Using Wavelets To Analyze AFM Images of Thin Films: Surface

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Using Wavelets To Analyze AFM Images of Thin Films: Surface Micelles and Supported Lipid Bilayers Matt Carmichael, Ruxandra Vidu, Alisher Maksumov,† Ahmet Palazoglu, and Pieter Stroeve* Department of Chemical Engineering and Materials Science, University of California, Davis, One Shields Avenue, Davis, California 95616 Received May 19, 2004. In Final Form: September 24, 2004 This paper presents micro- and nanoanalysis of thin films based on images obtained by atomic force microscopy (AFM). The analysis exploits the discrete wavelet transform and the resulting wavelet spectrum to study surface features. It is demonstrated that the wavelet technique can characterize micro- and nanosurface features and distinguish between similar surface structures. The use of a feature extraction method is shown. The method involves the separation of certain frequency content from the original AFM images and analyzing the data independently to gain quantitative information about the images. By using the feature extraction method, soft surfaces in water are analyzed and nanofeatures are measured. The packing of surface micelles of sodium dodecyl sulfate on a self-assembled monolayer is analyzed. The characteristics of pore formation, due to penetration of the antibacterial peptide protegrin, into a solidsupported lipid bilayer are quantified. The sizes of the pores are obtained, and it is observed that the line tension of the pores reduces the fluctuations of the lipid bilayer.

1. Introduction Among the key objectives in the analysis of organic films, one can cite the ability to observe various features on the surface, to interpret the observations, and to predict features that can be verified through observations. Surface characterization abilities are important in areas such as surfactant adsorption and pore formation but can also be extended to the characterization of inorganic thin films through defect detection and failure analysis. The search for new methods to characterize organic surfaces naturally necessitates the understanding of surface measurements at the atomic scale, which are now available through imaging techniques such as scanning probe microscopy (e.g., scanning tunneling microscopy (STM) and atomic force microscopy (AFM)). For organic surfaces, it is important to understand how films interact in the presence of certain chemicals or organic molecules such as proteins. Although the development of appropriate tools has been continuing for the past several years and there have been various methods developed, there is still considerable room for improvement. The most common tools used for characterization are based on simple statistical measures such as rootmean-square (RMS) roughness and power spectral density (PSD). RMS is a simple statistical calculation that measures the deviation of the surface profile from its mean height. Although it is simple to calculate, RMS cannot give a complete description of surface morphology because it relies only on vertical information of microscopic images and ignores spatial variations. As a result, one can have the same quantitative description of two different surfaces based on these statistical measures. PSD helps relate spatial variation, or a better term may be “spatial wavelength” (frequency information), to surface roughness by representing microscopic images based on their frequency content. PSD has many advantages over simple * To whom correspondence should be addressed. E-mail: [email protected]. Voice: (530) 752-8778. Fax: (530) 752-1031. † Current address: 777 Davis St., Suite 250, OSIsoft, San Leandro, CA 94577.

statistical measures, since it can map spatial information into frequency content and allows comparison of surface roughness based on frequency distributions. Such spectral analysis is capable of revealing spatial periodicity and amplitude of the roughness. Most surface characterization techniques utilize the Fourier transform (FT) in some form and may yield erroneous or incomplete results due to the inherent limitations of FT. FT assumes that the surface profile data are stationary and infinitely continuous. Stationarity implies that all frequency components are present within the whole profile length. However, in most cases, a microsurface profile would not be stationary. Instead, it may have discontinuities and abrupt changes. The complexity of surface data makes FT-based methods suffer from crude estimation of spectral components. As FT is localized in frequency only, it does not retain the space information. Hence, FT cannot be effectively used if locating certain features (e.g., surface damages, cracks, etc.) is a primary goal of the analysis. To overcome this drawback, a modified method, the short-time Fourier transform (STFT) can be used.1 The STFT allows the surface profile to be represented both in space and frequency, thus making spectral analysis more effective. It is achieved by using a window function of specified length that specifies a constant space and frequency resolution of the transformation. However, due to Heisenberg’s uncertainty principle, a perfect space and frequency resolution cannot be achieved simultaneously. Thus, for short windows, a good space but poor frequency, and for long windows, a good frequency but poor space resolution would be achieved.1 These deficiencies of FT and STFT are overcome in wavelet theory. Wavelets offer an effective alternative technique for spectral analysis of surface roughness, specifically for nonstationary surface measurements.2 Wavelets also provide the opportunity to study surface deposition independent of the initial surface. This (1) Strang, G.; Nguyen, T. Wavelets and Filter Banks; WellesleyCambridge Press: Wellesley, MA, 1996. (2) Maksumov, A.; Vidu, R.; Palazoglu, A.; Stroeve, P. J. Colloid Interface Sci. 2004, 272, 365.

