Study of the Intercalation Equilibrium between the Polynucleotide Poly

The intercalation equilibrium between the polynucleotide poly(adenylic)-poly(uridylic) acid and the dye ethidium bromide was studied using molecular ...
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Anal. Chem. 1999, 71, 4328-4337

Study of the Intercalation Equilibrium between the Polynucleotide Poly(adenylic)-Poly(uridylic) Acid and the Ethidium Bromide Dye by Means of Multivariate Curve Resolution and the Multivariate Extension of the Continuous Variation and Mole Ratio Methods M. Vives, R. Gargallo, and R. Tauler*

Department de Quı´mica Analı´tica, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain

The intercalation equilibrium between the polynucleotide poly(adenylic)-poly(uridylic) acid and the dye ethidium bromide was studied using molecular absorption spectrophotometry, spectrofluorimetry, and circular dichroism. The presence of an intercalation complex, its pure spectrum, and its concentration profile were clearly deduced using Multivariate Curve Resolution and a multivariate extension of the classical continuous variation and mole-ratio methods. The value of the polynucleotide/ dye ratio (rpoly/dye) in the intercalation complex and of its apparent formation log constant were estimated to be 4 and 6.2, respectively. The proposed multivariate methodology allowed an accurate qualitative and quantitative description of the intercalation process. DNA and RNA, the genetic material in living cells, can interact with certain classes of drugs, carcinogens, mutagens, and dyes, all of which are characterized by extended cyclic aromatic chromophores.1 Owing to nucleic acid’s central role in biological replication and protein biosynthesis, modification by such interaction greatly alters cell metabolism, diminishing and, in some cases, terminating cell growth.2 Many applications in medicine have been found, and these compounds are extensively used in laboratory studies of DNA and RNA structure and function.3 For one category of these substances, the interaction with the nucleic acids is by means of chemical modification. Another category binds to the nucleic acid double helix, doing so either at the periphery or by means of intercalation between adjacent base pairs. This latter interaction is accomplished without disrupting Watson-Crick hydrogen bonding.1 The study of DNA and RNA intercalation processes is usually performed by X-ray crystallography, for the structure elucidation in solid state, and by absorption spectrophotometry, molecular * Corresponding Author. E-mail: [email protected]. Tel: 34-934021545. Fax: 34-934021233. (1) Saenger, W. Principles of Nucleic Acid Structure; Springer-Verlag: New York, 1988. (2) Waring, M. J. Annu. Rev. Biochem. 1981, 50, 159-192. (3) Chu, W.; Shinomiya, M.; Kamitori, K. Y.; Samitori, S.; Carlson, R. G.; Weaver, R. F.; Takusagawa, F. J. Am. Chem. Soc. 1994, 116, 7971-7982.

4328 Analytical Chemistry, Vol. 71, No. 19, October 1, 1999

fluorescence, circular dichroism (CD), NMR, etc. for the study of these processes in solution. Despite the advances in the field of hyphenated spectroscopic techniques and computer applications, data analysis in Biophysics and Biochemistry is still mostly performed by means of univariate data-analysis methods. Qualitative studies are performed by visual comparison of the changes in absorption, molecular fluorescence, or CD spectra of a polynucleotide solution with and without an intercalator. On the other hand, quantitative studies using the continuous-variation and moleratio methods for the determination of the polynucleotide/dye ratio (rpoly/dye) monitor the spectral changes only at a single wavelength.4-6 Several univariate least squares curve fitting methods have been traditionally proposed to interpret the experimental data7-8 and they have shown its power to determine the value of the rpoly/dye and of the formation constants. However, much more information can be extracted if multivariate spectroscopic data from intercalation studies are analyzed by means of an appropriate multivariate data analysis method. Multivariate curve resolution has been shown to be a powerful method to analyze spectroscopic data from polynucleotide equilibria (ref 9 and references therein). Extension of the traditional univariate melting studies to multivariate data by means of Multivariate curve resolution (MCR) has been recently proposed as a means to recover both qualitative and quantitative information.10 In this work, the continuous-variation and mole-ratio methods used traditionally to elucidate the stoichiometries of the ligand/metal ion complexation systems11-12 are extended to the study of the interaction equilibria between polynucleotides and possible dye intercalators using multivariate spectral data from UV-vis absorption, molecular fluorescence, and CD spectrometries. In particular, in the present work the study of the intercalation equilibria between the polynucleotide poly(adenylic)-poly(uridylic) (poly(A)-poly(U)) and the dye ethidium bromide is studied in detail. Poly(A)-poly(U) is a synthetic polynucleotide constituted (4) Krugh, T. R.; Reinhardt, C. G. J. Mol. Biol. 1975, 97, 133-162. (5) Gaugain, B.; Barbet, J.; Capelle, N.; Roques, B. P.; Le Pecq, J. B. Biochemistry 1978, 17, 5078-5088. (6) Dutton, M. D.; Varhol, R. J.; Dixon, D. G. Anal. Biochem. 1995, 230, 353355. 10.1021/ac990131m CCC: $18.00

© 1999 American Chemical Society Published on Web 08/20/1999

Table 1. Experimental Conditions of the Experiments Performed at 37 °C; Neutral pH; KH2PO4, 0.021 M; Na2HPO4, 0.029 M; and NaCl, 0.15 M, Itotal ) 0.26 M data matrices experiment

method

CEt (M)

Cpoly (M)

pH

no. of spectra

absa

1 2 3

continuous-variation mole-ratio (constant CEt) mole-ratio (constant Cpoly)

0-2.12 × 10-5 1.04 × 10-5 0-2.08 × 10-5

2.12 × 10-5 - 0 0-1.49 × 10-4 2.44 × 10-5

6.85 6.85 6.80

21 21 22

Dabsvar DabsEt Dabspoly

fla

CDa

Dflvar DflEt Dflpoly

DCDvar DCDEt DCDpoly

a For each experiment, absorption (220-600 nm, N labs ) 381 wavelengths), molecular fluorescence (530-850 nm, Nlfluo ) 321 wavelengths), and CD (210-600 nm, NlDC ) 391 wavelengths) spectra were recorded.

