INTRODUCTION

Top Abstract Introduction Theory Materials and methods Results and discussion Conclusion References

Fourier transform infrared (FTIR) spectroscopy has been widely used for the study of biological molecules (Mantsch and Chapman, 1996) since the shape, intensity, and position of infrared bands are sensitive to the structure and motion of the molecular species. In addition, due to the fact that the absorption of the infrared radiation depends on the angle between the polarization of the incident radiation and the transition moment of a given vibration, it is also possible to characterize the molecular orientation in samples deposited on different types of substrates by means of polarized FTIR spectroscopy. For that purpose, different techniques have been used, namely polarized transmission spectroscopy (Rothschild and Clark, 1979; Chollet and Messier, 1982; Vogel et al., 1983), infrared reflection absorption spectroscopy (IRRAS) (Allara and Swallen, 1982; Rabolt et al., 1983; Umemura et al., 1990; Blaudez et al., 1998), polarization-modulation (PM) IRRAS (Golden et al., 1981; Buffeteau et al., 1991; Blaudez et al., 1993), and polarized attenuated total reflection (ATR) spectroscopy (Harrick, 1967; Fringeli and Günthard, 1981; Kimura et al., 1986; Ahn and Franses, 1992). ATR spectroscopy is a very effective technique for studying biological materials because the sample can be readily oriented on the ATR crystal and kept in an aqueous environment. This sampling technique has been used extensively to study proteins (Goormaghtigh et al., 1990), phospholipid multilayers and monolayers (Fringeli and Günthard, 1981; Okamura et al., 1985; Brandenburg and Seydel, 1986; Lotta et al., 1988), lipid-protein complexes (Okamura et al., 1986; Brauner et al., 1987; Cornell et al., 1989; Frey and Tamm, 1991; Subirade et al., 1995; Axelsen et al., 1995a), and membrane receptors (Baenziger et al., 1992). Even though polarized transmission and IRRAS results can be interpreted in a straightforward manner, it is not the case for ATR spectroscopy, since the electric field amplitudes of the infrared evanescent wave along the three coordinates of the ATR crystal have to be calculated to determine the order parameter from the linear dichroism of the infrared bands (Harrick, 1967; Mirabella and Harrick, 1985).

Some thirty years ago, Harrick (1967) derived analytical equations to calculate these electric field amplitudes for the limiting cases known as the thin-film approximation and the thick-film approximation. According to the Harrick thin-film approximation, the film thickness is very small compared to the penetration depth of the evanescent wave and the electric field amplitudes calculated are those at the surface of the ATR crystal. Thin films of phospholipids and proteins deposited either by the Langmuir-Blodgett technique (Lukes et al., 1992; Axelsen et al., 1995a, b; Subirade et al., 1995), by evaporation from organic solvent (Fringeli and Günthard, 1981; Brauner et al., 1987), or by fusion of small unilamellar vesicles of phospholipids (Frey and Tamm, 1991) have often been considered as Harrick thin films.

Recently, the thin film approximation has been questioned because it failed to give reliable results concerning the orientation of the helical polypeptides poly--benzyl-L-glutamate and poly--benzyl-L-aspartate, and the bee venom toxin melittin (Citra and Axelsen, 1996). It was then proposed that for very thin films, such as supported lipid monolayers and bilayers, the optical constants of the film are highly perturbed by the optical properties of the adjacent media and that the optical properties of the film should be neglected. This model, named the two-phase approximation (Citra and Axelsen, 1996), had already been used in the literature by other investigators (Higashiyama and Takenaka, 1974; Takenaka et al., 1980; Cropek and Bohn, 1990; Jang and Miller, 1995). With the two-phase approximation, Citra and Axelsen (1996) have obtained good results for the orientation of poly--benzyl-glutamate deposited on a hydrophobic substrate that were in agreement with those obtained by other spectroscopic techniques. In addition, this approach seems to eliminate the divergence between the results obtained in the controversial case of melittin bound to lipid membranes (Vogel et al., 1983; Brauner et al., 1987; Frey and Tamm, 1991). However, the Harrick thin film approximation has been used successfully for orientation measurements of dry phospholipid monolayers (Subirade et al., 1995; Labrecque, 1995) and for the orientation of dimyristoylphosphatidylcholine (DMPC) in supported DMPC-gramicidin monolayers deposited on a hydrophobic crystal covered with water (Axelsen et al., 1995a).