10.1021/la048753c CCC: $27.50 © 2004 American Chemical Society Published on Web 11/25/2004

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is because wavelet subimages allow certain frequency ranges to be isolated. If a surface deposition has different frequency characteristics from the initial base layers, wavelet analysis will allow the deposition to be analyzed without the inherent masking caused by periodicities of the support layers. In this work, we present wavelet theory as an advanced tool for morphological analysis and characterization of micro- and nanostructural surfaces of organic films. A necessary mathematical background on wavelet theory is briefly introduced in section 2. Here, the emphasis is given toward shifting wavelet concepts from time-frequency to space-frequency framework. Specifically, we emphasize the applicability of wavelet tools for 2D image analysis. As case studies, we first demonstrate how wavelets can be used to characterize a micro- and nanosurface based on AFM images and make distinctions between bilayers before and after the insertion of a protein in section 3. Another case study involves the characterization of a micelle surface below and above the critical micelle concentration (cmc). All calculations are performed in the MATLAB environment using our custom codes. 2. Wavelet Theory for Image Analysis Wavelets have been applied successfully as a tool for processing signals and 2D images as well as many other areas.3,4 Wavelets can be seen as a logical extension of FT based on time-frequency or space-frequency methods. In this section, we introduce the main concepts of the wavelet theory in the space-frequency framework. More detailed information on wavelet theory can be found in the literature.1,3,5 2.1. Continuous Wavelet Transform of 1D Signals. We shall start with the definition of STFT to motivate the introduction of the wavelet transform (WT). The STFT of a continuous signal f(x) is given as

STFT(l,ω) )

∫-∞∞ f(x)w(s - l)e-jωs dx

(1)

where w is a window function. STFT is a convolution of the signal, f(x)e-jωs, with a window function, w(x). The WT is described in a similar fashion as STFT, but instead of using periodic functions that are infinite in length as the transformation kernel, it uses a waveform function, the so-called wavelet function. The WT allows a perfect resolution for both space and frequency, which is achieved by dilating and translating a finite wavelet function at different frequency ranges. In contrast, STFT uses a constant length window for all frequency ranges, and the basis functions are sine and cosine functions, which are periodic in space. The main wavelet function is referred to as the mother wavelet and is used to obtain wavelet basis functions. Since the wavelet transform is not unique, there are different types of mother wavelet functions that can be used to obtain a WT. Among the most common mother wavelet functions, one can cite the Daubechies family of wavelets (Daubn, where n stands for the number of vanishing moments) as well as the Symlet (Symn) and Coiflet (Coifn) families. For details on the specific families of wavelets, the reader is referred to the literature.1,5 The basis functions are expressed as (3) Mallat, S. IEEE Trans. Pattern Anal. Mach. Intell. 1989, 11, 674. (4) Mallat, S. Proc. IEEE 1996, 84, 604. (5) Mallat, S. A Wavelet Tour of Signal Processing; Academic Press: San Diego, CA, 1998.

ψa,b(x) )

x-b 1 ψ a x|a|

(

)

a,b ∈ R a * 0

(2)

where ψa,b(x), the mother wavelet, is a space function with finite energy and fast decay, and a and b represent the dilation and translation parameters, respectively. Then, the continuous wavelet transform (CWT) can be defined as

CWT(a,b) )

/ (x) dx ∫-∞∞ f(x)ψa,b

(3)

where * denotes the complex conjugate. Hence, with the CWT, a one-dimensional signal is decomposed into its frequency components by scaled wavelet functions. Since wavelet functions are scaled according to frequency and space, such a decomposition results in the so-called “space-frequency localization”. 2.2. Discrete Wavelet Transform of 1D Signals. The discrete wavelet transform (DWT) is a shortened version of the CWT designed to remove the redundancy in the CWT and represents a 1D signal with a limited number of wavelet decomposition levels. This is achieved by sampling the wavelet function ψa,b(x) using a dyadic scale, i.e., a ) 2j and b ) k2j where j and k are positive integers. Thus, the discrete wavelet function becomes

ψj,k(x) ) 2-j/2ψ(2-jx - k)

(4)

and

DWT(j,k) )

∫-∞∞f[x]ψj,k/ (x) dx

(5)

where f[x] now represents a discrete function. A triangular decomposition algorithm, known as the multiresolution analysis (MRA), obtains the DWT. This is an algorithm that decomposes the signal into scales with different space and frequency resolutions based on wavelets. While performing DWT, a set of low-pass and high-pass filters is used for decomposing the data into a coarse approximation and a detail information. The relation between the filters and the wavelet functions can be stated as

∑n h[k]φ(2x - k)

(6)

∑n g[k]φ(2x - k)

(7)

φ(x) ) x2

ψ(x) ) x2

where h[k] and g[k] are high-pass and low-pass filters, respectively. These filters are related to each other by5

h(k) ) (-1)kg(1 - k)

(8)