by two complementary strands, which is used as a RNA model and also as an activator of in vivo interferon biosynthesis.13-14 Ethidium bromide (EtBr) is a very fluorescent dye which has been shown to interact with double-stranded polynucleotides:

As a drug, it has trypanocidal, antibacterial, and antiviral activities.15 As an indicator it is used to study the tertiary structures of DNA and RNA by measuring the fluorescence polarization anisotropy.16 Finally, as a dye, its application to the development of DNA-based biosensors has been reported.17 The stoichiometry of the DNA-EtBr and RNA-EtBr intercalation complexes is not yet completely known, and there is still a controversy. Some authors propose that the intercalation occurs every 4-5 nucleotides, both in DNA15,18,19 and in RNA.19 However, intercalation every 2-3 nucleotides in DNA and poly(A)-poly(U)20 and every 10 in RNA21 has been also proposed. It is therefore of interest to study this system and to show the applicability of the multivariate extension of the continuous variation and mole-ratio methods and multivariate curve resolution to the study of the intercalation equilibria of nucleic acids. EXPERIMENTAL SECTION Reagents and Solutions. Sodium chloride (Merck, a.r.), potassium monohydrogenphosphate (Carlo Erba a.r.), sodium (7) Scatchard, G. Ann. N. Y. Acad. Sci. 1949, 51, 660-672. (8) Crothers, D. M. Biopolymers 1968, 6, 575-584. (9) de Juan, A.; Izquierdo-Ridorsa, A.; Gargallo, R.; Tauler, R.; Fonrodona, G.; Casassas, E. Anal. Biochem. 1997, 249, 174-183. (10) Gargallo, R.; Tauler, R.; Izquierdo-Ridorsa, A. Anal. Chem. 1997, 69, 17851792. (11) Job, P. Ann. Chim. 1928, 9, 113-203. (12) Yoe, J. H.; Jones, A. L. Anal. Chem. 1944, 16, 111-115. (13) Dover, S. D.; Fuller, W.; Hodgson, A. R. J. Mol. Biol. 1973, 81, 207. (14) Thang, M. N.; Guschlbauer, W. Pathol. Biol. 1992, 40, 1006-1014. (15) Douthard, R. J.; Burnett, J. P.; Beasley, F. W.; Frank, B. H. Biochemistry 1972, 12, 214-219. (16) Duhamel, J.; Kanyo, J.; Dinter-Gottlieb, G.D.; Lu, P. Biochemistry 1996, 35, 16687-16697. (17) Mecklenburg, M.; Grauers, A.; Rees Jo¨nsson, B.; Weber, A.; Danielsson, B. Anal. Chim. Acta 1997, 347, 79-86. (18) Yguerabide, J.; Ceballos, A. Anal. Biochem. 1995, 228, 208-220. (19) Waring, M. J. J. Mol. Biol. 1965, 13, 269-282. (20) Bresloff, J. L.; Crothers, M. D. Biochemistry 1981, 20, 3547-3555. (21) LePecq, J. B.; Paoletti, C. J. Mol. Biol. 1967, 27, 87-106.

dihydrogenphosphate (Panreac, a.r.), ethidium bromide (SIGMA), and poly(A)-poly(U) acid (SIGMA) were used without further purification. Solutions of polynucleotide were prepared from a known amount of the solid reagent dissolved in the ionic medium used in this study. A pH value of 6.8 was adjusted by means of a buffer solution, monohydrogenphosphate/dihydrogenphosphate. The concentration of the synthetic polynucleotide solutions refers to the concentration of the cyclic monophosphate nucleotides cAMP and cUMP, which are the monomeric units in the polynucleotide chains. Table 1 summarizes the experimental conditions of the experiments performed. Apparatus. UV-vis absorption spectra were recorded on a Perkin-Elmer lambda-19 spectrophotometer. Fluorescence spectra were recorded on an Aminco-Bowman series 2 spectrofluorimeter (λex ) 520 nm, slits: 4/4). CD spectra were recorded on a Jasco J-720 spectropolarimeter. Instrumental control, data acquisition, and spectra preprocessing were carried out using personal computers. pH measurements were performed with an Orion model 701A pH meter (with a precision of (0.1 mV) and a combined Ross pH electrode (Orion 81-02). Experimental Procedure. The experimental conditions of the experiments performed are given in Table 1. Three different experiments were carried out at 37 °C and 0.26 M ionic strength. Experiment 1 is based on the traditional continuous-variation method,11 which consists of recording the absorbance of a set of solutions with different polynucleotide/dye concentration ratios, ranging from χEtBr (molar fraction) equal to 0 to χEtBr equal to 1. Traditionally, this method is based on the monitoring of the absorbance changes due to the formation of the complex at one single wavelength. This implies that this wavelength must be selective, i.e., only the complex must absorb at this wavelength. Experiments 2 and 3 are based on the mole-ratio method, which has been traditionally used in the study of the metal ionligand interactions.12 This method is based on monitoring the absorbance changes of a metal-ion solution upon the addition of a ligand stock solution. As in the continuous-variation method, absorbance changes are monitored at one single selective wavelength at which only the complex absorbs. Two different approaches have been used in this work. In experiment 2, EtBr concentration (CEt) was kept constant along the experiment whereas poly(A)-poly(U) concentration (Cpoly) was increased, i.e., rpoly/dye was increased along the experiment. On the contrary, Cpoly was kept constant whereas CEt was increased in experiment 3. Multivariate extension of these methods implies that for all the solutions prepared in experiments 1-3, the whole UV-vis absorption (220-600 nm), molecular fluorescence (530-850 nm), and CD (210-600 nm) spectra were recorded. Analytical Chemistry, Vol. 71, No. 19, October 1, 1999

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Figure 1. Data matrices arrangement: (a) Analysis of a single spectroscopic data matrix, (b) simultaneous analysis of several spectroscopic data matrices corresponding to the same experiment and different spectroscopic technique, c) simultaneous analysis of several spectroscopic data matrices corresponding to the same spectroscopic technique and different experiments, (d) simultaneous analysis of several spectroscopic data matrices corresponding to different spectroscopic techniques and different experiments.