The origin of the problems encountered with quantitative orientation measurements using polarized ATR spectroscopy may come from the miscalculation of the mean-square electric field amplitudes. As pointed out recently by Axelsen and Citra (1997), the electric field amplitudes may not be suitably calculated from the Harrick thin film equations. These equations are approximate and do not take into account the film thickness and the absorption of the different media. A wrong evaluation of the physical properties of the film, such as the refractive index or the thickness (thin or thick films) may also lead to the miscalculation of the electric fields. It has also been suggested that the optical properties of an ultra-thin film, and consequently the electric field amplitudes in the film, may be modified by the adjacent media (Axelsen and Citra, 1997).

To address these problems, we have made a detailed analysis of the ATR spectra of supported single bilayers of dimyristoylphosphatidic acid (DMPA) covered by either air or water. A phospholipid has been chosen since it is well known that phospholipids can form highly oriented bilayers whose orientation has been studied by x-ray diffraction (Harlos et al., 1984; Pascher et al., 1987). In addition, the acyl chains for lipid bilayers in the gel phase are in the all-trans conformation and the transition moments of the methylene stretching vibrations are perpendicular to the chain axis. In the present study, DMPA was in part chosen because of its high gel-to-liquid crystalline phase transition temperature (48°C) (Van Dick et al., 1978). Therefore, the spectra obtained at room temperature (~25°C below the phase transition temperature) should be representative of lipids in the gel phase.

The anisotropic optical constants (real refractive index and extinction coefficient in and out of the plane of the film) were first determined from the polarized ATR spectra. Then, the mean-square electric field amplitudes along the three axes of the ATR crystal were calculated using a matricial formalism (Hansen, 1965, 1968, 1972, 1973) that takes into account the number of layers, their complex refractive index, and their thickness. These electric field amplitudes were then compared with those calculated from the Harrick thin film equations and from the two-phase approximation. To test the validity of the different models used to calculate the mean-square electric field amplitudes, s- and p-polarized ATR spectra of a 40-Å lipid layer were simulated for different molecular tilt angles. For each spectrum simulated with a given tilt angle ("real tilt angle"), we have calculated the dichroic ratio and the associated order parameter and tilt angle ("calculated tilt angle"). The difference between the real and calculated tilt angles has been analyzed to determine which model gives better values of the electric field amplitudes. Finally, the different factors affecting the orientation measurements have been analyzed.

	THEORY

Top Abstract Introduction Theory Materials and methods Results and discussion Conclusion References

The computer programs developed to calculate the ATR spectra of multilayer systems and the intensity of the electric fields in each layer use the Abelès's matricial formalism (Abelès, 1967). This formalism is based on the fact that the equations that govern the propagation of light are linear and that the continuity of the tangential fields across an interface between two isotropic media can be regarded as a 2 × 2 linear matrix transformation. In this section, the complex refractive index, _j, is defined as follows:

(1)

where i is equal to , n_j is the refractive index, and k_j is the extinction coefficient of the jth layer.

Spectral simulation

In the Abelès's matrical formalism, the relationship between the components of the electric (E) and magnetic (H) field vectors at the upper and lower sides of the jth layer is governed by the characteristic matrix (Hansen, 1968):

(2)

where _j = 2d_jjcos _j/ represents the phase thickness, g_j = cos _j/_j for p polarization (electric field vector parallel to the plane of incidence, which is defined by the (x, z) plane), and g_j = _j cos _j for s polarization (electric field vector perpendicular to the plane of incidence, along the y axis).

In these terms,  is the wavelength of the incident light in vacuum, d_j is the thickness of the jth layer, and _j is the angle of refraction in layer j; _j is related to the incidence angle ₁ by Snell's law and satisfies n₁ sin ₁ = _j sin _j.

The two tangential fields at the first boundary are related to those at the final boundary by

(3)

where M is the characteristic matrix of an N phase system (i.e., N  2 layers between semi-infinite initial (j = 1) and final (j = N) phases), and U_k and V_k are the tangential components of the field amplitudes at the boundary k. U_k = E_yk and V_k = H_xk for s polarization while U_k = H_yk and V_k = E_xk for p polarization.

With the use of the components of M, the reflection coefficients of the multilayer system are expressed, for each polarization, as follows:

(4)

The polarized and unpolarized reflectances, which can be directly measured, are given by

(5)

As a result, ATR spectra for a multilayer system can be simulated considering the first phase as the denser medium (refractive index of the crystal) and knowing the complex refractive index and the thickness of each layer. It should be mentioned that the matrix method can be generalized for anisotropic layers, as shown by Yamamoto and Ishida (1994). In this case, _j must be replaced by _yj and _xj for s and p polarizations, respectively. However, the Snell's law for p polarization becomes n₁ sin ₁ = _zj sin _j.

