Detection of Minute Chemical Species by Principal-Component

Anal. Chem. 1999, 71, 3085-3091

Detection of Minute Chemical Species by Principal-Component Analysis Takeshi Hasegawa

Kobe Pharmaceutical University, Motoyama-kita, Higashinada-ku, Kobe 658-8558, Japan

A novel analytical technique based on the detection of minute bands in a mixture spectrum with the use of principal-component analysis (PCA) is presented. This new aspect of PCA indicates that overlapped spectra of some components can be separated with no a priori knowledge of the components when the absorbances of the components vary greatly. This technique can be used for the detection of minute chemical species. The concept was confirmed by computer simulations. In the simulations, abstract spectra (loading vectors) were successfully obtained, and the changes of the component absorbances were also successfully followed semiquantitatively by calculating their scores. The method developed with PCA was applied to the analysis of infrared reflection-absorption (RA) spectra to study molecular interaction mechanism between alkyl-deuterated dipalmitoylphosphatidylcholine (DPPC-d62) monolayer and sucrose. The samples were Langmuir-Blodgett (LB) films of the DPPC-d62 monolayer that was prepared on a sucrose solution. The LB films consisted of the following phases: air/DPPCd62 + sucrose/sucrose/substrate (gold). The abstract spectra corresponding to “DPPC-d62 + sucrose” and “sucrose” phases were successfully separated by PCA, and the absorbance change of sucrose in each phase was semiquantitatively calculated from the score. The absorbance change was experimentally confirmed with quartzcrystal microbalance (QCM) experiments. In addition, minute water molecules that remained in the LB films after drying were readily detected from an abstract spectrum, and their binding site was found to be the phospholipid moiety in the head group of DPPC-d62. In recent decades, mathematical or physical analyses for spectra have rapidly progressed.1-21 In addition, experimental methods have improved.22-25 If examples are limited only to the (1) Li, S.; Hamilton, J. C.; Gemperline, P. J. Anal. Chem. 1992, 64, 599-607. (2) Gemperline, P. J.; Miller, K. H.; West, T. L.; Weinstein, J. E.; Hamilton, J. C.; Bray, J. T. Anal. Chem. 1992, 64, 523A-532A. (3) Gemperline, P. J.; Boyer, N. R. Anal. Chem. 1995, 67, 160-166. (4) Gemperline, P. J.; Cho, J.-H.; Aldridge, P. K.; Sekulic, S. S. Anal. Chem. 1996, 68, 2913-2915. (5) Haaland, D. M.; Robinson, M. R.; Koepp, G. W.; Thomas, E. V.; Eaton, R. P. Appl. Spectrosc. 1992, 46, 1575-1578. (6) Haaland, D. M.; Thomas, E. V. Anal. Chem. 1988, 60, 1193-1202. (7) Nødland, E.; Libnau, F. O.; Kvalheim, O. M. Vib. Spectrosc. 1996, 12, 163176. (8) Førland, G. M.; Liang, Y.; Kvalheim, O. M.; Høiland, H.; Chazy, A. J. Phys. Chem. B 1997, 101, 6960-6969. (9) Liang, X.; Andrews, J. E.; de Haseth, J. A. Anal. Chem. 1996, 68, 378-385. 10.1021/ac981430z CCC: $18.00 Published on Web 06/24/1999

