overlapping signal.18 Since it was developed in the 1990s, ICA has been used in many different applications, e.g., medical signal analysis,19 sound separation,20 image processing,21 dimension reduction,22 fault detection,23 (10) Shao, X. G.; Leung, A. K. M.; Cau, F. T. Acc. Chem. Res. 2003, 36, 276283. (11) Shao, X. G.; Cai, W. S.; Sun, P. Y.; Zhang, M. S.; Zhao, G. W. Anal. Chem. 1997, 69, 1722-1725. (12) Shao, X. G.; Ma, C. X. Anal. Lett. 2003, 36, 1261-1277. (13) Shao, X. G.; Yu, Z. L.; Sun, L. TrAC, Trends Anal. Chem. 2003, 22, 59-69. (14) Sun, L.; Cai, W. S.; Shao, X. G. Fresenius J. Anal. Chem. 2001, 37, 16-21. (15) Shao, X. G.; Sun, L. Anal. Lett. 2002, 35, 2375-2387. (16) Shao, X. G.; Yu, Z. L.; Sun, L. Spectrochim. Acta, A 2003, 59, 1075-1082. (17) Richard, S. J.; Peter, R. G. Anal. Chem. 1991, 63, 2557-2763. (18) Comon, P. Signal Processing 1994, 36, 287-314. (19) Vigrio, R. N. Clin. Neurophysiol. 1997, 103, 395-404. (20) Brown, G. D.; Yamada, S.; Sejnowski, T. J. Trends Neurosci. 2001, 24, 5463. (21) Makeig, S.; Westerfield, M.; Jung, T. P.; Enghoff, S.; Townsend, J.; Courchesne, E.; Sejnowski, T. J. Science 2002, 295, 690-694. (22) Wersing, H.; Korner, E. Neural. Comput. 2003, 15, 1559-1588.

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statistical process monitoring,24 and near-infrared spectral data analysis.25 In this study, an adaptive immune algorithm (AIA) was proposed, in which the spectral information of the ICs is directly extracted from the measured overlapping signal by means of ICA, and then by using an IA, the chromatographic profiles of the ICs are calculated by the immune operation.13-16 The number of the ICs is determined by the differences between the reconstructed and the original data. The proposed AIA approach was used to resolve the overlapping GC/MS signal in the analysis of the pyrolysates of DL-β-phenylalanine. In the total ion current curve (TIC) of the pyrolysates, large amounts of the signal of the components, including the polycyclic aromatic hydrocarbons, are overlapping. Results show that the mass spectra and the chromatographic profiles of the components in the overlapping signal, including that of the background, are successfully resolved by the AIA approach. Moreover, one component that is hard to find by the conventional method was identified by using the resolved chromatographic profiles and the mass spectra. Compared with the results by a SIMPLISMA method, it is shown that the resolution by using the proposed AIA approach is better for both the simulated data and the experimental data, especially for the resolved information of the background. THEORY AND ALGORITHM Immune Algorithm. An overlapping signal can be described as the linear combination of the standard signal (signal of the reference substance with known concentration) of every component, i.e., d

V)

∑

zero, each element of T is defined as Ti ) V0i/〈V0i,V0i〉 (i ) 1,2,...,d), and 〈,〉 denotes the inner product or projection. When dc(k) approaches to zero in the above iterations, VF will be the information of the components in the overlapping signal, and ci (i ) 1, 2, ..., d) will be the concentration of the ith component at the retention time. Therefore, the mass spectrum of the ith component at this retention time can be calculated, and the chromatographic profiles of the components can also be obtained by the calculation at each retention time, respectively. With the given V0i, the intensity information of the corresponding components can be accurately resolved by the IA.13-16 However, it is difficult to obtain the standard information of the components in the GC separation of the complex samples. Therefore, ICA was used to adaptively extract the MS information of the components directly from the overlapping GC/MS signal. Independent Component Analysis. ICA is a well-established statistical signal processing technique that aims at decomposing a set of multivariate signals into a base of statistically independent components with the minimal loss of information content.18,26-28 Statistically, the variables x1 and x2 are said to be independent if none of them carry any information about the other; i.e., information on x1 dose not give any information on x2 and vice visa. In a mass spectrum, the different m/z positions can be regarded as different independent variables, and the intensities correspond to the magnitudes of the variables. In terms of the statistic theory, x1 and x2 are independent if their joint probability density p(x1,x2) is the factorial of their marginal probability density p(x1) and p(x2), i.e.,

