68 Volume 58, Number 1, 2004 APPLIED SPECTROSCOPY0003-7028 / 04 / 5801-0068$2.00 / 0q 2004 Society for Applied Spectroscopy

Analysis of 1H/2H Exchange Kinetics Using ModelInfrared Spectra

VINCENT RAUSSENS, JEAN-MARIE RUYSSCHAERT, and ERIK GOORMAGHTIGH*Laboratory for the Structure and Function of Biological Membranes, Structural Biology and Bioinformatics Center, Free Universityof Brussels, CP 206/2, Boulevard du Triomphe, B-1050 Brussels, Belgium

This paper investigates the different approaches that best retrieveband shape parameters and kinetic time constants from series ofprotein Fourier transform infrared (FT-IR) spectra recorded in thecourse of 1H/2H exchange. In this � rst approach, synthetic spectrawere used. It is shown that 1H/2H exchange kinetic measurementscan help resolve spectral features otherwise hidden because of theoverlap of various spectral contributions. We evaluated the ef� cien-cy of Fourier self-deconvolution, synchronous/asynchronous corre-lation, difference spectroscopy, principal component analysis, in-verse Laplace transform, and determination of the underlying spec-tra by global analysis assuming � rst-order kinetics with eitherknown or unknown time constants. It is demonstrated that somestrategies allow the extraction of both the time dependence and thespectral shape of the underlying contributions.

Index Headings: Fourier transform infrared spectroscopy; FT-IR;Deuterium; Exchange; Stability; Infrared.

INTRODUCTION

Hydrogen isotope exchange has long been used for theanalysis of protein structure and dynamics1–3 (for a re-view, see Refs. 4 and 5). It appears to be one of the maintechniques able to identify submolecular motional do-mains including fast exchanging protons of the proteinsurface, somewhat slower exchanging protons of the � ex-ible (loop) regions buried in the protein or involved insome secondary structures, and the slowly exchangingprotons from the protein core formed by the most rigidclusters (knots) of amino acids (for a review, see Ref. 6).

1H/2H exchange kinetics has also been widely used inthe � eld of membrane proteins. It allows the character-ization of the protein stability in different experimentalconditions7–15 and of conformational changes relevant toan enzyme catalytic cycle.16–19 Fourier transform infrared(FT-IR) data usually yield rough estimates of the ex-change rate for the protein as a whole. Recently it wasshown to help improve secondary structure predictionsfrom infrared (IR) spectra.14 Previous attempts have beendirected at the resolution of the exchange kinetics at thelevel of the secondary structure type,20–22 but because ofthe dif� culties of the approach, only a few works describeachievements of this type.20,23 Yet, obtaining such a res-olution is highly desirable for dissecting protein structuralchanges at submolecular levels. When membrane pro-teins are used, 1H/ 2H exchange kinetics also contain in-formation on the shielding by the lipid environment ofpart of the protein from the solvent. Recently, it has beenshown that combining linear dichroism and 1H/2H ex-change measurement allows the exchange rate to be re-

Received 14 May 2003; accepted 25 August 2003.* Author to whom correspondence should be sent. E-mail: egoor@

ulb.ac.be.

corded speci� cally for the oriented secondary structuresof a membrane-embedded protein.24 When compared tomass spectrometry or 1H/3H exchange, the great advan-tage of monitoring the exchange by FT-IR is that themeasure is focused on the amide protons only, yieldingdata proportional to the number of residues in the protein.Yet, so far, the lack of resolution of the underlying spec-tral contributions corresponding to submolecular entitiessuch as secondary structures has limited the use of FT-IR. For a more general review on the application of 1H/2H exchange kinetics for the study of membrane peptidesor proteins, the reader is referred to Ref. 25.

The FT-IR spectra are de� ned as a series of absorptionbands, some disappearing, others appearing in the courseof the 1H/ 2H exchange process. The most important vi-bration modes are called amide I and amide II. Withinthe major amide bands the contributions of the differentsecondary structures occur at slightly different frequen-cies. In practice, bandwidths are large with respect toband separation. It turns out that the individual compo-nents underlying the amide bands can generally not beresolved. Furthermore, the time-dependent evolution ofthe system is characterized by multiple time constantsthat also cannot be resolved.

The interest of a correct and accurate analysis of the1H/ 2H exchange kinetics is two fold. First, as just men-tioned, the exchange rate contains important informationon the structure and structure stability of a protein at asubmolecular level. Second, the 1H/ 2H exchange acts asa perturbation that can help reveal otherwise hidden com-ponents in the spectra.

In the present paper, using model kinetics we built withparameters closely related to those observed in real pro-teins, we explore several ways of analyzing the data. Weshow that the time behavior can be resolved and thatunderlying spectral components can be obtained when aseries of spectra recorded in the course of the exchangeis available. Furthermore, the exchange rate of differentprotein secondary structures can be retrieved. The presentwork evaluates the potentiality of different approaches toobtain as much information as possible on the protein.

METHODS

All the computations were carried out in an integratedapplication written in our laboratory and running underMATLAB 6 (The Mathworks, Natick, MA). The programcan also open spectra in the JCAMP international formatand is available on simple request. It requires MatLab torun.

Kinetic Model Spectra. Series of spectra were builtas Gaussian/Lorentzian band combinations. In infrared

APPLIED SPECTROSCOPY 69

TABLE I. Time constants and band characteristics for model helical and sheet structures in the 1800 and 1400 cm21 spectral region.a

StructureAbsorbance atmaximum An0

FWHH(cm21)

Frequencyn0 (cm21) fG

Time constant(min21)

a-helix (H form)(amide I) 700 45 1656 0.5 1022

(amide II) 310 35 1546 0.4 1022

a-helix (D form)(amide I9)(amide II9)

700310

4535

16501455

0.50.4

1022

1022

1022

b-helix (H form)(amide I)(amide I)(amide II)

1000180340

351340

163816841527

0.40.50.7

5 3 1024

5 3 1024

5 3 1024

b-helix (D form)(amide I9)(amide I9)(amide II9)

100018040

351340

162816791445

0.40.50.7

5 3 1024

5 3 1024

5 3 1024

a Bands are described as a combination of Lorentzian and Gaussian shapes.2 2FWHH 4(n 2 n )i 0,iA 5 (1 2 f )A 1 f A exp ln(2)On G n G ni 0,i i 0,i2 2 2[ ]FWHH 1 4(n 2 n ) FWHHi i 0, i i

where is the fraction of Gaussian component i, n0, i is the frequency of the maximum, and FWHH i is the full width at half-height. Each line offG i

the table describes a single component i. The time dependence is described by Eqs. 1 or 2. is the absorbance at the maximum of the band forAn0,i

either the 1H component or the 2H component.

