Application of Eigenstructure Tracking Analysis and SIMPLISMA to the

Each window is decomposed by singular value decomposition, and the I first singular values are plotted as function of the window number. The analysis ...
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Anal. Chem. 1996, 68, 2241-2247

Application of Eigenstructure Tracking Analysis and SIMPLISMA to the Study of the Protonation Equilibria of cCMP and Several Polynucleotides R. Gargallo,† F. Cuesta Sa´nchez,‡ A. Izquierdo-Ridorsa,*,† and D. L. Massart‡

Departament de Quimica Analitica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain, and ChemoAC, Vrije Universiteit Brussel, Laarbeeklaan 103, B-1090 Brussels, Belgium

The application of eigenstructure tracking analysis (ETA) and SIMPLISMA for the investigation of the protonation equilibria of a monomer and several polynucleotides is proposed. Both approaches have been applied in the pH and in the wavelength direction to the spectroscopic data matrices obtained in the study of each equilibrum. ETA provides information about the number of components in the system, their evolution along the titration, and the local rank. SIMPLISMA is also used to obtain the number of compounds in the system, the concentration profiles, and the unit spectrum of each compound. The results obtained with SIMPLISMA and those obtained previously with the alternating least-squares approach are compared. This work is part of a wider study concerning the interpretation of metal ions and proton interactions with nucleic acids and their constituents in aqueous solution under physiological conditions (37 °C and 0.15 M ionic strength).1-6 The study of equilibria between metal ions and macromolecular ligands is a field of great interest, owing to its environmental and biological importance. This study, however, is hindered by the fact that the law of mass action ruling the equilibria is valid only separately for each of the reaction sites of the macromolecule, and several additional or secondary effects must be considered. These secondary effects have been classified into three types:7 (a) polyfunctional effects assigned to differences in chemical nature and in electrostatic and steric environments of the coordination sites in the macromolecule; (b) conformational changes caused by the changes in pH, temperature, and ionic strength of the medium or by the content of complexed ion; and (c) polyelectrolytic effects caused by the ionization of major sites of the macromolecule yielding changes in the local electric field at the surface of the macromolecule. All these effects contribute to the stability of the formed species, and their relative importance is difficult to define since it varies with †

Universitat de Barcelona. Vrije Universiteit Brussel. (1) Casassas, E.; Gargallo, R.; Gime´nez, I.; Izquierdo-Ridorsa, A.; Tauler, R. Anal. Chim. Acta 1993, 283, 538-547. (2) Casassas, E.; Gargallo, R.; Gime´nez, I.; Izquierdo-Ridorsa, A.; Tauler, R. J. Inorg. Biochem. 1994, 56, 187-199. (3) Tauler, R.; Izquierdo-Ridorsa, A.; Gargallo, R.; Casassas, E. Chemom. Intell. Lab. Syst. 1995, 27, 163-174. (4) Casassas, E.; Gargallo, R.; Izquierdo-Ridorsa, A.; Tauler, R. React. Polym. 1995, 27, 1-14. (5) Izquierdo-Ridorsa, A.; Casassas, E.; Gargallo, R.; Marque´s, I.; Tauler, R. React. Polym. 1996, 28, 127-137. (6) Casassas, E.; Tauler, R.; Marque´s, I. Macromolecules 1994, 27, 1729-1737. (7) Buffle, J. Complexation Reactions in Aquatic Systems. An Analytical Approach; John Wiley and Sons, New York, 1988.