d

Vi )

i)1

∑c V

i 0i

(1)

where V represents the overlapping signal (in this study, it represents the overlapping MS signal at each retention time), d is the number of components in the overlapping signal, and Vi, V0i, and ci are the measured MS signal, the standard signal, and the concentration in the mixture of the ith component in the overlapping signal, respectively. If V0i (i ) 1, 2, ..., d) is given, the concentration information of the components in the overlapping signal can be obtained by the following operations:13-16 - 1) dc(k) ) 〈(V - V (k ),T〉 F

(2)

c(k) ) c(k - 1) + dc(k)

(3)

d

V (k) F )

p(x1,x2) ) p(x1)p(x2)

(5)

i)1

∑c

(k) i V0i

(4)

In terms of information entropy, statistical independence between x1 and x2 is equivalent to the situation of maximum joint entropy H(x1,x2) between the two variables, or the minimum mutual information I(x1,x2) that x1 and x2 carry about each other, because

H(x1,x2) ) H(x1) + H(x2) - I(x1,x2)

(6)

Assume that there are m observations X ) [x1,x2, ‚‚‚ ,xm]T of d independent source signals S ) [s1,s2, ‚‚‚,sd]T. For the observation of a GC/MS measurement, m represents the scan number, and d represents the number of components with different mass spectra (source signals) contained in the overlapping signal (observations). A generalized model can be represented as

X ) AST

(7)

i)1

where k is the number of iterations, VF represents the “eliminated” (extracted) information of the components and its initial value is (23) Kano, M.; Tanaka, S.; Hasebe, S.; Hashimoto, I.; Ohno, H. AIChE J. 2003, 49, 969-976. (24) Lee, J. M.; Yoo, C.; Lee, I. B. J. Chem. Eng. Jpn. 2003, 36, 563-577. (25) Chen, J.; Wang, X. Z. J. Chem. Inf. Comput. Sci. 2001, 41, 992-1001.

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where A is a matrix describing the mixing system from S to X. The goal of the ICA is to estimate the mixing matrix A and the independent source S from the observed signal X. This goal is (26) Hyva¨rinen, A. IEEE Signal Proc. Lett. 1999, 6, 145-175. (27) Bell, A.; Sejnowski, T. J. Neural Comput. 1995, 7, 1129-1159. (28) Cardoso, J. F.; Souloumiac, A. Proc. Inst. Electr. Eng. F 1993, 40, 362370.

principal components are used as the starting ICs in the calculation, which can accelerate the convergence of the optimization procedure. 3. Resolution of the Chromatographic Profiles of the ICs. The chromatographic profiles (C ˆ ) [cˆ1,cˆ2,...,cˆm]T) of the ICs are resolved by the immune operation with the spectral information extracted from the overlapping signal in step 2. 4. Calculation of the Difference of the Reconstructed and the Original Data. The reconstructed data Xrec can be calculated by,

ˆ Sˆ T Xrec ) C

Figure 1. Simulated overlapping chromatogram (TIC). 1-5 denote the four simulated components and background, respectively; 6 denotes the overlapping chromatogram (TIC).

The RRSSQ is used to express the differences,

RRSSQ )

(8)

where Sˆ is the estimation of the S. When W is an inverse of the mixing matrix A, the estimated source signal should equal the original source signal S, because

Sˆ T ) WX ) WAST ) ST

(9)