MRA is designed to give good spatial and poor frequency resolution at high frequencies and good frequency and poor spatial resolution at low frequencies. This is desirable because the high-frequency component of the signal is typically associated with signal noise, and therefore, good frequency resolution at higher scales is not necessary. As a result of DWT with the MRA algorithm, the data can be decomposed into approximation and detail coefficients at different levels, which represent the frequency content of the original signal at different scales. 2.3. DWT of 2D Images. Wavelets and MRA also allow particular frequency subbands to be isolated within an image. Here, AFM images are treated as two-dimensional signals, with x and y representing the independent

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Figure 1. Schematic of one-level, two-dimensional wavelet decomposition.

variables and z, the height of the surface, as the dependent variable. An AFM image can then be thought of as an equally spaced two-dimensional matrix with the numerical values corresponding to the height at a given position (x,y). In moving from 1D to 2D wavelet transform, the rows and columns of the matrix are treated as independent. Therefore, the 2D filters are the tensor products of their 1D counterparts and are given by6

φLL(x,y) ) φ(x) φ(y) ψHL(x,y) ) ψ(x) φ(y)

ψLH(x,y) ) φ(x) ψ(y) ψHH(x,y) ) ψ(x) ψ(y) (9)

Applying the filters to image data results in

fL(x,y) )

1

∑ g[i] f((2x + i) mod N,y)

Nl i)0

Nh-1

1

fH(x,y) )

Nl-1

∑ h[k] f((2x + k) mod N,y)

Nh k)0

(10)

for x ) 0, 1, 2, ..., (N/2) - 1 and y ) 0, 1, 2, ..., N - 1. And furthermore,

fLL(x,y) )

fLH(x,y) )

1

g[i] fL(x, (2y + i) mod N)

Nh-1

∑ h[k] fL(x, (2y + k) mod N)

Nh k)0

fHL(x,y) )

fHH(x,y) )

∑

Nl i)0

1

Nl-1

∑ g[i] fH(x,(2y + i) mod N)

Nl i)0 1

Nh-1

∑ h[k] fH(x,(2y + k) mod N)

Nh k)0

(11)

for x ) 0, 1, 2, ..., (N/2) - 1 and y ) 0, 1, 2, ..., (N/2) - 1. A schematic for a one-level decomposition of a 2D signal is shown in Figure 1. A high-pass and a low-pass filter (eqs 6 and 7) are applied to the image in the x-direction (across the rows of the matrix), and the results are downsampled by deleting every other column. This results in two images of approximately half the size of the original, one containing high-frequency components of the rows, fH, and the other containing low-frequency components, (6) Tsai, D.; Chiang, C. Image Vision Comput. 2003, 21, 413.

f(x,y) ) NJ-1

∑ k,i

Nl-1

1

fL. These two images are then each filtered down the columns using high-pass and low-pass filters and downsampling the results along the rows (deleting every other row). The resulting four images are approximately onefourth the size of the original image. These subimages are denoted by fLL(x′,y′), fLH(x′,y′), fHL(x′,y′), and fHH(x′,y′) and represent the smoothed approximation, the horizontal detail, the vertical detail, and the diagonal detail subimages, respectively. The algorithm described above represents a single-level decomposition. The process can be iterated on the smoothed approximation subimage, fLL(x′,y′), to obtain a decomposition in the next level. This results in new (j) (j) (j) subimages f (j) LL(x′,y′), f LH(x′,y′), f HL(x′,y′), and f HH(x′,y′), where j denotes the level of the decomposition and f 0LL(x′,y′) is the original image, f(x,y). The size of each image at level j is approximately (N/2j) by (N/2j). The original image can be reconstructed from the final approximation and details at each level by reversing the decomposition algorithm. The equation for reconstruction of a j-level wavelet decomposition can be shown as follows:7

J Nj-1

(J) f LL,k,i

LL φJ,k,i (x,y)

+

(j) B ψj,k,i (x,y) ∑ ∑ ∑ f B,k,i

(12)

B∈Β j)1 k,i)0

LL B where φj,k,i (x,y) and ψj,k,i (x,y) represent the (k,i)th element of the scaling and wavelet functions at level j as defined (j) (j) and f B,k,i are the (k,i)th in eq 9, respectively, f LL,k,i element of scaling and wavelet coefficients at level j as defined in eq 11, Β ) {LH, HL, HH}, and Nj ) N/2j. Figure 2 shows a schematic for a single level, twodimensional reconstruction. The approximation and details are first upsampled by adding a column of zeroes between each column, and the rows are convolved with a one-dimensional filter. A row of zeroes is then inserted between each row and the columns are again convolved with a one-dimensional filter. Perfect image reconstruction can be observed in Figure 3a,b where a generated image is shown as well as the reconstructed image after a seven-level wavelet decomposition. The algorithm uses the Symlet (Sym8) wavelet, and the number of levels depends on the image resolution (i.e., for a 512 × 512 image, 29, one can have 9 levels) and the presence of features in each level. We note that, generally, the results may depend on the choice of the wavelet function. However, in this particular application,

(7) Tsai, D.; Hsiao, B. Pattern Recognit. 2001, 34, 1285.