TABLE II. Time constants and band characteristics for random, turn, helix, sheet, and slow b-sheet model structures in the amide II/amide II9 range.a

StructureAbsorbance atmaximum An0,i

FWHH (cm21)Frequency n0, i

(cm21) fG,i

Time constant(min21)

randomturnsa-helixb-sheetslow b-sheet

210500310340340

5940354040

1545 ® 14501545 ® 14451546 ® 14551527 ® 14451527 ® 1445

0.70.50.40.70.7

5 3 1021

5 3 1022

1 3 1022

5 3 1024

1 3 1025

a Bands are described as a combination of Lorentzian and Gaussian shapes. The parameters fG, FWHH, and are supposed to be the same for theAn0

corresponding deuterated and undeuterated contributions. The speci� c frequencies of the absorption maximum are indicated under Am II and AmII9 for amide II and amide II9, respectively.

spectroscopy, assignments, band shapes, frequencies ofthe maximum, and extinction coef� cients could be dis-cussed at length. Yet, for building model spectra, we shallkeep those assignments that are familiar to IR spectros-copists. The a-helix, b-sheet, turn, and random structureswere modeled according to reported literature consensus.Band shapes, intensities, and widths have been describedfor every secondary structure.26–28 Frequencies for the ab-sorption maxima selected here are the average values re-ported earlier from a compilation of literature data.29–31

The time constants were selected according to realistictime constants determined earlier on real proteins.21,22

Most of the actual values used here are described in Ta-bles I and II. In the course of the exchange process, theintensity of these bands evolves with time according toa � rst-order kinetic process characterized by a speci� ctime constant (Eq. 1). The time points used to model thespectra in the course of the exchange process were notequally spaced in order to better describe the fasterchanges at the beginning of the kinetics. We selected herethe time points used in our classical experimental pro-tocols,17 i.e., (in minutes) [.00; .25; .50; .75; 1.00; 1.20;1.50; 1.70; 2.00; 2.50; 3.00; 3.50; 4.00; 5.00; 6.00; 7.00;8.00; 10.00; 12; 14; 16; 20; 24; 28; 32; 40; 48; 56; 64;

80; 96; 112; 128; 160; 192; 224; 256; 320; 384; 448;512; 640; 768; 896; 1024; 1280; 1536; 1792; 2560]. Thedisappearance of the protonated form of a structure (1H-form) results in a decay of the corresponding band. Forany component i, the time dependent evolution of theabsorbance An ,i(t) at wavenumber n is characterized by atime constant k i and is described by:

0 2k tiA (t) 5 A · e (1)n,i n,i

New components related to the deuterated form of theamide (2H-form) are simultaneously rising. The absor-bance An,j at wavenumber n of any given component jrises according to its time constant k j:

0 2k tjA (t) 5 A · (1 2 e ) (2)n, j n , j

The ‘‘0’’ superscript indicates that it is the absorbance ofthe pure component, i.e., the pure 1H-form in the case ofEq. 1 and the pure 2H-form in the case of Eq. 2. Equa-tions 1 and 2 were used to build model spectra accordingto the data reported in Tables I and II.

Addition of Noise. Most of the results of the presentstudy do not consider the presence of noise in the spectra.Yet, simulations were also carried out in the presence ofwhite noise added to the simulated spectrum series. When

70 Volume 58, Number 1, 2004

this was the case, noise characterized by its standard de-viation was added to all the spectra of the series. Typi-cally, the critical noise level for the outcome of the anal-yses occurred when its standard deviation was between0.1% and 1% of the spectral maximum intensity.

Fourier Self-Deconvolution. Fourier self-deconvolu-tion was performed according to Refs. 32–34. The bandparameters used are similar to those used for experimen-tal spectra.35 Deconvolution was performed with a Lor-entzian line (full width at half-height, FWHH 5 30 cm21)and apodization with a Gaussian line (FWHH 5 12.5cm21), resulting in a so-called ‘‘line-narrowing’’ factor of2.4.

It must be noted that while the narrowing effect ofFourier self-deconvolution has been widely used in thepast, the shape and width of the deconvoluting line shapeare usually unknown, resulting in less ef� cient band nar-rowing, as clearly illustrated in the past36,37 and more re-cently by Lorenz-Fonfria et al.38

Synchronous/Asynchronous Correlations. Two-di-mensional (2D) correlation spectra were calculated ac-cording to Noda39–41 and as recently described by Nabetand Pezolet.42 From the measured intensity y at time t 1t, a reference intensity measured at time t is subtractedaccording to the following equation:

y(n, t) 5 y(n, t 1 t) 2 y(n, t) (3)

The Fourier transform in the time domain of the N col-lected spectra is calculated according to the followingequation:

N211 2iptgY (n, g) 5 y (n, t)exp 2 (4)O 1 2N Nt50

Synchronous (F(n1,n2)) and asynchronous (C(n1,n2)) spec-tra are then calculated according to, respectively:

N1 ˜ ˜F(n , n ) 5 [Re(Y (n , g))Re(Y (n , g))O1 2 1 2pN g50

˜ ˜1 Im(Y (n , g))Im(Y (n , g))] (5)1 2

N1 ˜ ˜C(n , n ) 5 [Im(Y (n , g))Re(Y (n , g))O1 2 1 2pN g50

˜ ˜2 Re(Y (n , g))Im(Y (n , g))] (6)1 2

Computation was carried out using the Hilbert transform,as recently described.43

The two-dimensional (2D) correlation spectra can beinterpreted using the rules described by Noda44 and morerecently by Ekgasit et al.45

The ratio:F (n1, n2) 5 C(n1, n2)/F(n1, n2) (7)

or:F (n1, n2) 5 tan(F(n2) 2 F(n1)) (8)

describes the difference phase angle. For an exponentialdecay, it measures the degree of correlation between rateconstants for two bands located at n1 and n2. F has beensuggested by Buchet et al.46 to be a useful � lter for iden-tifying true synchronous or asynchronous correlations innoisy spectra since true maxima of the synchronous cor-relation must have F close to zero while the F should bevery large for true asynchronous peaks.

RESULTS

In order of increasing secondary structure complexity,the model kinetics we have submitted to analysis are (1)the pure a-helix, (2) the a-helix 1 b-sheet whose bandsare relatively well separated, (3) a-helix 1 b-sheet 1random that presents a strong overlap between the helixand random structures in the amide I band, and (4) a-helix 1 b-sheet 1 random 1 slowly exchanging b-sheet.The last b-sheet structure has a spectral shape identicalto the � rst one but is characterized by an exchange con-stant k 5 1025 instead of 5 3 1024 min21. Equimolarmixtures were used throughout.

Synchronous/Asynchronous Correlations. This ap-proach is presently one of the most popular for analyzing1H/ 2H exchange, temperature dependence, or other per-turbations applied to proteins. Because it is not within thescope of this publication to discuss correlations that arerevealed by this approach among the various spectralcomponents, the results are discussed only for band fre-quency identi� cation purposes. Relationships among thecomponents in the course of the kinetics are not discussedat all.

a-Helix Structure. Before discussing complex sys-tems, it is necessary to observe the potentialities of theapproach on a simple model. For this purpose, we presenthere the correlation analysis of a 1H/ 2H exchange kineticspectrum series representing the exchange of a single a-helix structure. The evolution of the helix component isdescribed here (see Table I) in the amide I band regionas a single absorption band (maximum at 1656 cm21) thatexponentially decays while the deuterated amide I band(amide I 9) appears (maximum at 1650 cm21). The amideII decreases at 1546 cm21 while the amide II 9 band ap-pears at 1455 cm21. The series of spectra obtained atdifferent deuteration times (see Methods section) isshown in Fig. 1. While the amide II/amide II 9 picture isclear, little can be seen in the amide I range, where theshift is small (from 1656 to 1650 cm21) with respect tobandwidth (FWHH 5 45 cm21). Fourier self-deconvolu-tion (right panel of Fig. 1) does not dramatically improveresolution in the amide I range.