Therefore, the main task of ICA is to find out the separating matrix W based on the principle that the output Sˆ becomes as independent as possible. Thus, the task turns into an optimization problem under the constraints of independency, which is generally reflected by nonGaussianity. Several approaches have been proposed to achieve this task, such as the FastICA,26 Infomax,27 and JADE (joint approximate diagonalization of eigenmatrixes).28 In this study, the Infomax was used for the calculations. The source signals are the mass spectra of the components in the overlapping GC/MS signal, the observed signal is the measured GC/MS data matrix, and the output of the ICA, i.e., the estimated source signals, will be the extracted mass spectra of the components in the overlapping GC/MS signal, which will be used as the standard spectra (antibody) in our AIA algorithm. Adaptive Immune Algorithm. The AIA is an unsupervised algorithm, the standard information (mass spectra) and the intensity profiles (chromatographic profiles) of the ICs will be adaptively calculated from multicomponent overlapping data matrix, and the number of the ICs will be determined when the relative root of sum of square differences (RRSSQ) approaches to a minimum value.29 The following steps are included: 1. Input of the Overlapping Signal and Set the Initial Number of the ICs. Input the overlapping signal X to the algorithm, and the initial number of ICs in the overlapping signal is set to one (d ) 1). 2. Resolution of the Spectral Information from the Overlapping Signal. By maximizing the likelihood of the ICs in the overlapping signal, the spectral information of the ICs is achieved. The (29) Windig, W.; Antalek, B.; Lippert, J. L.; Batonneau, Y.; Bremard, C. Anal. Chem. 2002, 74, 1371-1379.

x

m

n

∑∑(x

equivalent to find a separating (unmixing) matrix W that satisfies

Sˆ T ) WX

(10)

ij

2 - x rec ij )

i)1 j)1

m

(11)

n

∑ ∑x

2 ij

i)1 j)1

rec where xij and x rec ij are the elements of X and X , respectively. The original data X and the reconstructed data Xrec should be very similar and the RRSSQ value should be minimum when the proper number of ICs is determined. 5. Determination of IC Number or Output of the Resolution Results. If the proper number of ICs is reached, the spectral information and the chromatographic profiles of the ICs, which correspond to the components in the overlapping signal, can be obtained, the process will end and output the resolution results. Otherwise, increase the number of ICs (d ) d + 1) and circulate the process (goto step 2).

EXPERIMENTAL SECTION Data Simulation. The EMG equation30 was adopted to simulate the GC peaks.

V(t) )

(

)

As0 σg2 t - tg exp 2 τ τ 2τ

( )

1 - x2 exp dx (12) -∞ 2 x2π

∫

Z

where t is the retention time, As0 is the area of the peak with A being a coefficient and s0 being the standard information of the component, tg determines the position of the peak on retention time axis, τ is the time constant of the exponential decay, σg controls the tailing of the peak, the ratio τ/σg is a measure of its asymmetry, and Z ) [(t - tg)/σg] - (σg/τ). The parameters used in the simulation for the four peaks are 700, 180, 200, and 400 for A, 38.526, 38.600, 38.649, and 338.763 (min) for tg, 0.0172, 0.0172, 0.0172, and 0.0172 for τ, and 0.0189, 0.0189, 0.0189, 0.0189 for σg, respectively. The chromatographic background is supposed to be nearly constant during the whole retention time range (38.404-38.901 min, 62 sampling points). Figure 1 shows the simulated chromatogram (TIC) of the four components and the background with 10% random noise. The simulated mass spectra (relative (30) Foley, J. P. Anal. Chem. 1987, 59, 1984-1987.

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Figure 2. Mass spectra used in the simulation.

Figure 4. RRSSQ versus the number of the ICs used in AIA for the simulated data.

Figure 3. TIC of the pyrolysates of phenylalanine and the studied overlapping range.

Figure 5. Resolved mass spectra of the simulated overlapping signal.

abundance) used for the simulation are shown in Figure 2 and denoted as a-e, respectively. By multiplying the two matrices of the simulated chromatography and mass spectra, the GC/MS data matrix will be obtained. Experimental Information. DL-β-Phenylalanine (99% purity, Kangda Amino Acid Factory, Shanghai, China) was pyrolyzed by using a SGE microfurnace pyrojector (II). The pyrojector was directly interfaced to an HP 6890 gas chromatograph equipped with a HP 5973 MSD. HP-5MS capillary column (50 m × 0.20 mm i.d., 0.33-µm film thickness). The carrier gas was helium with a flow rate of 1.0 mL/min (constant pressure, 30.00 psi), and the split rate was 1/50. The temperatures of the GC injector and the MSD were controlled at 300 and 230 °C, respectively. The electron impact ionization was tuned at 70 eV. The mass range for the MS detection was 25-400 amu. The program temperature was used; i.e., the GC oven was set to 50 °C for the first 5 min, then heated with a rate of 5 °C/min up to 280 °C, and held for 30 min. Figure 3 shows the chromatogram (TIC) of the pyrolysates. The studied overlapping chromatogram was enlarged and shown in right top of the figure. The measured overlapping signal from 38.404 to 38.901 min was exported by Tools/Export 3-D Data provided in the Agilent GC/MS ChemStation and saved to a file in ASCII format (62 by 250 data matrix). Each row of the data matrix consists of an overlapping mass spectrum at a retention time. The precision of the raw measured data is 0.1 amu; however, the m/z values in the exported data are rounded to the nearest integer mass. Therefore, the precision of the extracted mass spectra and the standard mass spectra in the NIST MS library are both 1 amu. 5146 Analytical Chemistry, Vol. 76, No. 17, September 1, 2004