© 1999 American Chemical Society

field of infrared (or near-infrared) spectroscopy, chemometrics for solution chemistry,1-10 generalized two-dimensional (2D) correlation analyses,11-16 and electric field distribution analyses for surface chemistry17-21 have been extensively developed. These analytical methods enable us to understand physical or chemical processes in a system of interest that are difficult to recognize in raw spectra. Above all, chemometrics22 has been widely used as a multivariate calibration method. One of the most important purposes of chemometrics is to quantitatively estimate a component’s concentration in a mixture. For this purpose, measured spectra are mathematically expressed in a vector format, and a calibration matrix is estimated. For the calibration, test vectors of known concentrations must be prepared in advance. With these test vectors, the concentration matrix is produced to estimate the calibration matrix. This is true for almost all regression methods.22 Chemometrics has, on the other hand, a unique data-compression method, factor analysis (FA).22 One of the important goals of FA is to produce pure-component spectra and their concentration changes that reconstruct the series of spectra observed. Ideal pure-component spectra obtained by FA from the observed spectra are called real factors, and their concentration changes are evaluated by score values. In other words, the observed spectra can be reconstructed by the several real factors and score values only. This is the main idea of the data-compression by FA. (10) Shimoyama, H.; Maeda, H.; Matsukawa, K.; Inoue, H.; Ninomiya, T.; Ozaki, Y Vib. Spectrosc. 1997, 14, 253-259. (11) Noda, I. J. Am. Chem. Soc. 1989, 111, 8116-8118. (12) Noda, I. Appl. Spectrosc. 1993, 47, 1329-1336. (13) Noda, I.; Dowrey, A. E.; Marcott, C. Appl. Spectrosc. 1993, 47, 1317-1323. (14) Ozaki, Y.; Liu, Y.; Noda, I. Appl. Spectrosc. 1997, 51, 526-535. (15) Czarnecki, M. A.; Wu, P.; Siesler, H. W. Chem. Phys. Lett. 1998, 283, 326332. (16) Ekgasit, S.; Ishida, H. Appl. Spectrosc. 1995, 49, 1243-1253. (17) Hasegawa, T.; Takeda, S.; Kawaguchi, A.; Umemura, J. Langmuir 1995, 11, 1236-1243. (18) Hasegawa, T.; Nishijo, J.; Kobayashi, Y.; Umemura, J. Bull. Chem. Soc. Jpn. 1997, 70, 525-533. (19) Dluhy, R. A. J. Phys. Chem. 1986, 90, 1373-1379. (20) Parikh, A. N.; Allara, D. L. J. Chem. Phys. 1992, 96, 927-945. (21) Hansen, W. N. Symp. Faraday Soc. 1970, 4, 27-35. (22) For example: (a) Kramer, R. Chemometric Techniques for Quantitative Analysis; Marcel Dekker: New York, 1998. (b) Massart, D. L., et al., Eds. Handbook of Chemometrics and Qualimetrics: Parts A and B; Elsevier Science: Amsterdam, 1998. (23) Baumruk, V.; Pancoska, P.; Keiderling, T. A. J. Mol. Biol. 1996, 259, 774791. (24) Malins, D. C.; Polissar, N. L.; Gunselman, S. J. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 3611-3615. (25) For example: Malinowski, E. R. Factor Analysis in Chemistry, 2nd ed.; WileyInterscience: New York, 1991.

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Principal-component analysis (PCA)9,22,23 is usually employed as the first step of FA to estimate the real factors by calculation. PCA contains a orthogonalization procedure such as singular-value decomposition (SVD),25 eigenvector calculation with the use of a covariant matrix, nonlinear iterative partial least-squares (NIPALS),25 and successive average orthogonalization (SAO).9,26 In other words, PCA has a strong constraint that all the estimated spectra (loading vectors) obtained by calculation are mutually orthogonal, which is not necessary for real factors.22 That is why, in general, there is discrepancy between the real factors and the estimated spectra. The spectra estimated by PCA are called abstract spectra that are representations of the loading vectors. Abstract spectra are often not pure-component spectra but mixture spectra. Therefore, it has been frequently noted that abstract spectra obtained by PCA are meaningless chemically. This means that the loading vectors have to be rotated in factor space to fit in with real factors by using target factor analysis (TFA)27 or a related method.9,25 Nevertheless, we often come across the cases that PCA without any TFA process gives a nearly pure component spectrum. Such a case has been categorized as a “special case”. In textbooks or papers on chemometrics, it is sometimes pointed out that there are the special cases, although the special cases are not discussed in detail.22,28 In the present study, the special case has been investigated by theoretical discussion, computational simulation, and an application to observed infrared spectra. As a result, it has been found that PCA is applicable to band separation of a mixture spectrum when band intensities of the compounds are very different, even when there is no a priori knowledge of component identity. For example, when the amount of one compound, A, is much smaller than that of another compound, B, in the mixture, PCA proved to be able to find a very good abstract spectrum of component A which is very close to the real factor. The application of PCA also proved to reveal the intensity change of the weak component A in the mixture spectra by calculation of the score. This property of PCA has not been demonstrated by other analytical methods. An application to an infrared reflection-absorption (RA)29,30 study of monolayer Langmuir-Blodgett (LB) films of phospholipid with sucrose31 was successful. The LB film consists of distinct phospholipid + sucrose and sucrose layers.32,33 The residual minute water molecules bound to the head group of the phospholipid were readily detected by the method. The change in the absorbance of sucrose in each layer was also individually investigated by PCA. The potential and limitations of this method are also discussed in comparison to other analytical methods. EXPERIMENTAL DETAILS AND CALCULATIONS PCA calculations used an eigenvalue algorithm22,25 and were performed with the MathWorks (Natick, MA) MATLAB software version 4.0 for Windows with Chemometrics Toolbox purchased (26) Donahue, S. M.; Brown, C. W. Anal. Chem. 1991, 63, 980-985. (27) Weiner, P. H.; Malinowski, E. R.; Levinstone, A. R. J. Phys. Chem. 1970, 74, 4537-4542. (28) Sˇ asˇic´, S. Analyst 1998, 123, 1193-1197. (29) Greenler, R. G. J. Chem. Phys. 1966, 44, 310. (30) Takenaka, T.; Umemura, J. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier Science: Amsterdam, 1991; Vol. 19, p 215. (31) Blodgett, K. B. J. Am. Chem. Soc. 1934, 56, 495.

