J. Phys. Chem. B 2000, 104, 4537-4544
4537
Anisotropic Optical Constants of r-Helix and β-Sheet Secondary Structures in the Infrared T. Buffeteau,*,† E. Le Calvez,† S. Castano,† B. Desbat,† D. Blaudez,‡ and J. Dufourcq§ Laboratoire de Physico-Chimie Mole´ culaire, UMR 5803 du CNRS, and Centre de Physique Mole´ culaire Optique et Hertzienne, UMR 5798 du CNRS, UniVersite´ Bordeaux I, 33405 Talence, France, and Centre de Recherche Paul Pascal, CNRS, AVenue A. Schweitzer, 33600 Pessac, France ReceiVed: NoVember 8, 1999; In Final Form: February 22, 2000
Pure R-helices and antiparallel β-sheets were obtained using poly-γ-benzyl-L-glutamate (PBG) and model synthetic peptide K(LK)7, respectively. Monolayers of these polypeptides were transferred by the LangmuirBlodgett technique on calcium fluoride plates and gold mirrors. The optical constants (index of refraction and extinction coefficient) were determined in the space coordinate system from normalized polarized transmittance and reflectance spectra. Considering the symmetry of the two secondary structures, the anisotropic optical constants were calculated in the molecular coordinate system of the R-helix and the β-sheet. From anisotropic components of the extinction coefficients, oscillator strengths of amide I and amide II modes have been calculated for the two secondary structures. These data give important information on the relative intensities of the amide I and amide II modes; moreover, for PBG the angle between the transition moment of the amide I mode and the helix axis has been estimated to be 34-38°. Finally, on the basis of these anisotropic optical constants, PM-IRRAS spectra of a single monolayer at the air/water interface were simulated for the two secondary structures.
Introduction The determination of anisotropic optical constants (index of refraction n and extinction coefficient k) in the infrared range is particularly useful for organized thin films because it allows one to calculate the average orientation of each transition moment and of molecules when their conformation is known.1,2 Moreover, the anisotropic optical constants allow the simulation of infrared spectra of Langmuir and Langmuir-Blodgett (LB) monolayers on different substrates and under different experimental conditions. Then, by comparing the experimental and simulated spectra, the spectral changes due to optical and chemical effects can be distinguished.1-3 The knowledge of such optical data is of great interest in the study of thin films of biological molecules, in particular for the determination of the orientation of the main secondary structures (R-helices, β-sheets) found in proteins and polypeptides. We have thus attempted to determine the anisotropic optical constants of two synthetic polypeptides, each of them exhibiting only one secondary structure. Optical properties of the pure R-helix and the antiparallel β-sheet have been obtained with poly-γ-benzyl-L-glutamate (PBG) and model peptide K(LK)7 containing lysine (K) and leucine (L) residues, respectively. Indeed, PBG forms long R-helices oriented parallel to the surface when deposited onto solid surfaces.4,5 On the other hand, K(LK)7 forms perfect antiparallel β-sheets at the air/water interface because of its ideally amphipathic nature, and keeps its secondary structure after deposition onto solid substrates.6 As * To whom correspondence should be addressed. E-mail: thbuff@ lpct.u-bordeaux.fr. Fax: (33) 5 56 84 84 02. † Laboratoire de Physico-Chimie Mole ´ culaire, Universite´ Bordeaux I. ‡ Centre de Physique Mole ´ culaire Optique et Hertzienne, Universite´ Bordeaux I. § Centre de Recherche Paul Pascal, CNRS.
these polypeptides are not necessarily randomly oriented in the plane of the substrate, the optical constants have to be determined in the three directions of the space coordinate system. To evaluate the anisotropic optical constants of ultrathin films in the space coordinate system, we have used a calculation procedure which allows a direct determination of the refractive indexes from experimental FTIR spectra.1 In this procedure, the in-plane (X and Y) and out-of-plane (Z) refractive indexes are obtained from polarized normalized transmittance spectra at normal incidence and a p-polarized reflectance spectrum at grazing incidence (IRRAS), respectively. For ultrathin films (thickness d < 100 Å), a better sensitivity of the IRRAS spectra can be obtained using polarization modulation IRRAS (PMIRRAS).7 Then, the determination of the anisotropic optical constants in the molecular coordinate system can be performed considering the symmetry of the secondary structure of the studied polypeptides. This paper is organized as follows. After the Experimental Section, the procedure used to determine anisotropic optical constants in the space coordinate system from experimental spectra is presented. Then, the optical constants are calculated for the molecular coordinate system of PBG (R-helix) and K(LK)7 (antiparallel β-sheet). From anisotropic components of the extinction coefficients, the oscillator strengths of amide I and amide II modes have been calculated for the two secondary structures. Orientation of the “pseudo transition moment” of the amide I mode with respect to the helix axis is given, and the ratio rR/β between the oscillator strength of the two secondary structures has been calculated. Finally, the comparison between simulated and experimental PM-IRRAS spectra of a monolayer at the air/water interface is presented.
