Concatenated Two-Dimensional Correlation Analysis:A New Possibility for Generalized Two-DimensionalCorrelation Spectroscopy and Its Application to theExamination of Process Reversibility

LIPING ZHANG, ISAO NODA, and YUQING WU*State Key Lab for Supramolecular Structure and Material, Jilin University, No. 2699, Qianjin Street, Changchun, 130012 P. R. China (L.Z.,

Y.W.); The Procter & Gamble Company, 8611 Beckett Road, West Chester, Ohio 45069 (I.N.); and Jilin Business and Technology College, No.4728, Xi’an Road, Changchun, 130061, P. R. China (L.Z.)

We propose a new application of generalized two-dimensional (2D)

correlation spectroscopy called ‘‘concatenated’’ 2D correlation analysis,

which is useful in identifying the presence of strict similarity or very

subtle difference between two spectral data sets having a similar origin.

This approach is very efficient and can offer many potential applications.

In this study, the detailed examination of process reversibility is explored.

Two forms of concatenation, horizontal and vertical concatenation of data

matrices, are introduced and the latter is discussed in detail. Concate-

nated 2D correlation analysis allows one to investigate directly the

correlation between two independent but related spectral data sets. It can

extract more detailed information, such as the comparison of effects of

two different perturbations or different systems. We describe the principle

of the ‘‘mirror-image concatenation’’ in 2D correlation analysis, which is

applied to demonstrate its reliability and efficiency on three spectral

models: a synthetic simulation data set; experimental Fourier transform

infrared (FT-IR) spectra of the thermally induced unfolding–refolding

transition of bovine pancreatic ribonuclease A (RNase A) in aqueous

solution; and a set of FT-IR spectra of traditional Chinese medicines

(TCM) of similar origin. The concatenated 2D correlation analysis shows

its power in revealing the irreversibility of the thermally induced

conformation transition of RNase A as well as the comparison of different

species of TCM.

Index Headings: Two-dimensional correlation spectroscopy; 2D correla-

tion; Vertical concatenation; Process reversibility; Traditional Chinese

medicine.

INTRODUCTION

Since the introduction of the basic concept by Noda in1986,1 two-dimensional (2D) correlation spectroscopy hasbecome a popular tool applicable to a variety of analyticalscience problems.2–14 It enhances spectral resolution byspreading peaks along the second dimension and facilitatesthe extraction of information that cannot be obtained easilyfrom one-dimensional spectra.

With the rapid progress in the field of generalized 2Dcorrelation spectroscopy, hetero-spectral 2D correlation anal-ysis has recently become a subject of keen interest due to itspower in dealing with sets of completely different types ofspectra obtained for a system under the same perturbationconditions.15,16 Two types of hetero-spectral 2D correlationsare often used. The first one is concerned with the comparisonbetween closely related spectroscopic techniques, such asinfrared/near-infrared (IR/NIR) and Raman/NIR spectroscopy;the second one is hetero-correlation between completely

different types of spectroscopy or physical techniques such asIR and X-ray scattering. For example, Liu et al.17 used hetero-spectral 2D correlation based on the combination of visible andNIR spectroscopy to study the storage and treatment-processdependence of chicken meat. Czarnik-Matusewicz et al.3 usedIR/NIR hetero-spectral correlation to analyze the temperatureeffect on hydrogen bonded assembly of water. McNavage etal.18 developed a variant form of hetero-spectral correlationcalled cross-spectra correlation for time-resolved FT-IRemission study of photolysis reactions. Hyde et al.19 reportedhetero-correlation based on IR and gas chromatography.