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from Applied Chemometrics (Sharon, MA). The computer for the PCA calculations was a Toshiba (Tokyo) Libretto 20, i486-DX4 (CPU at 75 MHz) with a 230 MB HDD and a 16 MB RAM. The operating system was Microsoft Windows 95. 2D-correlation analyses were calculated by a privately provided software, 2D-Pocha, that runs on Windows 95. For more details, readers may refer to an earlier paper.33 All reagents for the study of molecular interactions between phospholipid monolayers and sucrose were the same as those described in the previous papers,32,33 and they are of extrapure grade or spectroscopic grade. The reagents were used without any further purification. For the infrared study, alkyl-deuterated L-R-dipalmitoylphophatidylcholine (DPPC-d62) was used for the preparation of the phospholipid monolayers. DPPC-d62 was purchased from Avanti Polar-Lipids (Alabaster, AL). Subphase water for preparation of LB films was obtained from a Millipore (Bedford, MA) Milli-Q laboratory water purifier after passing through a Yamato Scientific (Tokyo) model WG-25 water autodistiller. Any organic contaminant in the distilled water was removed by a Millipore Millipak 40 filter (pore size is ∼0.22 µm). The purity was checked by monitoring the electric resistance (>18.3 MΩ cm) and Fourier transform infrared (FT-IR) measurements of a collapsed film formed on the water. The LB trough for preparing LB films was the same as previously described.33 After 70 µL of a chloroform solution of DPPC-d62 was spread on a subphase water surface at an initial area of 916 cm2, 15 min was required to fully evaporate the solvent from the monolayer. The compression speed was set to 14 cm2 min-1. The surface pressure was monitored by a Wilhelmy balance with a glass plate. The LB transfer was carried out by the LB (vertical dipping) method,31 withdrawing a gold-evaporated glass slide upward. The withdrawing speed was 0.5 cm min-1. The pH of the subphase solution was fixed at 7.4 ( 0.1 by 2 mM Tris/ HCl buffer.33 The thermally hydrated DPPC-d62 monolayers32 were prepared by a thermal treatment process. A monolayer spread on a subphase solution was heated to 45 °C, and the temperature was maintained for 10 min. The thermally treated Langmuir (L, spread monolayer) film was cooled back to 25 °C, which provides a thermally hydrated DPPC-d62 L film. Although DPPC-d62 has a main transition (gel to liquid crystal) temperature of ∼35 °C,34 thermal hydration of the monolayers was performed at 45 °C for the same reason described in the previous paper.33 Gold-evaporated glass slides that have a 300 nm thick gold layer on a chromium layer evaporated on a glass slide (Sinyo, Osaka, Japan) were used for a substrate of LB films for the RA measurements. RA spectra were recorded on a Nicolet (Madison, WI) Magna 850 FT-IR spectrometer equipped with a deuterated triglycine sulfate (DTGS) infrared detector at 25 °C (fixed). The modulation frequency was set to 5 kHz, and the number of scans was 300. The p-polarized infrared ray was obtained with a Hitachi Au/AgBr wire grid polarizer. The RA measurements were performed with (32) Hasegawa, T.; Kawato, H.; Toudou, M.; Nishijo, J. J. Phys. Chem. B 1997, 101, 6701-6706. (33) Hasegawa, T.; Nishijo, J.; Umemura, J. J. Phys. Chem. B 1998, 102, 84988504. (34) Devlin, M. T.; Levin, I. W. J. Raman Spectrosc. 1990, 21, 441-451.