10.1021/jp9939524 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/19/2000
4538 J. Phys. Chem. B, Vol. 104, No. 18, 2000 Experimental Section Sample Preparation. Films of PBG and K(LK)7 were prepared by the conventional LB technique, using a NIMA 611 trough (Coventry, U.K.). PBG (molecular weight 22 000) was purchased from Sigma (St. Louis, MO). PBG monolayers were spread onto a MilliQ (Millipore) ultrapure water subphase from a 4 × 10-5 M chloroform solution. During the deposition, the surface pressure was sufficiently low to have only one monolayer on the water subphase and was maintained at a constant value of 5 mN/m corresponding to a molecular area of 19 Å2/monomer. K(LK)7 was provided by Neosystem (Strasbourg, France) and was solubilized in methanol at a concentration of 2.5 × 10-4 M. Peptide films at the air/water interface were formed by injection of a small volume into the subphase (ultrapure water + NaCl (0.1 M)). During the transfer, the surface pressure was maintained at a constant value of 20 mN/m. Films of the synthetic peptides were deposited onto calcium fluoride (CaF2) substrates for transmittance measurements, and onto gold-coated optical mirrors for infrared reflectance measurements. FTIR Measurements. Transmittance and PM-IRRAS spectra were recorded on a Nicolet 740 FTIR spectrometer at a resolution of 4 cm-1, by co-adding 300 scans. Polarized transmittance experiments were performed at normal incidence to obtain the infrared spectra in the substrate plane along the X and Y directions (Y being the direction of the withdrawal). A BaF2 wire grid polarizer (Specac, Paris, France) was used to select the polarized direction. The efficiency of the polarizer was specified to be better than 99% for wavenumbers lower than 3300 cm-1. PM-IRRAS experiments of synthetic peptide monolayers deposited onto a gold substrate and at the air/water interface were carried out at an incidence angle of 75°, using the setup and the experimental procedure described previously.7-9 A calibration procedure has been performed, by adding a linear polarizer oriented parallel or perpendicular to the incidence plane, to express the PM-IRRAS signal in terms of the IRRAS signal. Ellipsometry Measurements. The thickness of the synthetic peptide films has been determined using a GESP5 (SOPRA, Bois-Colombes, France) spectroscopic ellipsometer. This parameter has been obtained from the ellipsometric angles (ψ and ∆) measured with an angle of incidence of 70° in the 0.3-0.8 µm spectral range, using a regression procedure based on the second-order Cauchy dispersion law. Optical Constant Calculation Optical Constants in the Space Coordinate System (X, Y, Z). The optical constants along the X, Y, and Z directions of the substrate (space coordinate system) are calculated using an iterative procedure based on the inversion of spectral simulation programs.1 The optical constants in the plane of the layer (nX, kX, and nY, kY) are determined from the polarized transmittance spectra at normal incidence of a thin film deposited on a calcium fluoride substrate. Indeed, polarized radiation with the electric vector parallel (Y axis) or perpendicular (X axis) to the direction of the withdrawal interacts only with the Y and X components of the transition moments, respectively. On the other hand, the optical constants out of the plane of the layer (nZ, kZ) are determined from IRRAS or calibrated PM-IRRAS spectra of a thin film deposited on a metallic substrate. In this case, the electric vector is quasi perpendicular to the surface and interacts only with the normal (Z) component of the transition moment of the thin film.