Mean-square electric field amplitudes

Thickness- and absorption-dependent equations

(6)

1

(7)

1

j=k1

1

(8)

(9)

(10)

(11)

Approximate equations (Harrick equations)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

Determination of the optical constants of a uniaxial ultrathin film

A method for the determination of the optical constants of a uniaxial film (n_x = n_y, n_z and k_x = k_y, k_z) has recently been described (Buffeteau et al., 1997). In this method, the optical constants in the plane (n_x = n_y and k_x = k_y) of the thin film deposited onto a transparent substrate (calcium fluoride, zinc selenide, silicon ...) are determined from its transmittance spectrum at normal incidence. However, the optical constants perpendicular to the plane of the thin film (n_z and k_z) are determined from its p-polarized reflectance spectrum at grazing incidence (₁ = 85°) on a metallic substrate (IRRAS spectrum). Although this approach gives good results for ultrathin films, it requires that the molecular orientation is the same on all substrates used. In the current study, we have used a new method where the optical constants are determined directly from the s- and p-polarized ATR spectra (T. Buffeteau, unpublished results). The main advantage of this method is that all measurements are performed on the same sample.

A first estimation of the optical constants can be obtained using approximate equations of ATR spectra of ultrathin films in air (n₃ = 1). Indeed, using the thin film approximation (d ), the s-polarized ATR spectrum is given by

(19)

and the p-polarized ATR spectrum is given by

(20)

where R_s,p(d) and R_s,p(0) are the s- and p-polarized single reflection ATR spectra for the covered and uncovered crystal, respectively; n₁ is the refractive index of the ATR crystal, and  = ² is the complex dielectric constant of the film.

Equation 19 can be used to extract the imaginary part of the dielectric function _y = _x, and its real part can be calculated by Kramers-Kronig transformation of the imaginary part. Then, the initial real and imaginary parts of the dielectric function are used for calculating the s-polarized ATR spectrum and are perturbed by a Newton-Raphson method until the simulated and experimental spectra are sufficiently close to each other. Finally, the in-plane optical constants are calculated by simple arithmetical equations using the real and the imaginary parts of the dielectric function.

To calculate the optical constants perpendicular to the plane of the film from the p-polarized ATR spectrum, the imaginary part of (1/_z) is first calculated using Eq. 20 with the value of the dielectric function _y = _x obtained from the s-polarized ATR spectrum. Then, the same procedure as above is used to determine the final values of the out-of-plane optical constants.

	MATERIALS AND METHODS

Top Abstract Introduction Theory Materials and methods Results and discussion Conclusion References

Materials

The sodium salt of dimyristoylphosphatidic acid (DMPA) was obtained from Avanti Polar Lipids (Alabaster, AL) and used without further purification. The water used throughout this study was demineralized and deionized using a Barnstead NANOpurII system (Boston, MA) with four purification columns.

Sample preparation

The pH of the water used for all the experiments was adjusted to 6.5 with diluted NaOH using a microelectrode (Microelectrodes, Inc., Londonderry, NH). An aqueous dispersion of DMPA (2% wt/wt) was prepared by mixing the appropriate amount of solid in water. This dispersion was then heated to ~65°C for 10 min, stirred on a vortex mixer, and cooled down to 0°C for 10 min. This cycle was repeated at least five times to obtain multilamellar vesicles (MLV). Supported lipid bilayers were prepared by condensing small unilamellar vesicles (SUV) on the germanium ATR crystal as described previously for silica beads (Bayerl and Bloom, 1990; Picard et al., 1998). The SUV were prepared by extruding the MLV dispersion three times through a 0.1 µm polycarbonate filter (Nucleopore, Toronto, ON) at a temperature above the lipid gel-to-liquid crystalline phase transition temperature using a Lipex extruder (Vancouver, BC). The SUV were then diluted to obtain a lipid concentration of 1% (wt/wt). The lipid solution was then heated to 65°C and the ATR crystal was immersed in it for 15 min. The solution was cooled down below the lipid phase transition temperature (48°C) and the ATR crystal was pulled out and immersed twice in pure water to eliminate the excess of lipid. The single bilayers so obtained on each side of the ATR crystal were dried out with a gentle nitrogen stream.

FTIR measurements

Infrared spectra were recorded at room temperature (21°C) on a Nicolet Magna 550 (Madison, WI) Fourier transform infrared spectrometer equipped with a narrow-band mercury-cadmium-telluride detector and a germanium-coated KBr beamsplitter. A total of 1000 scans were averaged at 2 cm¹ resolution after triangular apodization. For polarization measurements, the infrared radiation was polarized with a ZnSe wire-grid polarizer (Specac, Orpington, UK).