For comparison or validation of the resolution results, phenanthrene (99% purity, Aldrich Chemical Co., Inc. Milwaukee, WI) and anthracene (99% purity, Acros Organics) were also analyzed by using the same GC/MS conditions. Retention times for phenanthrene and anthracene are 38.534 and 38.570 min, respectively. RESULTS AND DISCUSSION Resolution of the Simulated Data. At first the number of ICs in the overlapping signal was determined by the criterion RRSSQ between the reconstructed and the original simulated data. Figure 4 shows the variation of RRSSQ versus the number of the ICs (d) used in the AIA. It can be seen that the proper number is five (d ) 5) with a minimum RRSSQ ) 0.023. This means that there are five different mass spectra that are statistically independent. It is clear that the background is also considered as an IC. This is obviously consistent with the real number of the components used in the simulation. The five extracted mass spectra of the ICs are shown in Figure 5 and denoted as a-e, respectively. The mass spectra correspond to the five components shown in Figure 2. By comparison of Figure 2 and Figure 5, it can be seen that the resolved mass spectra are highly correlated with the corresponding original ones. By using the least-squares regression (linear regression, LR) method, the square correlation coefficients (R 2) between the resolved spectra and the corresponding standard ones are 0.9994, 0.9964, 0.9998, 0.9998, and 0.9982, respectively. It indicates that

Figure 6. Resolved profiles of the simulated data by AIA. The resolved chromatographic profiles and the simulated chromatographic profiles are shown as solid lines and dash lines, respectively.

Figure 7. Resolved profiles of the simulated data by SIMPLISMA. The resolved chromatographic profiles and the simulated chromatographic profiles are shown as solid lines and dash lines, respectively.

the mass spectra of the components, including the background, are accurately extracted from the overlapping signal by the AIA approach. It shows that the proposed AIA approach has a strong ability to extract the spectral information of the components from the overlapping signal, even with background. Using the extracted mass spectra as the standard information of the components, the chromatographic profiles of the ICs can be calculated by the AIA approach, which are shown as solid lines in Figure 6. The original chromatographic profiles used in the simulation are also shown as dash lines in the figure. It can be seen that the deviations are small and the resolved profiles are very similar to the corresponding original ones. This indicates that the chromatographic profiles are accurately resolved, and the five extracted ICs are respectively corresponding to the five components used in the simulation. From the resolution results shown in Figure 5 and Figure 6, it can be seen that the mass spectra and the chromatographic profiles of the components, not only for the overlapping components but also for the background, are accurately resolved by the proposed AIA approach. This indicates that the AIA approach has the abilities in both qualitative and quantitative analyses of the overlapping analytical signal by using the resolved mass spectra and the chromatographic profiles. As a comparison, the simulated data were also processed by the SIMPLISMA method. The resolved and the original chro-

Figure 8. RRSSQ versus the number of the ICs used in AIA for the experimental data.

Figure 9. Resolved and measured mass spectra of the ICs and of the reference substances. (a)-(c) Mass spectra (relative abundance) of the three ICs, respectively; (e) and (f) are the measured mass spectra of phenanthrene and anthracene, respectively.