Buffeteau et al. SCHEME 1 : Coordinate Axes and Euler Angles
A first estimation of the optical constants is obtained using approximate equations for the transmittance and IRRAS spectra. Using the thin film approximation (d , λ), the polarized normalized transmittance is given by norm T(X,Y) )
T(X,Y) sub T (X,Y)
[
) 1-
4πνjd Im(ˆ (X,Y)) (1 + ns)
]
(1)
and the IRRAS signal Rp(d)/Rp(0) is given by
Rp(d) Rp(0)
[
) 1-
( )]
8πνjd sin2 θ0 1 Im cos θ0 ˆ Z
(2)
where d is the thickness of the film, νj is the wavenumber, ns is the refractive index of the substrate, θ0 is the angle of incidence, and ˆ ) nˆ 2 is the complex dielectric constant of the film with nˆ ) n + ik.10-12 Equations 1 and 2 can be used to extract the imaginary parts of the dielectric functions, ˆ X, ˆ Y, and -1/ˆ Z, respectively, while their real parts are calculated by Kramers-Kronig transformations (KKT) of the associated imaginary parts.13 Then, the initial real and imaginary parts of the dielectric functions are used for calculating the polarized normalized transmittance or the IRRAS spectra and are perturbed, for each wavenumber, by a NewtonRaphson method until the simulated and experimental spectra are sufficiently close to each other. Since the real parts of the dielectric functions are not perturbed, this procedure must be repeated several times until no significant changes on the real and imaginary parts of the dielectric functions are observed. The final optical constants are calculated by simple arithmetical equations using the real and imaginary parts of the dielectric functions. Optical Constants in the Molecular Coordinate System (u, W, w). The optical constants can be calculated in the molecular coordinate system (u, V, w) using the rotation matrix:
() (
MX MY ) MZ cosψcosφ - cosγsinφsinψ -sinψcosφ - cosγsinφcosψ sinγsinφ cosψsinφ + cosγcosφsinψ -sinψsinφ + cosγcosφcosψ -sinγcosφ sinγsinψ sinγcosψ cosγ
)( ) Mu MV Mw
(3)
which relates the components of the transition dipole moment vector M in the space and molecular coordinate systems.14 The elements of the matrix represent the direction cosines expressed in terms of the Euler angles φ (azimuthal angle, rotation around Z), γ (tilt angle, rotation around u′), and ψ (twist angle, rotation around w) defined in Scheme 1.
Optical Constants of R-Helix and β-Sheet Structures
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4539
SCHEME 2: Schematic Representation of (a, top) an r-Helix and (b, bottom) a β-sheet in the Molecular Coordinate System
TABLE 1: Wavenumbers and Direction of the Transition Dipole Moments for the Amide I and Amide II Bands of PBG and K(LK)7 Polypeptides amide I conformation R-helix
cm-1 b
amide II directionc
cm-1 b
directionc
(u, V) w w V u
1548 (s) 1518 (w) 1536 (s) 1555 (m) 1540 (m)
(u, V) w w V u
(PBG)a
1656 (m) 1652 (vs) antiparallel β-sheet 1692 (m) K(LK)7 1650-1670 (w) 1628 (vs)
a The wavenumbers reported for the amide I and amide II bands of PBG are those observed in the polarized transmittance (w direction) and IRRAS (u and V directions) spectra of this work. b Intensity: vs, very strong; s, strong; m, medium; w, weak. c The direction assignment for the R-helix and for the antiparallel β-sheet is that reported in ref 16. The u, V, and w axes used in this study for the antiparallel β-sheet correspond to the Y, X, and Z axes of ref 16, respectively.