Hybrid 2D correlation spectroscopy was proposed in 2002.20

It deals with the 2D correlation analysis between twoseparately obtained data matrices.20–22 In hetero-spectral 2Dcorrelation, two sets of data matrices are obtained by makingtwo different types of spectroscopic measurements under thesame perturbation; in hybrid correlation, on the other hand, asingle type of spectroscopic measurement is usually carried outunder multiple perturbation variables. Most importantly, hybrid2D correlation spectroscopy is often applied to both sample–sample and variable–variable 2D correlation spectroscopy. Bycoupling with sample–sample correlation, hybrid 2D correla-tion furthermore can potentially explore the latent correlationbetween different perturbation variables. It explores thesimilarity or difference between two systems or processes byinvestigating the symmetry along the diagonal line in thesample–sample hybrid 2D cross-product. The technique so fardisclosed the presence of two different reaction mechanisms ofhydrogenation of nitrobenaene20 and the reversibility ofpolymer processes dependent on temperature and pressure.21

Here we propose a new application of generalized 2Dcorrelation spectroscopy called ‘‘concatenated’’ 2D correlationanalysis. By using this method, one can more clearly anddirectly identify the structural dissimilarity between twospectral data of related origin. In other words, concatenated2D correlation analysis deals with the correlation between twosets of spectra by concatenating them together into a new datamatrix, instead of separately performing 2D calculation on eachdata set. The technique may be regarded as a furtherdevelopment or an interesting extension of 2D hetero-spectral(with the same perturbation) or hybrid (with differentperturbations) correlation spectroscopy. Unlike the usual 2Dhetero-spectral or hybrid processes, concatenated 2D correla-tion analysis probes the correlation between two sets of spectraby means of the so-called vertical concatenation strategy. Thisapproach, we believe, is computationally easier and moreefficient and thus offers many potential applications, such as

Received 3 June 2009; accepted 22 December 2009.* Author to whom correspondence should be sent. E-mail: yqwu@jlu.edu.cn.

Volume 64, Number 3, 2010 APPLIED SPECTROSCOPY 3430003-7028/10/6403-0343$2.00/0

� 2010 Society for Applied Spectroscopy

diagnostics and classifications of samples, comparison ofsimilar samples, and assessment of the effect of differentstimuli on spectral changes of a given sample.

Ribonuclease A (RNase A) has long served as a model forstudies of protein stability, unfolding, structure, and chemis-try.23 Previous studies show that the unfolding of RNase A ishighly cooperative and exhibits a reversible two-state transitionin neutral and/or mildly acidic solutions.24–26 Using far-ultraviolet (UV) circular dichroism (CD) and nuclear magneticresonance (NMR), Yan et al. disclosed that there was a smallamount (approximately 5–10%) of irreversibility in the thermalunfolding of RNase A; using NMR, he found that the thermaldenaturation is nearly reversible (approximately 95%) in thetemperature range of 28 to 46 8C and irreversible when heatedto 50 8C.27 Besides, a recent investigation of protein structureby the bidirectional temperature-jumped method reported apath-dependent folding–unfolding mechanism of RNase A.28

In the present study, we will firstly describe the theoreticalbasis of the concatenated 2D correlation analysis. Then we willvalidate its reliability using a synthetic dataset. Finally, its truepower in actual application will be demonstrated both bydisclosing the irreversibility of thermally induced unfolding–refolding of bovine pancreatic ribonuclease A (RNase A) inaqueous solution and by comparison of different species oftraditional Chinese medicine (TCM).

THEORY

According to the basic theory of generalized two-dimen-sional correlation spectroscopy,29 2D correlation spectra maybe viewed as a product obtained by simple matrix multiplica-tion. In general, traditional variable–variable 2D correlation isa multiplication of the same data matrices. For a given datamatrix A, which is usually mean-centered, the synchronous andasynchronous spectra are proportional to the matrix products ofATA and ATNA, respectively, where N is the Hilbert–Noda

transformation matrix.16 Similarly, the hetero-spectral 2Dcorrelation can be viewed as the multiplication of two datasets of different spectral matrices, A and B. The synchronousand asynchronous hetero-spectral correlation can be achievedin a straightforward manner by ATB and ATNB.