Figure 1. Synthesized spectra (the thick spectrum and spectra I and II) made of components a and b. Spectrum I (solid curve) and the bottom thick spectrum keep the component ratio of 1:1. The component ratio of spectrum II (dashed curve) is different from that of spectrum I.

a Harrick Scientific (Ossining, NY) RMA-1DG/VRA variable-angle reflection attachment with retromirrors. The angle of incidence of the infrared ray on a sample was 80° from the surface normal. THEORY AND SIMULATIONS A. A Conventional Problem of Loadings. Figure 1 shows a simulated sample spectrum (the thick spectrum) that consists of two components (bands) a and b. If the spectrum comprises N distinct points as a result of digitization, the spectrum can be represented by the following vector form:

(a1, a2, ...., am, ..., an, ..., aN) ≡ a

(1)

where ai is absorbance (band intensity) at point i. The vector a can be considered to be a point in N-dimensional space. When the sample spectrum increases in intensity while keeping its band shape (to spectrum I in Figure 1), each ai on the spectrum increases proportionally (a f ka; k is a proportional coefficient). This makes the point, a, move in a direction that is collinear with the original vector (the movement image is available in the Supporting Information). When the two bands change independently (to spectrum II in Figure 1, for example), on the other hand, the movement of the point deviates from the original vector, since each ai increases nonproportionally. In other words, a mixture spectrum (nonproportional change) yields a movement that is out of the original vector. Simply stated, it may be convenient to consider only two points (m and n) in the sample spectrum (Figure 1). Two-point spectra correspond to measurements obtained with a dual-wavelength spectrometer. When the two bands individually arise from two independent compounds, the motions of the two bands do not correlate with each other. The aim of this study is to consider a case where the bands are separated by PCA only into two purecomponent bands. In the two-point spectral model, it is sufficient to use a twodimensional space (i.e., a plane). The plane is illustrated in Figure 2. The directions of the m and n axes in Figure 2 correspond to the two points (bands) m and n in the wavenumber domain spectra

Figure 2. Schematic images of the plot for dual-wavelength measurements. When the bands at the two wavenumbers have comparable band intensities, the plot would be like pattern a. When one component on the m axis is 100 times smaller in intensity than the other on the n axis, the plot would become like pattern b.

(Figure 1), respectively. Some points that correspond to changes of the measured spectra (Figure 1) are plotted schematically in Figure 2a. If the two bands change independently, the point moves along a line that does not pass through the origin of the plane. The dispersion of the plot around the line is caused by experimental error, noise, and other unexpected chemical changes (e.g., molecular interaction or dissociation). PCA is a method, in principle, that yields a line (a “loading” vector) to explain the most outstanding feature of the dispersed points, and the line is placed on the largest variance of the plot.22,25 In the present case, the fitted straight line determined by the least-squares method indicates the direction of the loading vector. Of particular note is that the loading vector in Figure 2a does not pass through the origin. This means that the loading vector obtained by PCA comprises m and n components. In this manner, in general, the loading vector is a linear combination of two or more components, which yields a mixture spectrum as an abstract spectrum. If the loading vector is directed along an axis perfectly, the calculated loading vector would indicate one pure-component spectrum that is overlapped with other components in the original spectrum. To solve this problem, TFA27 developed by Malinowski or iterative target transformation factor analysis (ITTFA)35 developed by Gemperline may be suitable. In particular, ITTFA is a powerful algorithm36 to obtain test vectors (pure-component spectra) theoretically without a priori knowledge of band identity. ITTFA was constructed to separate deeply overlapped peaks of a chromatogram. ITTFA is performed with the use of an iteration procedure to attain converged solutions where all concentrations are nonnegative, which is a physically meaningful constraint. A successful application of ITTFA combined with SAO26 for infrared spectra was reported9 recently for the resolution of mixture components. This study placed a nonnegative “absorbance” constraint to have the calculations converge. In infrared external reflection spectra17 and circular dichroism (CD) spectra, however, negative bands often appear. Therefore, even ITTFA is not suitable for these applications. In the following sections, the band separation by PCA only is discussed with simulations and a novel aspect of PCA is presented. (35) Gemperline, P. J. Anal. Chem. 1986, 58, 2656-2663. (36) Gemperline, P. J. J. Chem. Inf. Comput. Sci. 1984, 24, 206-212.