A bilayer was deposited on the two sides of a germanium ATR plate (50 × 20 × 2 mm, 45° parallelogram, 24 reflections). Prior to the deposition, the germanium crystal was cleaned with ethanol and water and placed for 5 min in a plasma cleaner (Harrick, NY). The crystal covered with the lipid bilayers was placed in a variable angle ATR unit (Harrick, NY). To obtain hydrated bilayers, the germanium crystal was covered with a thermoregulated stainless steel recess jacket fitted with holes allowing liquid circulation above the ATR crystal. The clean and dry ATR crystal was first heated to 65°C and the SUV solution of DMPA (~1 ml) was introduced into the thermoregulated cell for 10 min. The temperature was then cooled down to room temperature for an additional 10 min. Approximately 10 ml of pure water was gently introduced into the cell to eliminate the excess of lipids and to keep the bilayers hydrated on each side of the ATR plate.

All spectral manipulations were performed with the SpectraCalc software (Galactic Industries Corp., Salem, NH). The spectra in the CH stretching mode region (3050-2750 cm¹) were first baseline-corrected using either a linear function in the case of the spectra of the dry bilayers or a quadratic function in the case of the spectra of the hydrated bilayers. The baseline corrected spectra were then interpolated with one level of zero filling to better define the band maxima. Since the CH stretching mode region is composed of several overlapping bands, the dichroic ratio of the 2850 and 2918 cm¹ bands were calculated from the height of the bands at the maximum intensity. Band-fitting of the whole CH stretching mode region did not decrease the error on the determination of the dichroic ratio.

	RESULTS AND DISCUSSION

Top Abstract Introduction Theory Materials and methods Results and discussion Conclusion References

Preparation of dry and hydrated single DMPA bilayers

The preparation of a single lipid bilayer is not straightforward. A well known method is the Langmuir-Blodgett (LB) technique because it allows control of the number and the surface density of the lipid layers. Because of the hydrophilic nature of the germanium crystal used in this study, the first DMPA monolayer was easy to transfer with the LB technique. However, the deposition of the second monolayer was not possible because the first monolayer was always retransferred back on the surface of the Langmuir trough when the covered substrates were immersed in the subphase. Other groups have reported similar redeposition problems with phospholipids (Lotta et al., 1988; Fringeli and Günthard, 1981; Hasmonay et al., 1979; Cui et al., 1990).

Fringeli et al. (1989) have proposed a method for the preparation of a supported single bilayer which consists of depositing a first monolayer by the LB method while the second monolayer is self-deposited by immersing the covered substrate in an SUV solution. Good results were obtained for DMPA using this method. Indeed, we have observed that the absorbance of the bands in the ATR spectra of a bilayer is twice that of a monolayer deposited in the liquid-condensed state by the LB technique with a transfer ratio of 1.0. Identical results were also obtained with a simpler method that has often been used for NMR measurements of phospholipid bilayers on spherical solid supports (Bayerl and Bloom, 1990; Picard et al., 1998). This technique, described in the Materials and Methods section, consists of immersing clean germanium crystals directly into an SUV solution.

Polarized attenuated total reflection of a DMPA bilayer

S and p-polarized ATR spectra of a dry and of a hydrated single DMPA bilayer deposited on each side of a germanium ATR crystal are shown in Fig. 1 for the 3050-2750 cm¹ region. Four bands can easily be distinguished: the antisymmetric CH₃ stretching band (_a(CH₃)) at 2959 cm¹, the antisymmetric CH₂ stretching band (_a(CH₂)) at 2918 cm¹, the symmetric CH₃ stretching band (_s(CH₃)) at 2870 cm¹, and the symmetric CH₂ stretching band (_s(CH₂)) at 2850 cm¹. The position of the maximum of the methylene bands clearly indicates that both the dry and hydrated films are well ordered with the acyl chains in the all-trans conformation as observed for phospholipid dispersions in the gel phase (Mendelsohn and Mantsch, 1986; Mantsch and McElhaney, 1991). The close examination of these bands reveals that they are slightly broader in the spectra of the hydrated bilayers (by ~4 and 2 cm¹ for the 2918 and 2850 cm¹, respectively), suggesting that the acyl chains of DMPA are more mobile in the hydrated film (Casal and Mantsch, 1984; Mantsch and McElhaney, 1991). The absorbance of the 2918 and 2850 cm¹ bands for both polarization states is 0.048 and 0.033 for the dry bilayers, respectively, which is twice that observed by Labrecque (1995) for a dry DMPA monolayer deposited on a germanium crystal by the LB method at a surface pressure of 20 mN/m. For the hydrated bilayers, the maximum intensity of the methylene bands is very close to that of the dry bilayer. However, the bands associated with the antisymmetric and symmetric CH₃ stretching vibrations at 2959 and 2870 cm¹, respectively, are stronger in the ATR spectrum recorded with the infrared radiation polarized in the plane of incidence, suggesting that the acyl chains are less tilted in the hydrated film.