Data Treatment. Linear Model, Data Arrangement, and Data Pretreatment. Each of the proposed experiments using either the continuous-variation method or the mole-ratio method and one of the three spectrometric methods gave a set of experimental spectra which were arranged in a table or data matrix D of dimensions Nr × Nl, where Nr is the number of different spectra recorded at different concentration ratios of polynucleotide to ethidium dye, and Nl is the number of wavelengths of these spectra. As there were three types of experiments and three types of spectroscopies, a total number of nine data matrices were obtained in these experiments. In Table 1, the details of these nine experiments are given. The experimental data in each experiment are assumed to follow a linear model based in the multivariate extension of Beer’s law, which can be described by the following matrix equation (Figure 1a):

D ) C ST + E

(1)

In this equation, matrix C gives the changes of concentration of the species detected during the experiment and has dimensions 4330 Analytical Chemistry, Vol. 71, No. 19, October 1, 1999

Nr × N, where N is the number of detected species. Matrix ST gives the pure spectra of these detected species and has dimensions N × Nl. Matrix E is the matrix which has the data variance unexplained by the proposed model and number of species and which hopefully only describes experimental error. Matrix E has dimensions Nr × Nl. In Figure 1a, a graphical representation of this equation for the case of absorption data is given. The experimental data obtained using any one of the three spectroscopies, molecular absorption, fluorescence, or circular dichroism, are assumed to follow the linear model described by eq 1 and Figure 1a. Moreover, since the same samples were analyzed simultaneously by the three spectrometric methods, a new data arrangement is possible as shown in Figure 1b and described by eq 2

[DabsDflDCD] ) C[SabsSflSCD]T + [EabsEflECD]

(2)

or in a more compact form

[Dabs, Dfl, DCD] ) C[Sabs, Sfl, SCD]T + [Eabs, Efl, ECD] (2′)

where now [Dabs, Dfl, DCD] is the row-wise augmented data matrix obtained by setting the data matrices, obtained using the same chemical experiment but measured using the three different spectrometric methods, one beside the other. The dimensions of this new row-wise augmented data matrix are Nr × (Nlabs+ Nlfl + NlDC). C is the matrix giving the changes of concentration of the N species detected in the considered experiment, and it has the dimensions Nr × N, the same dimensions as in eq 1. [Sabs, Sfl, SCD]T is the row-wise augmented matrix of species spectra, where each row has, for each species, its pure spectrum in the three spectroscopies, absorption, fluorescence, and CD. It has dimensions N × (Nlabs+ Nlfl + NlDC). [Eabs, Efl, ECD] is the row-wise augmented error matrix in the three spectrometries, and it has the dimensions Nr × (Nlabs + Nlfl + NlDC). In this new data arrangement, the three individual matrices, Dabs, Dfl, and DCD share their row space, defined by concentration matrix C; i.e., the species concentration profiles are exactly the same in the three experiments (see Experimental Section). As three types of experiments were performed on the same polynucleotide-ethidium chemical system and in the three cases the same spectroscopy method was applied, a different data arrangement and model are possible for each spectrometric technique defined by eq 3 (see Figure 1, part c)

dimensions) (Nrvar + NrEt + Nrpoly) × Nl. Note that in this data arrangement it is implicitly assumed that some or all of the species formed in the three experiments are common (have the same spectrum), although their concentration or concentration profiles are different in the different experiments. Finally, a last possible data arrangement and model is possible as described by the equation (see Figure 1d)

Dvar Cvar Evar T Et Et ) C S + EEt D Dpoly Cpoly Epoly

where [Dvar; DEt; Dpoly] is the columnwise augmented matrix obtained by setting one individual matrix on top of the other. The data matrices Dvar, DEt, and Dpoly correspond to the three different experiments, the continuous-variation method, the mole-ratio method with constant CEt, or the mole ratio method with constant Cpoly concentration, analyzed by the same spectrometric method, for instance by absorption spectrophotometry. The dimensions of this new columnwise augmented data matrix are: (Nrvar + NrEt + Nrpoly) × Nl. [Cvar; CEt; Cpoly] is the corresponding augmented columnwise concentration matrix with dimensions (Nrvar + NrEt + Nrpoly) × Nl. Each column of this augmented matrix has the concentration profile of one species in each of the three different experiments. For each species, its concentration profile using the continuous-variation method or any of the two mole-ratio methods has a different shape.22,23 The matrix ST has the pure spectra of the detected species in the considered spectrometric method. and has dimensions N × Nl (the same as in eq 1). As common species are supposed to be formed in the different experiments, they share the same pure species spectrum, for the considered spectroscopy. [Evar; EEt; Epoly] matrix is the columnwise augmented error matrix for the three types of chemical experiments performed with