guished (in view of the uniaxial symmetry of the helical chain). The wavenumbers and the direction of the corresponding transition dipole moments observed for the amide I and amide II bands of PBG are reported in Table 1. Considering the uniaxial symmetry of the R-helix (ku ) kV ) ku,V), cos2 ψ and sin2 ψ have to be averaged in eqs 4 (i.e., both equal to 0.5). This is equivalent to setting ψ ) 45° in the calculation. Equations 4 become:
kX ) (cos2 φ)ku,V + (sin2 φ)kw kY ) (sin2 φ)ku,V + (cos2 φ)kw Considering that the extinction coefficients are proportional to the square of the transition dipole moments and assuming that the R-helices and antiparallel β-sheets are oriented parallel to the surface (γ ) 90°), we easily obtain the relationships between the extinction coefficients in the two coordinate systems:
kX ) (cos2 ψ cos2 φ)ku + (sin2 ψ cos2 φ)kV + (sin2 φ)kw (4) kZ ) (sin ψ)ku + (cos ψ)kV 2
kZ ) ku,V The extinction coefficient perpendicular to the helix axis ku,V is given by the calculation of the optical constants along the Z axis from the IRRAS spectrum. On the other hand, the extinction coefficient along the helix axis kw can be related to the extinction coefficients in the space coordinate system from eq 5 by the relation
k w ) kX + kY - kZ
kY ) (cos2 ψ sin2 φ)ku + (sin2 ψ sin2 φ)kV + (cos2 φ)kw 2
As shown in eqs 4, the determination of ku, kV, and kw, needs the knowledge of the Euler angles φ and ψ. Nevertheless, it can be done from symmetry considerations on the secondary structure of the peptides or on the studied transition dipole moments. The representations in the molecular coordinate system of the R-helices and β-sheets are reported in parts a and b, respectively, of Scheme 2. The R-helix axis is along the w axis (Scheme 2a). For β-sheets, the chain axis is along the w axis and the interchain hydrogen bonds are along the u axis (Scheme 2b). R-Helix. In helical polypeptides the vibrations of the CONH group (amides A, B, I, II, III) may be specified by the phase difference (δ) between corresponding atoms in adjacent repeat units. Thus, the infrared absorption arises either from the A symmetry class vibrations with the phase difference δ ) 0 (the transition moment being parallel to the helix axis, w) or from the E symmetry class vibrations with the phase difference equal to the angle which separates the corresponding atoms of the adjacent units (the transition moment being perpendicular to the helix axis).15,16 In this last degenerate symmetry class, the u and V directions of the transition moment cannot be distin-
(5)
(6)
The refractive indexes in the molecular coordinate system are calculated by Kramers-Kronig transformations of the corresponding extinction coefficients. Equations 5 can be used to calculate the azimuthal angle φ, which defines the angle between the helix axis and the withdrawing direction; this angle is given by the relation
φ ) arc tan
[( ) ] k X - kZ k Y - kZ
1/2
(7)
Antiparallel β-Sheets. The symmetry and the selection rule of the antiparallel β-sheet structure have been studied in the literature.16-18 For this structure, four peptide groups constitute the two-dimensional unit cell with a punctual group D2. For this point group, four symmetry classes are expected for the amide modes with three infrared-active vibrations along the w (B1), u (B2), and V (B3) axes. The wavenumbers and the direction of the corresponding transition dipole moments observed for the amide I and amide II bands of K(LK)7 are presented in Table 1. The amide II components along the u, V, and w axes appear at wavenumbers very close to each other, and the corresponding bands could be overlapped. In contrast, for the amide I mode, the vibration along the u axis (at about 1630 cm-1) is isolated and can be used to determine the twist and azimuthal angles of
4540 J. Phys. Chem. B, Vol. 104, No. 18, 2000
Buffeteau et al.
Figure 1. (A) Infrared normalized polarized transmittance spectrum of three monolayers of PBG deposited on each side of a CaF2 substrate measured at normal incidence. (B) PM-IRRAS spectrum (expressed in terms of the IRRAS signal) of one monolayer of PBG deposited on a gold substrate measured with an angle of incidence of 75°.
Figure 2. (A) Anisotropic extinction coefficients in the space coordinate system (kX, kY, and kZ) of PBG monolayers deposited on solid substrates. (B) Anisotropic extinction coefficients in the molecular coordinate system (ku, kV, and kw) of PBG monolayers deposited on solid substrates.
the antiparallel β-sheets. If we consider a transition dipole moment oriented along the u axis (i.e., MV ) Mw ) 0), eqs 4 become
Results
kX ) (cos2 ψ cos2 φ)ku kY ) (cos2 ψ sin2 φ)ku
(8)
kZ ) (sin2 ψ)ku Combining eqs 8, the twist angle ψ is given by
ψ ) arc tan
[(
)]
(9)
)
(10)
kZ kX + kY
1/2
and the azimuthal angle φ is given by:
(
k X - kY 1 φ ) arc cos 2 kX + kY
The knowledge of the angles φ and ψ allows the determination of the extinction coefficients in the molecular coordinate system by inversion of eqs 4. As mentioned above, the refractive indexes in the molecular coordinate system are calculated by Kramers-Kronig transformations of the corresponding extinction coefficients.