View larger version (21K): [in this window] [in a new window]   FIGURE 1   S and p-polarized ATR spectra of (A) dry and (B) hydrated single bilayers of DMPA deposited on each side of a germanium crystal.

To determine the orientation of the acyl chain with respect to the normal to the ATR crystal, the dichroic ratio, R_ATR, was calculated from the polarized spectra of Fig. 1, using the following equation:

(21)

where A_p and A_s are the absorbances of the bands obtained with the infrared radiation polarized parallel and perpendicular to the plane of incidence, respectively. Highly reproducible dichroic ratios were obtained for four different dry and hydrated samples. For the dry bilayers, dichroic ratios of 1.00 ± 0.01 were calculated for both the 2918 and 2850 cm¹ methylene bands, while for the hydrated bilayers, dichroic ratios of 1.02 ± 0.02 and 1.00 ± 0.02 were obtained for these bands, respectively. The lower accuracy for the results obtained for the hydrated bilayers is essentially a result of the difficulty in eliminating the water contribution in the ATR spectra.

Assuming a uniaxial distribution of orientation of the acyl chains with respect to the normal to the ATR crystal (z axis), the order parameter, S_z, of the transition moment of a given vibration can be calculated from the three mean-square orthogonal electric field amplitudes, E_x,y,z², using the following equation (Fringeli and Günthard, 1981):

(22)

For acyl chains with cylindrical symmetry, the order parameter of the chain axis, P₂ (cos ), can be calculated from the order parameter of the transition moment, S_z, using the Legendre addition theorem:

(23)

where  is the angle between the acyl chain axis and the normal to the ATR crystal, and  is the angle between the transition moment and the acyl chain axis. In the case of the _a(CH₂) and _s(CH₂) vibrations,  is equal to 90° if the acyl chains are in the all-trans conformation. If the orientation distribution of the acyl chains is infinitely narrow, it is possible to calculate the tilt angle  from Eq. 23 (Lafrance et al., 1995).

Equation 22 shows clearly that it is very important to accurately know the mean-square electric field amplitudes along the x, y, and z axis to perform orientation measurements by ATR spectroscopy. Since the mean-square electric field amplitudes depend on the film thickness as well as on the refractive indexes of the ATR crystal, film, and environment, it is important to use proper values for these parameters. The refractive index of germanium is equal to 4.0 and is fairly independent of the wavelength in the infrared region (Palik, 1985). The complex refractive index of water in the infrared region has recently been accurately determined by Bertie and Lan (1996). To our knowledge, the infrared dependence of the complex refractive indexes of phospholipid bilayers have not yet been published. We have thus determined these parameters for a DMPA bilayer, as described in the following section.

Determination of the optical constants for a bilayer of DMPA

To determine the optical constants of thin films using the procedure described in the Theory section, it is first necessary to know the thickness (d) and the refractive index of the film. The value used in this study for the thickness of a bilayer of DMPA is 40 Å, as determined by x-ray crystallography (Harlos et al., 1984). In the literature, values for the real refractive index of phospholipids of 1.4 (Citra and Axelsen, 1996), 1.44 (Brauner et al., 1987), and 1.5 (Frey and Tamm, 1991) have been used. Moreover, spectroscopic ellipsometry measurements on thin films of dimyristoylphosphatidylcholine have shown that the refractive index at 3000 cm¹ is 1.46 (D. Blaudez, unpublished results). In this study we have thus used a value of 1.45 for the refractive index of DMPA. The in-plane (n_x = n_y and k_x = k_y) and out-of-plane (n_z and k_z) optical constants determined from the s- and p-polarized ATR spectra of the dry DMPA bilayers, respectively, are presented in Fig. 2 for the 3050-2750 cm¹ region. The values of the refractive index and the extinction coefficient at 2918 and 2850 cm¹ are reported in Table 1. The higher values of the in-plane extinction coefficient compared to the out-of-plane values for the methylene bands clearly confirm that the film is anisotropic and that the transition moments of the methylene stretching vibrations are rather parallel to the surface.