[[Dabs, Dfl, DCD]var; [Dabs, Dfl, DCD]Et; [Dabs, Dfl, DCD]poly] is the row- and columnwise augmented experimental data matrix, which contains all the data in the three different experiments and spectroscopies. A total number of nine individual data matrices are simultaneously analyzed using model eq 4. The dimensions of this row-and-column-wise augmented matrix are (Nrvar + NrEt + Nrpoly) × (Nlabs + Nlfl + NlDC). [Cvar; CEt; Cpoly] is the columnwise augmented concentration matrix like in eq 3′, [Sabs, Sfl, SCD]T is the row-wise augmented spectra matrix like in eq 2′, and + [[Eabs, Efl, ECD]var; [Eabs, Efl, ECD]Et; [Eabs, Efl, ECD]poly] is the row- and columnwise augmented error matrix corresponding to all different experiments and spectroscopies of dimensions (Nrvar + NrEt + Nrpoly) × (Nabs + Nlfl + NlDC). Experimental data obtained in different spectroscopies were scaled to have similar maximum values when analyzed simultaneously in the row-wise augmented data arrangements (eqs 3 and 4). In this way, the scale of the different units of the different spectrometric methods are changed to a common scale with a maximum value of one. This data scaling helps to give similar weight to the three spectroscopies during their simultaneousresolution process. Multivariate Curve Resolution. The number of species present in the different spectroscopies and experiments was initially estimated by singular-value decomposition (SVD) of the experimental data matrices D.24 The number of larger singular values found in this analysis is related to the number of different species spectroscopically active. Conversely, small-size singular values are associated with experimental noise. Evolving factor analysis of individual data matrices D 25 was used to confirm this number of species and to have an estimate of how their concentrations changed during the experiments. As one particular chemical species may be spectrally active in one spectroscopic method and

(22) Tauler, R., Izquierdo-Ridorsa, A.; Casassas, R. Chemom. Intell. Lab. Syst. 1993, 18, 293-300. (23) Tauler, R.; Smilde, A.; Kowalski, B. J. Chemom. 1995, 9, 31.

(24) Golub, G. H.; Van Loan, C. F. Matrix Computations; The Johns Hopkins University Press: Baltimore, 1989. (25) Maeder, M.; Zillian, A. Chemom. Intell. Lab. Syst. 1988, 3, 205-313.

[ ][ ] [ ]

(3)

or in a more compact form

[Dvar; DEt; Dpoly] ) [Cvar; CEt; Cpoly]ST + [Evar; EEt; Epoly] (3′)

[

][ ]

[

]

var var var var Dvar Evar Cvar abs Dfl DCD abs Efl ECD Et Et Et Et DEt ) CEt [SabsSflSCD]T + EEt abs Dfl DCD abs Efl ECD poly poly poly Dpoly Dpoly Epoly ECD Cpoly abs Dfl CD abs Efl (4)

or in a more compact form

[[Dabs, Dfl, DCD]var; [Dabs, Dfl, DCD]Et; [Dabs, Dfl, DCD]poly] ) [Cvar; CEt; Cpoly] [Sabs, Sfl, SCD]T + [[Eabs, Efl, ECD]var; [Eabs, Efl, ECD]Et; [Eabs, Efl, ECD]poly] (4′)

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inactive in another spectroscopic method, the number of detected species may be different in the different experimental data sets. For instance, the poly(A)-poly(U) species is detected by CD, but it is nearly not detected by fluorescence under the conditions of the experiments (pH ) 6.8). On the other hand, EtBr dye is strongly fluorescent but is not optically active, and it is not detected by CD. Both, poly(A)-poly(U) and EtBr, do absorb in the UV region. Singular-value decomposition (SVD) of row-wise and columnwise augmented data matrices provided an estimation of the total number of spectroscopically active species and of their correspondence in the different experiments and spectroscopies. Equations 1-4 describe four different data arrangements in which the linear model holds. Initially, only the experimental data matrices D are known, and the goal of multivariate curve resolution (MCR) is the deduction of the true concentration and spectra matrices, C and ST, including the possible detection of new intercalation species. The proposed MCR method has been described in previous publications (refs 9, 22, 23, 26, 27 and references therein) and only a short description of how this method is adapted to the analysis of the experimental data of this work is given. Once an initial estimation of the number of species is available for every individual data matrix, evolving factor analysis (EFA 25) and pure variable detection methods28 are applied to each of the nine individual data matrices, respectively, to obtain initial estimates of the concentration or of the spectra matrix, (C)0 or (St)0. Once these initial estimations are available, an alternating least squares (ALS) iterative optimization is initiated using the two following equations and constraints (considering that the initial estimation available is the matrix C): Let M be equal to the number of required iterations for convergence, at each iteration (k ) 0:M - 1) solve the equations

STk+1 ) (Ck)+ D subject to:

(5)

ST g 0 (for absorption and fluorescence data only)

and

(Ck+1) ) D (Sk+1T)+ subject to:

(6)

Cg0

where C+ in eq 5 and (ST)+ in eq 6 refer, respectively, to the pseudoinverses24 of the nonsquare matrices C and ST. Equations 5 and 6 are solved iteratively using a nonnegative least squares algorithm.29,30 Apart from the nonnegativity constraint in eqs 5 and 6, concentration profiles obtained by solution of eq 6 are constrained to fulfill a closure constrain. As the total concentration of EtBr is known for each experimental point of the different experiments, a simple mass balance equation is established for (26) Tauler, R. Chemom. Intell. Lab. Syst. 1995, 30, 133-146. (27) Tauler, R.; Gargallo, R.; Vives, M.; Izquierdo-Ridorsa, A. Chemom. Intell. Lab. Syst. 1999, 46, 275-295. (28) Windig, W.; Stephenson, D. A. Anal. Chem. 1991, 64, 2735. (29) Lawson, C. L.; Hanson, R. J. Solving Least Squares Problem; Prentice-Hall: Englewood Cliffs, N. J., 1974. (30) Bro, R.; de Jong, S. J. Chemom. 1997, 11, 393-401.