matographic profiles are shown as solid lines and dash lines in Figure 7, respectively. It can be seen that the resolution has interference from the background.8,9,29 By comparing the results shown in Figure 6 and Figure 7, it can be seen that the resolution results of the simulated data by using the proposed AIA approach is much better than that by using the SIMPLISMA method, especially for the resolved information of the background. Resolution of the Experimental Overlapping Signal. The experimental data are processed by the AIA approach similar to that of the simulated data. Figure 8 shows the variation of RRSSQ versus the number of the ICs (d) used in the AIA. It can be seen from the figure that the number of ICs in the overlapping signal is three (d ) 3) with the minimum RRSSQ ) 0.191. The mass spectra (relative abundance) of the three ICs (IC1, IC2, IC3) extracted from the experimental overlapping signal are shown in Figure 9 and denoted as a-c, respectively. With the resolved spectral information, the chromatographic profiles corresponding to the ICs are calculated by using the immune operation in AIA and shown in Figure 10. From Figure 9 and Figure 10, it can be found that IC1 corresponds to component 1 and 3, IC2 corresponds to component 2, and IC3 corresponds to the background. It is interesting that two peaks appeared in the chromatographic profile corresponding to IC1. The reason is that these two peaks correspond to two different components with very similar mass spectra but different retention behavior. They are Analytical Chemistry, Vol. 76, No. 17, September 1, 2004

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Figure 10. Resolved profiles of the experimental data by AIA. 1 and 3 correspond to IC1; 2 and 4 correspond to IC2 and IC3, respectively; 5 and 6 are the resolved TIC and the experimental TIC, respectively.

Figure 11. Resolved profiles of the experimental data by SIMPLISMA. 1-3 correspond to the three components, respectively; 4 corresponds to the background; 5 and 6 are the resolved TIC and the experimental TIC, respectively.

recognized as one IC in the AIA calculation. By converting the mass spectra of the ICs to the format of the NIST MS Search 2.0 program, the components denoted as 1, 2, and 3 in Figure 10 are identified as phenanthrene, isopropyl(p-methoxyphenyl)malononitrile, and anthracene, respectively. The retention time of the resolved chromatographic profiles of phenanthrene and anthracene are 38.526 and 38.575 min, respectively, while retention times of the reference substances under the same GC conditions are 38.534 and 38.570 min, respectively. This indicates that the resolution result of the AIA is reliable. The mass spectra (relative abundance) of phenanthrene and anthracene obtained from the experimental data are shown in Figure 9 and denoted as (d) and (e), respectively. Comparing the mass spectra a, d, and e shows that they are very similar. The R 2 of LR between the spectra denoted as (a) and (d), (a) and (e), and (d) and (e) in Figure 9 are 0.9831, 0.9847, and 0.9977, respectively. It shows that the mass spectra of phenanthrene and

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anthracene are almost identical and have been accurately resolved from the overlapping GC/MS signal with background. By using the resolved mass spectra, the identification matching procedure should be more reliable. The component denoted as 2 in Figure 10 is hardly to be found by conventional method. Unfortunately, we cannot get the reference substance to validate it, but from the mechanism of the pyrolysis of DL-β-phenylalanine, the identification is reasonable. Furthermore, the two larger shoulder peaks in the original experimental chromatographic profile are most likely produced by combination of the background and the noise, not generated by two or more other specific components. The chromatographic profiles are also resolved by the SIMPLISMA method with its optimum number of components; the results are shown in Figure 11. By comparison of the results shown in Figure 10 and Figure 11, it can be seen that the resolution results of the AIA approach are better than that of the SIMPLISMA method, especially for the background. The difference may be accounted for by the fact that the determination of the pure variables may be interfered by the backgrounds in the SIMPLISMA method,8,9,29 while AIA takes the background as an independent component. CONCLUSION An AIA was proposed. By using the AIA approach, the mass spectra and the chromatographic profiles of the components, including the background, can be accurately resolved from the overlapping GC/MS signal. The number of independent components is determined by the differences of the reconstructed and the original data. The resolved mass spectra can be used to identify the components more reliably by matching the standard mass spectra library. Both the simulated data and the experiment data are satisfactorily resolved and the resolution results by the AIA approach are better than that by the SIMPLISMA method. The component in an overlapping signal that is very difficult to identify by the conventional method may be identified by using the resolved information. The AIA approach may be a promising tool for resolution of overlapping GC/MS signal. ACKNOWLEDGMENT This project is supported by the Teaching and Research Award Program for Outstanding Yong Teachers in Higher Educations of MOE, P.R.C (TRAPOYT), and the outstanding fund (20325517) from the National Natural Science Foundation of China (NNSFC). SUPPORTING INFORMATION AVAILABLE Flowchart of the AIA calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review December 19, 2003. Accepted June 17, 2004. AC035521U