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Figure 2. Schematic of one-level, two-dimensional wavelet reconstruction.

Figure 3. Computer-generated image (a), perfect image reconstruction after seven-level wavelet decomposition (b), image reconstruction without the vertical component (c), and the vertical components removed from the image (d). All wavelet analysis used Sym8 wavelet.

we have found that the results are quite insensitive to the choice of the wavelet, and thus, Sym8 is used throughout the paper. The reconstruction algorithm also allows us to selectively reconstruct the image by only using subimages of particular interest in the reconstruction. An example of this is shown in Figure 3c,d where the generated image is separated into two subimages, one representing the diagonal and horizontal components of the original image and the other representing the vertical components. In reconstructing an image without the vertical lines, all of the vertical detail matrices (f (j) HL(x′,y′), j ) 1, 2, ..., 7) were replaced by matrices of zeroes. The standard reconstruction algorithm is then applied to the subimages producing Figure 3c. To reconstruct with just the vertical lines as shown in Figure 3d, the process was repeated but the original f (j) HL(x′,y′) matrices were retained and the (j) f (j) LH(x′,y′) and f HH(x′,y′) matrices were replaced with matrices of zeroes.6 Although the reconstructed images

do not have the perfect background color, it is seen from Figure 3 that the important components (vertical, horizontal, and diagonal lines) are preserved in the reconstruction and thus can be studied independently. This method can be extended to isolating certain frequencies contained in an image. An application of this is shown in the results section where detail levels with a particular frequency content are reconstructed so that part of the surface can be analyzed independently of the support structure. 3. Experiments Detailed sample preparation and experimental procedures for the preparation of adsorbed sodium dodecyl sulfate (SDS) admicelles on self-assembled monolayers (SAMs) on gold surfaces have been described previously in detail.9 In situ imaging of surfactant layers was (8) Fan, G. IEEE Trans. Circuits Syst. 2003, 50, 106.


Figure 4. Original AFM image of SDS on a SAM.

performed in a liquid cell using a NanoScope III AFM apparatus (Digital Instruments, CA). The surface structures of SDS were imaged directly by using soft contact

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mode. The soft imaging mode can be achieved by using a delicate force, which is insufficient to displace the surfactant but has sufficient force gradient and stability to resolve the surface structures.10 The procedures, materials, and solution concentrations for the preparation of supported lipid bilayers have been described by Zhang et al.10 The metal surfaces were gold films (50 nm thick) deposited onto freshly cleaved mica substrates using an electron beam evaporator. The gold film on mica was annealed at 650 °C for 30 s resulting in a stepped Au(111) surface. The samples were covered with a self-assembled monolayer of alkylthiol by immersing the gold-covered mica in a solution of alkylthiol in ethanol for at least 18 h at room temperature. The slides were then rinsed with ethanol and dried with N2 immediately prior to use. Negatively charged lipid membranes were then formed on a polyion/alkylthiol layer pair on gold, and the pore-forming activities of regular protegrin on this model membrane system were investigated. This

Figure 5. Wavelet-denoised image of SDS on a SAM (a), isolated admicelle ridges (b), and base structure (c) with corresponding PSDs.

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Figure 6. Two-dimensional PSD of admicelles.

model system includes a water-containing polyion layer and an organic SAM of an alkylthiol that serve as “cushions” to lift the lipid membrane away from the solid surface. Compared to a charged lipid bilayer deposited directly onto an alkylthiol layer, the polyion-containing system is more fluid, facilitating the interaction of a transmembrane peptide (protegrin) with the watercontaining polyion layer. 4. Results and Discussion 4.1. Admicelles of SDS on Self-Assembled Monolayers. Understanding ionic surfactant adsorption on solid-aqueous interfaces is of crucial importance in many practical applications including pharmaceuticals, cosmetics, detergency, decontamination, and oil recovery. AFM has been recently used to image surface-adsorbed surfactant structures directly in surfactant solutions, facilitating our knowledge of admicelles (e.g., surface micelles of hemicylinders, cylinders, hemispheres, or spheres) formed by ionic and nonionic surfactants on surfaces.11 Knowledge of the aggregate structure of the adsorbed surfactant layer as well as the surface excess concentration and the rates of adsorption and desorption is necessary to fully characterize the adsorption behavior which is dependent on the interaction of a soluble surfactant with surfaces of different nature and charge. Here, we present a wavelet approach for microstructural analysis of SDS admicelles on undecanethiol on gold. The annealed gold film deposited on mica presents a typical surface with large atomically flat terraces and relative high density of steps. The surface of Au covered by a SAM of undecanethiol presents the same surface (9) Levchenko, A. A.; Argo, B. P.; Vidu, R.; Talroze, R. V.; Stroeve, P. Langmuir 2002, 18, 8464. (10) Zhang, L.; Vidu, R.; Waring, A. J.; Longo, M. L.; Stroeve, P. Langmuir 2002, 18, 1318. (11) Tiberg, T.; Brinck, J.; Grant, L. Curr. Opin. Colloid Interface Sci. 2000, 4, 411.