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the concentration of the species containing EtBr. This constraint is applied during each step of the ALS optimization, and it allows the estimation of the concentration profiles to be in the true concentration scale. The concentration and pure-spectra profiles of each species obtained in the analysis of individual data matrices by the MCRALS method can be different from the true ones because of the unresolved underlying factor analysis rotational and intensity ambiguities.22,23 Whether the final solutions are equal to the true ones depends on the data selectivity, i.e., on the presence of rpoly/dye regions where only one species predominates or on the presence of wavelengths at which mostly only one species absorbs23 and on local rank conditions, i.e., how the regions are where the different species are simultaneously present or are simultaneously absorbing.31 Multivariate curve resolution analysis of an individual data matrix where selectivity or local rank conditions are present provides solutions which are the true ones or are very close to the true ones. As it has also been shown in previous works,9,22,23,27 when different correlated-data matrices are simultaneously analyzed by the MCR-ALS method, the number of possible solutions of eqs 2, 3, and 4 and Factor Analysis rotational ambiguities are drastically reduced and, eventually, convergence to a unique solution is found. In fact, when the local rank conditions of resolution31 are met for one species in one matrix, then the resolution of this species is also obtained for the same species in the other matrices, even if its resolution was not possible in the individual analysis of the other matrices. In the particular case under study, resolution conditions may be easily achieved in the simultaneous analysis of the different spectral data matrices because of the absence of signal in some spectroscopies for some species and because of the inherent selectivity for some of the species in the continuous-variation and mole-ratio methods. The stoichiometry of the polynucleotide/dye complex was determined from the MCR-ALS estimated concentration profile of the intercalation complex. For the continuous variation method, rpoly/dye was calculated from the abscissa of the maximum of the concentration profile (χEtBrmax), calculated by drawing tangents to the initial and final parts of the profile.11 For the mole-ratio method, the abscissa of the point of intersection of the two tangents drawn to the initial and final parts of the concentration profile gives the value of rpoly/dye in the complex.12 From the MCR-ALS estimated concentration profiles it is also possible to calculate a value of the apparent formation constant of the intercalation complex using the equation

Kapp ) [complex]/[poly][EtBr]

(7)

where [complex], [poly], and [EtBr] are the estimated concentrations for the intercalation complex, free poly(A)-poly(U), and free EtBr, respectively, at each point of the concentration profiles. The values of log Kapp shown in Table 2 are the mean values of log Kapp in the points where the three species coexist at significant concentrations. RESULTS AND DISCUSSION There are three types of experiments, continuous-variation (var), mole-ratio at constant ethidium bromide concentration (Et), and mole-ratio at constant polynucleotide (poly) (see Table 1).

Table 2. Results of the MCR-ALS Analysis of the Different Experiments Carried Out in This Work data matrix Dabsvar Dflvar DCDvar [Dabsvar,Dflvar,DCDvar] [DabsEt,DflEt,DCDEt] [Dabspoly,Dflpoly,DCDpoly] [Dabsvar,Dflvar,DCDvar; DabsEt,DflEt,DCDEt; Dabspoly,Dflpoly,DCDpoly]

ALS lofa

rpoly/dyeb

mean value of log(Kapp)

3.4 3.6 10.1 4.1 4.3 3.6 3.7

1.4 4.8 4.0 4.0 4.2 4.0 4

d d d 5.9 (1.7) 7.1 (1.2) 6.4 (1.1) 6.2 (2.1)

a

lack of fit (lof) ) 100 ×

∑(d - d ) ∑d

x

/ 2 ij

ij

2 ij

where dij are the absorbance, CD, or fluorescence data at rpoly/dye i and wavelength j, and dij* are the ALS recalculated data using the specified number of components. b rpoly/dye was calculated according to the equation χpoly rpoly/dye ) 1 - χpoly c

For the calculation of Kapp see text. Standard deviations are also included in brackets. d Too few experimental points were available for a reliable estimation.

Each one of these experiments has been monitored using three different spectrometric methods: absorption (abs), molecular fluorescence (fl), and circular dichroism (CD). This gives a total of nine data sets arranged in the corresponding nine data matrices shown in Table 1. Apart from the individual analysis of these nine individual data matrices (Figure 1a), other data arrangements were possible. Summarizing, these arrangements were: (1) three rowwise augmented data matrices corresponding to the analysis of one of the three experiments (var, Et or poly) monitored simultaneously with the three different spectroscopic methods (abs, fl, and CD, Figure 1b); (2) three columnwise augmented data matrices corresponding to the simultaneous analysis of the three experiments (var, Et, and poly) monitored using only one of the three spectroscopic methods (abs, fl, or CD; Figure 1c); and (3) one row- and columnwise superaugmented data matrix built up using all nine different individual data sets (Figure 1d). The more relevant results of these analyses are given. Method of Continuous Variation. Individual Analysis of Absorption Data. Data Matrix Dabsvar. Figure 2a shows the absorption data obtained in the experiment 1. Whereas poly(A)poly(U) (bottom spectrum) shows only one maximum at 259 nm, EtBr (top spectrum) shows several maxima at 285 and 480 nm and a higher absorption intensity in the whole spectral range. From the UV data of Figure 2a it is difficult to deduce the formation of an intercalation complex because of the high spectral overlap. On the contrary, as the absorption in the visible region is only due to EtBr containing species, the shift of the maximum in the visible region from 480 nm for free EtBr to 490 nm at χEtBr ≈ 0.14-0.34 is an indication of the intercalation process. Finally, at χEtBr ≈ 0 the visible region of the spectra disappears because poly(A)-poly(U) does not show any absorption in this region, and no EtBr is present. In the whole absorption region no wavelength is fully selective for the intercalation complex, since the spectrum of this complex is completely

Figure 2. Experimental data matrices. Experiment 1: (a) absorption (data matrix Dabsvar); (b) fluorescence (Dflvar); (c) CD (DCDvar). Experiment 2: (d) absorption (DabsEt); (e) fluorescence (DflEt); (f) CD (DCDEt). Experiment 3: (g) absorption (Dabspoly); (h) fluorescence (Dflpoly); (i) CD (DCDpoly).