Synchronous correlation analysis (Fig. 2) in the amideI region reveals the presence of two components alongthe main diagonal at 1668 and 1637 cm21, i.e., far fromthe correct values of 1656 and 1650 cm21. When the anal-ysis is run over deconvolved spectra, the result is slightlybetter (1663 and 1644 cm21), but not good enough toidentify the frequency of the 1H and 2H helical contri-butions. On the other hand, in the amide II/amide II 9region where the overlap is weak (1546 and 11 455cm21), the frequencies are correctly identi� ed before orafter Fourier self-deconvolution.

Asynchronous correlation (not shown) is very weakand fails the F test everywhere (see the Methods section),even if a phase difference angle as small as 1 degree isconsidered for the threshold, underlying the fact that nosigni� cant asynchronous correlation is present, as ex-pected in this one-structure model.

It can be concluded from these observations that in thesynchronous analysis, while the number of underlyingcontributions is correctly identi� ed, their frequency is in-correctly de� ned in the amide I region because of the

APPLIED SPECTROSCOPY 71

FIG. 1. (Left) Series of spectra in the course of the deuteration for an a-helix model structure. Spectral shape and time dependence is computedas described in Table I. (Right) Fourier self-deconvolution of the series is computed as described in the Methods section. The � rst spectrum of theseries is computed for t 5 0 min. The spectra (from bottom to top) correspond to deuteration times reported in the Methods section. Spectra havebeen offset for clarity.

FIG. 2. Contour plots of the synchronous correlation computed as described in the Methods section. (Left) Performed on the original spectrareported in Fig. 1, for the exchange of an a-helix structure. (Right) Performed on the Fourier self-deconvolved spectra reported in Fig. 1. Theanalysis is performed (upper panels) between 1700 and 1600 cm 21, as well as (bottom panels) between 1700 and 1400 cm 21.

72 Volume 58, Number 1, 2004

FIG. 3. (Left) Series of model spectra in the course of the deuteration for an equimolar mixture of helix and sheet structures. Spectra are computedas described in Table I. (Right) Fourier self-deconvolution of the series is computed as described in the Methods section. The � rst spectrum of theseries is computed for t 5 0 min. The spectra (from bottom to top) correspond to deuteration times reported in the Methods section. Spectra havebeen offset for clarity.

large overlap between the 1H and 2H contributions. Bothfeatures are correctly analyzed in the amide II/amide II 9region.

a-Helix 1 b-Sheet Structures. Contributions and timedependence of the a-helix 1 b-sheet structures are re-ported in Table I. We now have six contributions in theamide I region, two in the amide II region, and two inthe amide II 9 region (see Table I). The series of spectraappear in Fig. 3 before (left panel) and after (right panel)self-deconvolution.

Synchronous correlation analysis (Fig. 4) in the amideI region reveals the presence of four components alongthe main diagonal at 1685 and 1678 cm21, and at 1663and 1628 cm21. The � rst couple of values matches the1684/1679 cm21 value for the high-frequency b-sheetcontribution before and after deuteration. The good res-olution of this weak component is due to its narrow band-width (FWHH 5 13 cm21). The major a-helix and b-sheet contributions are not resolved. After Fourier self-deconvolution, four contributions show up in the syn-chronous map in the amide I region, but their frequenciesare incorrect. Furthermore, in the amide II and amide II 9regions, the a-helix 1 b-sheet contributions are not re-solved. Applying Fourier self-deconvolution to the spec-tra before correlation analysis (Fig. 4, right panel) doesnot improve the resolution in the amide II and amide II 9regions. In the amide I, a � fth component becomes vis-ible at 1640 cm21, but simultaneously a ghost contribu-tion appears at 1695 cm21 because of the over-deconvo-lution of the narrow high-frequency b-sheet contribution.

On the other hand, asynchronous correlation analysis(Fig. 5) in the amide II and II 9 regions does resolve thea-helix from the b-sheet structures. Two asynchronouslycorrelated bands at 1545 and 1530 cm21 in the amide IIregion are in agreement with the underlying data (Table

I). Similarly, two contributions at 1458 and 1445 cm21

are correctly identi� ed. Remarkably, these contributionsare as well identi� ed before (Fig. 5, left panel) as after(Fig. 5, right panel) Fourier self-deconvolution. In theamide I region, � ve major frequencies can be identi� edonly after self-deconvolution. Reading the abscissa fromleft to right in Fig. 5 (right bottom panel), these frequen-cies have been numbered. The � rst two frequencies(1685/1678 cm21) are again clearly identi� ed and can besafely assigned to the high-frequency b-sheet contribu-tion. The third frequency (1663 cm21) represents the un-deuterated helix contribution (nominally 1656 cm21). Thefourth frequency, at 1645 cm21, mixes the rising deuter-ated helix contribution and the decreasing undeuteratedb-sheet contribution. Careful analysis of the � gure sug-gests that there are indeed two different frequencies inthis region labeled #4. The � fth frequency at about 1626cm21 clearly represents the rising deuterated b-sheet con-tribution.

In conclusion, the asynchronous correlation is clearlymore potent for identifying underlying contributions. Itallows a clear identi� cation of the two-structure contri-butions in the amide II and amide II 9 regions where thesynchronous analysis fails. In the amide I region, onlythe sharp high-frequency contribution of the anti-parallelb-sheet structure is easily resolved and found at the rightfrequency. Other contributions are only partially resolvedand are shifted with respect to their true position. Thedeuterated main b-sheet contribution, however, is suf� -ciently remote from the others and is correctly de� ned.

a-Helix 1 b-Sheet 1 Random Structures . In thismodel, a third structure has been added. As the randomcontribution largely overlaps the helical contribution inthe amide I region shifts from 1654 to 1645 cm21 (FWHH

APPLIED SPECTROSCOPY 73

FIG. 4. Contour plots of the synchronous correlation computed as described in the Methods section. (Left) Performed on the original spectrareported in Fig. 3, for the exchange of an a-helix/b-sheet mixture. (Right) Performed on the Fourier self-deconvolved spectra reported in Fig. 3.The analysis is performed (upper panels) between 1700 and 1600 cm21, as well as (bottom panels) between 1700 and 1400 cm21.

5 55 cm21, data not shown), resolution of features fromthe random structure is not possible (data not shown).