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Figure 3. Simulated pure-component source spectra for generating a series of synthesized spectra. Two source spectra are prepared: the strong pure-component spectrum (solid line) and the small purecomponent spectrum (dashed line) that is 100 times its actual intensity. The band intensity change of each source spectrum is shown in Figure 4.

B. Application of PCA for the Recognition of Minute Absorbances of Chemical Species. As mentioned earlier, band separation by PCA alone can be achieved if the loading vector is collinear with an axis in multidimensional space and passes through the origin. In this section, let us consider such a special case. It is of interest to consider a mixture sample that consists of a small amount of compound A and a 100 times larger amount of compound B. This results in a large relative band intensity ratio. Here, it is assumed that the two band peaks (wavenumbers), derived from compounds A and B, correspond to the directions of the m and n axes, respectively. In this case, components on the m axis in Figure 2a are 100 times reduced and plotted again in Figure 2b. The variance of the plot along the m axis becomes very small, and only the variance along the n axis is predominant and explains the entire plot. In this case, the loading vector should be placed nearly along the n axis. As the n direction is derived from compound B, the loading vector indicates that the major spectral change is caused by the band intensity change in the spectrum of component B. It is taken for granted that the major spectral change is dominated by the sample with the strong intensity. Regardless, PCA is able to pick up the small bands that are almost totally overlaid by the strong-intensity bands in the raw spectra. The first loading vector should be orthogonal to the next loading vector that reflects the weak spectral change due to the small absorbance of compound A. The most important concept of this paper is that PCA provides a significant detection level for a chemical species with very low absorbance, even when the minute compound hidden in other dominant compounds can not be chemically separated. In principle, any weak-intensity spectra can be extracted by PCA alone from other strong bands, within the limitation of the noise and the resolution of digital signal acquisition. To confirm the theoretical speculation above, the following simulations were performed. Figure 3 shows two generated independent source spectra. Both source spectra have two bands, 3088 Analytical Chemistry, Vol. 71, No. 15, August 1, 1999

Figure 4. (a) Intensity change (open circles) of the solid spectrum (Figure 3) and (b) that of the dashed spectrum, for generating the series of spectra (available in the Supporting Information). The scores for the first and second loadings calculated by PCA are shown by solid circles in (a) and (b), respectively.

and one of the spectra (dotted line) is 100 times its actual intensity. The two bands of the higher absorbance spectrum are located at channels 80 and 120, and those of the weaker spectrum are located at channels 90 and 130. The full widths at half-maximum (fwhm’s) of the two bands are 10 and 15 channels, respectively. The dotted and solid spectra are considered to be derived from two distinct chemical species A and B, respectively. In other words, the amount of compound A is much smaller than that of compound B, and the compounds show similar spectra and occur at similar channel numbers. An experimental case was considered where the concentrations of the compounds change independently. Spectral shape was kept unchanged. The two independent spectra were individually (asynchronously) changed in intensity and summed to obtain a series of synthesized spectra (available in the Supporting Information). The intensity change of each band is shown by open circles in Figure 4. Random noise (white noise) was generated and added to the spectra. In infrared spectrometry, the absorbance spectra are obtained from transmission spectra through a common logarithm function. Therefore, the noise was added to the transmission domain spectra, and they were transformed into absorbance domain spectra. The final noise level in the absorbance domain spectra was about 20% of that of the weak-intensity spectra. The infrared absorbance spectra were generated to show Gaussianshaped bands. The series of synthesized spectra seemed to comprise only the spectra of compound B at a glance. The weak bands arising from compound A were too weak to recognize, and the artificial noise was also unrecognizable due to its weak intensity. An attempt to elucidate the small bands in the simulated spectra was undertaken with the use of second derivatives,37 but no information was obtained for the minute bands and the noise was largely emphasized (not shown). Since the second-derivative technique can be expressed by Fourier transformation,37,38 it is believed that Fourier self-decon(37) Griffiths, P. R.; de Haseth, J. A. Fourier Transform Infrared Spectrometry; Wiley-Interscience: New York, 1986; p 101. (38) Cameron, D. G.; Moffatt, D. J. Appl. Spectrosc. 1987, 41, 539-544.