features as the Au film when the surface is imaged on a micrometer scale, because the thiol monolayer follows the topography of the gold film surface.9 After the SAM surface is imaged, the SDS solution is exchanged into the AFM liquid cell and the system is allowed to equilibrate. Figure 4 shows an AFM image of the SDS surface micelles (admicelles) formed on the SAM for a section of a partially flat gold terrace (in water) obtained at a SDS bulk concentration of 100 mM, which is well above the critical micelle concentration (the cmc is 8.1 mM).9 The window is 295 by 295 nm. The gold terrace steps are visible as broad, light (yellow) striations running mainly diagonally from the top left to the bottom right side. Some terrace steps are also visible in the bottom left corner of the figure. The SDS hemicylinders on the SAM of undecanethiol are observed as very thin parallel stripes9 running diagonally from lower left to upper right. A blowup of a region of the surface micelles is shown in Figure 13 in Appendix A for a 66 by 66 nm window. The most striking feature of these hemicylinder stripes is that they retain a degree of parallelism across the surface steps (i.e., the stripes are not reoriented by surface steps), indicating that there are no significant interactions between surfactant aggregates and step sites. These results contrast with SDS adsorption on gold (at a concentration 2 times the cmc) where the stripes are straight and parallel, but they are oriented at angles of 30°, 90°, or 270° relative to the crystallographic faceted steps on the gold surface.12 Figure 5a shows a wavelet-denoised AFM image of the adsorbed SDS admicelles on the undecanethiol SAM interface. Next, we shall demonstrate how wavelets can be used for feature extraction that involves the separation of a certain frequency content from the original image (Figure 4) and analyzing the data independently. This allows us (12) Hayter, J. B. In Proceedings of the International School of Physics: Physics of Amphiphiles, Vesicles and Macroemulsions, Vesicles and Macroemulsions; Degiorgio, V., Ed.; Elsevier: Amsterdam, 1985; pp 59-93.


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to improve visibility of “interesting” features by isolating them from the remaining, less important, content. Figure 5a was obtained by imaging the surface in soft contact mode, as described above, and then applying a wavelet-denoising algorithm, which removes the first detail levels (high-frequency component) of the image. The first detail levels contain random noise effects that are spatially uncorrelated. The PSD of the denoised image (right panel) shows a large peak around a frequency of 0.076 Hz, which is believed to represent the distance between the SDS micelle ridges. Figure 5b illustrates the hemicylinder ridges that were isolated from the original image. It was obtained by performing two-dimensional wavelet reconstruction using only the detail levels that contained significant power at a frequency of 0.076 Hz. This can be done based on the observation that suggests that the thiol film decreases the interaction between gold and SDS.12 In this case, the detail level 2 horizontal and detail level 3 vertical and diagonal subimages were used in the reconstruction. This allows the Au/SAM base structure and noise to be removed so that the admicelles can be analyzed independent of the substrate. The PSD of the admicelles, shown on the right side of Figure 5b, shows that 77% of the original power at 0.076 Hz is captured by the reconstruction. Figure 5c shows the reconstruction of the original image with the details associated with the admicelle ridges and noise removed. It is apparent from both the image and its corresponding PSD that the admicelle ridges have been almost completely separated from the original image. As stated above, it is believed that the peak at 0.076 Hz is important because it corresponds to the peak-to-peak distance between the admicelle ridges, which is essential in characterizing the admicelle structure. From previous work, it has been estimated that the distance between the ridges is 6.0 ( 0.5 nm.9 The distance can be corroborated by the following equation that relates the PSD frequencies to the length scale:

length distance ) (f)-1 spacings

(13)

where f is the frequency in Hz, length is the total length of the image in the x-direction in nanometers, and spacings is the number of points in the x-direction. For this image, the length is 279 nm and the number of spacings is 512. Therefore, 0.076 Hz corresponds to 7.2 nm, which is on the order of the expected distance. However, the onedimensional PSDs shown in Figure 5 do not correspond to the exact distance between the hemicylinder ridges because the 1D PSD calculates the periodicity only in the x-direction and does not take into account the fact that the micelle ridges are not aligned along the x- or y-axis. This can be resolved by studying the two-dimensional PSD of the admicelle image, shown in Figure 6. As shown in Figure 6, the 2D PSD has peaks that correspond to both x- and y-directions, which allow for a more accurate determination of the distance between the ridges of the hemicylinders. The two-dimensional PSD gives distances of 7.0 and 5.8 nm in the x- and y-directions, respectively. However, these distances are also not yet correct because the image is not perfectly aligned with the ridges parallel to either the x- or y-direction. As shown in Appendix B, Figure 5a needs to be rotated by an angle θ so that one of the axes is orthogonal and the other axis is parallel to the ridges. As discussed in Appendix B, when the angle is 20.5° the minimum distance d1 between the ridges of the hemicylinders is 6.0 nm. The value of 6.0 nm for the periodicity of the surface aggregates in 100 mM

Figure 7. The original AFM images of a bilayer before (a) and after (b) protegrin adsorption.