In conclusion, the asynchronous correlation approachachieves remarkable results for resolving overlappedbands in the amide I, amide II, and amide II 9 regions ofthe spectra. Yet some contributions are too broad and tooclose to be resolved in the amide I region. Resolution ofthe helix and random structures is impossible. It remains,however, a valuable tool to analyze the kinetic relationbetween components when resolved (not discussed in thispaper). The b–n correlation developed by Dluhy et al.47,48

is most helpful in this sense.Difference Spectroscopy. As the analysis of the pure

a-helix exchange (Fig. 1) is straightforward, we do notpresent the results here.

a-Helix 1 b-Sheet Structures. Because of the differ-ence in the time constant characterizing the exchange ofthe different secondary structure types (k 5 0.01 min21

for the a-helix and 5 3 1024 min21 for the b-sheet, seeTable I), it is expected that a difference spectrum com-puted between two successive spectra recorded in the � rstminutes of the exchange process would contain essen-tially contributions from the fast-exchanging part of theprotein. On the other hand, a difference spectrum ob-tained between two successive spectra recorded after sev-eral hours of exposure to 2H2O would contain featurescharacterizing the parts of the protein that exchange more

slowly. At that stage, fast-exchanging structures shouldhave no signi� cant contribution. In order to monitor thesedifferences, the global exchange rate was � rst evaluatedfrom the evolution of the amide II integrated area (Fig.6, panel B). In order to produce difference spectra whoseintensities are large enough with respect to the noisewhen dealing with experimental spectra, a series of spec-tra couples characterized by a difference of about 10%in deuteration extent were selected and their differencecomputed. For the a-helix structure alone, as expected,all the differences are similar in shape (not shown). Forthe a-helix 1 b-sheet mixture, the difference spectra arereported in Fig. 6, panel A. Clearly, the � rst differencespectrum (Fig. 6, panel A, bottom curve) contains mainlyhelical contributions. No b-sheet contribution is visibleon the � rst difference spectrum. While the original bandfrequencies cannot be read on the curve in the amide Iregion, a curve-� tting procedure could reveal them withgood accuracy (see below). On the contrary, the last dif-ference spectrum (Fig. 6, panel A, top curve) containsmainly b-sheet contributions characterized by the high-frequency 1684/1679 cm21 shift and its main contributionshifting from 1638 to 1628 cm21. The characteristic fre-quency of the a-helix and b-sheet contributions in theamide II and amide II 9 regions are also clearly resolvedin this series of difference spectra. When working onFourier self-deconvolved spectra, a small but signi� cant

74 Volume 58, Number 1, 2004

FIG. 5. Contour plots of the asynchronous correlation computed as described in the Methods section. (Left) Performed on the original spectrareported in Fig. 3, for the exchange of an a-helix/b-sheet mixture. (Right) Performed on the Fourier self-deconvolved spectra reported in Fig. 3.The analysis is performed (upper panels) between 1700 and 1600 cm21, as well as (bottom panels) between 1700 and 1400 cm21.

contribution from the b-sheet exchange is already visibleat the beginning of the exchange (not shown).

Assuming that only two structures are present, the en-tire series of spectra can be rebuilt from the � rst spectrumand the two extreme difference spectra. For the 49 timepoints and the 401 wavenumber points (between 1800and 1400 cm21, spacing 5 1 cm21), the time series ofspectra Ht (Fig. 3, left panel) can be expressed as a linearcombination of (1) the � rst spectrum of the series, (2)the � rst difference, and (3) the last difference (P matrix).

Ht(401,49) 5 P (401,3)·C (3,49) (9)

the coef� cients C are easily obtained by matrix inversionand describe the time dependence of the contribution ofeach of the three basic spectra contained in P. The timedependence of the � rst contribution (the � rst spectrum ofthe series) is 1 everywhere, as expected. The time-de-pendent contribution of the � rst and last differences ap-pears in Fig. 6, panel C. They reveal the kinetics of theexchange curve for the two individual secondary struc-tures. The kinetics of exchange of the a-helix structure(time constant k1 5 1022 min21) and of the b-sheet struc-ture (time constant k2 5 5 3 1024 min21) can be accu-rately determined.

In more complex systems (more structures and moretime constants), intermediate difference spectra will ap-pear. Fitting the spectrum series with only the two ex-

treme differences results in a reconstruction of the data(Eq. 9) that is characterized by a large standard deviationwhere the intermediate difference spectra are missing (notshown). Iterative strategies can be designed to obtainthese intermediates but were found to be dif� cult to applywith real spectra. We therefore suggest limiting the anal-ysis described above for the two-structure case and withlarge differences in the time constants. The standard de-viation of the difference between the reconstructed series(Eq. 9) and the original series of spectra should be usedto check whether the two-structure hypothesis is valid.

In conclusion, this approach makes use of the differ-ence in the time dependence of the exchange processesto gain information on the main structures that are ex-changed at different stages of the experiment. Using sim-ple linear algebra allows the resolution of the kinetics ofeach of the two secondary structures involved.

Principal Component Analysis. In principal compo-nent analysis, the covariance between wavenumber i andwavenumber k, si, k for n spectra in the series is computedas:

n1s 5 (a 2 a ) · (a 2 a ) (10)Oi,k j, i i j,k kn j51

where a i and a k are respectively the means at wavenum-bers i and k. The covariance matrix is diagonalized and

APPLIED SPECTROSCOPY 75

FIG. 6. (A) Selected difference spectra computed on the kinetic series presented in Fig. 3, left panel (evolution of an equimolar mixture of helixand sheet structures in the course of the deuteration). Each computed difference SpB 2 SpA is computed with SpB being 10% more deuteratedthan SpA. From the bottom to the top, the % of deuteration of SpA is incremented by 5%. The bottom spectrum is then the difference 10% 2 0%deuteration, the next one is 15% 2 5%, and so on. The level of deuteration was estimated from the area of amide II and 100% deuteration isassumed for a zero area in amide II. (B) Evolution of the area of amide II. The series of kinetic spectra (Fig. 3, left panel) was rebuilt from the� rst spectrum of the series and the � rst and last difference spectra presented in the left panel (Eq. 9). (C ) Contribution of the � rst and last differencespectra.

FIG. 7. Decomposition of the kinetic series presented in Fig. 3, leftpanel (evolution of an equimolar mixture of helix and sheet structuresin the course of the deuteration) by PCA. Spectra have been mean-centered prior to PCA decomposition. The � rst two principal compo-nents are presented in the left panels and their corresponding contri-bution to the kinetics in the right panels. Together, they represent morethan 99.9999% of the variance.

the so-obtained eigenvectors are orthogonal and have anull covariance. They can then be used to describe thekinetic spectrum series. It is expected that a small numberof eigenvectors is necessary to fully describe the varia-tions that exist in the kinetic spectrum series. Further-more, because the eigenvectors have a null covariance,they are describing ‘‘independent’’ events. They provideus, therefore, with a potential method for extracting in-dividual spectra features.