Figure 5. The first and second abstract spectra that represent the first and second loading vectors by determined PCA. The second abstract spectrum is multiplied by -1. The third abstract spectrum is shown by the scattered thin zigzag pattern.

volution also has the same limitation of being unable to reveal small bands in strong-band spectra. C. Investigation of 2D-Correlation Analysis for the Detection of Minute Bands. Only one conventional candidate other than PCA for the recognition of minute absorbances of chemical species in the presence of large absorbances is generalized 2Dcorrelation analysis.12 It has been widely shown that the asynchronous map of generalized 2D-correlation analysis has great potential to find small bands overlaid by large ones. In particular, small changes in a band hidden in a large background (frequently found in near-infrared spectra) have provided good examples to show the potential of the asynchronous map. Nevertheless, it is unfortunate that the asynchronous map greatly responds to noise when the noise level approaches band intensities. (Figures of simulations are available in Supporting Information.) The cross-peaks in the asynchronous map are largely distorted by the noise, and discussion with the map becomes impossible. In practice, it is difficult to obtain noise-free spectra, especially when the total amount of sample is small. In other words, even the asynchrounous 2D-correlation method is not suitable for analysis of spectra of thin-layer materials. In the next section, a great advantage of PCA will be presented by showing that PCA is impervious to noise. D. Advantage of PCA for Spectra with Noise. Abstract spectra for the synthesized series of spectra with white noise were calculated by PCA. The abstract spectra are shown in Figure 5. The solid and dotted lines correspond to the first and second abstract spectra, respectively. Since the sign of an abstract factor (loading vector) is arbitrary and depends on the PCA algorithm,22 the second abstract spectrum was multiplied by -1. The abstract spectra are very similar to the original components (Figure 3), although the second abstract spectrum exhibits small negative peaks at the large band positions. The widely scattered zigzag pattern (noise only) in Figure 5 is the third abstract spectrum and suggests that the first two abstract spectra are sufficient to explain the original spectral changes. It should be noted that PCA is a powerful method even in the presence of large spectral noise. The score for each loading was calculated. The calculated scores for the first and second loadings are plotted by solid circles

in Figure 4. The scores are consistent with the original quantities, at least, semiquantitatively. Since the loadings are normalized in the process of PCA calculations, the scores will not necessarily be quantitatively consistent with the original quantities. Therefore, the semiquantitative consistency strongly indicates that almost real factors are obtained by PCA. In other words, the quantitative change of the chemical species are indicated by PCA alone when the band intensity ratio (IA/IB) of targeting chemical compounds is large. In summary, PCA is theoretically expected to obtain nearly pure component spectra from a series of changing spectra when the chemical components differ greatly in absorbance. It is not necessary to know the identity of any of the components a priori, and the scores semiquantitatively follow the concentrations. This property can be widely used to detect a minute absorbance of chemical species hidden by other dominant species, such as a tiny quantity of species in a chemical equilibrium system. E. The Case of Completely Overlapped Bands. The example shown in Figure 5 was devoted to partially overlapped bands. In this section, a case where the band centers are the same is briefly discussed. When the band positions are exactly the same, the band separation by PCA can be summarized in the following two manners. (1) When both band positions and bandwidths are close to each other, the separation by PCA only is impossible. This case corresponds to that in which the two bands have many common axes (deep overlap) in multidimensional space. Having too many common axes means that the discrimination of the two spectra by orthogonalization calculation can not be performed. Therefore, it is reasonable that this case is not amenable to PCA separation (not shown). (2) When the bandwidths are very different, the band separation by PCA is readily performed, even when the band centers are completely the same. In this case, the large-width band has many axes different from those of the small-width band in multidimensional space, which permits a successful separation. (An example is available in the Supporting Information.) RESULTS AND DISCUSSION As an application of this technique, reflection-absorption spectra of monolayer Langmuir-Blodgett (LB) films of DPPC with sucrose have been analyzed by PCA. Infrared RA spectra of monolayer LB films of DPPC-d62 with varying concentration of sucrose in the subphase solution are shown in Figure 6. The spectra are almost identical to previously published spectra of the same LB films,33 but the present spectra are remeasured with a common gold surface reference for PCA calculations. As described in the previous paper, the LB films consist of two phases: a sucrose layer and a DPPC-d62 + sucrose layer (see inset in Figure 6). The sucrose layer is formed after drying of the LB films, since the sucrose aqueous solution is transferred to the gold-evaporated glass slide (substrate) with the DPPC-d62 monolayers. As the quantity of dried sucrose is large and the bands of sucrose absorb the infrared radiation in the fingerprint region strongly, the sucrose layer is expected to play a dominant role in the sucrose-concentration-dependent RA spectra. In fact, the main spectral features in Figure 6 are due to the RA spectrum of sucrose. Analytical Chemistry, Vol. 71, No. 15, August 1, 1999