the degree of site occupation (complexation or protonation). The interpretation of the experimental data using traditional leastsquares curve-fitting approaches is consequently rather cumbersome and unsafe,7-9 and there is a demand for the development of new approaches free from the constraints of the law of mass action and free from the prior postulation of a chemical model. In this work, the acid-base properties of the compounds cyclic cytidine 3′-5′-monophosphate (cCMP), poly(inosinic acid) (poly(I)), poly(cytidylic acid) (poly(C)), and heteropolynucleotide poly(I)-poly(C) are studied by means of the eigenstructure tracking analysis (ETA)10 and SIMPLISMA11-14 approaches. The acidbase properties of poly(I),3 cCMP, and poly(C)4,5 have been already studied with the alternating least-squares (ALS) approach, which is based on the previously developed SPFAC procedure.15,16 The study of conformational and structural transitions in synthetic polynucleotides such as poly(I), poly(C), and poly(I)poly(C) is important to better understand the structures and interactions in naturally occurring nucleic acids.17 These polynucleotides allow evaluation of constants of ion binding to predetermined types of bases. The study of monomers, such as cCMP, helps in understanding the phenomena involved in the equilibria of polynucleotides. Furthermore, cyclic nucleotides can be considered as model compounds since they contain the same coordinating centers as polynucleotides. ETA has been used to reveal the noise pattern (heteroscedasticity) in instrumental profiles of IR spectra.10 It has also shown to be useful in determining the local rank and selective regions in a data matrix. The application of ETA to the systems studied here is another way to determine the number of components present in these systems in addition to the methods previously used in the study of equilibria of polynucleotides.1,3-6 The determination of the pH-selective regions of each compound is also helpful information for the further application of SIMPLISMA and ALS. SIMPLISMA11-14 is a self-modeling approach based on the selection of what are called pure variables. A pure variable is

‡

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© 1996 American Chemical Society

(8) Marinsky, J. A. Coord. Chem. 1976, 19, 125. (9) Barbucci, R.; Casolaro, M.; Nocentini, M.; Corezzi, S.; Ferruti, P.; Barone, V. Macromolecules 1986, 19, 37. (10) Toft, J.; Kvalheim, O. M. Chemom. Intell. Lab. Syst. 1993, 19, 65-73. (11) Windig, W.; Guilment, J. Anal. Chem. 1991, 63, 1425. (12) Windig, W.; Heckler, C. E.; Agblevor, F. A.; Evans, R. J. Chemom. Intell. Lab. Syst. 1992, 14, 195. (13) Windig,W.; Stephenson, D. A. Anal. Chem. 1992, 64, 2735. (14) Cuesta Sa´nchez, F.; Massart, D. L. Anal. Chim. Acta 1994, 298, 331-339. (15) Tauler, R.; Casassas, E.; Izquierdo-Ridorsa, A. Anal. Chim. Acta 1991, 248, 447. (16) Tauler, R.; Casassas, E. Analusis 1992, 20, 255. (17) Eisenberg, H.; Felsenfeld, G. J. J. Mol. Biol. 1967, 30, 17.

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defined as a variable the intensity of which is due to only one of the compounds in the mixture under consideration. In this paper, the application of SIMPLISMA to the resolution of the spectral data into the concentration profiles and unit spectra of the different species present in the protonation equilibria of several polynucleotides and cCMP is investigated. The results obtained with SIMPLISMA are compared with those obtained previously with ALS. The present study is the first attempt to show that the results obtained with SIMPLISMA and EFA-ALS are similar, despite of their different mathematical bases. ALS presents a series of constraints (i.e., concentration closure, unimodality, the concentrations and/or spectra are nonnegative) that are not present in SIMPLISMA. Thus, the results of both methods, while qualitatively very similar, can differ in the quantitative aspects, and the introduction in SIMPLISMA of some constraints can give more chemical meaning to the mathematical results obtained with SIMPLISMA. THEORY ETA. A detailed explanation of ETA has been given elsewhere.10 ETA is a dynamic and evolving procedure revealing the local rank in the pH or wavelength direction. Within each run of ETA, when applied in the pH direction, a moving window embracing I successive spectra or objects is defined. The first window contains the I first spectra, the second window contains spectrum 2 to I + 1, and so on until the last spectrum is included. Each window is decomposed by singular value decomposition, and the I first singular values are plotted as function of the window number. The analysis is repeated with an increasing size window until the optimum is found. The optimum window size should be one unit higher than the maximum number of compounds present simultaneously. SIMPLISMA. The mathematical basis of SIMPLISMA have been explained elsewhere.11-14 SIMPLISMA is a self-modeling approach based on the selection of pure variables (wavelengths) or objects (pHs). If pure objects or pure variables exist, i.e., pH values where a single species is present or wavelength values where a single species absorbs, then they are determined. Once the pure objects or pure variables are known, the spectrum of each compound or the concentration profiles (depending on whether the study has been carried out in the wavelength or in the pH direction) can be determined by a least-squares procedure. When the correct number of pure variables or pure spectra is selected, the variance in the data is well explained, and the process finishes. A single titration can be analyzed with SIMPLISMA, and the final results obtained are the concentration profiles and the unit spectra for each compound in this titration. When pure variables are not present, the individual calculated concentrations or spectra contain contributions from other components.14 While the purity of a variable is not an absolute requirement when SIMPLISMA is used as an interpretation tool, it can be important when quantitative information, such as stability constants, should be extracted from the results. ALS. The ALS approach1,3-6,15,16 also resolves the experimental data matrix into the concentration profiles and unit spectra. The first step in the procedure is the determination of the number of components present in the system. The number of components to be considered is that needed to reproduce the original data matrix within the experimental error, and it should be intrinsically related to the number of species in equilibrium in the system. ALS does not determine the number of components by itself, and 2242