SDS is comparable to the micellar diameter in solution of 5.1 nm measured by small-angle neutron scattering in a 100 mM SDS solution.13 Curiously the value of d2 at θ equal to 20.5° does not vanish but is 4.0 nm. The 4.0 nm represents a periodicity along the hemicylindrical ridges and is clearly visible in Figure 13. This is an unexpected result that will need more study. We think the periodicity may be due to how the surfactant needs to pack into the hemicylinder. 4.2. Protegrin Insertion in Supported Lipid Bilayers. Structural aspects of protein and peptide assemblies in a membrane are a major challenge in structural biology. In situ AFM observation in an aqueous environment remains a powerful surface characterization technique, but feature extraction techniques used in image processing, such as that offered by wavelets, are necessary for a better understanding of the mechanism of protegrin insertion into a lipid bilayer. Of particular interest are defects such as holes or pores formed during the assembly process or formed as a result of protein adsorption to the assembled membrane. Such defects can be advantageous (such as in the deliberate formation of ion channels) or disadvantageous when one desires an electrically sealed system. Solid-supported lipid bilayers have been used extensively as models of biological membranes.14-22 These (13) Hu, K.; Bard, A. J. Langmuir 1997, 13, 5418. (14) Sackmann, E. Science 1996, 271, 43. (15) Stelzle, M.; Weissmuller, G.; Sackmann, E. J. Phys. Chem. 1993, 97, 2974. (16) Majewski, J.; Wong, J. Y.; Park, C. K.; Seitz, M.; Israelachvili, J. N.; Smith, G. S. Biophys. J. 1998, 75, 2363. (17) Sohling, U.; Schouten, A. J. Langmuir 1996, 12, 3912.

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Figure 8. Wavelet-denoised images (left) and PSDs (right) of lipid bilayer before (a, top) and after (b, bottom) protegrin insertion.

model membranes have been used to determine the molecular function and mechanisms of membrane-bound molecules, such as molecule recognition, ion sensing, channel formation, antigen-antibody binding, and energy conversion.23-27 Unlike conventional model membranes, such as spherical liposomes and black lipid membranes, the supported membranes allow the application of various powerful surface techniques such as surface plasmon resonance and atomic force microscopy.20,21,28-30 In a previous study, we conducted in situ atomic force microscopy studies of the insertion of an antibacterial peptide into mobile, supported phospholipid bilayers on a polyion/alkylthiol layer pair.10 The ion-channel-forming peptide used in this study, protegrin-1, is an 18 amino (18) Salafsky, J.; Groves, J. T.; Boxer, S. G. Biochemistry 1996, 35, 14773-14781. (19) Kalb, E.; Tamm, L. K. Thin Solid Films 1992, 210/211, 763765. (20) Knoll, W.; Frank, C. W.; Heibel, C.; Naumann, R.; Offenhausser, A.; Ruhe, J.; Schmitt, E. K.; Shen, W. W.; Sinner, A. Rev. Mol. Biotech. 2000, 74, 137. (21) Cheng, Y.; Ogier, S. D.; Bushby, R. J.; Evans, S. D. Rev. Mol. Biotech. 2000, 74, 159. (22) Schouten, S.; Stroeve, P.; Longo, M. L. Langmuir 1999, 15, 8133. (23) Ottova, A. L.; Tien, H. T. Bioelectrochem. Bioenerg. 1997, 42, 141. (24) Asaka, K.; Ottova, A.; Tien, H. T. Thin Solid Films 1991, 354, 201. (25) Ottova, A.; Tvarozek, V.; Racek, J.; Sabo, J.; Ziegler, W.; Hianik, T.; Tien, H. T. Supramol. Sci. 1997, 4, 101. (26) Asaka, K.; Tien, H. T.; Ottova, A. J. Biochem. Biophys. Methods 1999, 40, 27. (27) Tien, H. T.; Wurster, S. H.; Ottova, A. L. Bioelectrochem. Bioenerg. 1997, 42, 77. (28) Lingler, S.; Rubinstein, I.; Knoll, W.; Offenhausser, A. Langmuir 1997, 13, 7085. (29) Zhang, L.; Longo, M. L.; Stroeve, P. Langmuir 2000, 16, 5093. (30) Zhang, L.; Booth, C. A.; Stroeve, P. J. Colloid Interface Sci. 2000, 229, 82.

