- Email: [email protected]
New strategy to identify radicals in a time evolving EPR data set by multivariate curve resolution-alternating least squares
Accepted Manuscript New strategy to identify radicals in a time evolving EPR data set by Multivariate Curve Resolution-Alternating Least Squares Maya Abou Fadel, Anna de Juan, Hervé Vezin, Ludovic Duponchel PII:
S0003-2670(16)31240-5
DOI:
10.1016/j.aca.2016.10.028
Reference:
ACA 234851
To appear in:
Analytica Chimica Acta
Received Date: 7 July 2016 Revised Date:
14 October 2016
Accepted Date: 17 October 2016
Please cite this article as: M.A. Fadel, A. de Juan, H. Vezin, L. Duponchel, New strategy to identify radicals in a time evolving EPR data set by Multivariate Curve Resolution-Alternating Least Squares, Analytica Chimica Acta (2016), doi: 10.1016/j.aca.2016.10.028. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT
New strategy to identify radicals in a time evolving EPR data set by
RI PT
Multivariate Curve Resolution-Alternating Least Squares
Maya Abou Fadel(a), Anna de Juan(b) Hervé Vezin(a), Ludovic Duponchel(a,*).
(a) LASIR CNRS UMR 8516, Université Lille 1, Sciences et Technologies, 59655 Villeneuve
SC
d’Ascq Cedex, France.
645, 08028 Barcelona, Spain.
M AN U
(b) Chemometrics Group, Section of Analytical Chemistry, Universitat de Barcelona, Diagonal
(*) Corresponding author, Email: [email protected], Tel: +33 320434902.
TE D
Abstract
Electron paramagnetic resonance (EPR) spectroscopy is a powerful technique that is able to characterize radicals formed in kinetic reactions. However, spectral characterization of individual
EP
chemical species is often limited or even unmanageable due to the severe kinetic and spectral
AC C
overlap among species in kinetic processes. Therefore, we applied, for the first time, multivariate curve resolution-alternating least squares (MCR-ALS) method to EPR time evolving data sets to model and characterize the different constituents in a kinetic reaction. Here we demonstrate the advantage of multivariate analysis in the investigation of radicals formed along the kinetic process of hydroxycoumarin in alkaline medium. Multiset analysis of several EPR-monitored kinetic experiments performed in different conditions revealed the individual paramagnetic
1
ACCEPTED MANUSCRIPT
centres as well as their kinetic profiles. The results obtained by MCR-ALS method demonstrate its prominent potential in analysis of EPR time evolved spectra.
AC C
EP
TE D
M AN U
SC
Resonance spectroscopy, radicals, multiset analysis, chemometrics.
RI PT
Keywords: Multivariate Curve Resolution-Alternating Least Squares, Electron Paramagnetic
2
ACCEPTED MANUSCRIPT
1. Introduction
The study of kinetics chemical reactions by spectroscopic methods is still very often based on
RI PT
univariate approach. Typically, a series of spectra are measured as a function of time and the evolution of single peaks is independently analyzed. In simple cases, the evolution of a particular compound is followed by modeling the increase or decrease of a given spectral band during such
SC
analysis. However, this approach can lead to erroneous interpretation when signals from different species overlap i.e. when the selected spectral variable is not specific to the compound of
M AN U
interest. Thus, multivariate methods are indispensable in the analysis of complex systems to overcome most of the problems reported by univariate approaches. Many multivariate methods, known under the denomination of hard-modeling methods, require knowledge about the initial concentrations of reactants and the mechanistic kinetic model. This model is then assumed and
TE D
experimental data are fitted according to it. However, the choice of the correct kinetic model is sometimes difficult or not possible at all. Multivariate soft modeling methods, which are datadriven procedures and do not need any mechanistic model, are needed to solve this kind of the
EP
problems. Among these latter methods, Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) has been successfully applied to different time evolving data [1] as well as other
AC C
kinds of sequence ordered data sets, such as chromatographic runs[2,4], or other kinds of other kinds of reactions and processes monitored by spectroscopic and voltammetric measurements[5, 8]. It is, hence, a useful tool for kinetic studies. MCR-ALS is able to retrieve, with no a priori, the pure time profiles and related spectral signatures of all the components in a studied system.
In spite of this fact, MCR-ALS has not yet been applied to the analysis of time-resolved EPR spectra. Considering that EPR is an irreplaceable tool in the study of kinetics for many kinds of 3
ACCEPTED MANUSCRIPT
paramagnetic centres and that the examination of kinetic reactions involving radicals by EPR has often to contend with strongly overlapped and multicomponent spectra, MCR-ALS appears as a suitable alternative to study this kind of systems. It was demonstrated in our previous articles that
RI PT
MCR-ALS is an effective approach in the analysis of entangled EPR signals coming from a mixture of non-interacting paramagnetic centers [9] as well as for the study of hyperspectral EPR images[10]. These results prompted us to apply MCR-ALS on EPR time evolving data because it
SC
seems to be a promising tool in the study of the reactions of radicals[11]. The objective of this work is to demonstrate the applicability of MCR-ALS to an EPR data set from a reactive mixture
M AN U
of paramagnetic radicals. As a model system for our study, one of the derivatives of 3hydroxycoumarin (see Figure 1) (3,6,7-trihydroxycoumarin) was chosen because it can be oxidized and can form different radicals in alkaline conditions. Moreover, this molecule is interesting in itself and has been intensively studied due to its promising antioxidant
TE D
properties[12].
Antioxidants interact with the free radicals and prevents them from causing damage[13].
EP
Therefore, they are also known as free radical scavengers. Free radicals are highly reactive metabolites and are naturally produced by the body as a result of normal metabolism and energy
AC C
production. These incomplete molecules aggressively attack other molecules in the body to refill the missing electrons. This oxidation severely affects the cells and leads to different diseases and antioxidants defend the body against such damages[14]. There exist endogenous and exogenous antioxidants. Exogenous sources come primarily from diet, particularly from fruits, vegetables and grains[15]. 3-hydroxycoumarin is an antioxidant that belongs to the coumarin-related compounds. The former is rare in nature and is formed from the hydroxylation of the coumarins at the 3-position by liver microsomes[16]. In 1990, Aihara el al. described their first chemical 4
ACCEPTED MANUSCRIPT
preparation from coumarins[17]. The 3-hydroxylation turned out to significantly improve antioxidant activity and, for instance, increased the 5-lipoxygenase and α-glycosidase inhibitory activities of coumarins. One of the derivatives of this molecule which exhibits very promising
RI PT
antioxidant properties is 3,6,7-trihydroxycoumarin presented in Figure 1.
In this work, EPR spectra of this molecule measured in alkaline conditions as a function of time
SC
are analysed by MCR-ALS in order to extract knowledge about the intermediate species formed
M AN U
and the related reaction pathway.
2. Experimental Section
2.1. Sample preparation
TE D
3,6,7-trihydroxycoumarin was synthesized as described by Cotelle et al.[11]. Two experimental solutions were prepared by mixing 1 mg of the compound with 500 µL of sodium hydroxide
EP
with two different concentrations, 1M and 2M, respectively.
AC C
2.2. Spectral acquisition
Samples were analyzed with a continuous wave-electron paramagnetic resonance spectrometer (CW-EPR). EPR spectra were recorded at a constant room temperature of 20°C, using a Bruker ELEXSYS 500 spectrometer operating at the X-Band. All spectra were recorded at a modulation field frequency of 100 kHz and a microwave frequency of 9.80 GHz, with an amplitude modulation of 0.002 mT and a microwave power of 0.1 mW corresponding to non-saturation
5
ACCEPTED MANUSCRIPT
conditions. The weak pitch from Bruker was used as standard reference and contained a known concentration of spin/mass (1.29 × 1013 spins/g). The following spectrometer parameters were used during the spectral acquisition: receiver gain 68 dB, time constant 40.96 ms, conversion
RI PT
time 81.92 ms. The spin concentration is given by the double integration of the first derivative of the EPR signal. Spectra were measured over a spectral range from 3473 Gauss to 3486 Gauss. Each sample was monitored as a function of time with 900 second intervals. 80 time-resolved
SC
spectra were recorded for both samples covering 20 hours time range.