In the present study, we will further explore the concatena-tion of two data matrices, which will bring a very interestingand insightful result. Generally, there are two forms ofconcatenation, named horizontal and vertical concatenation.The former (as shown in Scheme 1a) is performed by joiningtwo matrices side by side and expressed as [A B] in MATLABlanguage. Anther type of concatenation, named verticalconcatenation, shown in Scheme 1b, is more significant inthe present study. It is performed by joining the two matricestop to bottom and is expressed as [A;B]. Matrices A and Bmust have the same spectral range and each spectral trace musthave the same number of data points to perform a verticalconcatenation. It is similar to the case for hetero sample–sample or variable–variable 2D correlation. The synchronousand asynchronous spectra of this vertically concatenated matrixwill be represented as [A;B]T[A;B] and [A;B]TN[A;B],respectively. The synchronous spectrum is actually nothingbut the sum of ATA and BTB, which is not particularlyinteresting. The asynchronous spectrum, however, will have afascinating property if matrix A is related to matrix B in acertain way. The asynchronous spectrum of the verticallyconcatenated data matrix [A;B] will most vividly identify thestrict similarity or subtle difference between the two originaldata matrices A and B. This conclusion will be reached by thefollowing deduction.

Before proceeding further, let us firstly introduce themathematical operation of ‘‘perversion’’30 or ‘‘flip’’ of a datamatrix, which results in a ‘‘mirror-image matrix’’ of the originalone. In parallel to the two kinds of data matrix concatenation,there are also two forms of flips, as shown in Scheme 2,‘‘horizontal flip’’ and ‘‘vertical flip’’, which can be easilyperformed by using the ‘‘fliplr’’ and ‘‘flipud’’ functions inMATLAB.

Now let us resume the vertical concatenation of the datamatrices discussed above. If matrices A and its vertical mirror-image matrix Aflipud are vertically concatenated into a newmatrix, it can be expressed horizontally as [A;Aflipud ]. We cannow calculate the synchronous and asynchronous spectra of thevertically concatenated mirror-image data as

U ¼ ½A; Aflipud�T½A; Aflipud� ¼ ATA ð1Þ

W ¼ ½A; Aflipud�TN½A; Aflipud� ¼ 0 ð2Þ

The calculated synchronous spectrum of the concatenatedmatrix will remain ATA according to Eq. 1, which is nothingnew as after calculation it goes back to the original product ofmatrix A, ATA. What is fascinating here is the asynchronousspectrum, which will become zero according to Eq. 2. Theresult indicates that no cross-peak will show up in theasynchronous spectrum for a mirror-image concatenatedmatrix, even if asynchronous spectra generated from individualmatrices A and Aflipud may have several asynchronous peaks.Indeed, [A;Aflipud]TN[A;Aflipud] has absolutely no correlationintensity what so ever!

Scheme 3 illustrates the cause of the disappearance of the

SCHEME 1. Illustration of two types of concatenation: (a) horizontalconcatenation and (b) vertical concatenation.

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asynchronous cross-peaks. It is seen that the concatenation of adata matrix with its flipped matrix in the perturbation axis willalways produce an even function (Scheme 3a), while theHilbert–Noda transformation of an even function will producean odd function (Scheme 3b). The asynchronous correlation isgiven by the convolution of signal at some wavenumber m1 andthe Hilbert–Noda transform of some other signal at m2.16 It isknown that the convolution of any pair of an even function andodd function is always zero, regardless of shape, sign, ormagnitude. Thus, asynchronous correlation intensity betweenany set of even functions, such as those created by the mirror-image concatenation, will be zero. That is the cause of the total

absence of cross-peaks in the asynchronous spectrum of thevertically mirror-image concatenated matrix [A;Aflipud].

This property can be used as a powerful diagnostic tool toidentify the presence of strict similarity or very subtledissimilarity between two spectral data matrices of similar orrelated origins. For example, let us consider two spectral datasets A and B obtained from a roundtrip perturbation process,such as heating and cooling, compression and decompression,etc. One can join them into a vertically concatenated matrix inwhich B is attached at the bottom of A sequentially. Then, oneapplies 2D correlation analysis to the newly created verticallyconcatenated matrix, i.e., [A;B]. If no meaningful cross-peakappears in the asynchronous 2D spectrum for the concatenateddata, there is a good chance we can draw a conclusion that B¼Aflipud according to Eq. 2. That is, the original two data sets Aand B have exactly the same spectral response behavior, exceptthat their behavior is opposite in the direction along theperturbation or sampling axis.