The pure a-helix structure exchange model has a singlePC that is the difference between the 1H and 2H formsof the helix components. The results are not presentedgraphically here.

a-Helix 1 b-Sheet Structures. Figure 7 reports the� rst two eigenvectors obtained from the a-helix 1 b-sheet mixture series described in Fig. 3. The results com-pare well to the difference spectroscopy approach (Fig.6A). The � rst eigenvector (Fig. 7, top) mainly describesthe helix exchange but also contains a small contributionfrom the b-sheet exchange. The contribution of each ei-genvector to the series is reported as a function of time(Fig. 7), yielding information on their time-dependentcontribution to the series. It can be observed that neitherthe shape of the PCs nor the time dependence of theircontribution correctly describes the exchange of the pure

76 Volume 58, Number 1, 2004

FIG. 8. (A) Evolution of the absorbance at selected frequencies in the amide II range in the kinetic series presented in Fig. 3, left panel (evolutionof an equimolar mixture of helix and sheet structures in the course of the deuteration). (B) Contour map of the inverse Laplace transform of thedata presented in panel A. (C ) Evolution of the absorbance at selected frequencies in the amide II range in the Fourier self-deconvolved kineticseries presented in Fig. 3, right panel. (D ) Contour map of the inverse Laplace transform of the data presented in panel C.

secondary structures. Therefore, the potentialities of PCAwill not be investigated any further.

Inverse Laplace Transform. This approach is basedon the idea that the time-dependence behavior of thespectra can be described as the superimposition of vari-ous � rst-order kinetics. Considering a continuous distri-bution of the time constants f (k), the fraction of the 1H-form of the protein amide bonds at any time t can bedescribed by:

1`

H (t) 5 f (k)exp(2kt) dk 5 L{ f (k)} (11)E2`

That is in fact the Laplace transform L of f (k). In turn,the inverse Laplace transform L21 immediately yields thedistribution shape f (k):

f (k) 5 L21{H (t)} (12)

Knox and Rosenberg49 suggested a dimensionless presen-tation of the distribution function obtained after rewritingof the integral expression:

1`

H (t) 5 kf (k)exp(2kt) d ln(k) (13)E2`

Solving the inverse Laplace transform L21 can be ap-proached analytically after � tting H (t) to a suitable func-tion or can be approached numerically. For reasons de-tailed by Gregory and Lumry,1 the numerical approachis subject to several artifacts if not carefully treated.3,50–

53 We used the program ‘‘CONTIN’’ from Provench-er,3,50,53 which provides a regularized solution to the prob-lem. It was found in the course of this work that, usingCONTIN, stable solutions could only be obtained inspectral regions where it can be assumed that all the com-ponents are decaying (i.e., the amide II region). Typically,the behavior of amide II corresponds to this description.A similar approach based on a maximum entropy regu-larized method 20 has been recently used.

The use of the inverse Laplace transform on the 1H/ 2Hexchange on the pure a-helix structure (Fig. 1) revealsthe exact exchange rate constant (k 5 0.01 min21, notshown). For the a-helix 1 b-sheet structure exchange,spectral intensities sampled every 2 cm21 from 1580 to1510 cm21 are plotted on Fig. 8, panels A and C, and aresubmitted to inverse Laplace transform. Figure 8 (panelsB and D) reports k.f (k) (Z axis) as a function of log(k)between 1580 and 1510 cm21. A remarkable separation

APPLIED SPECTROSCOPY 77

FIG. 9. (A) Inverse Laplace transform of the evolution of the absorbance in the amide II range in a kinetic series containing contributions froma-helix, random, sheet, turn, and slowly exchanging b-sheets. The characteristics of the band shapes and of the exchange time constants aredescribed in Table II. (B) Contour map of the 3D plot presented in panel A.

of the different contributions occurs in the log(k) dimen-sion, without any interfering effect of band overlap. Bothband positions and time constants are correct. The ap-proach also successfully resolves the 3-structure problem(not shown). In the most complex system studied, � vestructures are present: a-helix, b-sheet, random, andslowly exchanging b-sheet. Band parameters and timeconstants are brie� y described in Table II. Figure 9 re-ports the result of the inverse Laplace transform on theamide II region. Again, the reverse Laplace transformresults in a remarkable resolution of all the different com-ponents, including the slowest one (k 5 1/105 min21),even though data points were available only for the � rst2.5 3 103 min of the exchange process. For the � rst fourstructures, both the time constant and the position of themaximum are accurately determined. It must be indicatedhere that the approach is successful as soon as the timeconstants differ by more than 15% (not shown).

In conclusion, the inverse Laplace transform accuratelyreveals the time constants of the exchange process andaccurately reveals the band shape and frequency of themaximum in the amide II range. Because the correlationbetween secondary structure and frequency of the maxi-mum is better assessed for the amide I region of the spec-trum, the approach might fail to identify the nature of the

secondary structures involved in the exchange. The nextapproach uses the time constants determined here to ex-tract information on the secondary structures involved.

Global Analysis. Using the Time Constants ObtainedFrom Inverse Laplace Transform in the Amide II Re-gion. As described before, the series of spectra Ht (401data points between 1800 and 1400 cm21, 49 spectra cor-responding to 49 time points) can be described as a linearcombination of a number of basic spectra P, each char-acterized by a particular exchange kinetic. We shall pre-sent here the results for the most complex system only.In the case of Fig. 9, � ve structures characterized by � vedistinct time constants were identi� ed by the inverse La-place transform of the kinetic data in the amide II range.Once the time constants are known from this analysis ofamide II, we show here that it is possible to extract thebasic kinetic spectra for the entire spectrum range. TheC matrix (Eq. 14) was constructed with rows 2 through6 containing the evolution of the kinetics for each of the� ve time constants according to exp(2k i.t) with i 5 1–5.Line 1 was � lled with ones to allow for the constant partof the data. The 49 spectra are then expressed as:

Ht(401,49) 5 P (401,6)·C (6,49) (14)

The global analysis minimizes in the least-square sense

78 Volume 58, Number 1, 2004

FIG. 10. Basic spectra decomposition of the kinetic series containing contributions from a-helix, random, sheet, turn, and slowly exchanging b-sheets (not shown). The characteristics of the band shapes and of the exchange time constants are described in Table II. The decomposition hasbeen carried out as described in the text and by Eq. 16. The time constants imposed for the decomposition are reported on the right side of the� gure.

the basic spectra P in order to obtain the best � t of theseries of spectra recorded in the course of the exchange(Ht) over the entire spectral range and for all the timepoints. At every wavenumber n and deuteration time t,the absorbance Ht(n, t) is given by:

n k t n k ti iHt (n, t) 5 A ·e 1 B (1 2 e ) (15)O O0,i 0,ii i

where A is the absorbance of the undeuterated structuren0, i

i and B is the absorbance of the fully deuterated struc-n0, i

ture i at the particular wavenumber. This can be re-writtenas:

n n 2k t niHt (n, t) 5 (A 2 B )e 1 B (16)O O0,i 0,i 0,ii i

indicating that the independent basic spectra are (1) Si

B , i.e., the fully deuterated spectrum, and (2) the spec-n0, i

tral differences A 2 B . The results of this decompo-n n0, i 0, i

sition carried out on the data used in Fig. 9 are reportedin Fig. 10. All the features present in the basic spectra ofFig. 10 are in perfect agreement with the underlyingstructure spectra, including the fully deuterated spectrumSi B that has a constant contribution to the series. Thisn