M AN U
2.3. Data treatment
Recorded spectra of both samples were gathered in two data sets. They were processed and analyzed in MATLAB environment version R2008b (The MathWorks Inc., Natick, MA, 2000)
TE D
by the MCR-ALS toolbox (see the method below) developed by J. Jaumot, R. Tauler and A. de Juan. It can be freely downloaded from the webpage http://www.mcrals.info[18].
EP
2.4 Multivariate resolution of spectroscopic data
AC C
The aim of multivariate curve resolution methods is to decompose a mixed signal into the contribution of the pure component profiles of the constituents, by means of a simple bilinear model, defined as follows[19,20] = + (eq.1)
6
ACCEPTED MANUSCRIPT where D ( × ) is the raw experimental data matrix containing the different EPR spectra
acquired as a function of time, the columns of C( × ) are the kinetic profiles of the k pure components involved in the kinetic process and the rows of ST( × ) are their related pure
RI PT
EPR spectral profiles. E( × ) is the error matrix that presents the data variance not explained
by the bilinear model. The model is optimized during an iterative process via an alternating
SC
least squares algorithm under constraints (see below).
MCR-ALS has the possibility to be applied simultaneously on more than one data set[21].
M AN U
Therefore, the procedure described above can be extended to the analysis of multiple data sets (experiments) simultaneously as long as they have at least one data mode, i.e. direction, in common. In the case of r different data sets acquired by the same spectroscopic technique, the possible data arrangement and extension of the bilinear model would be as follows:
EP
TE D
= + (eq.2) … ⋯ ⋯
In the context of this work, , , ..., , are EPR-monitored kinetic experiments performed in
AC C
different conditions sharing components in common, , , ..., contain the kinetic profiles
of the resolved components in each of the related Di submatrices (experiments), respectively,
is a single matrix that represents the EPR spectral profiles of the different components present in
the analysed Di submatrices, and , , ..., are the corresponding error submatrices containing the part of the measured data unexplained by the proposed bilinear model. The multiset equation can be written in a more compact form (i.e. an augmented one) as follows
7
ACCEPTED MANUSCRIPT = ; ; ⋯ ; = ; ; ⋯ ; + ; ; ⋯ ; = + (eq.3) where , and correspond to the column-wise augmented matrices containing,
RI PT
respectively, the EPR-monitored kinetic experiments, the kinetic profiles of the resolved
components in the different experiments, and the error of the unexplained modelled data in different experiments, respectively. The notation ';' in the previous equation is used to indicate
SC
the column-wise augmentation.
M AN U
MCR-ALS provides Caug and matrices solely from the information of the experimental matrix
Daug. The first step in MCR-ALS is to obtain an estimation of the number of pure components
involved in the reaction i.e. rank k of data matrix. This determination is performed by Singular Value Decomposition (SVD)[22]. Rank k is equal to the singular values related to the chemical
TE D
species that are larger than those linked to experimental errors or noise. Second, initial estimates, either of concentration profiles Cini or spectral profiles STini, are required to start the iterative Alternating Least Squares procedure (ALS). The pure variable selection method based on
EP
SIMPLe-to-use Interactive Self modeling Analysis (SIMPLISMA) is used for this purpose [23].
AC C
This method is based on selecting the purest or the more specific variables in the data set. It is often said that SIMPLISMA selects the more dissimilar variables from the data matric D. For better variable selection, this method is applied only on positive data set i.e. integrated spectra which is rather uncommon for EPR data analysis. Integrated spectra are generated by a homebuilt code. Considering that the initial estimates are the spectral profiles (in this specific case), an iterative alternating least squares optimization of matrices Caug and ST is done for each iteration according to the following equations 4 and 5: 8
ACCEPTED MANUSCRIPT = ( ) (eq.4)
RI PT
= ( ) (eq.5) Suitable constraints can be implemented during the iterative calculation of Caug and ST, to give physical meaning to the obtained results, and to decrease the extent of possible rotational
SC
ambiguities[24]. Rotational ambiguity is connected to the number of possible solution of MCRALS extractions. Thus our main aim is always to decrease it in order to obtain the uniqueness of
M AN U
extractions for concentrations and spectral profiles. Constraints are defined as chemical properties translated into mathematical conditions that concentration Caug and/or spectral profiles ST should fulfill (e.g. non-negativity, closure, unimodality, ...). Therefore, when a profile is constrained, its shape is modified in order to fulfill preselected properties. Iterations stop when
TE D
an optimal solution is obtained i.e. achieved the postulated constraints and the established convergence criteria. In general, it is achieved when the relative difference in lack of fit between two consecutive iterations is below a threshold or when a predefined number of iteration is
EP
reached. The lack of fit (eq. 6) is evaluated from the difference between the experimental data matrix Daug and the resolved data matrix, which is the product of concentration and spectral
AC C
profiles CaugST. The explained variance (r2), which is also used to evaluate the fit quality of MCR-ALS model, is defined in equation 7.
∑.,/ -./0
lack of fit (%) = 100+∑
0 .,/ 2./
(eq. 6)
9
ACCEPTED MANUSCRIPT 0 ∑ 7,8 -.,/
3 4 = 100 51 − ∑
0 7,8 2.,/
9 (eq. 7)
RI PT
where dij is an element of the input data matrix Daug (time i, magnetic field j) and eij is the related residual obtained from the difference between the input element and the MCR-ALS reproduction.
SC
The results obtained from multivariate curve resolution when applied to time evolving EPR data
M AN U
sets are pure kinetic and spectral profiles of all the compounds present in the studied samples. Resolved spectral profiles can be used to identify these components by comparing them with those obtained by EPR spectra simulations. On the other hand, the time profiles give the kinetic information of each component and a description of the full time-dependent process.
TE D
3. Results
EPR spectra of 3,6,7-trihydroxycoumarin in 1M and 2M NaOH recorded at different times after
EP
dissolution are presented in Figure 2. Spectra were gathered in two individual data sets, D1 (for 1M NaOH) and D2 (for 2M NaOH), respectively. The dimension of each data set is 80×1024
AC C
comprising 80 spectra and 1024 different magnetic fields. In the first attempts, the original raw EPR data sets were individually analyzed by MCR-ALS but the results suffered significant ambiguity and satisfactory resolution was not achieved.
10
ACCEPTED MANUSCRIPT
Therefore, the two data sets were combined into a single column-wise augmented data matrix to benefit from the ambiguity decrease provided by multiset analysis[25,26]. The simultaneous analysis of different mixtures of the same compounds, in different chemical or physical
RI PT
conditions such as time or pH is a powerful approach to extract more reliable knowledge on the individual species of the systems[25]. In this study, the same molecule in experiments performed in different alkaline conditions was present in each experiment. Thus, a magnetic field wise-
SC
augmented matrix, keeping the magnetic fields values in common, was built for multiset analysis. As a consequence, the pure spectra in both data sets are considered invariant and the
M AN U
matrix C allows the profiles of each compound in the concentration direction to be different for each individual matrix (experiment) (Figure 3).
First attempts of multiset analysis were aimed at performing MCR-ALS directly on the raw data
TE D
i.e. on EPR spectra represented in their first derivative form (Figure 2). However, this approach was not efficient to resolve various components with ubiquitous spectral overlapping. The implementation of only one constraint in MCR-ALS procedure i.e. non-negativity on the
EP
concentration profile on such complex data, gave high uncertainty in the final solution. For this reason, integrated spectra shown in Figure 2, were used instead of original first derivative
AC C
spectra. In this case, an additional constraint that is the non-negativity on the spectral direction can be added.