View larger version (23K): [in this window] [in a new window]   FIGURE 2   (A) Anisotropic refractive indexes (nx = ny and nz) and (B) extinction coefficients (kx = ky and kz) of DMPA determined from the s- and p-polarized ATR spectra of the dry single DMPA bilayers.

View this table: [in this window] [in a new window]   TABLE 1   Values of the anisotropic optical constants of a DMPA bilayer at 2918 and 2850 cm1

From the values of the extinction coefficients along the x, y, and z directions for a given absorption band, it is possible to calculate the maximum extinction coefficient, k_max, when all transition moments are oriented along the same direction and the isotropic extinction coefficient, k_iso, when the transition moments are randomly oriented, using the following equation:

(24)

The value of k_max that depends on the strength of the oscillator and the molecular density of the film is 0.652 and 0.443 at the maximum intensity of the 2918 and 2850 cm¹ bands, respectively (Table 1). A k_max of 1.07 for the 2918 cm¹ band has recently been determined by Flach et al. (1997) for a condensed monolayer film of behenic acid methyl ester (BAME) at the air-water interface. The value of k_max per methylene group being 0.053 for BAME and 0.050 DMPA suggests that the difference between the k_max for the two systems is essentially due to the difference in the number of methylene groups, and that the packing surface density of the methylene groups is essentially the same in the two systems.

Determination of the mean-square electric field amplitudes

The electric field amplitudes along the x, y, and z axes were calculated using the formalism described in the Theory section for an isotropic three-phase system. The isotropic optical constants at 2918 cm¹ of germanium, DMPA, and water used in these calculations are given in Table 2. Fig. 3 shows the effect of the film thickness, up to 2 µm, on the three calculated orthogonal mean-square electric field amplitudes in a dry DMPA bilayer, at the interface between the film and the ATR crystal (initial values), for a nonabsorbing film (k = 0) and for an absorbing film (k = 0.217). As predicted from the Harrick equations, the electric field amplitude along the z direction is much more sensitive to the film thickness than those along the x and y directions. The three electric fields change up to ~1 µm and then remain constant. For a nonabsorbing film, E_z² increases from an initial value of 0.515 to a maximum value of 2.651. However, for the same thickness range, E_x² decreases only from 1.991 to 1.954 while E_y² increases from 2.133 to 2.303. As seen in this figure, the limiting values of the electric field amplitudes are in perfect agreement with those calculated from the Harrick approximate equations for thin and thick films. However, for film thicknesses between 0 and 0.5 µm, the Harrick equations do not allow the accurate calculation of the mean-square electric fields. In addition, Figure 3 shows that for thick absorbing films, the electric field amplitudes calculated from the thickness-dependent formalism differ significantly from those calculated from the approximate Harrick equations, revealing the limitations of these equations. All initial values of the three electric field amplitudes are smaller for the absorbing film than those calculated for the nonabsorbing film.

View this table: [in this window] [in a new window]   TABLE 2   Values of the isotropic optical constants of germanium, DMPA bilayer, and water at 2918 cm1 used in the calculation of the electric field amplitudes

View larger version (23K): [in this window] [in a new window]   FIGURE 3   Effect of the film thickness on the three calculated orthogonal mean-square electric field amplitudes, Ei2, in a dry DMPA bilayer, at the interface between the film and the ATR crystal (initial values), for nonabsorbing film (k = 0) and absorbing films (k = 0.217). The open and filled squares are the values calculated using the Harrick thin and thick film equations, respectively.

The results of Figure 3 clearly show that it is important to consider both the film thickness and the extinction coefficient of the studied film to precisely determine the initial values of the three electric field amplitudes. However, it is also important to know the variation of the mean-square electric field amplitudes as a function of the depth in the film. Fig. 4 shows this variation for a 40-Å absorbing dry DMPA bilayer. As can be seen, even for an ultra-thin film, the electric field amplitudes are not constant throughout the film, E_x², E_y² and E_z² decreasing by ~2, 4, and 8%, respectively. Therefore, the error made in orientation measurements by using the initial values of the electric field amplitudes is not negligible, especially for the field along the z direction. The use of the mean values of the electric field amplitudes over the film thickness should be more appropriate. The initial and mean values of the mean-square electric field amplitudes are compared in Table 3 for an absorbing (k = 0.217) dry DMPA bilayer with a thickness of 40 Å.

View larger version (14K): [in this window] [in a new window]   FIGURE 4   Effect of the depth of penetration on the three calculated orthogonal mean-square electric field amplitudes, Ei2, in a 40 Å thick dry DMPA bilayer.