On the other hand, the appearance of any meaningful cross-peaks in the asynchronous 2D spectrum indicates that thebehaviors of the original two data sets are different, ether in thepathways or changing rate constants. To give a criterion of themeaningful asynchronous peaks, a series of vertical concate-nated matrices are built based on a data matrix S from thetemperature-dependent IR spectra of RNase A measured in thespectral range of 1600 to 1700 cm�1 from 25 8C to 40 8C. Oneof the matrices is the vertical mirror-concatenated one, denotedas [S;Sflipud]. The very weak cross-peaks (the magnitude ofintensity is approximately 10�22) in its asynchronous spectrumshould be ascribed to the noise. Other matrices are marked as[S;P](P ¼ aSflipud). By changing the value of a from 0.95 to1.05, a series of asynchronous spectra are calculated from thematrix [S;P]. The results indicate that a slight departure of P(i.e., a¼ 0.999 or a¼ 1.001, respectively) from Sflipud leads tothe magnitude of the asynchronous cross-peaks changing fromthe level of 10�22 to 10�6. Therefore, we assign the magnitudeat the level of 1.0 3 10�6 as a tentative criterion for theselection of the meaningful asynchronous peaks for RNase A.

SCHEME 2. Representation of two kinds of flipping operations: (top) vertical flip and (bottom) horizontal flip; matrix F is a perversion operator.

SCHEME 3. Mirror-image concatenation with the same data flipped in (a) theperturbation axis and (b) its Hilbert–Noda transformation form.

APPLIED SPECTROSCOPY 345

Further improvement on the criterion is still under investiga-tion.

The property thus can be applied to the diagnosis ordetermination of the reversibility of many practically importantprocesses. Suppose we carry out a spectral measurement undera usual physical perturbation protocol, such as the temperature-dependent IR measurement of a protein sample. This time,however, we use the so-called ‘‘mirror-image’’ or roundtripprotocol, where temperature is raised from the initialtemperature to a fixed point and then lowered in a similarmanner back to the initial condition in a single reversedexperiment. This process is equivalent to flipping the directionof the perturbation in the middle of the experiment.

If the spectral response is truly not only reversible but alsoindependent of path, then the profile during the cooling should bethe mirror image of that obtained in heating. Thus, theasynchronous spectrum of the data obtained under such aroundtrip perturbation protocol (i.e., data matrix of temperaturerise is vertically concatenated by data matrix of temperature drop)should be essentially like the case for [A;Aflipud]

TN[A;Aflipud]. Weshould not expect to see any meaningful cross-peaks. The partialflipping of spectral order is no longer necessary, because it isactually done for the portion of the perturbation process instead ofthe data when one reverses the course of the temperature change.

Conversely, any meaningful asynchronous cross-peaks froma data set obtained under the roundtrip perturbation willbecome a definite proof that there is some path-dependent (i.e.,nonlinear) process involved during the ‘‘flipping’’ of theperturbation direction from heating to cooling. In fact, thistype of situation is expected in the case of molecular responsefor a phase transition or any other order–disorder transitionprocess, where approaching the transition point from higher orlower temperature will be governed by different processes.

Interestingly, however, all the other asynchronicity amongthe spectral bands not related to the path dependence (e.g.,different susceptibility of band intensity to temperature change)will be completely cancelled out during the roundtripperturbation. Thus, even if many cross-peaks may appear inthe asynchronous spectrum for data collected during the one-way temperature rise or one-way temperature drop, they willdisappear in the roundtrip case, as long as the spectral intensitychange profiles are strictly mirror images of each other. Thisfeature becomes especially useful in detecting the specific partof molecular behavior that is responsible for the nonlinearresponse. It is noted that the sequential order rules are stillvalid, even for the 2D spectra constructed under the roundtripexperimental protocol.