embedded into the EtBr spectrum. Under these conditions, the classical univariate continuous-variation method could not have been applied to deduce the stoichiometry nor the nature of the intercalation complex, since this method needs selective wavelengths at which the measured absorption is only due to the complex. The data matrix Dabsvar was analyzed by the SVD method, and it confirmed the presence of three main components in the system. EFA plots 25 also showed the presence of three main components in the system, which were related, respectively, to the free polynucleotide, the free ethidium, and the possible intercalation complex. This number of components was also checked by detection of the purest spectra.28 The purest spectra found were those recorded at χEtBr ) 0, 0.19 and at χEtBr ) 1. Using the initial concentration profiles estimated by EFA,23 MCR-ALS resolved the pure absorption spectra and concentration profiles given in Figure 3. The same ALS optimization was also carried out using as initial estimations the purest spectra estimated using the SIMPLISMA method.28 The results obtained by MCR-ALS with the two initial estimations converged to a very similar final solution. However, from the recovered profiles, it is clear that the local rank conditions31 for a correct resolution of the intermediate intercalation complex species were not present, since this intermediate species existed from nearly the beginning to the end of the experiment, and its formation was always overlapped, both in concentration and in spectra, with the other two present species (see Figure 3). On the contrary, rotational freedom for the first and third pure species spectra, should be much lower than for the second species because of the high concentration selectivity present for these two species either at the beginning of the experiment (for poly(A)-poly(U) species) or at the end of the experiment (for EtBr species). The resolved absorption pure spectra already explained the main trends observed experimentally (Figure 3a). Hence, the absorption of poly(A)-poly(U) is consider(31) Manne, R. Chemom. Intell. Lab. Syst. 1995, 27, 89-94.

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Figure 3. Results of the data analysis in the absorption region of Experiment 1 (data matrix Dabsvar). (a) Pure absorption spectra; (b) concentration profiles. 1, EtBr; 2, intercalation complex; 3, poly(A)poly(U).

ably lower than that observed for EtBr and a shift in the maximum from 480 to 490 nm is also observed during the intercalation process. From the resolved concentration profiles, a value of rpoly/dye ≈ 1.4 (corresponding to a χEtBr ≈ 0.58) was initially estimated from the intersection of the tangent lines drawn from the first and last points of the experiment. MCR-ALS lack of fit values and estimated rpoly/dye and Kapp values are given in Table 2. ALS lack of fit values show that most of the data variance is explained by the proposed model; residual unexplained variance (3.4%) is supposed to be due to experimental noise and to experimental uncertainties in the total concentration of EtBr, CEt, when the closure constraint was applied. Individual Analysis of Molecular Fluorescence and of CD Data. Data Matrices Dflvar and DCDvar. Figure 2b shows the molecular fluorescence (data matrix Dflvar) spectra obtained in experiment 1. EtBr (bottom spectrum) shows a fluorescence maximum at 610 nm. Addition of poly(A)-poly(U), which is not fluorescent at this pH, produces a shift of the maximum to 592 nm together with a dramatic increase of the fluorescence intensity. Figure 2c shows the CD spectra obtained in experiment 1 (data matrix (DCDvar). Poly(A)-poly(U) shows a well-defined CD spectra, characterized by the maxima at 222 and 266 nm. Addition of EtBr, which does not have a CD signal, produces a slight shift of the two maxima up to 220 and 271 nm, the appearance of a band at 310-320 nm, and a small change in the noise pattern at 450-550 nm. For both techniques, fluorescence and CD, only two of the three species present in the system showed a spectroscopic signal, i.e., only the species containing ethidium showed fluorescence and only the species containing poly(A)-poly(U) showed optical properties in CD. SVD analysis suggested in both cases the presence of only two main components in the system. In both cases the ALS resolved concentration profiles for these two species were free from rotational ambiguities since selectivity conditions23 for the total resolution of these two species were present. MCRALS lack of fit values and estimated rpoly/dye and Kapp values are also given in Table 2. CD results gave worse fits than absorption 4334 Analytical Chemistry, Vol. 71, No. 19, October 1, 1999

Figure 4. Results of the simultaneous data analysis in the absorption, CD, and fluorescence regions of the experiment 1 (data matrix [Dabsvar, Dflvar, DCDvar]). (a) Pure absorption spectra; (b) CD spectra; (c) fluorescence spectra; (d) concentration profiles. Continuous line, EtBr; dotted line, intercalation complex; dashed line, poly(A)-poly(U).

or fluorescence results because of the lower signal-to-noise ratio of CD spectra compared with those of absorption and fluorescence spectra. As it is seen from values in Table 2, rpoly/dye results obtained by CD and fluorescence do agree, but, they disagree with those previously obtained by absorption results, in which rotational ambiguities were probably still present. Simultaneous Analysis of Absorption-Fluorescence-CD Data (eq 2). Row-wise Augmented Data Matrix [Dabs, Dfl, DCD]var. MCRALS data analysis was extended to the analysis of the row-wise augmented data matrix built up using the three spectroscopic techniques (Figure 1b and eq 2). This procedure allowed the simultaneous analysis of absorption, fluorescence, and CD data matrices for the three detected species. The absorption, CD, and fluorescence pure spectra and the concentration profiles obtained by the MCR-ALS procedure are given in Figure 4. The resolved absorption, CD, and fluorescence pure spectra showed the trends already observed in the experimental data. The intercalation process is characterized by hypochromic and bathochromic effects in the visible region, by a displacement of CD bands at 220 and 271 nm and the appearance of a new CD band at 310 nm, and by a dramatic increase in the fluorescence due to the intercalation complex with EtBr. Moreover, the absorption spectrum recovered for this intercalation complex is different from the absorption spectrum recovered in the individual analysis of the absorption data. The maximum in the visible region is located at 504 nm, slightly different from the maximum at 490 nm previously calculated for the intercalation complex. An isosbestic point at 510 nm was observed which agrees with previous results of Douthard et al.15 The difference between this spectrum and that obtained in the individual analysis of only the absorption data (eq 1) confirms that rotational ambiguities were still present. The MCR-ALS recovered concentration profiles obtained for the absorption data in the row-wise augmented data matrix treatment were also slightly different from those obtained in the individual analysis of absorption data. The maximum of the intercalationcomplex profile was now located at χEtBr ≈ 0.2 instead of at χEtBr 0.58 in the individual analysis. From these concentration profiles