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Figure 6. Sucrose-concentration-dependent infrared RA spectra of DPPC-d62 LB monolayers deposited on a gold-evaporated glass slide (substrate). The schematic layer structure of the monolayer LB film is shown above the spectra. The sucrose concentration range is 0-40 mM.

Prior to the analysis by PCA, three abstract spectra at least are expected. The first one should be derived from the bulk sucrose. The second one is expected to be derived from the DPPCd62 monolayer and incorporated sucrose molecules, since their quantities are comparable while they are much less than that of bulk sucrose. The sucrose molecules incorporated with DPPCd62 monolayers are expected to act as a single species. The third abstract spectrum would be derived from unexpected minute chemical species. The results are shown in Figure 7. The first abstract spectrum in Figure 7a is very similar to a pure-sucrose spectrum in both the low- and high-wavenumber regions as expected. This indicates that the major change in the RA spectra is governed by the concentration change in the bulk sucrose layer. The score for the first abstract spectrum is shown by open circles in Figure 8a. The score value increases almost linearly with the concentration of sucrose. In the previous study, the increase of mass due to the sucrose layer (out of the DPPC-d62 layer) was measured by a quartz-crystal microbalance (QCM) method.33 The results are shown by open circles in Figure 8b. The experimental results are consistent with the score change. This strongly supports our theory that the first abstract spectrum is mainly derived from the sucrose layer. The second abstract spectrum is shown in Figure 7b. The entire shape of the spectrum is very similar to that of an RA spectrum of a DPPC-d62 monolayer overlapped with a sucrose spectrum, except for the O-H stretching vibration (δ(O-H)) band at 3435 cm-1. The finely separated C-H stretching vibration bands indicate the resolution enhancement ability of PCA. On closer inspection, the antisymmetric PO2- stretching vibration (νas(PO2-)) band is observed to be split into two peaks at 1278 and 1264 cm-1. In general, the νas(PO2-) band of the DPPC-d62 monolayer appears below 1260 cm-1.39,40 In our case, however, the DPPC-d62 (39) Okamura, E.; Umemura, J.; Takenaka, T. Biochim. Biophys. Acta 1990, 1025, 94-98. (40) Mantsch, H. H., Chapman, D., Eds. Infrared Spectroscopy of Biomolecules; Wiley-Liss: New York, 1995.

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Figure 7. The (a) first, (b) second, and (c) third abstract spectra of the RA spectra in Figure 6 yielded by PCA.

monolayers had been thermally hydrated, resulting in a different film packing in the LB films. For the thermally hydrated DPPCd62 monolayer LB films, the νas(PO2-) band is found to appear at 1278 cm-1 as a single peak. According to Crowe et al.,41 the νas(PO2-) band shifts to a lower wavenumber (over 10 cm-1) when DPPC is hydrated. Therefore, the new band at 1264 cm-1 in the second abstract spectrum (41) Crowe, J. H.; Crowe, L. M.; Carpenter, J. F.; Rudolph, A. S.; Wistrom, C. A.; Spargo, B. J.; Anchordoguy, T. J. Biochim. Biophys. Acta 1988, 947, 367384.

that is specific to hydrogen-bonded water molecules.42 At the same time, the O-H bending vibration band appears at 1650 cm-1. This abstract spectrum strongly indicates that there remains a minute concentration of water molecules even after adequate drying of the monolayer LB films. The remaining water proved to be bound to the PO2- group in the head moiety of DPPC-d62. In other words, the residual water and bound PO2- groups are recognized as identical chemical species. The score of the third abstract spectrum was calculated, but it was meaningless as the scores were scattered because of their very small eigenvalues.