SPECTRAL MODELS

In order to verify the utility and potential of this new 2Dcorrelation technique, we chose three spectral datasets asmodels. Model I is composed of synthetic spectral data havingtwo overlapped Gaussian peaks: the one at 1400 cm�1 slowlydecreases exponentially, while the other at 1600 cm�1 rapidlyincreases and approaches to a fixed value, again exponentially.Model II involves the temperature-dependent IR spectra ofbovine pancreatic ribonuclease A (RNase A) in aqueoussolution; the heating process has been studied in previousreports, revealing the thermally induced pretransition of theprotein.31,32 The measurement and analysis of IR spectra incooling are identical to those of the heating. Model III is a setof IR spectral data measured from traditional Chinesemedicines (TCM) having similar origin.

RESULTS AND DISCUSSION

Concatenated Two-Dimensional Correlation Analysis ofSimulated Mirror-Image Data. Figure 1 shows a set ofsynthetic spectral data, the left is the original data set (Fig. 1a)and the right (Fig. 1b) is the vertically concatenation of (a) withits flipped counterpart. In the plot spectral traces are stacked inorder with a fixed incremental offset, where the trace found atthe top corresponds to the first row of the data matrix. It is clearthat, with progress, the spectral intensity of the band at 1400cm�1 decreases while that of the band at 1600 cm�1 increasesmonotonically in the original data set (Fig. 1a). For theconcatenated data (Fig. 1b), a local maximum and a saddlepoint, respectively, are observed around the midway positionfor the spectral intensities at 1600 and 1400 cm�1.

The calculated 2D correlation spectra of the two datamatrices in Figs. 1a and 1b are shown in Fig. 2. It is obviousthat the synchronous spectra of the two matrices (Figs. 2a and2c) look exactly the same, which accords with the conclusion

FIG. 2. (a) Synchronous and (b) asynchronous 2D contour maps of datamatrix A used in Model I; (c) synchronous and (d) asynchronous 2D contourmaps of the vertically concatenated matrix in Fig. 1b.

FIG. 1. A set of synthetic spectra of Model I: (a) original data set and (b) thevertically concatenated one with its flipped counterpart.

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deduced from Eq. 1. Here, what inspired us mostly are themarked differences in 2D correlation asynchronous spectra inFigs. 2b and 2d. Two cross-peaks in the asynchronousspectrum of the original dataset (Fig. 2b) clearly show theasynchronicity of the behavior of bands at 1400 and 1600cm�1, while, after the ‘‘mirror-image’’ concatenation treatment,there is no apparent cross-peak left in the asynchronousspectrum except for some noise, which arises from thenumerical truncation during the machine calculation. It isconsistent with the prediction by Eq. 2 and demonstrates thatthis ‘‘mirror-image’’ concatenation indeed eliminates cross-peaks from asynchronous spectrum.

Concatenated Two-Dimensional Correlation Analysis ofRoundtrip Experimental Data. Spectral data matrices used inModel II are built based on the temperature-dependent IRspectra of RNase A relating to the amide I0 band (Fig. 3). Thissystem was studied in the previous publication investigatingthe thermally induced pretransition in the heating process.31,32

A significant band-shift from 1636 to 1651 cm�1 is observed inthe heating process (Fig. 3a), which corresponds to theunfolding of the protein.31,32 A similar band shift in theopposite direction from 1651 to 1636 cm�1 can also beobserved in the reversed process of cooling (Fig. 3b).Apparently, from the 1D IR spectra, it looks as if the thermallyinduced unfolding and refolding is completely reversible,

FIG. 5. (a) Synchronous and (b) asynchronous 2D contour maps of spectraldata matrix H obtained during the heating process; (c) asynchronous spectra ofthe vertical mirror-image concatenated data V, and (d) the roundtrip data R.

FIG. 6. (a) The dynamic spectra of the vertical mirror-image concatenated dataV and (b) the roundtrip data R after mean centering by subtracting the averagedspectrum from each one.

FIG. 4. The plot of temperature-dependent intensity change at eachwavenumber of data matrix R.

FIG. 3. Temperature-dependent IR spectra of RNase A in the region of 1700–1600 cm�1: both in (a) heating and (b) cooling. The spectra were measuredbetween 25 8C and 75 8C with an interval of 1 8C.

