Free Radicals Identification from the Complex EPR Signals by

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Free Radicals Identification from the Complex EPR Signals by Applying Higher Order Statistics Aleksandar G. Savić† and Miloš Mojović*,‡ †

Institute for Multidisciplinary Research, University of Belgrade, Kneza Višeslava 1, 11000 Belgrade, Serbia Faculty of Physical Chemistry, University of Belgrade, Studentski Trg 12-16, 11000 Belgrade, Serbia

‡

ABSTRACT: EPR spin-trapping technique, using spin-trap DEPMPO, has been shown to be capable of simultaneous detection of multiple free radical species which are generated in the same system. However, such approach proved to be unsuitable due to the complexity of the obtained composite EPR signal of the spin-adducts. Although rather unique, each individual spin-adduct signal is composed of at least eight EPR peaks, thus many of them could be overlapped, making the signal separation process almost impossible to accomplish by using ordinary chemometrics methods such as fast independent component analysis (FastICA), factor analysis (FA), or parallel factor analysis (PARAFAC). We have proposed a new approach which involves cumulative usage of two different statistical techniques. Applied algorithms are based on the second order statistics, second order blind identification with the robust orthogonalization algorithm (SOBI-RO), and the constrained independent component analysis (CICA).

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almost impossible to accomplish using common chemometrics techniques. EPR signals may be considered as sparse signals because the peaks of individual components are split with the regions without signals.3,4 Thus, signal separation techniques based on the signal correlation may not be efficient. Many techniques based on multivariate analyses have been found to have the usage in the analysis of spectroscopic data, such as fluorescence and FTIR spectra.5−10 The core of the FA based techniques, like PARAFAC,11−13 is finding the least possible number of components (factors) to describe the spectral matrix, in which each individual spectrum represents one experimental spectrum. However, sparsity and customary low signal-to-noise ratio makes FA useless in the EPR signal analysis. Frequently, even the number of free radical species which are present in the system could hardly be revealed. As it has been found in our tests, FA has the tendency to reduce the number of components by considering similar components as one. The best, but not satisfactory, results were obtained by using factor analysis with orthogonal rotations, which is the most similar to independent component analysis (ICA). By using this method, it was possible to distinguish mixtures of two significantly different shaped spin-adduct species (e.g., hydroxyl and superoxide anion radicals) using spectral matrix which contained about 10 spectra, what is rather inconvenient for real experimental usage.

n this era of intense study of free radicals and antioxidants, electron paramagnetic resonance (EPR) spin-trapping is arguably the best-suited technique for such research, particularly when considering biochemical and biological systems where multiple free radical species are frequently involved in metabolic paths. The proper choice of a spin-trap is essential for the successful application of EPR technique. The suitability of a certain spin-trap is defined through its ability to selectively trap a selected free radical or to have characteristic EPR spectra of adducts so that different trapped radicals can be easily distinguished. Numerous spin-traps are currently available for the detection of different types of free radicals. Among them, spin-trap DEPMPO, a phosphorylated analogue of a previously widely exploited spin-trap DMPO, attracted a lot of attention because of its high sensitivity, adduct stability, and the ability to differentiate between various trapped radical species.1 Chemical structure of the spin trap DEPMPO (5-(diethoxyphosphoryl)5-methyl-1-pyrroline-N-oxide) provides the additional hyperfine splitting of the EPR spectral lines due to the presence of 31 P, so each of the obtained spin-adducts derived from trapping of various radical species, e.g., hydroxyl radical, superoxide anion radical, methyl radical, methoxy, or carbon dioxide anion radical, has a unique multiple peak EPR signal which represents the specific radical fingerprint. Unfortunately, the composite EPR spectrum obtained from multiple DEPMPO adducts is consequently rather complicated, especially in biological systems where more than three different radical types could be easily generated.2 Furthermore, in the obtained mixed EPR signal, many of the EPR peaks will overlap, making the signal separation and adduct identification problem © 2012 American Chemical Society

Received: January 19, 2012 Accepted: March 1, 2012 Published: March 1, 2012 3398

dx.doi.org/10.1021/ac300200y | Anal. Chem. 2012, 84, 3398−3402

Analytical Chemistry

Article

Methods based on ICA,14 for example FastICA algorithm, may be efficient if two distinctive spin-adduct signals are present, such as hydroxyl and the superoxide anion radical.15−17 However, when overlapping of spectral components becomes significant, such as the examples of mixtures that include methyl and methoxy adducts, FastICA algorithm also fails to determine the number of components, its origin, and consequently its relative contributions in the integral signal. Still, FastICA has been shown to be better than the FA for the EPR signal separation purpose. It provides better decomposition and requires a spectral matrix which contains the number of spectra equal to the number of components. In this paper, SOBI-RO algorithm was used to roughly estimate the presence of spectral components. After the components were recognized, fine determination was performed in order to increase the reliability for the relative contribution. We have found that the constrained independent component analysis (CICA) method allows spectral components to be fitted from reference signals as well as provides freedom for source signal shape estimation. As the reference signals, EPR signals of spin-adducts experimentally obtained from the pure radical generator systems were used. The efficiency of this SOBI-RO/CICA approach has been demonstrated on a semisimulated spectral data. Composite signals were generated by implementing randomly generated coefficients of the linear combination (multipliers) of each individual experimental spectrum and the summation of all components.