The first step of multiset MCR-ALS was the evaluation of the data matrix rank corresponding to the number of independent components present in the experimental mixture. It is worth noting that MCR-ALS is a real blind signal unmixing procedure since no prior knowledge about the total number of pure components is used. For this purpose, SVD was applied on the multiset 11
ACCEPTED MANUSCRIPT
Daug. Figure 4 presents the plot of the first 20 eigenvalues indicating the presence of four distinct contributions in terms of the broken stick concept. Indeed four significant eigenvalues are distinguished from the rest due to the sudden change of the slopes. All further eigenvalues
RI PT
represent variance associated with noise. In order to develop this assumption, we have done resolutions with a rank of five or six without letting us to extract more pure contributions and even generate worse extractions.The next step in MCR-ALS was the estimation of the initial
SC
spectral or concentration profiles by a SIMPLISMA-based algorithm. In this case, STini matrix was obtained in order to begin the ALS iterations. In the optimization process, non-negativity
M AN U
constraints were imposed on the concentration as well as spectral profiles. The results obtained after the application of MCR-ALS on the augmented matrix Daug are shown in Figure 5. They represent the pure spectra ST of all species (Figure 5A,B,C and D) present in both experiments and corresponding concentration profiles (Figure 5, C1 and C2) which are different in two
TE D
experiments due to different alkaline conditions. The quality of the final resolution was verified and given the signal-to-noise in the integrated EPR data, a lack of fit of 3.45% and explained
AC C
EP
variance of 99.88% were accepted as good figures of merit for the proposed resolution.
4. Discussion
Identification of the spectra extracted by MCR-ALS (see Figure 5) is not a trivial task. As described in the literature, 3-hydroxycoumarin can be oxidized under alkaline conditions and form various radicals [11]. According to Cotelle et al. six radicals can be formed in the reaction
12
ACCEPTED MANUSCRIPT
of 3,6,7-trihydroxycoumarin in the presence of NaOH [11]. The proposed structures and reaction paths for these radicals are presented in Figure 6.
RI PT
Six radicals may be formed by transformation from one to another. Thus association of the extracted MCR-ALS spectra with some of these radicals require some simulations. The theoretical calculations for the postulated radicals revealed that they should exhibit characteristic
SC
patterns in EPR spectra. In addition to the previous literature data, a new set of simulations of the radical spectra was performed using WinSim software[27] considering the hyperfine constants
M AN U
(presented in Table 1) provided by Cotelle et al.[11]. The results of these simulations are presented in
TE D
.
Radical I is represented by a spectrum formed by 8 equally distributed EPR lines (Figure 7a) and it is not observed in the set of MCR-ALS results (see Figure 5). Indeed, this radical is known to
EP
be only observed in weakly alkaline solution (for example 0.1M of NaOH). It possesses three doublets that are attributed to the coupling between the unpaired electron and the three protons
AC C
(H4, H5 and H8). In the considered experimental conditions, radical I is rapidly transformed into other radical forms. At this step, two possible pathways are postulated. The first one assumes that radical II is formed, however, it rapidly decays and is replaced by radical III that is more stable. The EPR spectra of radicals II and III are very similar so they are difficult to distinguish. Actually, in highly basic medium (1 or 2M of NaOH) the spectra of these two radicals are nearly identical. They possess characteristic EPR pattern with 32-line spectrum due to the interaction between the unpaired electron and five protons; however, only four quartets and two pentets can 13
ACCEPTED MANUSCRIPT
be shown due to the overlap of the bands (see Figre 7b). Radical III can be further transformed into radical VI which exhibits an 8-line spectrum presented in Figure 7e. The parallel reaction path includes the transition from Radical I to radicals IV and V which are in equilibrium. They
RI PT
have different EPR signals presented in Figure 7c and Figure 7d respectively. The former possesses triplet of quartets due to the coupling between the unpaired electron and four protons, among which two protons are equivalent. The latter has an 8-line EPR spectrum due to the
SC
interaction between the unpaired electron and three protons. In the context of this established reactions scheme, the presence of signal from radicals III, IV, V and VI can be observed in the
M AN U
studied dataset.
Comparing spectral profile extracted by MCR-ALS (Figure 5) and the simulated spectra (Figure 7) the assignment of the radicals is possible. The first extracted spectrum (in blue) corresponds very well to initially formed pure radical II. The second spectrum (in green) in Figure 5 can be
TE D
undoubtedly attributed to the EPR spectrum of radical VI. The third spectrum (in red) is not a pure one. Indeed, it is a mixture of radical VI (central part of the spectrum) and radical IV recognized by characteristic four peaks at the left and the right of the central part. The fourth
EP
spectrum (in orange) cannot be easily assigned and it is probably a mixture of several radicals IV, V and VI. It is important to note that there are species in equilibrium and parallel reactions
AC C
and, therefore, rotational ambiguity still exists in this data set. As a consequence, a doubt on the rank number could be built. However, in the case of a rank modification, even radicals II and IV were not purely extracted by MCR-ALS. This confirms the fact that the rank estimated in this work (four) is relevant. In spite the fact that the third and fourth spectra extracted by MCR-ALS are not yet completely pure, the extracted concentration profiles of radicals II and VI can provide valuable information
14
ACCEPTED MANUSCRIPT
about the kinetics of the reactions. Considering concentration profiles of radical II (blue) and radical VI (green) in D1 and D2, in both cases, a decay of radical II corresponds to the growth of radical VI which confirms a postulated reaction path (Figure 6). However in D2, a decay of
RI PT
radical II is clearly faster than in D1. This makes perfect sense with respect to higher alkaline conditions (2M NaOH instead of 1M NaOH) observed for data set D2.The concentration profile of the third and fourth component, which are the only ones including EPR features of radicals IV
SC
and V have a lower presence in both experiments, especially in the experiment at 2 M NaOH, which could confirm that the formation of radical IV is a less promoted mechanism than the
M AN U
formation of radical II.
5. Conclusions
TE D
The results presented in this paper demonstrate the applicability of MCR-ALS to the analysis of multicomponent time evolving EPR data. The presented results are the first MCR-ALS application on this type of EPR data sets. The analysis confirmed that a complex system of
EP
paramagnetic species can be resolved by multivariate analysis giving valuable information about the reaction pathways. In addition, it was demonstrated the usefulness of multiset analysis in this
AC C
context. Some of the spectral signatures and kinetic profiles of four pure radicals were retrieved from the kinetic reaction of hydroxycoumarin in alkaline medium. Furthermore, results obtained by MCR-ALS (multiset analysis) seem appropriate but not yet optimal due to the presence of rotational ambiguity that still exists due to the complexity in both the kinetic and the spectral directions. In order to fully resolve the pure components from this challenging system, richer experimental data, such as experiments at different conditions, are required. An experiment with varied acquisition speed is needed for further exploration of the reaction, especially in its initial 15
ACCEPTED MANUSCRIPT
part, since most of the reactions occur in this part. If information is more complete, the inclusion of mechanistic models within the framework of MCR, successfully done in other examples.
dimensions in the interpretation of EPR results.
SC
6. Acknowledgement
RI PT
could also be envisioned. We are convinced that such an approach will open new analytical
Anna de Juan acknowledges funding support from the Spanish government through project
Captions
TE D
Figure 1: 3,6,7-trihydroxycoumarin.
M AN U
CTQ2015-66254-C2-2-P.
Figure 2: 80 EPR time-resolved spectra obtained for 3,6,7-trihydroxycoumarin in 1M NaOH (upper left) and corresponding integrated form (upper right). 80 EPR time-resolved spectra obtained for 3,6,7-
EP
trihydroxycoumarin in 2M NaOH form (lower left) and corresponding integrated form (lower right).