APPLIED SPECTROSCOPY 347

considering both the band intensity and its central position inthe original IR spectra. In other words, the slight irreversibilitybetween unfolding and refolding can not be expressed easily by1D IR spectra. Here, we will demonstrate the potential of thevertically concatenated 2D correlation analysis in revealing thedeparture from the reversibility in this important transitionprocess.

The original spectral data obtained during the heatingprocess (25 8C ! 75 8C with an interval of 1 8C) is markedas matrix H. Likewise, the matrix C represents the spectral dataduring the cooling process (75 8C ! 25 8C). The matrix Vdenotes the vertical mirror-image concatenation of H withHflipud, i.e., V ¼ [H;Hflipud]. The matrix R represents thespectral data measured in the whole temperature span as aroundtrip process, i.e., R¼ [H;C]. Figure 4 shows columns ofthe matrix R, illustrating temperature-dependent intensitychanges in the round trip at each wavenumber. Of note isthat the bilateral symmetry of the plots also indicates thereversibility of unfolding and refolding between heating andcooling.

Figure 5 presents the calculated synchronous 2D contourmap of matrix H and asynchronous 2D contour maps ofmatrices H, V, and R. The negative cross-peak (1670, 1630)cm�1 in the synchronous spectrum of the heating step datamatrix H (Fig. 5a) shows the different directions of intensitychanges for these two bands during the heating. The positivecross-peak (1670, 1630) cm�1 in the asynchronous spectrum ofH (Fig. 5b) indicates that the decrease of the band at 1630 cm�1

occurs at a lower temperature than the increase of the band at1670 cm�1. The synchronous spectra of the mirror-imageconcatenated matrix V is just the same as that of matrix H, inaccordance with Eq. 1, while synchronous spectra of theroundtrip data matrix R (not shown) are the average of thosegenerated from matrices H and C.

Figure 6 shows the dynamic spectra of V and R obtainedafter mean centering by subtracting the averaged spectrumfrom each set. It can be seen that a very regular changingpattern can be observed in Fig. 6a, while the case in Fig. 6b is alittle more complex and somewhat irregular, leading todifferent asynchronous spectra for matrices V and R.

The asynchronous spectrum of the mirror-image data matrixV is shown in Fig. 5c. It can be clearly seen that there are nomeaningful cross-peaks except a bit of noise. This result is incontrast to the definite appearance of several well-definedcross-peaks in the asynchronous spectrum of matrix H. Such aresult is very similar to the case for Model I. It confirms that 2Dcorrelation analysis based on the concatenated matrix seems toreveal only the inter-asynchronicity between two matrices. Themirror-image concatenation completely eliminates the effect ofintra-asynchronicity within a matrix. No meaningful cross-peakexists in the asynchronous spectrum of the mirror-imageconcatenated matrix V, since matrix H and its mirror imagehave no inter-asynchronicity with each other.

The asynchronous spectrum of roundtrip data matrix R (Fig.5d) does show apparently significant cross-peaks at (1660,1630) and (1643, 1630) cm�1. The result indicates that the data

FIG. 7. 3D view of asynchronous spectra calculated from spectral data matrix of (a) vertical mirror-image concatenation V, (b) roundtrip measurement R, (c)selective data matrix S1, and (d) selective data matrix S2.

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matrices H and C are not mirror images of each other. It canalso be taken as proof of the existence of certain inter-asynchronicity between matrices H and C, demonstrating thatthe thermally induced unfolding of RNase A is path dependent.This conclusion is consistent with recent reports.28 The positivecross-peaks at (1660, 1630) and (1643, 1630) cm�1 uncover thefact that the variation of the intensity of the band at 1630 cm�1

occurs much earlier than that of the band at 1660 cm�1 inheating than in cooling. It indicates that the spectral changes atthese wavenumbers are path dependent. It is the truemanifestation of the inter-asynchronicity of RNase A betweenthe unfolding and refolding transition observed at themolecular level. Apparently, this inter-asynchronicity can beclearly revealed by the concatenated 2D correlation analysis,which is impossible to perform with the 1D IR spectra.