a value of rpoly/dye ≈ 4 was calculated. This value is more in agreement with those obtained for the CD and fluorescence data and confirms that rotational ambiguities present in the individual analysis of data matrix Dabs were solved in the analysis of augmented matrix [Dabs, Dfl, DCD]var. Mole-Ratio Method. Table 1 shows the experimental conditions of the two approaches used for the mole-ratio method developed in this work. Results of the individual analysis of each spectrometric data set (absorption, fluorescence, and circular dichroism) with the MCR-ALS method are not given here for brevity and because most of the information obtained from these analyses is also obtained in the simultaneous analysis of these data sets given below. CEt Constant. Simultaneous Analysis of Absorption-FluorescenceCD Data (eq 2). Row-Wise Augmented Data Matrix [Dabs, Dfl, DCD]Et. In experiment 2, CEt was kept constant along the experiment whereas Cpoly was increased. The intercalation process was detected in experiment 2 by a bathochromic effect in the visible region, by the appearance of new bands in the CD spectrum of poly(A)-poly(U), and by a dramatic increase in the fluorescence of EtBr. As in the continuous-variation method, data analysis was first performed for the individual spectrometric methods (eq 1) and then extended to the analysis of the row-wise augmented data matrix containing the data from the three spectroscopic techniques. As in the analysis of data from experiment 1, three components were needed to explain the whole variation in the experimental data. These components were also related to free EtBr, to an intercalation complex, and to free poly(A)-poly(U). Table 2 gives the final achieved results. The maximum of the intercalation-complex profile is again located at rpoly/dye ≈ 4. The same considerations about the removal of factor-analysis ambiguities associated with the individual analysis of absorption data compared with the individual analysis of fluorescence and CD data apply here. As for the continuous-variation data, the simultaneous analysis of the three spectrometric data matrices gave a more reliable explanation of the concentration and spectra profiles of the three detected species than did the individual analysis of each of them. Cpoly(A)-poly(U) Constant. Simultaneous Analysis of AbsorptionFluorescence-CD Data (eq 2). Row-Wise Augmented Data Matrix [Dabs, Dfl, DCD]poly. In this experiment, Cpoly was kept constant whereas CEt was increased along the experiment 3 (Table 1). The intercalation process was detected in the absorption spectrum by the appearance of two bands at 280 and 505 nm, respectively, shifting the latter to 490 nm upon increase of CEt. In the fluorescence spectrum, the appearance of a band upon addition of EtBr was also observed. Finally, the CD spectrum shows the formation of the complex by the appearance of a band at 310 nm (Figure 2). Three components were needed to explain the whole variation in the experimental data, which were also related to free EtBr, to an intercalation complex, and to free poly(A)-poly(U). Table 2 shows the calculated ALS lack of fit, rpoly/dye and log Kapp values, which agreed with those obtained previously in the simultaneous analysis of absorption, fluorescence, and CD data of experiments 1 and 2. The same considerations about the removal of factor-analysis ambiguities associated with the individual analysis of absorption data as compared with the individual analysis of fluorescence and CD data can be done.

Figure 5. Results of the simultaneous data analysis of experiments 1, 2, and 3, in the absorption, CD, and molecular fluorescence regions (data matrix [Dabsvar, Dflvar, DCDvar; DabsEt, DflEt, DCDEt; Dabspoly, Dflpoly, DCDpoly]). (a) Pure absorption spectra; (b) fluorescence spectra; (c) CD spectra; concentration profiles for the experimental conditions of experiment 1 (d), experiment 2 (e) and experiment 3 (f). Lines as in Figure 4.

Simultaneous Analysis of Continuous-Variation and MoleRatio Experiments Using the Three Spectrometric Methods (eqs 4 and 4′). Row-Wise and Column-Wise Augmented Data Matrix [[Dabs, Dfl, DCD]var; [Dabs, Dfl, DCD]Et; [Dabs, Dfl, DCD]poly]. Finally, MCR-ALS was applied to the row-and-columnwise superaugmented data matrix, i.e, to all nine experimental data matrices (eqs 4 and 4′). Table 2 and Figure 5 give the final obtained results. The concentration profiles obtained by MCR-ALS for this superaugmented matrix are similar to those obtained in analysis of rowwise augmented data matrices. The value of 510 nm found for the visible maximum of the intercalation complex is slightly different from that found by Bresloff et al. using a univariate approach (518 nm).20 The value of rpoly/dye, ∼4, is confirmed. That means than only 25% of potential intercalation sites between base pairs are occupied by dye molecules. This implies that three of every four potential intercalation sites along the poly(A)-poly(U) double helix are not occupied by the intercalated ethidium molecules. These results do agree with those obtained for DNA15,18,19 and RNA.19 From concentration profiles of Figure 5, a value of log Kapp equal to 6.2 was estimated, which is similar to the value reported by Bresloff et al. at lower temperature and higher ionic strength for the poly(A)-poly(U)-EtBr complex (log Kapp ) 5.0 at 19 °C and 1 M 20). The slight disagreement of these values could be due to the differences in the experimental conditions of temperature and ionic strength, which could affect the structure of the polynucleotide.27 Comparison of Results Obtained with Different Data Treatments. To summarize the results obtained in the different data arrangements and see which one is better, correlation coefficients between the recovered absorption spectrum of the intercalation complex (Table 3) and its concentration profile using the different data arrangements given in Table 1 were calculated. It has been considered a very good agreement between two data treatments when the correlation coefficient, r, between the two corresponding recovered profiles is higher than 0.99. The absorption spectrum recovered in the individual analysis of the continuAnalytical Chemistry, Vol. 71, No. 19, October 1, 1999