AC C
Figure 3: Scheme of the MCR-ALS decomposition of augmented matrix by column-wise augmented matrix of two experimental data sets.
Figure 4: Logarithm of eigenvalues obtained by Singular Value Decomposition of the spectral data matrix Daug.
16
ACCEPTED MANUSCRIPT
Figure 5: Pure concentration profiles Caug (top) and corresponding pure spectra ST (bottom) of four components resolved by MCR-ALS on augmented data set Daug.
RI PT
Figure 6: Scheme representing radicals formed in the reaction of 3,6,7-trihydroxycoumarin in alkaline solution[11].
SC
Figure 7: Simulated EPR spectra of the pure radicals in their integrated form.
AC C
EP
TE D
M AN U
Table 1: Experimental hyperfine constants obtained by simulation (in Gauss, in absolute value).
17
ACCEPTED MANUSCRIPT
References
M. Garrido, F.X. Rius, M.S. Larrechi, Multivariate curve resolution-alternating least
RI PT
[1]
squares (MCR-ALS) applied to spectroscopic data from monitoring chemical reactions processes., Anal. Bioanal. Chem. 390 (2008) 2059–66.
S. Mas, A. Carbo, S. Lacorte, A. De Juan, R. Tauler, Comprehensive description of the
SC
[2]
photodegradation of bromophenols using chromatographic monitoring and chemometric
[3]
M AN U
tools, Talanta. 83 (2011) 1134–1146.
R. Gargallo, R. Tauler, F. Cuesta-Sánchez, D.L. Massart, Validation of alternating leastsquares multivariate curve resolution for chromatographic resolution and quantitation, Trac- Trend. Anal. Chem. 15 (1996) 279–286.
K. De Braekeleer, A. De Juan, D.L. Massart, Purity assessment and resolution of
TE D
[4]
tetracycline hydrochloride samples analysed using high-performance liquid chromatography with diode array detection, J. Chromatogr. A. 832 (1999) 67–86. A. Izquierdo-Ridorsa, J. Saurina, S. Hernández-Cassou, R. Tauler, Second-order
EP
[5]
multivariate curve resolution applied to rank-deficient data obtained from acid-base
AC C
spectrophotometric titrations of mixtures of nucleic bases, Chemometr. Intell. Lab. 38 (1997) 183–196.
[6]
J. Saurina, S. Hernández-Cassou, R. Tauler, a Izquierdo-Ridorsa, Procedure for the quantitative determination of mixtures of nucleic Acid components based on multivariate spectrophotometric Acid-base titrations., Anal. Chem. 71 (1999) 126–134.
[7]
J. Diewok, A. de Juan, R. Tauler, B. Lendl, Quantitation of Mixtures of Diprotic Organic Acids by FT-IR Flow Titrations and Multivariate Curve Resolution, Appl. Spectrosc. 56 18
ACCEPTED MANUSCRIPT
(2002) 40–50. [8]
A. Safavi, B. Hemmateenejad, F. Honarasa, Chemometrics assisted resolving of net faradaic current contribution from total current in potential step and staircase cyclic
[9]
RI PT
voltammetry, Anal. Chim. Acta. 766 (2013) 34–46.
M. Abou Fadel, A. De Juan, N. Touati, H. Vezin, L. Duponchel, New chemometric
approach MCR-ALS to unmix EPR spectroscopic data from complex mixtures, J. Magn.
[10]
SC
Reson. 248 (2014) 27–35.
M. Abou Fadel, X. Zhang, A. De Juan, R. Tauler, H. Vezin, L. Duponchel, Extraction of
M AN U
Pure Spectral Signatures and Corresponding Chemical Maps from EPR Imaging Data Sets: Identifying Defects on a CaF2 Surface Due to a Laser Beam Exposure, Anal. Chem. 87 (2015) 3929–3935. [11]
P. Cotelle, H. Vezin, EPR of free radicals formed from 3-hydroxyesculetin and related
[12]
TE D
derivatives., Res. Chem. Intermediat. 29 (2003) 365–77.
F. Bailly, C. Maurin, E. Teissier, H. Vezin, P. Cotelle, Antioxidant properties of 3hydroxycoumarin derivatives, Bioorganic Med. Chem. 12 (2004) 5611–5618. B. Halliwell, Free radicals, antioxidants, and human disease: curiosity, cause, or
EP
[13]
consequence?, Lancet. 344 (1994) 721–4. B.N. Ames, M.K. Shigenaga, T.M. Hagen, Oxidants, antioxidants, and the degenerative
AC C
[14]
diseases of aging., P. Natl. Acad. Sci. U. S. A. 90 (1993) 7915–7922.
[15]
J. Bouayed, T. Bohn, Exogenous Antioxidants—Double-Edged Swords in Cellular Redox State: Health Beneficial Effects at Physiologic Doses versus Deleterious Effects at High Doses, Oxid. Med. Cell. Longev. 3 (2010) 228–237.
[16]
A. Heliangolide, C. Zdero, A heliangolide, 3-hydroxyumbelliferone Derivatives
19
ACCEPTED MANUSCRIPT
Diterpenes From Bahia Ambroszozdes, Phytochemistry. 29 (1990) 205–208. [17]
K. Aihara, T. Higuchi, M. Hirobe, 3-Hydroxycoumarins - 1st Direct Preparation From Coumarins Using a Cu-2+ Ascorbic-Acid O2 System, And Their Potent Bioactivities.,
[18]
RI PT
Biochem. Biophy. Res. Com. 168 (1990) 169–75.
J. Jaumot, A. De Juan, R. Tauler, MCR-ALS GUI 2.0: New features and applications, Chemometr. Intell. Lab. Syst. 140 (2015) 1–12.
J.H. Jiang, Y. Liang, Y. Ozaki, Principles and methodologies in self-modeling curve
SC
[19]
resolution, Chemometr. Intell. Lab. Syst. 71 (2004) 1–12.
A. De Juan, R. Tauler, Chemometrics applied to unravel multicomponent processes and
M AN U
[20]
mixtures: Revisiting latest trends in multivariate resolution, Anal. Chim. Acta. 500 (2003) 195–210. [21]
A. de Juan, R. Tauler, Multivariate Curve Resolution (MCR) from 2000: Progress in
[22]
TE D
Concepts and Applications, Crit. Rev. Anal. Chem. 36 (2006) 163–176. G.H. Golub, C. Reinsch, Singular value decomposition ans least squares solutions, Numer. Math. 420 (1970) 403–420.
W. Windig, J. Guilment, Interactive Self-Modeling Mixture Analysis, Anal. Chem. 63
EP
[23]
(1991) 1425–1432.
A. De Juan, Y. Vander Heyden, R. Tauler, D.L. Massart, Assessment of new constraints
AC C
[24]
applied to the alternating least squares method, Anal. Chim. Acta. 346 (1997) 307–318.
[25]
A. de Juan, A. Izquierdo-Ridorsa, R. Tauler, G. Fonrodona, E. Casassas, A soft-modeling
approach to interpret thermodynamic and conformational transitions of polynucleotides., Biophys. J. 73 (1997) 2937.
[26]
C. Ruckebusch, A. De Juan, L. Duponchel, J.P. Huvenne, Matrix augmentation for
20
ACCEPTED MANUSCRIPT
breaking rank-deficiency: A case study, Chemom. Intell. Lab. Syst. 80 (2006) 209–214. D.R. Duling, Simulation of multiple isotropic spin-trap EPR spectra., J. Magn. Reson. Ser.
EP
TE D
M AN U
SC
RI PT
B. 104 (1994) 105–110.
AC C
[27]
21
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT
A new strategy to identify radicals in a time evolving EPR data set.
•
Extraction of pure EPR spectral signatures and corresponding kinetic profiles.
•
The proposed method does not require any prior knowledge of the chemical system.