acid cationic peptide first isolated from porcine leukocytes.10,31-33 It is active against a broad range of microorganisms, yet does not harm many types of host cells significantly at peptide concentrations that destroy microorganisms.32 In vitro, protegrin-1 kills various bacteria, such as Escherichia coli.31,33 It is also active against fungi and HIV virus infection.34 Like other antimicrobial peptides, protegrin-1 inserts into the microbial lipid membrane, changes membrane permeability, and impairs internal homeostasis.34-38 Cysteines in protegrin form disulfide bonds, holding the peptide in a structure resembling a hairpin. Positively charged arginine residues are present at both ends of the hairpin-like molecule, while hydrophobic and uncharged amino acids form the remainder of its structure. Protegrin-1’s reported preference for negatively charged bacterial cell membranes over host cell membranes31,39,40 makes it a good candidate to insert (31) Vidu, R.; Zhang, L.; Waring, A. J.; Longo, M. L.; Stroeve, P. Mater. Sci. Eng. 2002, B96, 199. (32) Heller, W. T.; Waring, A. J.; Lehrer, R. I.; Huang, H. W. Biochemistry 1998, 37, 17331. (33) Heller, W. T.; Waring, A. J.; Lehrer, R. I.; Harroun, T. A.; Weiss, T. M.; Yang, L.; Huang, H. W. Biochemistry 2000, 39, 139. (34) Kokryakov, V. N.; Harwig, S. S. L.; Panyutich, E. A.; Shevchenko, A. A.; Aleshina, G. M.; Shamova, O. V.; Korneva, H. A.; Lehrer, R. I. FEBS Lett. 1993, 327, 231. (35) Tamanura, H.; Murakami, T.; Horiuchi, S.; Sugihara, K.; Otaka, A.; Takada, W.; Ibuka, T.; Waki, M.; Yamamoto, N.; Fujii, N. Chem. Pharm. Bull. 1995, 43, 853. (36) Waring, A. J.; Harwig, S. S. L.; Lehrer, R. I. Protein Pept. Lett. 1996, 3, 177. (37) Kagan, B. L.; Selsted, M. E.; Ganz, T.; Lehrer, R. I. Proc. Natl. Acad. Sci. U.S.A. 1990, 8, 210. (38) Cociancich, S.; Ghazi, A.; Hetru, C.; Hoffmann, J. A.; Letellier, L. J. Biol. Chem. 1993, 268, 19239. (39) Mangoni, M. E.; Aumelas, A.; Charnet, P.; Roumestand, C.; Chiche, L.; Despaux, E.; Grassy, G.; Calas, B.; Chavanieu, A. FEBS Lett. 1996, 383, 93.


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Figure 9. Level 3 approximation of the bilayer before protegrin insertion (a, top) and after protegrin insertion (b, bottom).

into the supported anionic lipid membrane.10 The formation of holes (pores) by protegrin was observed by AFM, which explained the electrochemical behavior of protegrin association with anionic supported lipid bilayers. One goal of analyzing AFM data of protegrin insertion into a supported lipid bilayer is to try to understand the mechanism by which protegrin inserts into a lipid bilayer and causes holes. Here, we present the application of wavelet analysis to AFM images of supported, mobile, phospholipid bilayers on polyion/alkylthiol layer pairs to characterize the size and shape of the holes formed by protegrin insertion in the bilayer. Figures 7 and 8 present the original and the waveletdenoised AFM images, respectively, in an aqueous solution of a bilayer before and after protegrin adsorption. Protegrin insertion causes large undulations (holes) in the bilayer.10 The one-dimensional PSD for the bilayer after protegrin insertion shows a large peak at 0.0078 Hz. This corresponds to 44 nm, but as stated before, this is only in the x-direction and does not give an accurate distance, merely a general idea of the distances being dealt with. A distance of 44 nm is not unreasonable. The mechanism for protegrin insertion is not well understood, but it is believed that the peptides insert into a bilayer in a method similar to that shown in ref 41 in their Figure 3. It takes a number of protegrin molecules to create a hole of a certain size. The estimated width of an individual protegrin molecule is 0.8 nm, while the length is approximately 3 nm.40 The hole size of 44 nm could represent a depression formed by (40) Fahrner, R. L.; Dieckmann, T.; Harwig, S. S. L.; Lehrer, R. I.; Eisenberg, D.; Feigon, J. Chem. Biol. 1996, 3, 543. (41) Yang, L.; Weiss, T. M.; Lehrer, R. I.; Huang, H. W. Biophys. J. 2000, 79, 2002.