0, i

is remarkable in the sense that the deuteration process isfar from being over in the kinetic series of spectra usedhere. Yet, the fully deuterated spectrum obtained (Fig. 10)is correctly extrapolated. Further resolving the differencespectra A 2 B into their original contribution A andn n n

0, i 0, i 0, i

B is possible by curve � tting, assuming a particular linen0, i

shape for the absorption bands.Nonlinear curve � tting with a difference between the

band before deuteration (centered around n0,1) and afterdeuteration (centered around n0,2):

2FWHHA (n) 5 (1 2 f )AG 0 2 2FWHH 1 4(n 2 n )0,1

24(n 2 n )0,11 f A exp 2ln(2)G 0 2[ ]FWHH2FWHH

2 (1 2 f )AG 0 2 2FWHH 1 4(n 2 n )0,2

24(n 2 n )0,21 f A exp ln(2) (17)G 0 2[ ]FWHH

yields accurate values for the frequency of the originalbands (error , 1 cm21 except for the deuterated randomamide I component (error 5 2.5 cm21, not shown). Thereader is referred to Table I for the description of thesymbols used in Eq. 17.

In conclusion, this approach uses the time constantsdetermined by inverse Laplace transform in the amide IIregion to reveal the shape of the difference spectra (1Hform– 2H form) for each exchanging structure in the am-ide I region. It succeeds in resolving all the structuretypes, including the strongly overlapping helix and ran-dom structures and the fully overlapped b-sheets.

Time Constant Unknown. The previous approach re-quires knowledge of the various time constants charac-terizing the exchange process. Even though the time con-stants are best evaluated from the evolution of amide IIin the course of the exchange, the procedure requires thedetermination of the baseline from which the intensities(or area) are measured. It also assumes that the intensityof amide II can only decrease proportionally to the ex-change progression. In real proteins, it may happen thatside chains also present a contribution in the amide I andamide II range, whose contribution increases as a func-tion of time (for a review on side-chain contributions seeRefs. 28, 30, 54, and 55). The overlap of increasing anddecreasing intensities might result in bias when using theinverse Laplace transform analysis because, as statedabove, the analysis as set here assumes decreasing con-

APPLIED SPECTROSCOPY 79

FIG. 11. Global � tting basic spectra decomposition of the kinetic series containing contributions from a-helix, random, sheet, turn, and slowlyexchanging b-sheets (not shown). The characteristics of the band shapes and of the exchange time constants are described in Table II. Thedecomposition has been carried out as described in the text and by Eq. 16. The time constants determined in the course of the � tting are reportedin the right margin of the � gure along with the assignments. The different components are numbered from 1 to 6. The time-dependent contributionof each is reported in Fig. 12.

FIG. 12. Time-dependent contribution of the global � tting basic spectra reported in Fig. 11. The numbers refer to the numbering present inFig. 11.

tributions only. Global � tting of the whole spectral rangebetween 1700 and 1400 cm21 is a potential approach tosolve this matter.56 The global � tting problem can be de-scribed exactly as above by Eqs. 14 through 16, but inaddition, a nonlinear curve-� tting procedure (Levenberg–Marquardt) is used to determine the k i that result in thebest � t of the entire series of spectra between 1750 and1400 cm21.

As previously, we present the results for the most com-plex case only. The resulting basic spectra are reportedin Fig. 11 along with the corresponding determined timeconstants. There is obviously an excellent agreement withthe previous method and with the underlying data. In ad-dition, this procedure determines simultaneously the ex-change rate that characterizes each basic spectrum (Fig.12). Only the slowest time constant (k 5 1.03 3 1024

instead of 1025 min21) is incorrect (Fig. 11). This is notsurprising when it is considered that the spectral shape isthe same as for the other b-sheet component and that thekinetic series provided for the global � tting decomposi-tion reaches only 2560 min while the time constant is1025 min21, i.e., the decay for this component is less than2.5% of its total amplitude.

The only necessary input parameter in this approach isthe number of time constants necessary to � t the kineticdata. An insight into the problem of the evaluation of thenumber of necessary time constants is provided by ananalysis of the quality of the � t. The residuals of the � tare easily computed as Ht(401,49) 2 P (401,6)·C (6,49) (see Eq.14) for each time point. Further insight into the time re-gions that are not well described by the determined basicspectra and the corresponding time constants is providedby the standard deviation of the difference Ht 2 P. Cobtained at each time point (not shown). The mean ofthese standard deviations is reported in Fig. 13 as a func-tion of the number of time constants allowed for the glob-al � tting. When dealing with real spectra, the signi� cantnumber of time constants will ultimately depend on thequality of the spectra.

In conclusion, this approach provides us with a tool tosimultaneously obtain the basic spectra and their contri-butions in the course of the kinetics. As described above,more precise information on the frequencies of the ex-changing structures requires a curve � tting of the basicspectra.

Individual Secondary Structure Exchange. In the

80 Volume 58, Number 1, 2004

FIG. 13. Evolution of the mean standard deviation of the � t as a func-tion of the number of time constants allowed.

FIG. 14. (A) Evolution of the absorbance of a kinetic series (equimolar mixture of a-helix, b-sheet, and random structures) at selected wavenumbers.The characteristics of the band shapes are described in the text. The label a indicates the monitoring of the a-helix structure at the isobestic pointfor the random structure. The label a1r indicates that both the a-helix and the random structure are monitored at 1640 cm21. The b-sheet structuredeuteration curve is indicated by b. (B) a-helix, b-sheet, and random (r) contributions resolved as explained in the text and rescaled between 0and 1.

analysis described so far, we have assumed that one ex-change rate de� nes one secondary structure type. Eventhough the spectral features reported in Fig. 10 do notsuppose an assignment to a speci� c secondary structure,we described the A 2 B curves (Eq. 16) as belongingn n

0, i 0, i

to a single, well-de� ned structure. Yet it might be desir-able to monitor the exchange rate of a given secondarystructure, should this secondary structure be characterizedby several rate constants. It has been reported earlier20–22

that monitoring amide I (where assignments to secondarystructure are rather well established) can bring this typeof information. Monitoring the shifts in amide I is dif� -cult because of the broadness of the contributions. In par-ticular, a-helix and random contributions absorb at almostthe same wavenumbers. We have found that the problemcan be relatively easily sorted out for the three-structuremixture a-helix 1 b-sheet 1 random. We built a kineticmodel in the amide I range with the a-helix and b-sheetparameters described in Table I and a random structure