View this table: [in this window] [in a new window]   TABLE 3   Values of the mean-square electric field amplitudes at 2918 cm1, acyl chain order parameter, and tilt angle calculated with different formalisms for a dry and a hydrated bilayer of DMPA in ATR infrared spectroscopy

Finally, the mean-square electric field amplitudes for the two-phase approximation, where the film is not considered, have also been calculated and the values obtained are presented in Table 3. E_x² and E_y² have values similar to those obtained using approximate Harrick thin film equations, whereas E_z² is much stronger because the two-phase approximation does not take into account the refractive index of the film.

The mean-square electric field amplitudes along the x, y, and z directions have also been calculated for a hydrated DMPA bilayer using the different models described above for the dry film, and are presented in Table 3. As can be seen, the change of E_z² with the film thickness is drastically reduced when the DMPA bilayer is covered with water and the value of E_z² is nearly independent of the model used for the calculation of the electric fields. This effect is essentially due to the fact that the refractive index of water is very close to that of the phospholipid (Table 2).

From the values of the mean-square electric field amplitudes calculated using the different models and the experimental dichroic ratios of dry and hydrated DMPA bilayers, the order parameter, P₂ (cos ), and the average tilt angle, , of the acyl chains have been calculated using Eqs. 22 and 23, and are presented in Table 3. For the dry bilayer, the tilt angle ranges from 28 to 30°, except for the two-phase approximation that gives a tilt angle of 14°; for the hydrated bilayer, however, the tilt angle is always between 22 and 23°, no matter which model is used to calculate the electric fields.

Because the different models for the calculations of the electric fields give different results for the acyl chain tilt angle for a dry DMPA bilayer, it is important to determine which model is the best one. For that purpose, s- and p-polarized ATR spectra of a 40-Å lipid layer were simulated for different molecular tilt angles. For each spectrum simulated with a given tilt angle ("real tilt angle"), we have calculated the dichroic ratio and the associated order parameter and tilt angle ("calculated tilt angle") using the different sets of electric fields given in Table 3. Finally, the difference between the real and the calculated tilt angles has been analyzed to determine which set of electric fields gives the best results.

Effect of the acyl chain tilt angle on the dichroic ratio

To simulate the polarized ATR spectra of a thin phospholipid film, we have used a single Lorentzian band centered at 2918 cm¹ with a maximum extinction coefficient k_max = 0.652 and a width at half-height of 18 cm¹. These parameters are typical of the band due to the antisymmetric methylene stretching vibration in the DMPA spectra. For each tilt angle, , the extinction coefficients k_x, k_y, and k_z were calculated from k_max using the following equations (Fraser and MacRea, 1973), assuming that the symmetry of orientation of the acyl chains is uniaxial and that the angle between the transition moment and the chain axis, , is 90°:

(25)

(26)

The refractive indexes along the x, y, and z directions were calculated by the Kramers-Kronig transformation of the corresponding extinction coefficients, using n = 1.45. The s- and p-polarized ATR spectra were then simulated using the formalism described in the Theory section, and the dichroic ratio was determined from these spectra.

Fig. 5 shows the dependence of the dichroic ratio on the tilt angle for the 0-40° range for both the dry and hydrated films. This range of angles has been chosen since lipid acyl chains tend to orient rather vertically with respect to the ATR crystal. As can be seen in Fig. 5, the variation of the dichroic ratio with the tilt angle is more important for the hydrated film than for the dry film. This is due to the fact that in the hydrated film, E_z² is ~5 times higher than in the dry film, allowing a better sensitivity for the determination of the orientation of the acyl chains. Furthermore, the variation of the dichroic ratio for tilt angles below 15° is very small. It can thus be concluded that the ATR bands resulting from the methylene stretching vibrations are not suitable for precise orientation measurements of acyl chains with tilt angles <15°. In such a case, vibrations with transition moment parallel to the chain axis, such as the wagging progression vibrations, should be used (Brauner et al., 1987; Ahn and Franses, 1992). Fig. 5 also stresses the importance of determining the dichroic ratio with the highest possible accuracy. For DMPA, the dichroic ratio determined experimentally for the 2918 cm¹ band is 1.00 ± 0.01 for the dry film and 1.02 ± 0.02 for the hydrated film, giving tilt angles of 28 ± 2° and 23 ± 2°, respectively. Nevertheless, the results obtained for the dry film show that the chain tilt angle in the DMPA bilayers is close to the 31° value determined by x-ray diffraction on crystalline DMPA (Harlos et al., 1984).

View larger version (24K): [in this window] [in a new window]   FIGURE 5   Effect of the acyl chain tilt angle on the dichroic ratio obtained from the simulated ATR spectra of both dry and hydrated 40-Å-thick lipid bilayers for a vibration with a transition moment perpendicular to the chain axis.