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several methods based on factor analysis can be used for the estimation of the number of species in equilibrium.18-20 The initial estimation of the concentration profiles to be used in the ALS approach is usually provided by evolving factor analysis (EFA)21,22 Thus, the main difference between ALS and the alternating regression (AR) proposed by Karjalainen23 is the use of an initial estimation of the concentration profiles or unit spectra, usually provided by EFA. Once the number of species present in each titration is known and an initial estimation of the concentration distributions is obtained from EFA, an ALS regression procedure is started with a series of constraints: (1) UV-vis absorptivities must be positive, whereas circular dichroism (CD) unit absorptivities can be positive or negative; (2) the concentrations are constrained to be positive and unimodal, i.e., each compound has only one maximum in the pH range; and (3) the system is forced to be closed, i.e., the total concentration at each pH is constant. ALS allows also the simultaneous study of more than one titration in order to solve the different ambiguities (rotational and intensity ambiguities) that can be present in the resolution of only one data matrix.15,16 The most difficult to remove is the rotational ambiguity, which is due to the lack of selectivity for any of the species formed. pKa Calculation. From the concentration profiles, obtained either by SIMPLISMA or ALS, an estimation of the pKa values, related to the different acid-base equilibria, can be calculated. In a first step, for each acid-base equilibrium, a pKa value is calculated at each point of the titration, in order to evaluate its dependence with the degree of protonation. Then, two different situations can be discerned: (a) When no secondary effects (i.e., polyfunctional, conformational, or polyelectrolytic effects) are present, the pKa has a constant value along the titration. In these cases, the final pKa value may be obtained by averaging the pKa values calculated, for that equilibrium, at each point of the titration. (b) When secondary effects are present, a dependence of the pKa on the degree of protonation is observed,4-6 i.e., the law of mass action ruling the equilibria is valid only separately for each of the reaction sites of the macromolecule. However, in order to carry out a comparative study between the acid-base behaviors of the different polynucleotides, a single pKa value should be given to each of the acid-base equilibria. In this paper, the pKa value chosen for each acid-base equilibrium is that obtained graphically from the crossing point between the concentration profiles of the two species involved in the equilibrium. EXPERIMENTAL SECTION The experimental data consist of several potentiometric titrations, with sodium hydroxide or hydrochloric acid, of slightly acid or neutral solutions containing different nucleotide or polynucleotide concentrations.3-5 The titration vessel was termostated at 37 °C, and the ionic strength was kept at 0.15 M with sodium chloride. With the aid of a peristaltic pump, the medium under study is introduced in the UV-vis spectrophotometer. In the case (18) Malinowski, E. R. Factor Analysis in Chemistry, 2nd ed.; Wiley: New York, 1991. (19) Malinowski, E. R. Anal. Chem. 1977, 49, 612. (20) Wold, S. Technometrics 1978, 20, 397. (21) Gampp, H.; Maeder, M.; Meyer, Ch. J.; Zuberbu ¨ hler, A. D. Talanta 1985, 32, 1133. (22) Gampp, H.; Maeder, M.; Meyer, Ch. J.; Zuberbu ¨ hler, A. D. Talanta 1986, 33, 943. (23) Karjalainen, E. J. Chemom. Intell. Lab. Syst. 1989, 7, 31.