•
A multiset analysis in order to decrease rotational ambiguity.
AC C
EP
TE D
M AN U
SC
RI PT
•
S0003-2670(16)31240-5
DOI:
10.1016/j.aca.2016.10.028
Reference:
ACA 234851
To appear in:
Analytica Chimica Acta
Received Date: 7 July 2016 Revised Date:
14 October 2016
Accepted Date: 17 October 2016
Please cite this article as: M.A. Fadel, A. de Juan, H. Vezin, L. Duponchel, New strategy to identify radicals in a time evolving EPR data set by Multivariate Curve Resolution-Alternating Least Squares, Analytica Chimica Acta (2016), doi: 10.1016/j.aca.2016.10.028. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT
New strategy to identify radicals in a time evolving EPR data set by
RI PT
Multivariate Curve Resolution-Alternating Least Squares
Maya Abou Fadel(a), Anna de Juan(b) Hervé Vezin(a), Ludovic Duponchel(a,*).
(a) LASIR CNRS UMR 8516, Université Lille 1, Sciences et Technologies, 59655 Villeneuve
SC
d’Ascq Cedex, France.
645, 08028 Barcelona, Spain.
M AN U
(b) Chemometrics Group, Section of Analytical Chemistry, Universitat de Barcelona, Diagonal
(*) Corresponding author, Email: [email protected], Tel: +33 320434902.
TE D
Abstract
Electron paramagnetic resonance (EPR) spectroscopy is a powerful technique that is able to characterize radicals formed in kinetic reactions. However, spectral characterization of individual
EP
chemical species is often limited or even unmanageable due to the severe kinetic and spectral
AC C
overlap among species in kinetic processes. Therefore, we applied, for the first time, multivariate curve resolution-alternating least squares (MCR-ALS) method to EPR time evolving data sets to model and characterize the different constituents in a kinetic reaction. Here we demonstrate the advantage of multivariate analysis in the investigation of radicals formed along the kinetic process of hydroxycoumarin in alkaline medium. Multiset analysis of several EPR-monitored kinetic experiments performed in different conditions revealed the individual paramagnetic
1
ACCEPTED MANUSCRIPT
centres as well as their kinetic profiles. The results obtained by MCR-ALS method demonstrate its prominent potential in analysis of EPR time evolved spectra.
AC C
EP
TE D
M AN U
SC
Resonance spectroscopy, radicals, multiset analysis, chemometrics.
RI PT
Keywords: Multivariate Curve Resolution-Alternating Least Squares, Electron Paramagnetic
2
ACCEPTED MANUSCRIPT
1. Introduction
The study of kinetics chemical reactions by spectroscopic methods is still very often based on
RI PT
univariate approach. Typically, a series of spectra are measured as a function of time and the evolution of single peaks is independently analyzed. In simple cases, the evolution of a particular compound is followed by modeling the increase or decrease of a given spectral band during such
SC
analysis. However, this approach can lead to erroneous interpretation when signals from different species overlap i.e. when the selected spectral variable is not specific to the compound of
M AN U
interest. Thus, multivariate methods are indispensable in the analysis of complex systems to overcome most of the problems reported by univariate approaches. Many multivariate methods, known under the denomination of hard-modeling methods, require knowledge about the initial concentrations of reactants and the mechanistic kinetic model. This model is then assumed and
TE D
experimental data are fitted according to it. However, the choice of the correct kinetic model is sometimes difficult or not possible at all. Multivariate soft modeling methods, which are datadriven procedures and do not need any mechanistic model, are needed to solve this kind of the
EP
problems. Among these latter methods, Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) has been successfully applied to different time evolving data [1] as well as other
AC C
kinds of sequence ordered data sets, such as chromatographic runs[2,4], or other kinds of other kinds of reactions and processes monitored by spectroscopic and voltammetric measurements[5, 8]. It is, hence, a useful tool for kinetic studies. MCR-ALS is able to retrieve, with no a priori, the pure time profiles and related spectral signatures of all the components in a studied system.
In spite of this fact, MCR-ALS has not yet been applied to the analysis of time-resolved EPR spectra. Considering that EPR is an irreplaceable tool in the study of kinetics for many kinds of 3
ACCEPTED MANUSCRIPT
paramagnetic centres and that the examination of kinetic reactions involving radicals by EPR has often to contend with strongly overlapped and multicomponent spectra, MCR-ALS appears as a suitable alternative to study this kind of systems. It was demonstrated in our previous articles that
RI PT
MCR-ALS is an effective approach in the analysis of entangled EPR signals coming from a mixture of non-interacting paramagnetic centers [9] as well as for the study of hyperspectral EPR images[10]. These results prompted us to apply MCR-ALS on EPR time evolving data because it
SC
seems to be a promising tool in the study of the reactions of radicals[11]. The objective of this work is to demonstrate the applicability of MCR-ALS to an EPR data set from a reactive mixture
M AN U
of paramagnetic radicals. As a model system for our study, one of the derivatives of 3hydroxycoumarin (see Figure 1) (3,6,7-trihydroxycoumarin) was chosen because it can be oxidized and can form different radicals in alkaline conditions. Moreover, this molecule is interesting in itself and has been intensively studied due to its promising antioxidant
TE D
properties[12].
Antioxidants interact with the free radicals and prevents them from causing damage[13].
EP
Therefore, they are also known as free radical scavengers. Free radicals are highly reactive metabolites and are naturally produced by the body as a result of normal metabolism and energy
AC C
production. These incomplete molecules aggressively attack other molecules in the body to refill the missing electrons. This oxidation severely affects the cells and leads to different diseases and antioxidants defend the body against such damages[14]. There exist endogenous and exogenous antioxidants. Exogenous sources come primarily from diet, particularly from fruits, vegetables and grains[15]. 3-hydroxycoumarin is an antioxidant that belongs to the coumarin-related compounds. The former is rare in nature and is formed from the hydroxylation of the coumarins at the 3-position by liver microsomes[16]. In 1990, Aihara el al. described their first chemical 4
ACCEPTED MANUSCRIPT
preparation from coumarins[17]. The 3-hydroxylation turned out to significantly improve antioxidant activity and, for instance, increased the 5-lipoxygenase and α-glycosidase inhibitory activities of coumarins. One of the derivatives of this molecule which exhibits very promising
RI PT
antioxidant properties is 3,6,7-trihydroxycoumarin presented in Figure 1.
In this work, EPR spectra of this molecule measured in alkaline conditions as a function of time
SC
are analysed by MCR-ALS in order to extract knowledge about the intermediate species formed
M AN U
and the related reaction pathway.
2. Experimental Section
2.1. Sample preparation
TE D
3,6,7-trihydroxycoumarin was synthesized as described by Cotelle et al.[11]. Two experimental solutions were prepared by mixing 1 mg of the compound with 500 µL of sodium hydroxide
EP
with two different concentrations, 1M and 2M, respectively.
AC C
2.2. Spectral acquisition
Samples were analyzed with a continuous wave-electron paramagnetic resonance spectrometer (CW-EPR). EPR spectra were recorded at a constant room temperature of 20°C, using a Bruker ELEXSYS 500 spectrometer operating at the X-Band. All spectra were recorded at a modulation field frequency of 100 kHz and a microwave frequency of 9.80 GHz, with an amplitude modulation of 0.002 mT and a microwave power of 0.1 mW corresponding to non-saturation
5
ACCEPTED MANUSCRIPT
conditions. The weak pitch from Bruker was used as standard reference and contained a known concentration of spin/mass (1.29 × 1013 spins/g). The following spectrometer parameters were used during the spectral acquisition: receiver gain 68 dB, time constant 40.96 ms, conversion
RI PT
time 81.92 ms. The spin concentration is given by the double integration of the first derivative of the EPR signal. Spectra were measured over a spectral range from 3473 Gauss to 3486 Gauss. Each sample was monitored as a function of time with 900 second intervals. 80 time-resolved
SC
spectra were recorded for both samples covering 20 hours time range.