characterized by a shift from 1658 ® 1646 cm21, FWHH5 55 cm21, and a time constant k 5 0.5 min21. At 1620cm21, only the b-sheet contribution is sensed, providingus with the opportunity to record the shape of the ex-change curve for the b-sheet structure alone (Fig. 14,panel A). After rescaling between 0 and 1, the data arereported in Fig. 14, panel B. Resolving the random anda-helix contributions is more complex. As previously in-dicated by de Jongh et al.,22 we searched in the 1656–1645 cm21 region for an isobestic point present at thevery beginning of the exchange process, when most ofthe changes are due to the fast exchanging random struc-ture only. The isobestic point for the random structure isobtained by � tting the time dependence of the data (be-tween 0.5 and 5 min) at every wavenumber by a simpleexponential decay. Figure 15 reports the result of such a� t for the a-helix 1 b-sheet 1 random kinetic model justdescribed. Clearly, there is a good agreement between thetime constant for the exchange of the random structurereported in the ordinate (0.5 min21) and the isobesticpoint reported at the beginning of the exchange processindicated by the sign change (1651 cm21). According tode Jongh et al.,22 once the isobestic point of the randomstructure is identi� ed, monitoring the long-term kineticsat this wavenumber allows the recording of the helix ex-change only, with no interference of the random structureexchange. The evolution of the absorbance at the isobes-tic point of the random structure is shown in Fig. 14(panel A, a). A contribution from the b-sheet structureexchange is obvious in the long run as the intensity � rstincreases, then decreases because of the b-sheet ex-change. The contribution of the b-sheet exchange can beremoved as follows. Because the exchange of the b-sheetstructure is thought to be the slowest one,21 when lookingat 1652 cm21 in the time region beyond 300 min it canbe assumed that only the b-sheet contributes to the ki-netic curve. The absorbance at 1651 cm21, t . 300 min,can therefore be written as:

A1651, t.300 5 a·A sheet, t.300 1 b (18)

A sheet, t.300 is the curve recorded at 1620 cm21 in the region

APPLIED SPECTROSCOPY 81

FIG. 15. Determination of the isobestic point position at the beginningof the exchange process for a model kinetic series containing an equi-molar mixture of a-helix, b-sheet, and random structures. At everywavenumber, the evolution of the absorbance was � tted as a singleexponential decay. The portion of the kinetic analyzed was 0.5 to 5 minand 300 and 2000 min (not shown). The determined time constant k isreported (ordinate) for every frequency. The constant was multiplied by11 where the intensity decreases and 21 where it increases for astraightforward visualization of the frequency of the isobestic point. Theisobestic point is determined as the frequency where the line crossesthe 0 abscissa (dotted line).

beyond 300 min. Once the constant a is determined, theentire scaled b-sheet kinetic can be subtracted from thehelix kinetic recorded at 1651 cm21. Figure 14, panel B,presents the resolved kinetic curve for the a-helix struc-ture. The same correction is applied at 1640 cm21 whereonly the superimposed contributions of the a-helix andrandom structures remain. Subtraction of the a-helix con-tribution at 1640 cm21 is realized according to the sameprinciple. Because the exchange of the random structureis supposed to be very fast, when looking at 1640 cm21

in the time region beyond 48 min it can be assumed thatonly the a-helix contributes to the kinetic curve. The ab-sorbance at 1640 cm21, t . 48 min, can therefore bewritten as:

A1640, t.48 5 c·Ahelix, t.48 1 d (19)

Once the constant c is determined, the scaled helix kineticcan be subtracted from the helix 1 random kinetic re-corded at 1640 cm21. Figure 14, panel B, presents theresolved kinetic curve for the random structure.

When applied to more complex systems (4- or 5-struc-ture mix), the problem requires more corrections such asthose brought by Eqs. 18 and 19 and can no longer besolved satisfactorily unless the time constants of the ki-netics are all well separated.

In conclusion, this approach can resolve the kinetics atthe level of the secondary structure in the 3-structuremodel. A � ne analysis of the curves presented in Fig. 14,panel B, indicates signi� cant deviations from the expect-ed single exponential shape (not presented).

DISCUSSION

As a general conclusion for this study, a number ofdifferent approaches allow the resolution of the exchangerate at the level of submolecular entities. The methodcurrently used in the large majority of the published pa-

pers, i.e., the computation of the synchronous/asynchro-nous maps, is not the most potent. The approaches thatimplicitly include the known shape of the kinetics (� rst-order reactions) outperform the other methods. In partic-ular, the inverse Laplace transform and the global � tting(with or without previous knowledge of the kinetic timeconstants) were shown to resolve the most complex casesstudied.

It is of importance to stress here the fact that the datapresented only consider � rst-order kinetics in modelspectra and model kinetics. The effect of noise and thepossible shift of a component over a dispersion of wave-numbers have not been investigated in the present study.In order to evaluate the effect of noise on all the analyses,this study was repeated on spectrum series with variouslevels of noise added (see the Methods section, data notshown). It was found that the outcome of the analysesremains identical until the noise (its standard deviation)reaches a range of approximately 0.1–1% of the maxi-mum spectra intensity in the amide I region. The accept-able level of noise can then be increased by at least oneorder of magnitude by using speci� c processing. Eitherspectral smoothing (including the FSD used here that in-cludes an apodization of the Fourier transform of thespectra, see the Methods section) or by using publishedapproaches to analyze the correlation maps.46,57,58 The de-tailed analysis of the effect of the noise was consideredto be beyond the scope of the present paper.

Another potential problem when working with realproteins comes from the implicit assumption that the deu-teration is a two-state phenomenon. It is likely that partialdeuteration of protein segments would yield a spectrumthat is not simply a linear combination of the initial and� nal states because of the complex resonances that willinduce mutual in� uences. This has been particularly welldocumented in the case of speci� c 13C labeling in pep-tides.59 As far as the exchange of 1H by 2H is concerned,the problem is also much more complicated by the largenumber of amide groups in a protein. Amide groups fromdifferent regions of a helix (top, middle, end) may absorbat different frequencies. Yet, even though the deep com-plexity is recognized, previous studies indicated that theinfrared spectra exchange can be modeled by a super-imposition of a few bands similar to those described inthe present paper, at least within the accuracy limits ofthe recorded spectra.21,22 It therefore appears that the ap-proaches proposed here are of interest for the study ofreal protein spectra.

ACKNOWLEDGMENTS

This work was funded by a grant ARC (Action de Recherches Con-certees). Dr. Goormaghtigh is Research Director of the Belgian NationalFund For Scienti� c Research. Dr. Raussens is Research Associate ofthe Belgian National Fund for Scienti� c Research. We thank Dr. Prov-encher for providing us with the CONTIN program and helping usmodify a few lines of the code.

1. R. B. Gregory and R. Lumry, Biopolymers 24, 301 (1985).2. D. G. Knox and A. Rosenberg, Biopolymers 19, 1049 (1980).3. S. W. Provencher and V. G. Dovi, Can. J. Biochem. 1, 313 (1979).4. S. W. Englander and N. R. Kallenbach, Q. Rev. Biophys. 16, 521

(1984).5. P. S. Kim, Methods Enzymol. 131, 136 (1986).

82 Volume 58, Number 1, 2004

6. R. Lumry, Protein-solvent interactions, R. B. Gregory, Ed. (MarcelDekker, New York, 1994).

7. T. Heimburg and D. Marsh, Biophys. J. 65, 2408 (1993).8. S. Meskers, J. M. Ruysschaert, and E. Goormaghtigh, J. Am. Chem.