Table 1. Experimental Conditions of the Spectroscopic Titrations Performed system cCMP-H poly(I)-H poly(C)-H poly(I)poly(C)-H

a

technique UV-vis UV-vis UV-vis CD UV-vis CD

titration [molecule]0 no. (×104) 1 2 3 4 5 6

0.99 1.35 1.40 2.05 0.64 0.70

pH interval

no. of spectra

2.08-7.10 2.13-11.68 7.30-3.24 6.48-3.42 2.07-10.54 1.93-9.72

23 20 35 35 56 34

b

Figure 1. UV-vis study of the cCMP-H system. (a) ETA results in the pH direction. (b) ETA results in the wavelength direction.

of CD measurements, a sample of the medium is taken from the vessel and introduced into the spectropolarimeter. In both cases, the spectra are registered, and the pH value is read. The experimental conditions of the titrations performed are given in Table 1. The experimental conditions of the potentiometric titrations in the study of the poly(C)-H system were different from those of the other systems studied, since they were performed from neutral to acid pH in order to avoid the precipitate that appears in the system at pH lower than 3.2.4 The spectral data were measured with a Perkin-Elmer λ-19 spectrometer and a JASCO J-720 spectropolarimeter. pH measurements were performed with a Radiometer PHM-64 pH meter (with a precision of (0.1 mV) and a combined Ross pH electrode (Orion 81-02). Concentrated titrant was added with a Metrohm Dosimat 655 autoburet equipped with an exchange unit of 5 cm3. cCMP, poly(I), poly(C), and poly(I)-poly(C) were made by Sigma and used without further purification. Deionized water distilled twice was also used in all titrations. Sodium chloride, sodium hydroxide, and hydrochloric acid were analytical reagent grade. A data set has been collected from each potentiometric titration followed by UV-vis or CD spectroscopy. The experimental data are contained in several data matrices, where the rows correspond to different spectra obtained at different pH values and the columns correspond to the different wavelengths at which the absorptions were measured. RESULTS AND DISCUSSION (a) cCMP-H System. The results obtained by ETA in the pH direction with a window of size 3 are shown in Figure 1a. The changes in the singular values show clearly the presence of at least two species in the system. The first singular value does not change practically in the whole pH range. To understand the system, the evolution of the second and third singular values has to be studied. The second singular value changes only slightly in the initial windows (acidic pH values), which indicates that there is no change in the number of components in the system. Afterward, the second singular value increases with the window number, while the third singular value does not vary. This fact

Figure 2. UV-vis study of the cCMP-H system. Results with SIMPLISMA in the pH direction: (a) concentration profiles, (b) unit spectra. Results with SIMPLISMA and concentration constraint (solid line) compared with those of EFA-ALS (symbols): (c) concentration profiles, (d) unit spectra. (1) Protonated form of cCMP, (2) deprotonated form of cCMP.

indicates the presence of a new factor in this pH region. At neutral pH values (window number higher than 15), the second singular value decreases and the third one remains constant, indicating the presence of the same number of species as at the beginning of the titration. The same result is obtained with other window sizes (4-5 spectra). Figure 1b shows the results obtained by ETA in the wavelength direction with a window of size 3. The evolution of the singular values indicates the presence of at least two factors. The third singular value represents the noise level. The presence of two selective zones in windows 20 (240 nm) and 80 (300 nm) is observed. Similar results have been obtained with other window sizes (4-5 variables). SIMPLISMA has been applied to the experimental data in the pH direction and two pure spectra are found at pH 2.08 and 7.10. Both pH values are in the selective zones found with ETA in the pH direction (Figure 1a). The results obtained with SIMPLISMA are shown in Figure 2a,b. The concentration profiles show a pKa value close to 4.0, very similar to the value obtained previously from the potentiometric study (pKa ) 3.89).5 These concentration profiles indicate the presence of two selective regions, at the initial and final pH values, where only one species is present. The protonated form of cCMP is present in the selective region at acidic pH values, and the deprotonated form is present in the selective region at neutral pH values. At intermediate pH values, both species coexist. These results agree with those obtained with ETA in the pH direction (Figure 1a). Two selective regions at the initial and final window numbers were observed, as well as an overlapped region where both compounds are present. Since the system under study is closed, i.e., the sum of the concentration of all the compounds present at each pH is constant, the concentration profiles obtained with SIMPLISMA are normalized according to this constraint by dividing the concentration of the compounds at each pH by the total concentration at the pH considered. The constrained concentration profiles obtained with SIMPLISMA and those obtained with the EFA-ALS approach are shown in Figure 2c. The unit spectra are recalculated from the Analytical Chemistry, Vol. 68, No. 13, July 1, 1996