To further explore which temperature range contributes mostto the irreversibility, the spectral data are divided into severalsegments along temperatures. For example, two new datamatrices (denoted as S1 and S2) are thus created by verticallyconcatenating the spectral data set selected from temperatureranges of 25–40 8C/40–25 8C and 50–75 8C/75–50 8C,respectively. The three-dimensional view of the asynchronousspectra of spectral data matrices V, R, S1, and S2 in Fig. 7illustrates more clearly their intensity differences. It is obviousthat the peaks in Fig. 7c are rather weaker than those in Fig. 7b,indicating that the temperature range from 25 8C to 40 8C does

not contribute largely to the inter-asynchronicity of unfoldingand refolding of RNase A, while the similarity of Fig. 7d toFig. 7b indicates that the behavior of RNase A in thetemperature range from 50 8C to 75 8C (in the vicinity of 668C, corresponding to the main unfolding of RNase A)contributes most to the irreversibility of the conformationtransition. The conclusion is also supported by the literature.27

Such a result illustrates that this new technique is rathersensitive to the specific inter-asynchronicity between heatingand cooling.

Concatenated Two-Dimensional Correlation Analysis ofDifferent Traditional Chinese Medicine Samples. Inaddition to the investigation of the process reversibility, thisnew technique may offer many other interesting potentialapplications, such as diagnostics and classifications of samples,comparison of similar samples, etc. Among these potentials, wewill demonstrate the comparison of samples of TCM in thepresent study. Three samples of TCM (named Astragaluszhengheiqi) from Shanxi Hunyuan area are selected and IRspectra are measured for the analysis. Figure 8 shows thecalculated three-dimensional asynchronous spectra based onthe three matrices from samples of A, B, and D: matrix[A;Aflipud] (Fig. 8a), matrix [A;Dflipud] (Fig. 8b), and matrix[B;Dflipud] (Fig. 8c). It is obvious that asynchronicity betweensamples B and D is much larger than that between A and D,indicating that samples A and D are similar, but sample B is

FIG. 8. The calculated asynchronous spectra based on IR spectral data matrix from different TCM samples: (a) data matrix [A;Aflipud], (b) [A;Dflipud], and(c) [B;Dflipud].

APPLIED SPECTROSCOPY 349

different. This result demonstrates that the new methodperforms well in the comparison of different samples, whichinspires us to explore its other applications such as theexamination of process reversibility.

CONCLUSION

We have proposed a novel application of generalized 2Dcorrelation spectroscopy, concatenated 2D correlation analysis.Peculiar properties of so-called mirror-image concatenated 2Dcorrelation spectra enables one to effectively distinguish thestrict similarity and very subtle difference between two spectraldata sets having similar origin. This new method has beensuccessfully validated using a synthetic model dataset andapplied to experimentally measured IR spectra. One is thecomparison of different TCM samples. Another is theexamination of the reversibility of thermally induced unfoldingof RNase A in aqueous solution. The following conclusionshave been reached: (1) For a given data matrix A, the mirror-image concatenation of A and its vertically flipped form,Aflipud, brings no cross-peak in the asynchronous spectrum. (2)The vertical concatenation of different data matrices A and Bresults in some cross-peaks in the asynchronous spectrum, if B6¼ Aflipud. (3) Concatenated 2D correlation analysis selectivelyreveals the inter-asynchronicity between matrices A and B byremoving the contribution of the intra-asynchronicity within Aor B. (4) By using concatenated 2D correlation analysis, theirreversibility in the thermal-induced unfolding and refoldingconformation transition of RNase A is revealed clearly, whichis impossible to perform using 1D spectra analysis. (5) Inaddition to the investigation of the process reversibility, thisnew technique may offer many other interesting potentialapplications, such as diagnostics and classifications of samples,comparison of similar samples, and comparison of the effect ofdifferent stimuli on spectral changes.

ACKNOWLEDGMENTS

The present study is supported by the Project of NSFC (No. 20934002,20973073), the Major State Basic Research Development Program(2007CB808006), the Programs for New Century Excellent Talents inUniversity (NCET), and the 111 project (B06009), which are gratefullyacknowledged. The authors also thank Prof. Suqin Sun, Tsinghua University,for supplying IR spectral data of TCM.

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