Soc. 121, 5115 (1999).9. V. Raussens, V. Narayanaswami, E. Goormaghtigh, R. O. Ryan, and

J. M. Ruysschaert, J. Biol. Chem. 271, 23089 (1996).10. R. I. Saba, J. M. Ruysschaert, A. Herchuelz, and E. Goormaghtigh,

J. Biol. Chem. 274, 15510 (1999).11. N. Sonveaux, A. B. Shapiro, E. Goormaghtigh, V. Ling, and J. M.

Ruysschaert, J. Biol. Chem. 271, 24617 (1996).12. J. Sturgis, B. Robert, and E. Goormaghtigh, Biophys. J. 74, 988

(1998).13. H. H. de Jongh, E. Goormaghtigh, and J. M. Ruysschaert, Bio-

chemistry 34, 172 (1995).14. B. I. Baello, P. Pancoska, and T. A. Keiderling, Anal. Biochem.

280, 46 (2000).15. S. A. Tatulian, B. W. Chen, J. H. Li, S. Negash, C. R. Middaugh,

D. J. Bigelow, and T. C. Squier, Biochemistry 41, 741 (2002).16. F. Scheirlinckx, R. Buchet, J. M. Ruysschaert, and E. Goormagh-

tigh, Eur. J. Biochem. 268, 3644 (2001).17. L. Vigneron, J. M. Ruysschaert, and E. Goormaghtigh, J. Biol.

Chem. 270, 17685 (1995).18. E. Goormaghtigh, L. Vigneron, G. A. Scarborough, and J. M. Ruys-

schaert, J. Biol. Chem. 269, 27409 (1994).19. J. E. Baenziger and N. Methot, J. Biol. Chem. 270, 29129 (1995).20. N. Dave, V. A. Lorenz-Fonfria, J. Villaverde, R. Lemonnier, G.

Leblanc, and E. Padros, J. Biol. Chem. 277, 3380 (2002).21. H. H. de Jongh, E. Goormaghtigh, and J. M. Ruysschaert, Bio-

chemistry 36, 13603 (1997).22. H. H. de Jongh, E. Goormaghtigh, and J. M. Ruysschaert, Bio-

chemistry 36, 13593 (1997).23. M. Hollecker, M. Vincent, J. Gallay, J. M. Ruysschaert, and E.

Goormaghtigh, Biochemistry 41, 15267 (2002).24. V. Grimard, C. Vigano, A. Margolles, R. Wattiez, H. W. van-Veen,

W. N. Konings, J. M. Ruysschaert, and E. Goormaghtigh, Biochem-istry 40, 11876 (2001).

25. E. Goormaghtigh, V. Raussens, and J. M. Ruysschaert, Biochim.Biophys. Acta 105, 1422 (1999).

26. Y. N. Chirgadze and E. V. Brazhnikov, Biopolymers 13, 1701(1974).

27. Y. N. Chirgadze and N. A. Nevskaya, Biopolymers 15, 627 (1976).28. S. Y. Venyaminov and N. N. Kalnin, Biopolymers 30, 1259 (1990).29. J. L. R. Arrondo and F. M. Goni, Prog. Biophys. Molec. Biol. 72,

367 (1999).30. E. Goormaghtigh, V. Cabiaux, and J. M. Ruysschaert, Subcell.

Biochem. 23, 329 (1994).31. E. Goormaghtigh, V. Cabiaux, and J. M. Ruysschaert, Subcell.

Biochem. 23, 405 (1994).

32. J. K. Kauppinen, D. J. Moffat, H. H. Mantsch, and D. G. Cameron,Anal. Chem. 53, 1454 (1981).

33. J. K. Kauppinen, D. J. Moffat, H. H. Mantsch, and D. G. Cameron,Appl. Spectrosc. 35, 271 (1981).

34. J. K. Kauppinen, D. J. Moffat, and H. H. Mantsch, Appl. Opt. 20,1866 (1981).

35. E. Goormaghtigh, V. Cabiaux, and J. M. Ruysschaert, Eur. J. Bio-chem. 193, 409 (1990).

36. E. Goormaghtigh, V. Cabiaux, and J. M. Ruysschaert, Subcell.Biochem. 23, 405 (1994).

37. E. Goormaghtigh and J. M. Ruysschaert, ‘‘Polarized Attenuated To-tal Re� ection Infrared Spectroscopy as a Tool to Investigate theConformation and Orientation of Membrane Components’’, in Mo-lecular Description of Biological Membrane Components by Com-puter-Aided Conformational Analysis, R. Brasseur, Ed. (CRC Press,Boca Raton, FL, 1990).

38. V. A. Lorenz-Fonfria, J. Villaverde, and E. Padros, Appl. Spectrosc.56, 232 (2002).

39. I. Noda, Appl. Spectrosc. 44, 550 (1990).40. I. Noda, Appl. Spectrosc. 47, 1329 (1993).41. I. Noda, A. E. Dowrey, C. Marcott, G. M. Story, and Y. Ozaki,

Appl. Spectrosc. 54, 236A (2000).42. A. Nabet and M. Pezolet, Appl. Spectrosc. 51, 466 (1997).43. S. S† as†ic, A. Muszynski, and Y. Ozaki, Appl. Spectrosc. 55, 343

(2001).44. I. Noda, A. E. Dowrey, and C. Marcott, Appl. Spectrosc. 47, 1317

(1993).45. S. Ekgasit and H. Ishida, Appl. Spectrosc. 49, 1243 (1995).46. R. Buchet, Y. Wu, G. Lachenal, C. Raimbault, and Y. Ozaki, Appl.

Spectrosc. 55, 155 (2002).47. S. Shanmukh, P. Howell, J. E. Baatz, and R. A. Dluhy, Biophys. J.

83, 2126 (2002).48. D. L. Elmore and R. A. Dluhy, J. Phys. Chem. B 105, 11377

(2001).49. D. G. Knox and A. Rosenberg, Biopolymers 19, 1049 (1980).50. S. W. Provencher, Comp. Phys. Commun. 27, 229 (1982).51. M. Ameloot, Methods Enzymol. 210, 279 (1992).52. H. Halvorsen, Methods Enzymol. 210, 54 (1992).53. S. W. Provencher, Biophys. J. 16, 27 (1976).54. A. Barth, Prog. Biophys. Molec. Biol. 74, 141 (2000).55. A. Barth and C. Zscherp, Quarterly Rev. Biophys. 35, 369 (2002).56. R. Brudler, R. Rammelsberg, T. T. Woo, E. D. Getzoff, and K.

Gerwert, Nat. Struct. Biol. 8, 265 (2001).57. Y. M. Jung, H. S. Shin, S. Bin Kim, and I. Noda, Appl. Spectrosc.

56, 1562 (2002).58. Y. M. Jung, H. S. Shin, S. Bin Kim, and I. Noda, Appl. Spectrosc.

57, 557 (2003).59. S. Y. Venyaminov, J. F. Hedstrom, and F. G. Prendergast, Proteins-

Struct. Funct. Genet. 45, 81 (2001).