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Figure 3. UV-vis study of the cCMP system. Results with SIMPLISMA and concentration constraint in the wavelength direction (solid line) compared with those of SIMPLISMA in the pH direction (symbols). (a) Concentration profiles obtained, (b) unit spectra obtained. (1) and (2) as in Figure 2.

constrained concentration profiles and compared with the ones obtained with the EFA-ALS approach (Figure 2d). The results obtained with both approaches are quite similar. SIMPLISMA has been also applied to the data matrix in the wavelength direction, and two pure variables are found, 240 and 302 nm, both in the selective regions found with ETA (Figure 1b). However, in the first selective zone (240 nm), both species absorb (see Figure 2), and ETA and SIMPLISMA have noticed this region probably because there is a strong change in the absorbance when the second species appears. On the other hand, both approaches have correctly found that only one species absorbs in the second selective zone, despite the small change in the absorbance during the titration. The concentration profiles and unit spectra have been calculated with SIMPLISMA considering these two pure variables and also a concentration closure (Figure 3). The concentration profiles are similar in shape to those obtained previously with EFA-ALS and with SIMPLISMA in the pH direction, but in this case no selective regions are observed, and both species seem to be present along the whole pH range. This fact can be related to the pure variables chosen, i.e., a lack of selectivity in the first variable (240 nm) and a small change in the absorbance in the second one (300 nm) along the titration. It reinforces the fact that, when no real pure variables are found, no quantitative information can be extracted from the results obtained. The unit spectra obtained from this study, which are also different from those calculated with the EFA-ALS, are shown in Figure 3b. (b) Poly(I)-H System. The experimental data obtained along a spectrophotometric titration of the poly(I)-H system3 were analyzed with the ETA procedure. The results obtained in the pH direction using a window of size 3 are shown in Figure 4. The evolution of the three singular values obtained is similar to that previously explained for the cCMP-H system. The changes in the singular values show clearly the presence of at least two species in the system. The second singular value changes only slightly in the initial windows (acidic and neutral pH values), which indicates that there is no change in the number of species in this region. Between window numbers 7-10, an increase is observed for the second singular value. This fact indicates the presence of a new factor in this pH region. At higher window numbers (pH values near 11), the second singular value decreases, and the third one remains nearly constant, indicating the presence of the same number of species as at the beginning of the titration. The same result is obtained with different window sizes (4-5 spectra). SIMPLISMA is applied to the data matrix in the pH direction, and two pure spectra, at pH 2.13 and 10.74, are found. Both 2244 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996

Figure 4. UV-vis study of the poly(I)-H system. ETA results in the pH direction.

Figure 5. UV-vis study of the poly(I)-H system. Results with SIMPLISMA and concentration constraint (solid line) compared with those of EFA-ALS (symbols): (a) concentration profiles, (b) unit spectra. (1) Protonated form of poly(I), (2) deprotonated form of poly(I).

spectra belong to the selective zones found previously with ETA in the pH direction (Figure 4). The concentration profiles and spectra of the different species obtained with SIMPLISMA, after the constrain of constant total ligand concentration, and those obtained previously with EFA-ALS, are shown in Figure 5. The concentration profiles show a pKa value close to 8.8. This value is similar to the one from the potentiometric study (pKa ) 8.86).3 The concentration profiles show the presence of two selective regions. At the acidic and neutral pH values, only the protonated form of the polymer exists, while at the basic pH values, only the deprotonated form is present. Both species coexist at intermediate pH values. These results agree with those obtained with ETA in the pH direction, i.e., two selective regions at the initial and final window numbers and an overlapped region in the middle of the titration. The results obtained with SIMPLISMA after the application of the concentration constraint agree with those obtained with EFA-ALS. ETA and SIMPLISMA have not been applied to the data matrix in the wavelength direction due to the high overlapping between the unit spectra of protonated and deprotonated poly(I). (c) Poly(C)-H System. The poly(C)-H system has been studied by means of UV-vis and CD spectroscopic techniques (titrations 3 and 4).4 Figure 6 shows the ETA profiles obtained for both titrations using a window size of 3 in the pH direction. For the UV-vis data (Figure 6a), the first singular value in the ETA plot does not change practically in the whole pH range. The second singular value changes only slightly in the initial windows (1-7; i.e., pH values between 7.3 and 5.6), which indicates that

a

b

Figure 6. UV-vis and CD studies of the poly(C)-H system. (a) ETA results in the pH direction for the UV-vis titration. (b) ETA results in the pH direction for the CD titration.