r-Helix. Figure 1 shows the normalized polarized transmittances (along the X and Y axes) and IRRAS spectra of three monolayers of PBG deposited on each side of a CaF2 substrate and of one monolayer deposited on a gold mirror, respectively, in the 1850-1400 cm-1 spectral range. The main bands in these spectra at 1732, 1652, and 1548 cm-1 are assigned to the ester CdO stretching vibration of the residue and the amide I and amide II modes, respectively. The observed wavenumbers of the amide I and amide II bands reveal that the main conformation of the molecular chains in the monolayers is the R-helical structure. The intensities of the amide I and amide II bands are different in the two polarized transmittance spectra, indicating a preferential orientation of the R-helix with respect to the withdrawing direction (Y). On the other hand, the relative intensity of the amide I and amide II bands is slightly lower than 1.0 on the IRRAS spectrum. Considering the surface selection rule on a metallic substrate (only the electric field normal to the surface has a nonzero component) and the infrared spectra (parallel and perpendicular to the helix axis) obtained by Tsuboi on oriented PBG,19 we can conclude that the helices are parallel (i.e., γ ≈ 90°) to the substrate. A similar helix orientation has been found by Takenaka et al.4 on PBG monolayers deposited onto solid substrates. The extinction coefficients in the space coordinate system (kX, kY, and kZ), determined from the normalized polarized
Optical Constants of R-Helix and β-Sheet Structures
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4541
TABLE 2: Maximum Values of the Extinction Coefficients in the Space Coordinate System and Euler Angles (O and ψ) for the Amide I and Amide II Modes of PBG and K(LK)7 Polypeptides system PBG K(LK)7
mode (cm-1)
kX
kY
kZ
ester (1734) amide I (1652) amide II (1548) amide I (1692) amide I (1628) amide II (1536)
0.30 ( 0.02 0.43 ( 0.02 0.23 ( 0.02 0.15 ( 0.02a 0.58 ( 0.05 0.33 ( 0.02
0.30 ( 0.02 0.75 ( 0.02 0.13 ( 0.03 0.11 ( 0.02a 1.17 ( 0.05 0.18 ( 0.02
0.22 ( 0.03 0.22 ( 0.02 0.31 ( 0.02 0.02 ( 0.02a 0.10 ( 0.05a 0.14 ( 0.03
ψ (deg)
φ (deg)
45 45 45
45 ( 2 32 ( 2 34 ( 2 50 ( 4b 55 ( 2 54 ( 2b
13 ( 3
a The maximum k values have been obtained after subtraction of the contribution of the broad band located at 1650 cm-1. b These values have been calculated using the relation φ ) arc tan[(kX/kY)1/2], and assuming that the vibrations are purely along the w axis.
TABLE 3: Maximum Values of the Extinction Coefficients in the Molecular Coordinate System and Integrated Intensities for the Amide I and Amide II Modes of PBG and K(LK)7 Polypeptides system PBG
K(LK)7
mode (cm-1)
ku
kV
kw
Iu (cm-1)
IV (cm-1)
Iw (cm-1)
ester (1734) amide I (1656) amide I (1652) amide II (1548) amide II (1518) amide I (1692) amide I (1628) amide II (1555) amide II (1540) amide II (1536)
0.22 ( 0.03 0.23 ( 0.02
0.22 ( 0.03 0.23 ( 0.02
0.40 ( 0.02
8.6 ( 1.4 6.1 ( 0.7
8.6 ( 1.4 6.1 ( 0.7
10.2 ( 0.8
0.31 ( 0.02
0.31 ( 0.02
9.3 ( 1.1
9.3 ( 1.1
1.64 ( 0.05 0.06 ( 0.03
1.00 ( 0.02 0.04 ( 0.02 0.28 ( 0.03
0.15 ( 0.05
transmittances and the IRRAS spectra, are presented in Figure 2a. For these calculations, a thickness of 15 Å/monolayer has been used. This value has been evaluated from the crystalline structure of PBG and from ellipsometric measurements on a five-layer LB film. The maximum values of kX, kY, and kZ and the azimuthal angle φ calculated from eq 7 are reported in Table 2 for the ester, amide I and amide II modes. The helix axes form an angle of about 33° ( 2° with the withdrawing direction; this value is in very good agreement with that evaluated by Takenaka et al. (35° ( 2°).4 On the other hand, the ester groups of PBG are oriented at 45° with respect to the withdrawing direction. The extinction coefficients in the molecular coordinate system (ku, kV, and kw) have been calculated using eqs 5 and 6 and are presented in Figure 2b. The maximum values of these extinction coefficients have been reported in Table 3. For the amide I mode, the value of the extinction coefficient along the helix axis is very high (kw ) 1.00 ( 0.02) whereas the value of the extinction coefficients perpendicular to the helix axis are lower (ku ) kV ) 0.23 ( 0.02). For