constant 0.032 s. Experiments were performed at room temperature (22 °C). The spectra were processed by EW software (Scientific Software). Spectral simulations and analyses were performed by using Matlab 7.0 and ICALAB, software written for Matlab, developed by Andrzej Cichocki. Spectral Simulation. Obtained spectra of five free radical species, hydroxyl radical, superoxide anion radical, carbon dioxide anion radical, methyl radical, and methoxy radical, were normalized in range from −1 to 1, so the maximum EPR signal intensities of individual components were comparable (Figure 1).

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MATERIALS AND METHODS Free Radical Generator Reactions. Hydroxyl radicals (•OH) were generated using the standard Fenton reaction (0.2 mM FeSO4 and 0.2 mM H2O2), in the presence of 0.1 M DEPMPO (the concentration of DEPMPO was same in all generator systems). Methyl radicals (•CH3) were generated using reaction mixture composed of 20 mM diethylene triamine pentaacetic acid (DTPA), 0.2 mM FeSO4, 0.2 mM H2O2, and 10% v/v of dimethylsulfoxide (DMSO) in cacodylate buffered solution (pH = 7.1). Methoxy radicals (•CH2OH) were generated in reaction mixture composed of 20 mM DTPA, 0.2 mM FeSO4, 0.2 mM H2O2, and 10% v/v of methanol in cacodylate buffered solution (pH = 7.1). Carbon dioxide anion radicals (•CO2−) were generated in reaction mixture composed of 20 mM DTPA, 0.2 mM FeSO4, 0.2 mM H2O2, and 15 mM sodium formate in cacodylate buffered solution (pH = 7.1). Superoxide anion radicals (•O2−) were generated using riboflavin-light reaction. Starting mixture containing 0.05 mM riboflavin, 4 mM DTPA, and spin-trap DEPMPO was continuously flowed with gaseous oxygen. Finally, UV lamp (130 W) was applied for 30 s. All chemicals (analytical grade or higher) were used as received from Sigma-Aldrich without any further purification, except spin-trap DEPMPO which was purchased from Enzo Life Sciences and purified according to the procedure proposed by Jackson.18 All solutions were prepared with deionized water of resistivity not less than 18.2 MΩ cm. All EPR spectra were recorded using a Varian E104-A X-band ESR spectrometer under the following conditions: field center 3410 G, scan range 200 G, microwave frequency 100 kHz, modulation amplitude 2 G, microwave power 10 mW, time

Figure 1. EPR spectra of spin-adducts experimentally obtained from the pure radical generator systems: (a) hydroxyl radical adduct (DEPMPO/ • OH), (b) methoxy radical adduct (DEPMPO/•CH2OH), (c) methyl radical adduct (DEPMPO/•CH3), (d) carbon dioxide anion radical adduct (DEPMPO/•CO2−), and (e) superoxide anion radical adduct (DEPMPO/•OOH).

According to the established notation in chemometrics,7 simulated spectra may be described by following equation: Dm × n = Sm × nCn × n

Matrix Dm×n represents the matrix of simulated spectra which will be analyzed according to the specification of EPR spectrometer used in our measurements (Figure 2). Matrix Sm×n 3399



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Figure 3. Decomposed spectra after application of SOBI-RO algorithm to whole length signals. Estimated signals of (a) hydroxyl radical adduct (DEPMPO/•OH), (b) methoxy radical adduct (DEPMPO/•CH2OH), (c) methyl radical adduct (DEPMPO/•CH3), (d) carbon dioxide anion radical adduct (DEPMPO/•CO2−), and (e) superoxide anion radical adduct (DEPMPO/•OOH).

Figure 2. Five semisimulated EPR spectra (a−e). Composite signals are generated by multiplying each individual experimental spectrum with randomly generated coefficients and the summation of all the components.

denotes five source spectra, each one for the specific free radical, while matrix C n×n gives coefficients of linear combinations. The number of spectra needed to resolve the number and the origin of signals should be as small as possible, in the ideal case, equal to the number of components that should be extracted. Coefficients of linear combination were chosen by generating the random number matrix to avoid the subjectivity. Noise has already been contained in the matrix of source components, so there was no need to specify matrix that only represents noise. When signal of blank probe was tested, or when simulated spectra were compared with the experimental, it has been shown that the noise is Gaussian white noise. In the further text, noise will be denoted as n. Independent Component Analysis. Spectral analysis was performed in two different steps. The first step was based on SOBI-RO algorithm, which is used as a blind source analytical method. Blind source identification of spectral components starts without any a priori knowledge about the components. The second step involves a constrained method for independent component analysis which uses components identified by SOBI-RO as the source signals. Noisy spin-adduct signals were considered as the signals which contain temporally uncorrelated and spatially correlated noise. Robust whitening as the preprocessing step gives us the ability to identify the source components even when the signalto-noise ratio is low. Robust whitening consists of eigenvalue

decomposition of a set of correlation matrices taken at nonzero lags. The data model presented in the equation19,20 should be transformed in order to explain SOBI-RO algorithm: d(t ) = As(t ) + n(t )