M AN U
2.3. Data treatment
Recorded spectra of both samples were gathered in two data sets. They were processed and analyzed in MATLAB environment version R2008b (The MathWorks Inc., Natick, MA, 2000)
TE D
by the MCR-ALS toolbox (see the method below) developed by J. Jaumot, R. Tauler and A. de Juan. It can be freely downloaded from the webpage http://www.mcrals.info[18].
EP
2.4 Multivariate resolution of spectroscopic data
AC C
The aim of multivariate curve resolution methods is to decompose a mixed signal into the contribution of the pure component profiles of the constituents, by means of a simple bilinear model, defined as follows[19,20] = + (eq.1)
6
ACCEPTED MANUSCRIPT where D ( × ) is the raw experimental data matrix containing the different EPR spectra
acquired as a function of time, the columns of C( × ) are the kinetic profiles of the k pure components involved in the kinetic process and the rows of ST( × ) are their related pure
RI PT
EPR spectral profiles. E( × ) is the error matrix that presents the data variance not explained
by the bilinear model. The model is optimized during an iterative process via an alternating
SC
least squares algorithm under constraints (see below).
MCR-ALS has the possibility to be applied simultaneously on more than one data set[21].
M AN U
Therefore, the procedure described above can be extended to the analysis of multiple data sets (experiments) simultaneously as long as they have at least one data mode, i.e. direction, in common. In the case of r different data sets acquired by the same spectroscopic technique, the possible data arrangement and extension of the bilinear model would be as follows:
EP
TE D
= + (eq.2) … ⋯ ⋯
In the context of this work, , , ..., , are EPR-monitored kinetic experiments performed in
AC C
different conditions sharing components in common, , , ..., contain the kinetic profiles
of the resolved components in each of the related Di submatrices (experiments), respectively,
is a single matrix that represents the EPR spectral profiles of the different components present in
the analysed Di submatrices, and , , ..., are the corresponding error submatrices containing the part of the measured data unexplained by the proposed bilinear model. The multiset equation can be written in a more compact form (i.e. an augmented one) as follows
7
ACCEPTED MANUSCRIPT = ; ; ⋯ ; = ; ; ⋯ ; + ; ; ⋯ ; = + (eq.3) where , and correspond to the column-wise augmented matrices containing,
RI PT
respectively, the EPR-monitored kinetic experiments, the kinetic profiles of the resolved
components in the different experiments, and the error of the unexplained modelled data in different experiments, respectively. The notation ';' in the previous equation is used to indicate
SC
the column-wise augmentation.
M AN U
MCR-ALS provides Caug and matrices solely from the information of the experimental matrix
Daug. The first step in MCR-ALS is to obtain an estimation of the number of pure components
involved in the reaction i.e. rank k of data matrix. This determination is performed by Singular Value Decomposition (SVD)[22]. Rank k is equal to the singular values related to the chemical
TE D
species that are larger than those linked to experimental errors or noise. Second, initial estimates, either of concentration profiles Cini or spectral profiles STini, are required to start the iterative Alternating Least Squares procedure (ALS). The pure variable selection method based on
EP
SIMPLe-to-use Interactive Self modeling Analysis (SIMPLISMA) is used for this purpose [23].
AC C
This method is based on selecting the purest or the more specific variables in the data set. It is often said that SIMPLISMA selects the more dissimilar variables from the data matric D. For better variable selection, this method is applied only on positive data set i.e. integrated spectra which is rather uncommon for EPR data analysis. Integrated spectra are generated by a homebuilt code. Considering that the initial estimates are the spectral profiles (in this specific case), an iterative alternating least squares optimization of matrices Caug and ST is done for each iteration according to the following equations 4 and 5: 8
ACCEPTED MANUSCRIPT = ( ) (eq.4)
RI PT
= ( ) (eq.5) Suitable constraints can be implemented during the iterative calculation of Caug and ST, to give physical meaning to the obtained results, and to decrease the extent of possible rotational
SC
ambiguities[24]. Rotational ambiguity is connected to the number of possible solution of MCRALS extractions. Thus our main aim is always to decrease it in order to obtain the uniqueness of
M AN U
extractions for concentrations and spectral profiles. Constraints are defined as chemical properties translated into mathematical conditions that concentration Caug and/or spectral profiles ST should fulfill (e.g. non-negativity, closure, unimodality, ...). Therefore, when a profile is constrained, its shape is modified in order to fulfill preselected properties. Iterations stop when
TE D
an optimal solution is obtained i.e. achieved the postulated constraints and the established convergence criteria. In general, it is achieved when the relative difference in lack of fit between two consecutive iterations is below a threshold or when a predefined number of iteration is
EP
reached. The lack of fit (eq. 6) is evaluated from the difference between the experimental data matrix Daug and the resolved data matrix, which is the product of concentration and spectral
AC C
profiles CaugST. The explained variance (r2), which is also used to evaluate the fit quality of MCR-ALS model, is defined in equation 7.
∑.,/ -./0
lack of fit (%) = 100+∑
0 .,/ 2./
(eq. 6)
9
ACCEPTED MANUSCRIPT 0 ∑ 7,8 -.,/
3 4 = 100 51 − ∑
0 7,8 2.,/
9 (eq. 7)
RI PT
where dij is an element of the input data matrix Daug (time i, magnetic field j) and eij is the related residual obtained from the difference between the input element and the MCR-ALS reproduction.
SC
The results obtained from multivariate curve resolution when applied to time evolving EPR data
M AN U
sets are pure kinetic and spectral profiles of all the compounds present in the studied samples. Resolved spectral profiles can be used to identify these components by comparing them with those obtained by EPR spectra simulations. On the other hand, the time profiles give the kinetic information of each component and a description of the full time-dependent process.
TE D
3. Results
EPR spectra of 3,6,7-trihydroxycoumarin in 1M and 2M NaOH recorded at different times after
EP
dissolution are presented in Figure 2. Spectra were gathered in two individual data sets, D1 (for 1M NaOH) and D2 (for 2M NaOH), respectively. The dimension of each data set is 80×1024
AC C
comprising 80 spectra and 1024 different magnetic fields. In the first attempts, the original raw EPR data sets were individually analyzed by MCR-ALS but the results suffered significant ambiguity and satisfactory resolution was not achieved.
10
ACCEPTED MANUSCRIPT
Therefore, the two data sets were combined into a single column-wise augmented data matrix to benefit from the ambiguity decrease provided by multiset analysis[25,26]. The simultaneous analysis of different mixtures of the same compounds, in different chemical or physical
RI PT
conditions such as time or pH is a powerful approach to extract more reliable knowledge on the individual species of the systems[25]. In this study, the same molecule in experiments performed in different alkaline conditions was present in each experiment. Thus, a magnetic field wise-
SC
augmented matrix, keeping the magnetic fields values in common, was built for multiset analysis. As a consequence, the pure spectra in both data sets are considered invariant and the
M AN U
matrix C allows the profiles of each compound in the concentration direction to be different for each individual matrix (experiment) (Figure 3).
First attempts of multiset analysis were aimed at performing MCR-ALS directly on the raw data
TE D
i.e. on EPR spectra represented in their first derivative form (Figure 2). However, this approach was not efficient to resolve various components with ubiquitous spectral overlapping. The implementation of only one constraint in MCR-ALS procedure i.e. non-negativity on the
EP
concentration profile on such complex data, gave high uncertainty in the final solution. For this reason, integrated spectra shown in Figure 2, were used instead of original first derivative
AC C
spectra. In this case, an additional constraint that is the non-negativity on the spectral direction can be added.