there is no change in the number of components in the system. When the window number increases (7-12, i.e., pH values between 5.6 and 5.2), the second singular value also increases, indicating the presence of a new factor in this pH region. The peak found for the third singular values in this region probably reflects the appearance of another factor. In the pH region between pH 5.5 and the last points of the titration (acidic pH values), the second singular value decreases but does not reach the same level as at the beginning of the titration. This may be attributed to the presence of more than one species; i.e., this region seems not to be selective. The overall results indicate the formation of three different species in the system along the titration. At the beginning of the titration, only one species is present in the solution. At pH values around 5.5, a second species is formed and also probably a third one. Similar results are obtained for the different window sizes used in the ETA procedure (4-5). However, for the CD data, the ETA plot indicates the simultaneous presence of only two factors in the system (Figure 6b). The first singular value does not change practically in all the titration. The second singular value increases between pH values around 5.7 and 5.4 (window numbers 5-12), indicating the presence of a new factor in the solution. In the pH region between 5.5 and about 3.2, the second singular value decreases and reaches the same level as at the beginning of the titration. This fact can indicate the presence of only one species in this pH region; i.e., this region seems to be completely selective. The overall results indicate the formation of at least two different species in the system along the titration. At the beginning of the titration, only one species is present in the solution. At pH values around 5.5, a second species is formed, and at pH values around 4-3, the second singular value can indicate the only presence of one factor. Similar results are obtained for the different window sizes used in the ETA procedure (4-5). In the pH region between 4.0 and 3.2, there is a decrease in the CD intensity of the experimental spectra without any change in the position of the CD bands. When the spectra measured in the pH region 4.0-3.2 are normalized to equal length, one can see that all the spectra are identical, and the ETA approach only notices the presence of one factor (Figure 6b, window numbers 30-32). A possible explanation could be that the third species, which is probably present in a random coil conformation, has a CD spectrum of much lower intensity (similar to the baseline) compared to the other two spectra (both reflect ordered conformations of poly(C)).4 This fact is reflected in the experimental CD data as a decrease in the intensity of the spectra in the pH range where the acid-base equilibrium between the second and third species is present. However, only a certain decrease is observed, since the titrations cannot be carried out until complete

Figure 7. UV-vis and CD studies of the poly(C)-H system. Results with SIMPLISMA and concentration constraint (solid line) compared with those of EFA-ALS (symbols): (a) concentration profiles from the UV-vis titration, (b) UV-vis unit spectra, (c) concentration profiles from the CD titration, (d) CD unit spectra. (1) Deprotonated form of poly(C), (2) hemiprotonated form, (3) protonated form.4

protonation of the macromolecule due to the formation of precipitates at pH 3.2. Instead, the UV spectrum of the third species is different from that of the other two species, and the ETA approach clearly detects the presence of the three species when the UV data are analyzed. SIMPLISMA is applied to the UV data in the pH direction, and three pure spectra at pH values 6.44, 5.39, and 3.29 are found. The concentration profiles obtained from SIMPLISMA are constrained to have constant total concentration at each pH. The constrained concentration profiles, together with the ones obtained from EFA-ALS, are given in Figure 7a. The concentration profiles show the presence of a selective region in the neutral pH values (where only the deprotonated form of the polymer is present). In the pH values around 5.5, there is a region where two compounds are present simultaneously, and this fact was indicated in the ETA plot, with the presence of a peak in the second singular value (window numbers 7-12, Figure 6a). At pH values close to 5.0, the concentration profiles show a region where the second compound is coexisting with a small amount of the first (deprotonated) and third ones. This fact has been also reflected in the ETA plot in the peak in the third singular value. At the end of the titration (acidic pH values around 3.2), two species are present simultaneously in the solution. The results obtained with SIMPLISMA agree with those obtained with EFA-ALS. However, these results should be considered critically, since no selective zones are found for the second and third species, and the distribution species plot and individual spectra for these species might only be an unknown linear combination of the real ones. When SIMPLISMA is applied to the CD data in the pH direction, three pure spectra at pH values 6.48, 5.38, and 3.42 are found. The concentration profiles obtained from SIMPLISMA are constrained to have constant total concentration along the whole titration. The constrained concentration profiles, together with the ones obtained from EFA-ALS, are given in Figure 7c. In this case, the concentration profiles show the presence of two selective regions: one at neutral pH values and the other in the Analytical Chemistry, Vol. 68, No. 13, July 1, 1996