the amide II mode only the extinction coefficients perpendicular to the helix axis have a nonzero component. Antiparallel β-Sheets. Figure 3 shows the normalized polarized transmittances (along the X and Y axes) and IRRAS spectra of one monolayer of K(LK)7 deposited on each side of a CaF2 substrate and onto a gold mirror, respectively, in the 1800-1400 cm-1 spectral range. The main bands in these spectra at 1692, 1628, and 1536 cm-1 are assigned to the amide I modes along the peptide chain (w), the amide I modes along the interchain hydrogen bonds (u), and the amide II modes along the peptide chain, respectively. A weak band at 1650 cm-1 is observed in the polarized transmittance and IRRAS spectra; it can be due to the presence of water in the monolayer and/or to some weak random contribution from secondary structure. Moreover, the amide II band is overlapped by an absorption band at 1520 cm-1, assigned to the asymmetric bending of the NH3+ groups of lysine residues.20,21 The observed wavenumbers of the two amide I bands at 1692 and 1628 cm-1 indicate that the peptides adopt an antiparallel β-sheet conformation in the monolayer.16,17 The intensities of the amide I mode along the interchain hydrogen bonds are different in the two polarized
0.43 ( 0.02
36.5 ( 2.2 1.0 ( 0.6
26.9 ( 1.3 1.2 ( 0.7 3.7 ( 0.5
5.0 ( 1.9 14.9 ( 1.4
transmittance spectra, indicating a preferred orientation of the β-sheets in the (X, Y) plane. The extinction coefficients in the space coordinate system (kX, kY, and kZ) are presented in Figure 4a. For these calculations, a thickness of 10 Å/monolayer has been estimated. The maximum values of kX, kY, and kZ are reported in Table 2 for the amide I and amide II modes. The twist angle ψ and the azimuthal angle φ, calculated from eqs 9 and 10 for the amide I modes along the u direction, have also been reported in Table 2. The value calculated for ψ indicates that the plane containing the interchain hydrogen bonds is rather parallel to the surface, the nonzero value being most likely due to the slightly twisted structure of the antiparallel β-sheets. On the other hand, the β-sheet axes form an angle of about 55° ( 2° with the withdrawing direction. The extinction coefficients in the molecular coordinate system (ku, kV, and kw) have been calculated and are presented in Figure 4b. For the amide I modes, the maximum value of the extinction coefficient along the interchain hydrogen bonds (at 1628 cm-1) is very high (ku ) 1.64 ( 0.05) whereas the maximum value of the extinction coefficient along the β-sheet axis (at 1692 cm-1) is lower (kw ) 0.28 ( 0.03). The value of kV for the amide I mode has not been estimated because it is almost impossible to extract its contribution from the broad band near 1650 cm-1. For the amide II mode, the extinction coefficient along the β-sheet axis has the highest value (kw ) 0.43 ( 0.02). Discussion Oscillator Strengths of Amide I and Amide II Modes. The integrated extinction coefficients of the main characteristic bands of PBG and K(LK)7 polypeptides are reported in Table 3. These values have been calculated by a curve-fitting procedure, using a mixture of 90/10 Lorentzian/Gaussian line shapes. From the fitted parameters (frequency, height, and width) of each amide I and amide II component, we have calculated the model extinction coefficients of PBG and K(LK)7 polypeptides used to simulate the spectra presented in the following sections. For the simulation of infrared spectra of antiparallel β-sheet polypeptides the contribution of water and lysine residues has been removed.
4542 J. Phys. Chem. B, Vol. 104, No. 18, 2000
Buffeteau et al.
Figure 3. (A) Infrared normalized polarized transmittance spectrum of one monolayer of K(LK)7 deposited on each side of a CaF2 substrate measured at normal incidence. (B) PM-IRRAS spectrum (expressed in terms of the IRRAS signal) of one monolayer of K(LK)7 deposited on a gold substrate measured with an angle of incidence of 75°.
Figure 4. (A) Anisotropic extinction coefficients in the space coordinate system (kX, kY, and kZ) of K(LK)7 monolayers deposited on solid substrates. (B) Anisotropic extinction coefficients in the molecular coordinate system (ku, kV, and kw) of K(LK)7 monolayers deposited on solid substrates.