The first step of multiset MCR-ALS was the evaluation of the data matrix rank corresponding to the number of independent components present in the experimental mixture. It is worth noting that MCR-ALS is a real blind signal unmixing procedure since no prior knowledge about the total number of pure components is used. For this purpose, SVD was applied on the multiset 11
ACCEPTED MANUSCRIPT
Daug. Figure 4 presents the plot of the first 20 eigenvalues indicating the presence of four distinct contributions in terms of the broken stick concept. Indeed four significant eigenvalues are distinguished from the rest due to the sudden change of the slopes. All further eigenvalues
RI PT
represent variance associated with noise. In order to develop this assumption, we have done resolutions with a rank of five or six without letting us to extract more pure contributions and even generate worse extractions.The next step in MCR-ALS was the estimation of the initial
SC
spectral or concentration profiles by a SIMPLISMA-based algorithm. In this case, STini matrix was obtained in order to begin the ALS iterations. In the optimization process, non-negativity
M AN U
constraints were imposed on the concentration as well as spectral profiles. The results obtained after the application of MCR-ALS on the augmented matrix Daug are shown in Figure 5. They represent the pure spectra ST of all species (Figure 5A,B,C and D) present in both experiments and corresponding concentration profiles (Figure 5, C1 and C2) which are different in two
TE D
experiments due to different alkaline conditions. The quality of the final resolution was verified and given the signal-to-noise in the integrated EPR data, a lack of fit of 3.45% and explained
AC C
EP
variance of 99.88% were accepted as good figures of merit for the proposed resolution.
4. Discussion
Identification of the spectra extracted by MCR-ALS (see Figure 5) is not a trivial task. As described in the literature, 3-hydroxycoumarin can be oxidized under alkaline conditions and form various radicals [11]. According to Cotelle et al. six radicals can be formed in the reaction
12
ACCEPTED MANUSCRIPT
of 3,6,7-trihydroxycoumarin in the presence of NaOH [11]. The proposed structures and reaction paths for these radicals are presented in Figure 6.
RI PT
Six radicals may be formed by transformation from one to another. Thus association of the extracted MCR-ALS spectra with some of these radicals require some simulations. The theoretical calculations for the postulated radicals revealed that they should exhibit characteristic
SC
patterns in EPR spectra. In addition to the previous literature data, a new set of simulations of the radical spectra was performed using WinSim software[27] considering the hyperfine constants
M AN U
(presented in Table 1) provided by Cotelle et al.[11]. The results of these simulations are presented in
TE D
.
Radical I is represented by a spectrum formed by 8 equally distributed EPR lines (Figure 7a) and it is not observed in the set of MCR-ALS results (see Figure 5). Indeed, this radical is known to
EP
be only observed in weakly alkaline solution (for example 0.1M of NaOH). It possesses three doublets that are attributed to the coupling between the unpaired electron and the three protons
AC C
(H4, H5 and H8). In the considered experimental conditions, radical I is rapidly transformed into other radical forms. At this step, two possible pathways are postulated. The first one assumes that radical II is formed, however, it rapidly decays and is replaced by radical III that is more stable. The EPR spectra of radicals II and III are very similar so they are difficult to distinguish. Actually, in highly basic medium (1 or 2M of NaOH) the spectra of these two radicals are nearly identical. They possess characteristic EPR pattern with 32-line spectrum due to the interaction between the unpaired electron and five protons; however, only four quartets and two pentets can 13
ACCEPTED MANUSCRIPT
be shown due to the overlap of the bands (see Figre 7b). Radical III can be further transformed into radical VI which exhibits an 8-line spectrum presented in Figure 7e. The parallel reaction path includes the transition from Radical I to radicals IV and V which are in equilibrium. They
RI PT
have different EPR signals presented in Figure 7c and Figure 7d respectively. The former possesses triplet of quartets due to the coupling between the unpaired electron and four protons, among which two protons are equivalent. The latter has an 8-line EPR spectrum due to the
SC
interaction between the unpaired electron and three protons. In the context of this established reactions scheme, the presence of signal from radicals III, IV, V and VI can be observed in the
M AN U
studied dataset.
Comparing spectral profile extracted by MCR-ALS (Figure 5) and the simulated spectra (Figure 7) the assignment of the radicals is possible. The first extracted spectrum (in blue) corresponds very well to initially formed pure radical II. The second spectrum (in green) in Figure 5 can be
TE D
undoubtedly attributed to the EPR spectrum of radical VI. The third spectrum (in red) is not a pure one. Indeed, it is a mixture of radical VI (central part of the spectrum) and radical IV recognized by characteristic four peaks at the left and the right of the central part. The fourth
EP
spectrum (in orange) cannot be easily assigned and it is probably a mixture of several radicals IV, V and VI. It is important to note that there are species in equilibrium and parallel reactions
AC C
and, therefore, rotational ambiguity still exists in this data set. As a consequence, a doubt on the rank number could be built. However, in the case of a rank modification, even radicals II and IV were not purely extracted by MCR-ALS. This confirms the fact that the rank estimated in this work (four) is relevant. In spite the fact that the third and fourth spectra extracted by MCR-ALS are not yet completely pure, the extracted concentration profiles of radicals II and VI can provide valuable information
14
ACCEPTED MANUSCRIPT
about the kinetics of the reactions. Considering concentration profiles of radical II (blue) and radical VI (green) in D1 and D2, in both cases, a decay of radical II corresponds to the growth of radical VI which confirms a postulated reaction path (Figure 6). However in D2, a decay of
RI PT
radical II is clearly faster than in D1. This makes perfect sense with respect to higher alkaline conditions (2M NaOH instead of 1M NaOH) observed for data set D2.The concentration profile of the third and fourth component, which are the only ones including EPR features of radicals IV
SC
and V have a lower presence in both experiments, especially in the experiment at 2 M NaOH, which could confirm that the formation of radical IV is a less promoted mechanism than the
M AN U
formation of radical II.
5. Conclusions
TE D
The results presented in this paper demonstrate the applicability of MCR-ALS to the analysis of multicomponent time evolving EPR data. The presented results are the first MCR-ALS application on this type of EPR data sets. The analysis confirmed that a complex system of
EP
paramagnetic species can be resolved by multivariate analysis giving valuable information about the reaction pathways. In addition, it was demonstrated the usefulness of multiset analysis in this
AC C
context. Some of the spectral signatures and kinetic profiles of four pure radicals were retrieved from the kinetic reaction of hydroxycoumarin in alkaline medium. Furthermore, results obtained by MCR-ALS (multiset analysis) seem appropriate but not yet optimal due to the presence of rotational ambiguity that still exists due to the complexity in both the kinetic and the spectral directions. In order to fully resolve the pure components from this challenging system, richer experimental data, such as experiments at different conditions, are required. An experiment with varied acquisition speed is needed for further exploration of the reaction, especially in its initial 15
ACCEPTED MANUSCRIPT
part, since most of the reactions occur in this part. If information is more complete, the inclusion of mechanistic models within the framework of MCR, successfully done in other examples.
dimensions in the interpretation of EPR results.
SC
6. Acknowledgement
RI PT
could also be envisioned. We are convinced that such an approach will open new analytical
Anna de Juan acknowledges funding support from the Spanish government through project
Captions
TE D
Figure 1: 3,6,7-trihydroxycoumarin.
M AN U
CTQ2015-66254-C2-2-P.
Figure 2: 80 EPR time-resolved spectra obtained for 3,6,7-trihydroxycoumarin in 1M NaOH (upper left) and corresponding integrated form (upper right). 80 EPR time-resolved spectra obtained for 3,6,7-
EP
trihydroxycoumarin in 2M NaOH form (lower left) and corresponding integrated form (lower right).
AC C
Figure 3: Scheme of the MCR-ALS decomposition of augmented matrix by column-wise augmented matrix of two experimental data sets.
Figure 4: Logarithm of eigenvalues obtained by Singular Value Decomposition of the spectral data matrix Daug.