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Table 3. Comparison between the Pure Spectra of the Intercalation Complex Estimated by MCR-ALS in the Different Data Treatments (Values are Given As Correlation Coefficients (Similarities) between the Couple of Profiles)a

sabsvar,a sabsEt,a sabspoly,a sabsvar,b sabsEt,b sabspoly,b sabsc sabsd

sabsvar,a

sabsEt,a

sabspoly,a

sabsvar,b

sabsEt,b

sabspoly,b

sabsc

sabsd

1 0.94 0.95 0.96 0.92 0.91 0.92 0.93

1 >0.99 >0.99 >0.99 >0.99 >0.99 >0.99

1 >0.99 >0.99 >0.99 >0.99 >0.99

1 >0.99 >0.99 >0.99 >0.99

1 >0.99 >0.99 >0.99

1 >0.99 >0.99

1 >0.99

1

a Symbols are as in Figure 1 and Tables 1 and 2. Superscript a refers to the recovered spectra using the individual data treatment (scheme a in Figure 1). Superscript b refers to the recovered spectra obtained using the row-wise data augmentation (scheme b in Figure 1). Superscript c refers to the recovered spectra obtained using the column-wise data augmentation (scheme c in Figure 1). Superscript d refers to the recovered spectra obtained using superaugmented data matrix (scheme d in Figure 1).

Table 4. Comparison between the Concentration Profiles of the Intercalation Complex Estimated by MCR-ALS in the Different Data Treatments (Values are Given As Correlation Coefficients (Similarities) between the Couple of Compared Profilesa

cabsvar,a cflvar,a cCDvar,a cabsvar,c cflvar,c cCDvar,c cvar,b cvar,d

cabsvar,a

cflvar,a

cCDvar,a

cabsvar,c

cflvar,c

cCDvar,c

cvar,b

cvar,d

1 0.86 0.89 0.75 0.87 0.86 0.85 0.85

1 0.98 0.93 0.95 0.93 0.96 0.95

1 0.92 0.97 0.97 0.97 0.97

1 0.96 0.97 0.98 0.98

1 0.99 0.99 >0.99

1 >0.99 >0.99

1 >0.99

1

a Symbols are as in Figure 1 and Tables 1 and 2. Superscript a refers to the recovered profiles using the individual data treatment (scheme a in Figure 1). Superscript c refers to the recovered profiles obtained using the columnwise data augmentation (scheme c in Figure 1). Superscrpt b refers to the recovered profiles obtained using the row-wise data augmentation (scheme b in Figure 1). Superscript d refers to the recovered profiles obtained using the superaugmented data matrix (scheme d in Figure 1).

ous-variation data, sabsvar,a, differed somewhat from the same spectrum recovered in the individual analysis of mole-ratio data, either at constant Ethidium concentration, sabsEt,a (r ) 0.94) or at constant polynucleotide concentration, sabspoly,a (r ) 0.95). This tendency is also observed when the spectrum sabsvar,a is compared with the spectrum recovered in any other data arrangement (rowor columnwise or both simultaneously) as shown in the first column of Table 3, where r is always below 0.97. This confirms again that in the individual analysis of the continuous-variation data, rotational ambiguities were not totally solved for the spectrum of this species. Conversely, in the analysis of mole-ratio experiments, row-wise (Figure 1b), columnwise (Figure 1c), and super-augmentation (Figure 1d) data arrangements, the agreement between the recovered absorption spectrum of the intercalation complex was always very high (r > 0.99). From these results it is clear that either the simultaneous analysis of the absorption, fluorescence, and CD data (in row-wise data augmentation arrangements) or the simultaneous analysis of the continuousvariation and mole-ratio data (in columnwise data augmentation arrangements) improved the recovery of the absorption spectrum of the intercalation complex. Similar arguments can be given for the interpretation of the results obtained in the recovery of the concentration profile of the intercalation complex using the different data treatments (Table 4). Again, the higher disagreements (r values between 0.75 and 0.9 in Table 4) were found for the concentration profiles of 4336 Analytical Chemistry, Vol. 71, No. 19, October 1, 1999

the intercalation complex obtained in the individual analysis of continuous-variation data using absorption data, cabsvar,a. Individual analysis of fluorescent and circular dichroism data gave better results (r values higher than 0.92), especially for the mole-ratio data (correlation coefficients higher than 0.97, results not shown in Table 4). Columnwise and row-wise data augmentation treatments always gave concentration profiles very similar to those shown in Figure 5 for the superaugmented data matrix, confirming that rotational ambiguities were practically solved in both data augmentation schemes. However, for columnwise data augmentation (Scheme 1c in Figure 1) using absorption data, though data fitting was always very good (lack of fit (lof) values around 3.5%), recovery of the concentration profile of the intercalation complex in the continuous-variation experiment, cabsvar,c, was slightly worse (r values between 0.96 and 0.98 in Table 4) than for the other spectrometric methods cflvar,c, cCDvar,c, and cvar,b (r values equal or higher than 0.99 in Table 4). The interpretation of this is that columnwise data augmentation of absorption data did not completely solve the rotational ambiguities in the resolution of the concentration profile of the intercalation complex since no concentration selectivity was present for absorption data, whereas selectivity was present for fluorescent and CD data. From Figure 5 d,e,f, it is clearly seen that the intercalation-complex concentration profile in absorption data is mostly always embedded inside the concentration profiles of the free poly(A)-poly(U) and free Ethidium. In contrast, for fluorescence and CD data, only two species

were detected and concentration selectivity was always present for the intercalation complex (see Figure 5 d,e,f). As a conclusion, for the data set under study, row-wise data augmentation resulted in slightly better data than columnwise data augmentation owing to the higher selectivity associated with the use of fluorescence and circular dichroism data. However, for the safest resolution of the system, superaugmentation data treatment (row- and columnwise simultaneously, Figure 1d) was a useful check for the correct resolution of the whole system, and it provided a way to get better solutions for systems in which no selectivity is present either in the spectra or in the concentration profiles.

ACKNOWLEDGMENT The authors gratefully acknowledge helpful discussions with J. Mendieta and A. de Juan. This study was supported by the Ministerio de Educacio´n y Cultura (Grant DGICYT PB96-0377 and UE96-040). M.Vives aknowledges a PhD Grant from the University of Barcelona. Received for review February 10, 1999. Accepted June 20, 1999. AC990131M

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