The total integrated extinction coefficient I, defined by I ) Iu + IV + Iw, is a useful parameter in particular for analytical application. Indeed, assuming that the infrared spectra of proteins containing different secondary structures are additive, the determination of this parameter (as the integrated intensity for proteins in solution) for each type of structure allows their relative contents to be estimated. The total integrated extinction coefficient of the amide I mode is similar for PBG (I ) 39 ( 3) and K(LK)7 (I ) 40 ( 3) polypeptides. Consequently, the ratio rR/β between the amide I oscillator strength of the two secondary structures is close to 1. It is noteworthy that the value of this ratio is related to the two studied polypeptides and could differ for other systems, in particular for other types of β-sheet structures. On the other hand, the total integrated extinction coefficient of the ester groups of PBG is significantly lower (I ) 27 ( 4), indicating that the oscillator strength of the amide I mode is stronger than that of the ester vibration. This result is in agreement with intensities of amide I and ester modes determined by Y. N. Chirgadze et al.22 for PBG in solution. It is also interesting to evaluate the oscillator strength ratio of the amide I and amide II modes. This parameter has been determined for PBG and K(LK)7 polypeptides by ratioing the total integrated extinction coefficient of amide I and amide II modes. The calculated value of 2.1 for oriented PBG films is lower than that determined for PBG in solution (∼2.8).22 For K(LK)7 polypeptide films the oscillator strength ratio of the
amide I and amide II modes is equal to 1.9. This value should be taken with care because of the overlapping of different bands in the amide II spectral region. Finally, from the integrated extinction coefficient of amide I modes of PBG it is possible to determine the direction of the amide I transition moment. Indeed, the angle R between the amide I transition moment and the long axis of the R-helix is given by the relation23
R ) arc tan
[( ) ] 2Iu,V Iw
1/2
(11)
From the integrated intensities reported in Table 3 and other data obtained on thicker samples, the angle R is estimated to be 34-38°. This value is in good agreement with those determined on PBG experimentally by several groups.18,19 In such experiments, PBG films were oriented on IR plates and the angle R was determined from the dichroic ratio of the amide I band. A correction of this dichroic ratio was necessary to take into account the imperfect orientation of the helices. Following this procedure, values ranging from 29° to 34° were found by Miyazawa et al.,18 and a value of 39° was observed by Tsuboi.19 Likewise, the angle between the amide II transition moment and the long axis of the R-helix can be calculated using eq 11. A value of 76° ( 3° has been found from our data, which is in good agreement with that obtained by Tsuboi (75° ( 1°).19
Optical Constants of R-Helix and β-Sheet Structures
Figure 5. (A) Experimental and simulated PM-IRRAS spectra of a single PBG monolayer at the air/water interface. The surface pressure was 7 mN/m. (B) Experimental and simulated PM-IRRAS spectra of a single K(LK)7 monolayer at the air/water interface. The surface pressure was 20 mN/m.
Simulation of PM-IRRAS Spectra at the Air/Water Interface. From the anisotropic optical constants in the molecular coordinate system of polypeptide LB films, PM-IRRAS spectra of a single monolayer at the air/water interface can be calculated for different orientations of the R-helices or the antiparallel β-sheets, using an algorithm based on Berreman’s matricial formalism.24,25 The simulation of PM-IRRAS spectra can exhibit some optical effects on these monolayer systems, which have to be taken into account to understand experimental spectra. Moreover, the comparison of simulated and experimental spectra can reveal spectral changes associated with different orientations of R-helices or antiparallel β-sheets at the air/water interface and at the surface of a solid substrate, or associated with chemical effects due to specific interactions between the LB film and the substrate. The experimental and simulated normalized PM-IRRAS spectra of PBG and K(LK)7 monolayers at the air/water interface are presented in parts a and b, respectively, of Figure 5. PMIRRAS spectra of a single polypeptide monolayer at the air/ water interface S(d) and of the uncovered water surface S(0) were recorded under the experimental conditions as described in ref 8. The normalized PM-IRRAS spectra S(d)/S(0) have been calculated to eliminate the spectral contribution of the water subphase. The simulated normalized PM-IRRAS spectra were calculated using the anisotropic optical constants of PBG and K(LK)7 previously presented (considering a uniaxial orientation