Figure 8. (a) Scores calculated with the use of the abstract spectra (Figure 7) and the RA spectra (Figure 6). The scores corresponding to the first and second abstract spectra are shown by open and solid circles, respectively. (b) Observed mass increase of sucrose measured by QCM. The mass increase of sucrose out of the DPPC-d62 LB monolayer and in the layer are shown by open and solid circles, respectively.

indicates the existence of partially hydrated phosphate groups in the head group moiety of DPPC-d62. The negative δ(O-H) band at 3435 cm-1 is assigned to sucrose. In an abstract spectrum, negative bands mean that a band change has taken place in a direction opposite to that of other bands. Therefore, the second abstract spectrum shows a relative change of bands arisen from DPPC-d62 and incorporated sucrose simultaneously. The increase of sucrose in the DPPC-d62 layer was measured by QCM to give the result shown in Figure 8b (closed circles). The score of the second abstract spectrum was calculated. Since the second abstract spectrum shows a negative δ(O-H) band, which is a key band for following the incorporated sucrose molecules in the DPPC-d62 layer, the calculated score was multiplied by -1. The result is shown in Figure 8a by solid circles. The score change is expected to show the mass change of incorporated sucrose because the mass of the DPPC-d62 monolayer is not changed throughout the experiments. It should be noted here that the result is quite similar to the experimental result (solid circles in Figure 8b). This strongly indicates that the change in mass of sucrose in the DPPC-d62 layer was successfully followed by PCA. It is also noticed that the mass changes of sucrose in and out of the DPPC-d62 monolayer were followed individually by PCA without any chemical markers. The third abstract spectrum is displayed in Figure 7c. This spectrum shows nonnegative bands, although the second abstract spectrum contains mixed-component (DPPC-d62 and incorporated sucrose) spectra. This is because the third chemical component is much less in quantity than the other species. In the third abstract spectrum, the νas(PO2-) band at 1264 cm-1 is readily resolved as a sharp single peak. It should be noted that the δ(O-H) band appears at a very low wavenumber (3250 cm-1) (42) Givan, A.; Loewenschuss, A.; Nielsen, C. J. J. Phys. Chem. B 1997, 101, 8696-8706.

CONCLUSION The special case of PCA analysis was revealed and specified. PCA proved to be powerfully applicable to the detection of minute chemical species hidden in dominant species. An application of PCA was performed for the investigation of the molecular interaction between DPPC-d62 monolayers and sucrose. A novel aspect of PCA to record semiquantitative changes in the mass of chemical species has been demonstrated, with a theoretical speculation and simulations. For actual experimental data, the calculated mass changes from the original RA spectra are quite consistent with measured QCM results. PCA revealed the existence of residual water molecules in the monolayer LB films and their binding locations. Consequently, this new aspect of PCA was found to be a useful method for the detection of minute bands, and the method requires no a priori knowledge of component identity. It may prove to be a powerful tool for chemical equilibrium and surface science studies, especially when the minute chemical species of interest cannot be separated chemically. It is also important that this analytical method is impervious to spectral noise. ACKNOWLEDGMENT The author thanks Dr. Junzo Umemura, Institute for Chemical Research, Kyoto University, for allowing the frequent use of his FT-IR spectrometer. He thanks Professor James A. de Haseth, University of Georgia, for helpful suggestions and useful comments on the occasion of his visit to Japan. He also thanks Mr. Richard Kramer, Applied Chemometrics, Inc., for helpful discussions and Professor Yukihiro Ozaki, Kwansei Gakuin University, for warm encouragement and fruitful discussions. This work was financially supported by Grant-in-Aid for Scientific Research No. 09771955 from the Ministry of Education, Science, and Culture of Japan and by a grant from the Inoue Foundation for Science, Tokyo, whom the author expresses his thanks. SUPPORTING INFORMATION AVAILABLE Figures presenting (1) an elucidation of points in N-dimensional space, (2) a synthesized series of spectra with white noise, (3) the results of 2D-correlation analyses for the synthesized series of spectra, and (4) an example for text section E(2). This material is available free of charge via the Internet at http://pubs.acs.org. Received for review December 29, 1998. Accepted April 27, 1999. AC981430Z

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