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Figure 8. CD study of the poly(I)-poly(C)-H system. ETA results in the pH direction.

Figure 9. CD study of the poly(I)-poly(C)-H system. Concentration profiles obtained with SIMPLISMA and concentration constraint (solid line) compared with those of EFA-ALS (symbols+solid line).

acidic pH region. Around pH 5.5, there is a region where two compounds are present simultaneously. These results, which are similar to those obtained with the EFA-ALS treatment, do not agree with those observed experimentally; i.e., the continuous decrease in the CD intensity in the pH range 4.0-3.2 is not explained by this distribution plot, since it indicates that in this range a single species is present. This third species is assigned a spectrum similar to that obtained for the second one. Furthermore, there is no agreement between this distribution plot and that obtained with the UV data. From these results, it can be concluded that when no selective regions (either in the pH or in the wavelength direction) are found for each of the different species present in the system, the results obtained (distribution plot of species and unitary spectra) only provide semiquantitative information about the system. (d) Poly(I)-Poly(C)-H System. The next step in the study of polynucleotides is the study of heteropolynucleotides, such as poly(I)-poly(C). This study could reveal if the acid-base behavior of this mixture is the sum of that of poly(I) and poly(C) individually, or if new interactions between both polynucleotides are present. Figure 8 shows the ETA profile for titration 6 obtained using a window size of 4 in the pH direction. The changes in the singular values show the presence of at least four species in the system. The low value of the second singular value and the lack of variation in the third singular values in the two initial windows (acidic pH values) indicate the presence of a selective region. Afterward, the second singular value increases, indicating the presence of a new compound in the system (windows 6-8). The decrease in the second singular value in windows 9-11 shows the presence of a region with the same number of compounds as at the beginning of the titration. In windows 13-16, a new compound is observed, and this fact is repeated in windows 2628. In conclusion, the ETA results show the presence of four selective pH regions, three regions where two compounds are present simultaneously, and probably four main factors in all the pH range. Similar results are obtained with the window sizes used in the ETA procedure (3-5). SIMPLISMA has been applied to the experimental data in the pH direction, and four pure spectra at pH values 2.41, 9.72, 6.35, and 3.87 have been found. Figure 9 shows the concentration

profiles obtained after constraining the total concentration at each pH to be constant, together with those obtained with EFA-ALS. The results confirm what was observed in the ETA plot (Figure 8). In the acidic pH values lower than 3, only one compound is present; i.e., there is a selective region for the first compound. This fact was also observed in the initial windows of the ETA plot. A second compound appears at pH 3. The presence of two compounds is indicated by the peak in the second singular value from windows 6 to 8. Around pH 4.0, the first compound has disappeared, and only the second compound is present. This was indicated in the ETA plot by a valley around window 10 in the second singular value. Afterward, a third compound is formed, and two compounds are detected from windows 13 to 16 in the ETA plot. When the second compound disappears, only the third compound is left, which is reflected by another valley in the ETA plot around window 23. At pH higher than 8, a fourth compound is formed. The coexisting region of compounds 3 and 4 is observed in the ETA plot from windows 23 to 31. At the end, only the fourth compound is left. In Figures 9 and 10, the results obtained with SIMPLISMA and EFA-ALS are compared. In general, the profiles obtained with both methods are quite similar in shape and in the position of the maximum. The difference arises in the presence of some secondary peaks in the profiles obtained with SIMPLISMA, while the profiles obtained with ALS do not show more than one maximum because of the unimodality constraint imposed. The CD unit spectra obtained for each compound with both approaches are shown in Figure 10. The agreement between the two sets of results are quite good. The small differences in the spectra are related to the presence of these additional peaks in the concentration profiles obtained with SIMPLISMA. SIMPLISMA was applied to UV-vis data of titration 5, and the pure spectra found were 10.54, 2.07, 4.43, and 7.94. The number of compounds and shape of the concentration profiles are in agreement with those obtained from the study by CD. The differences found in the profiles obtained from the CD data with both procedures have been also found with the UV-vis data.