J. Phys. Chem. B, Vol. 104, No. 18, 2000 4543 of R-helices and antiparallel β-sheets with respect to the normal of the surface) and the isotropic optical constants of water determined by Bertie and Lan.26 The thicknesses of the PBG and K(LK)7 monolayers were taken to be equal to 15 and 10 Å, respectively. The calculated PM-IRRAS spectrum of PBG (Figure 5a) reproduces the intensity of the amide I and amide II modes very well, indicating that the orientation of the R-helices is nearly the same for monolayers at the air/water interface or deposited on a solid substrate (γ ≈ 90°). This result shows that the orientation with respect to the normal of the surface of the R-helices is not perturbed by the LB transfer. On the other hand, the simulated and experimental spectra are significantly different in the region of the ester mode. The integrated intensities of the experimental and simulated spectra are the same, but the heights and the widths of the band differ. This result can be explained considering that the ester groups are in different environments at the air/water interface (single hydrated monolayer) and deposited on solid substrates (multilayer systems). In conclusion, for the PBG system the vibrations associated with the benzyl glutamate residues seem to be perturbed by the water subphase whereas the vibrations associated with the R-helix structure (amide I and amide II modes) are unchanged. For K(LK)7 polypeptide (as shown in Figure 5b) the simulated and experimental PM-IRRAS spectra are quite similar, indicating that the antiparallel β-sheets lie on the water surface. The intensity of the amide I mode along the interchain hydrogen bonds (1628 cm-1) is lower in the experimental spectrum, but a broader band is observed. Moreover, this band appears at lower wavenumbers on the experimental spectrum (1622 cm-1 instead of 1628 cm-1). These observations suggest that the amide modes are sensitive to the interaction between the antiparallel β-sheets and the substrate. The frequency shift could also result from different degrees of molecular aggregation. The influence of the tilt angle γ on IRRAS and PM-IRRAS spectra of a single monolayer of PBG and K(LK)7 at the air/ water interface is presented in Supporting Information. Simulations are also given for a single monolayer deposited on a metallic substrate. These simulations allow a quantitative evaluation of the modification in the intensities of the amide I and amide II modes for different orientations of the R-helices and the antiparallel β-sheets. Conclusion The anisotropic infrared optical constants of synthetic polypeptide monolayers have been determined in the space coordinate system from normalized polarized transmittance spectra at normal incidence and the p-polarized reflectance spectrum at grazing incidence. Considering the secondary structure of the studied polypeptides (R-helices for PBG and antiparallel β-sheets for K(LK)7), the optical constants were calculated in their molecular coordinate system. The determination of these optical constants is useful for several reasons: (i) the oscillator strengths of amide I and amide II modes have been evaluated for the two secondary structures; (ii) the orientation of the transition moment of the amide I mode with respect to the helix axis has been estimated to be 34-38° for PBG; (iii) comparison between experimental and simulated PM-IRRAS spectra of a single monolayer at the air/water interface shows that the organization and the orientation of the R-helices are not perturbed by the LB transfer, whereas the amide modes of the K(LK)7 system are sensitive to interactions between the antiparallel β-sheets and the substrate; (iv) the very high sensitivity of the amide I/amide II ratio versus the orientation of the R-helices and
4544 J. Phys. Chem. B, Vol. 104, No. 18, 2000 antiparallel β-sheets has been shown in the simulated PMIRRAS and IRRAS spectra of a single monolayer at the air/ water interface or deposited on a metallic substrate (see the Supporting Information). Acknowledgment. We are indebted to the CNRS (Chemistry Department) and to Re´gion Aquitaine for financial support. We are thankful to Prof. M. Pe´zolet, De´partement de Chimie, Universite´ Laval, Que´bec, Canada, for several stimulating discussions and to the reviewers for their constructive comments. Supporting Information Available: Influence of the tilt angle γ on IRRAS and PM-IRRAS spectra of a single monolayer of PBG and K(LK)7 at the air/water interface or deposited on a metallic substrate. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Buffeteau, T.; Blaudez, D.; Pe´re´, E.; Desbat, B. J. Phys. Chem. B 1999, 103, 5020. (2) Blaudez, D.; Boucher, F.; Buffeteau, T.; Desbat, B.; Grandbois, M.; Salesse, C. Appl. Spectrosc. 1999, 53, 1299. (3) Ishino, Y.; Ishida, H. Langmuir 1988, 4, 1341. (4) Takenaka, T.; Harada, K.; Matsumoto, M. J. Colloid Interface Sci. 1980, 73, 569. (5) Citra, M. J.; Axelsen, P. H. Biophysical J. 1996, 71, 1796. (6) Castano, S.; Desbat, B.; Dufourcq, J. Biochim. Biophys. Acta 2000, 1463, 65.
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