16
ACCEPTED MANUSCRIPT
Figure 5: Pure concentration profiles Caug (top) and corresponding pure spectra ST (bottom) of four components resolved by MCR-ALS on augmented data set Daug.
RI PT
Figure 6: Scheme representing radicals formed in the reaction of 3,6,7-trihydroxycoumarin in alkaline solution[11].
SC
Figure 7: Simulated EPR spectra of the pure radicals in their integrated form.
AC C
EP
TE D
M AN U
Table 1: Experimental hyperfine constants obtained by simulation (in Gauss, in absolute value).
17
ACCEPTED MANUSCRIPT
References
M. Garrido, F.X. Rius, M.S. Larrechi, Multivariate curve resolution-alternating least
RI PT
[1]
squares (MCR-ALS) applied to spectroscopic data from monitoring chemical reactions processes., Anal. Bioanal. Chem. 390 (2008) 2059–66.
S. Mas, A. Carbo, S. Lacorte, A. De Juan, R. Tauler, Comprehensive description of the
SC
[2]
photodegradation of bromophenols using chromatographic monitoring and chemometric
[3]
M AN U
tools, Talanta. 83 (2011) 1134–1146.
R. Gargallo, R. Tauler, F. Cuesta-Sánchez, D.L. Massart, Validation of alternating leastsquares multivariate curve resolution for chromatographic resolution and quantitation, Trac- Trend. Anal. Chem. 15 (1996) 279–286.
K. De Braekeleer, A. De Juan, D.L. Massart, Purity assessment and resolution of
TE D
[4]
tetracycline hydrochloride samples analysed using high-performance liquid chromatography with diode array detection, J. Chromatogr. A. 832 (1999) 67–86. A. Izquierdo-Ridorsa, J. Saurina, S. Hernández-Cassou, R. Tauler, Second-order
EP
[5]
multivariate curve resolution applied to rank-deficient data obtained from acid-base
AC C
spectrophotometric titrations of mixtures of nucleic bases, Chemometr. Intell. Lab. 38 (1997) 183–196.
[6]
J. Saurina, S. Hernández-Cassou, R. Tauler, a Izquierdo-Ridorsa, Procedure for the quantitative determination of mixtures of nucleic Acid components based on multivariate spectrophotometric Acid-base titrations., Anal. Chem. 71 (1999) 126–134.
[7]
J. Diewok, A. de Juan, R. Tauler, B. Lendl, Quantitation of Mixtures of Diprotic Organic Acids by FT-IR Flow Titrations and Multivariate Curve Resolution, Appl. Spectrosc. 56 18
ACCEPTED MANUSCRIPT
(2002) 40–50. [8]
A. Safavi, B. Hemmateenejad, F. Honarasa, Chemometrics assisted resolving of net faradaic current contribution from total current in potential step and staircase cyclic
[9]
RI PT
voltammetry, Anal. Chim. Acta. 766 (2013) 34–46.
M. Abou Fadel, A. De Juan, N. Touati, H. Vezin, L. Duponchel, New chemometric
approach MCR-ALS to unmix EPR spectroscopic data from complex mixtures, J. Magn.
[10]
SC
Reson. 248 (2014) 27–35.
M. Abou Fadel, X. Zhang, A. De Juan, R. Tauler, H. Vezin, L. Duponchel, Extraction of
M AN U
Pure Spectral Signatures and Corresponding Chemical Maps from EPR Imaging Data Sets: Identifying Defects on a CaF2 Surface Due to a Laser Beam Exposure, Anal. Chem. 87 (2015) 3929–3935. [11]
P. Cotelle, H. Vezin, EPR of free radicals formed from 3-hydroxyesculetin and related
[12]
TE D
derivatives., Res. Chem. Intermediat. 29 (2003) 365–77.
F. Bailly, C. Maurin, E. Teissier, H. Vezin, P. Cotelle, Antioxidant properties of 3hydroxycoumarin derivatives, Bioorganic Med. Chem. 12 (2004) 5611–5618. B. Halliwell, Free radicals, antioxidants, and human disease: curiosity, cause, or
EP
[13]
consequence?, Lancet. 344 (1994) 721–4. B.N. Ames, M.K. Shigenaga, T.M. Hagen, Oxidants, antioxidants, and the degenerative
AC C
[14]
diseases of aging., P. Natl. Acad. Sci. U. S. A. 90 (1993) 7915–7922.
[15]
J. Bouayed, T. Bohn, Exogenous Antioxidants—Double-Edged Swords in Cellular Redox State: Health Beneficial Effects at Physiologic Doses versus Deleterious Effects at High Doses, Oxid. Med. Cell. Longev. 3 (2010) 228–237.
[16]
A. Heliangolide, C. Zdero, A heliangolide, 3-hydroxyumbelliferone Derivatives
19
ACCEPTED MANUSCRIPT
Diterpenes From Bahia Ambroszozdes, Phytochemistry. 29 (1990) 205–208. [17]
K. Aihara, T. Higuchi, M. Hirobe, 3-Hydroxycoumarins - 1st Direct Preparation From Coumarins Using a Cu-2+ Ascorbic-Acid O2 System, And Their Potent Bioactivities.,
[18]
RI PT
Biochem. Biophy. Res. Com. 168 (1990) 169–75.
J. Jaumot, A. De Juan, R. Tauler, MCR-ALS GUI 2.0: New features and applications, Chemometr. Intell. Lab. Syst. 140 (2015) 1–12.
J.H. Jiang, Y. Liang, Y. Ozaki, Principles and methodologies in self-modeling curve
SC
[19]
resolution, Chemometr. Intell. Lab. Syst. 71 (2004) 1–12.
A. De Juan, R. Tauler, Chemometrics applied to unravel multicomponent processes and
M AN U
[20]
mixtures: Revisiting latest trends in multivariate resolution, Anal. Chim. Acta. 500 (2003) 195–210. [21]
A. de Juan, R. Tauler, Multivariate Curve Resolution (MCR) from 2000: Progress in
[22]
TE D
Concepts and Applications, Crit. Rev. Anal. Chem. 36 (2006) 163–176. G.H. Golub, C. Reinsch, Singular value decomposition ans least squares solutions, Numer. Math. 420 (1970) 403–420.
W. Windig, J. Guilment, Interactive Self-Modeling Mixture Analysis, Anal. Chem. 63
EP
[23]
(1991) 1425–1432.
A. De Juan, Y. Vander Heyden, R. Tauler, D.L. Massart, Assessment of new constraints
AC C
[24]
applied to the alternating least squares method, Anal. Chim. Acta. 346 (1997) 307–318.
[25]
A. de Juan, A. Izquierdo-Ridorsa, R. Tauler, G. Fonrodona, E. Casassas, A soft-modeling
approach to interpret thermodynamic and conformational transitions of polynucleotides., Biophys. J. 73 (1997) 2937.
[26]
C. Ruckebusch, A. De Juan, L. Duponchel, J.P. Huvenne, Matrix augmentation for
20
ACCEPTED MANUSCRIPT
breaking rank-deficiency: A case study, Chemom. Intell. Lab. Syst. 80 (2006) 209–214. D.R. Duling, Simulation of multiple isotropic spin-trap EPR spectra., J. Magn. Reson. Ser.
EP
TE D
M AN U
SC
RI PT
B. 104 (1994) 105–110.
AC C
[27]
21
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
AC C
EP
TE D
M AN U
SC
RI PT
ACCEPTED MANUSCRIPT
ACCEPTED MANUSCRIPT
A new strategy to identify radicals in a time evolving EPR data set.
•
Extraction of pure EPR spectral signatures and corresponding kinetic profiles.
•
The proposed method does not require any prior knowledge of the chemical system.
•
A multiset analysis in order to decrease rotational ambiguity.
AC C
EP
TE D
M AN U
SC
RI PT
•