2246 Analytical Chemistry, Vol. 68, No. 13, July 1, 1996

CONCLUSIONS ETA was applied to build the rank analysis map of the data matrices and to detect the selective regions in the pH and

Table 2. pKa Values Obtained after the Data Treatment with SIMPLISMA and EFA-ALS

Figure 10. CD study of the poly(I)-poly(C)-H system. CD unit spectra obtained with SIMPLISMA and concentration constraint (solid line) compared with those of EFA-ALS (symbols).

wavelength directions. The evolution of the number of components along the titration and their concentration windows were also determined. The application of ETA in the wavelength direction was not very useful due to the lack of selectivity in the spectra. However, the application in the pH direction detects the selective pH regions and the number of compounds present at different pH values. For the cCMP-H and poly(I)-H systems, only two species are present, and selective regions have been found for these species. On the other hand, the ETA study of the UVvis data of the poly(C)-H system has shown the presence of at least three species, but only one selective region (at the start of the titration, i.e., neutral pH values) has been found. Finally, the study of the poly(I)-poly(C)-H has shown clearly the presence of at least four species and four selective zones. SIMPLISMA was applied to the experimental data in the pH direction in order to determine the number of components in the studied systems and their concentration profiles and unit spectra. When SIMPLISMA was applied in the wavelength direction, the purest wavelengths were selected, but the absence of truly pure variables makes the resolution process fail. The presence of selective pH values for the cCMP, poly(I), and poly(I)-poly(C) systems allows the resolution of these systems with the application of SIMPLISMA in the pH direction. The pure spectra found with SIMPLISMA agree with the selective regions found with ETA. The concentration profiles obtained with SIMPLISMA have been also compared with the information obtained with ETA. In general, the agreement between both types of information is total.

system

pKa1

pKa2

poly(I)-H poly(C)-H poly(C)-poly(I)-H

3.8 3.6

5.5 5.0

pKa3 8.8 9.4

The presence of pH regions where only one compound is present is reflected in the ETA plots, when the second singular values are low and reach the noise level. On the other hand, the presence of pH regions where two compounds are present simultaneously (usually in pH values close to the pKa) is reflected in the high second singular values. The results obtained for the equilibria of polynucleotides with SIMPLISMA agree only qualitatively with the ones obtained with the ALS approach. However, it is possible to have also a quantitative agreement between both sets of results if a closure constraint is introduced in the SIMPLISMA method. Finally, when selectivity is not present in the pH range, the results obtained with both approaches are not completely reliable, as has been observed for the poly(C)-H system. The pKa values obtained from SIMPLISMA for the poly(I)poly(C)-H system can be compared with the values obtained for the poly(I)-H and poly(C)-H systems. In the case of the polynucleotides, it is difficult to determine a single pKa value for each of the equilibria present because of the presence of several secondary effects above mentioned. So, the pKa values obtained for the polynucleotides are referred to the pH value where 50% of each compound is involved in the acid-base equilibrium. In Table 2, all the pKa values found in this work are listed. The pKa values of poly(I) and poly(C) when they are isolated are different from the pKa values obtained when they interact in the same system. On the other hand, the precipitate in the poly(C)-H system at acidic pH (smaller than 3.2) is not observed in this case. We can conclude that there are some interactions (probably by hydrogen bonding) between the two kinds of nitrogenated bases. The explanation is rather extensive and is not the subject of this work. ACKNOWLEDGMENT R.G. acknowledges a FI grant from Generalitat de Catalunya (Spain). J. Toft is thanked for his helpful discussions. Received for review June 15, 1995. Accepted March 26, 1996.X AC950596M X

Abstract published in Advance ACS Abstracts, May 15, 1996.

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