Matrix A∈Rn×n is analogous to matrix C. s(t) denotes ndimensional vector of mutually uncorrelated, not temporally correlated source signals, and it is analogous to matrix Sm×n. n(t) represents temporally white noise, with zero mean independent from the source signals.19 Correlation matrices take the following form: R x(0) = E{x(t )x T (t )} = AR s(0)AT + R n R x(i) = E{x(t )x(t − i)T } = AR s(i)AT for i = 1, ..., 0

Rn denotes covariance matrix which represents the noise, E denotes statistical expectation operator. The only known data are the observation data x(t), and the task of the algorithm is to estimate the mixing matrix A or its pseudo-inverse. SOBI algorithm estimates whitening matrix by using the linear combination of correlation matrices. If the eigenvalues of spectral components are close to each other, as in the case of EPR spectra, algorithm for multiple unknown signals extraction (AMUSE) or matrix pencil method is not suitable. While AMUSE exploits two different correlation 3400



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noise cannot be removed. The whitening method called robust whitening is not sensitive to the present white noise, and that is the main advantage compared to classical whitening. After some of the spin-adduct spectra were undoubtedly identified, CICA was applied. CICA analysis is a member of ICA analyses with the reference (ICA-R). Constraints provide the proper reduction of dimensionality and the rough templates of the source shape increase the proper estimation of sources. Because during the recording of spectra some of the signals may not be stationary, CICA is much more suitable than applying the brute force algorithm with the given sources.

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RESULTS The first step involved decomposition of all signals by applying the SOBI-RO algorithm. Estimated spectral components are presented in Figure 3. Some of the estimated components were easily recognizable, but some of them (like spectra b and d) were still not approximated well enough, and the calculation of relative contributions in the composite spectra would give wrong results. For the exact evaluation, obtained spectra should be used for the election of the reference signals for the constrained ICA method. After applying CICA method, more accurate matching with the source EPR signal was obtained (Figure 4). The best way to check the reliability of the CICA method is to compare the estimated mixing matrix Ce and the mixing matrix C that was applied to multiply the source matrix S. The comparison between these two mixing matrices is shown in Figure 5.

Figure 4. Decomposed spectra when CICA algorithm was applied: (a) hydroxyl radical adduct (DEPMPO/•OH), (b) methoxy radical adduct (DEPMPO/•CH2OH), (c) methyl radical adduct (DEPMPO/•CH3), (d) carbon dioxide anion radical adduct (DEPMPO/•CO2−), and (e) superoxide anion radical adduct (DEPMPO/•OOH).

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CONCLUSION Development of a new spin trap DEPMPO has provided simultaneous detection of multiple free radical species generated in the same system, which is represented as a mixed signal of adducts. That capability unfortunately could not be exploited without proper analytical methods. Perfect method, or procedure, should satisfy several demands: it must be robust enough for analysis of noisy spectra, the number of input spectra should be as small as possible, and the estimation of the spectral shape, thus spectral relative

matrices, SOBI is based on the joint approximate diagonalization of multiple time-delayed correlation matrices. An algorithm such as flexible joint approximate diagonalization of quadricovariance matrices (FJADE) was relatively successful, but not good enough as SOBI-RO. The whitening of the input data is an important preprocessing step. In the case of conventional whitening, the effect of additive

Figure 5. Comparison between estimated mixing matrix Ce and the used mixing matrix C. Circles refer to the values of the matrix C, and the squares refer to the matrix Ce. Values along the axes show the relative contribution of the individual DEPMPO adduct signal in the corresponding semisimulated spectra denoted with letters in the corners (the same as shown in Figure 2). 3401



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contribution, should be reliable. This paper describes the cumulative usage of two statistical techniques, proven in analyses of similar sparse, noisy, and overlapping signals. In the first step, implementation of second order blind identification with robust orthogonalization algorithm (SOBIRO) was performed to roughly estimate the components that may be included in the cumulative EPR spectra of DEPMPO adducts. In the following step, clearly identifiable and corresponding experimentally recorded spectra were used as starting components for constrained independent component analysis (CICA). Such an approach should be very usable for biochemical systems which produce several free radical species simultaneously. Further improvements of the described procedure may involve automatic recognition of estimated spectral components after application of SOBI-RO algorithm.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Grants 41005 and 173040 from the Ministry of Education and Science of Government of the Republic of Serbia.

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Free Radicals Identification from the Complex EPR Signals by

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