Validity of the different models used to calculate the mean-square electric fields

Fig. 6 shows the correlation between the tilt angle calculated from the dichroic ratio and the real tilt angle in the 0-40° range for the different models used to calculate the mean-square electric fields for dry and hydrated 40-Å lipid films. The results presented in Fig. 6 A for the dry film indicates that the Harrick thin film equations give overestimated tilt angles, the difference between the real and calculated tilt angles increasing as the tilt angle decreases. For example, the error made by using the Harrick equations is only 2° at a tilt angle of 25°, but it is 10° for a tilt angle of 0°. As seen in Fig. 6 A, the results obtained using the initial values of the mean-square electric fields calculated using the thickness- and absorption-dependent formalism are not better than those obtained from the Harrick thin films equations. However, when the mean values of the electric fields over the film thickness (see Table 3) are used to calculate the tilt angle, the thickness- and absorption-dependent formalisms give calculated tilt angles that are in almost perfect agreement with the real ones. Finally, it is clear from Fig. 6 A that the two-phase approximation is not adequate for the determination of the chain orientation in phospholipid thin films in air.

View larger version (36K): [in this window] [in a new window]   FIGURE 6   Correlation between the "calculated" and "real" acyl chain tilt angles for (A) a dry and (B) a hydrated 40-Å-thick lipid bilayer using electric field amplitudes obtained from the Harrick thin film equations (HTF), from the thickness- and absorption-dependent formalism using initial (TAD-Initial) and mean (TAD-Mean) values, and from the two-phase approximation (TPA).

These results show unambiguously that to obtain accurate values of acyl chain tilt angles in dry lipid films, it is important to use the more complete model to calculate the electric fields, such as the thickness- and absorption-dependent one, using the mean values of the electric field over the film thickness. However, such a model is not straightforward to use routinely, and the Harrick thin film approximation provides acceptable results for very thin films (d < 40 Å) where the variation of the electric fields over the film thickness is relatively small, and for tilt angle >15°. When the lipid film is covered with water (Fig. 6 B), however, all models give reasonably good correlations between the calculated and real tilt angles. This results from the fact that for the hydrated lipid film, the mean-square electric field amplitudes are nearly independent of the model used for the calculation (see Table 3).

Factors affecting the orientation measurements

Several factors may affect the accuracy of an orientation measurement done by ATR spectroscopy. Some of them are related to physical characteristics of the studied system, such as the refractive index and the thickness of the film, and others are related to the definition of the system itself, such as the width of the orientation distribution and the symmetry of the system.

Values of the real refractive index of phospholipids between 1.4 and 1.5 have been used in the literature (Citra and Axelsen, 1996; Frey and Tamm, 1991; Brauner et al., 1987). Fig. 7 shows the effect of the refractive index on the determination of the tilt angle. For the observed dichroic ratio of the dry DMPA bilayer (R_ATR = 1.00), the tilt angle increases from 26° for n = 1.4 to 30° for n = 1.5. The effect of the refractive index on the determination of the tilt angle increases with the tilt angle. However, for tilt angles <30°, which is the case for most phospholipids, the change of the tilt angle for refractive indexes between 1.4 and 1.5 is approximately the same as that due to the experimental error on the determination of the dichroic ratio, as seen in Fig. 7.

View larger version (27K): [in this window] [in a new window]   FIGURE 7   Effect of the lipid refractive index on the dichroic ratio obtained from the simulated ATR spectra of a dry lipid bilayer for a vibration with a transition moment perpendicular to the chain axis.

It has been shown above that the film thickness is important in the calculation of electric field amplitudes. Fig. 8 shows the effect of the film thickness on the determination of the tilt angle. Calculations were done for a single monolayer (20 Å), a single bilayer (40 Å), and a 60-Å thick film. As seen in this figure, for a dichroic ratio of 1.00, increasing the film thickness by a factor of three from 20 to 60 Å results in a change of the tilt angle of only 2°. This change in the tilt angle is lower than the error because of the experimental uncertainty of the determination of the dichroic ratio. Therefore, in the case of ultra-thin films of lipids, such as monolayers or bilayers, it is not necessary to precisely determine the film thickness to determine chain tilt angles. However, for film thicknesses between 200 Å and 0.5 µm, the results of Fig. 3 clearly show that the film thickness has to be known precisely for reliable orientation measurements by ATR spectroscopy. In this case it is necessary to use the thickness- and absorption-dependent formalism to determine the mean-square electric field amplitudes.