the peptides with a diameter of about 55 protegrin molecules. In Figure 8b, there do not appear to be domains or repeating patterns on the order of 40 nm, especially patterns in the x-direction, as would be expected from the one-dimensional analysis. Considering the approximation and detail levels of the pre- and post-protegrin-insertion images, we can make further observations about the bilayers. First, the waveletdenoised image of the preinsertion bilayer (Figure 8a) has more power in the higher frequencies. The postinsertion image (Figure 8b) has almost no power above 0.1 Hz, while the preinsertion image has some power, although the magnitude is small. These higher frequencies could be associated with signal noise, so it may be assumed that the preinsertion images have more noise associated with their measurement, but this may not necessarily be the case since a (linear) denoising algorithm has already been applied and the high frequencies in the preinsertion image may be due to the headgroups of the molecules in the bilayer. More information can be obtained by studying the level 3 approximations of the two images. Figure 9 shows that the level 3 approximation and wavelet-denoised images in Figure 8 for the postinsertion are much more similar to each other than the preinsertion images. This is because the higher frequencies are removed in detail levels 1 and 2. The preinsertion image contains a much greater amount of high-frequency content and therefore changes more between the original and the level 3 approximation, compared to the postinsertion image. This is shown in Figure 10 for the level 3 details (horizontal, vertical, and diagonal) of both images, where the detail images of the preinsertion images show significant power but the

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Figure 10. Horizontal, vertical, and diagonal details at level 3 before (a, left) and after (b, right) insertion of protegrin.

postinsertion images show almost no power in the given frequency range. From this, we can conclude that for the low-frequency levels, the postinsertion surface is rougher (higher power) probably due to the presence of holes, while for the highfrequency levels, the preinsertion surface shows more variation. The data suggest that, on the nanometer scale, the surface of the preinsertion lipid bilayer is rougher than the surface of a comparable region of lipid bilayer (i.e., a region without holes) for postinsertion. To further explore the lipid membrane fluctuations, we first need to obtain information on the holes created by the peptide. Next, we will attempt to isolate the holes in the supported bilayer, assuming these correspond to the peak at 0.0078 Hz, in the same manner that the micelle ridges were isolated in the previous section. The resulting images are shown in Figure 11 along with the PSDs of the original, base structure, and isolated holes. The isolation of the

holes (Figure 11, middle) maintains 63% of the original power at 0.0078 Hz of the original image (Figure 11, top). However, the new image also does not appear to show any periodicity occurring with a repeating distance of 44 nm. The two-dimensional PSD yields more plausible distances. Figure 12 shows the two-dimensional PSD of the protegrin image that yields distances of 22 and 11 nm in both x- and y-directions. These distances for sizes of the holes seem reasonable and are supported by the images of the holes. These distances correspond to the presence of approximately 28 and 14 protegrin molecules, respectively, in each hole.41 It seems reasonable to assume that the holes are round because the same distances are found in both x- and y-directions. It is important to understand how the insertion of the protegrin protein affects the bilayer region adjacent to the holes. Intuitively, one might expect the roughness of the surface to increase after insertion due to the head-


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Figure 11. Wavelet images (right) and PSDs (left) of original (top), isolated holes (middle), and base structure (bottom).

groups being compressed together after the insertion of the protegrin molecules. However, this does not appear to be the case, as shown in Table 1. Measuring the RMS roughness of the original images of two surfaces yields roughness values of 0.0044 and 0.0055 nm for the preand postinsertion surfaces, respectively. It appears that the surface is rougher after the protegrin molecules are inserted. However, by looking at the base structure of the surface after protegrin insertion (Figure 11), but with the holes removed, the roughness drops significantly to 0.0034 nm; while performing the same filtering on the preinsertion surface, the RMS roughness does not change significantly. The results lead us to conclude that although protegrin causes large holes, the lipid bilayer region away from the holes is smoother. The presence of a hole or pore in a bilayer leads to an increase in the surface tension of the curved edge of the lipid bilayer at the periphery of the hole,42-44 and consequently, the higher surface tension (42) May, S. Eur. Phys. J. E 2000, 3, 37.

pulls on the rest of the bilayer reducing the lipid bilayer fluctuations.45 Our conclusion is supported by the data in Figures 9 and 10. 5. Conclusions Wavelet analysis has been successfully applied in the characterization of two organic soft surfaces. The application of selective reconstruction of the images after wavelet decomposition allows us to isolate important patterns and analyze the images independently of the underlying base structure. Using this feature extraction method, hemicylinders of SDS surfactant on SAMs of thiols on gold were analyzed and the ridge distances between the aggregates were found to be 6.0 nm. Further, holes (43) Chernomordik, L. V.; Kozlov, M. M.; Melikyan, G. B.; Markin, V. S.; Chizmadzhev, Y. A. Biochim. Biophys. Acta 1985, 812, 643. (44) Fosnaric, M.; Kralj-Iglic, V.; Bohinc, K.; Iglic, A.; May, S. J. Phys. Chem. B 2003, 107, 12519. (45) Hategan, A.; Law, R.; Kahn, S.; Discher, D. E. Biophys. J. 2003, 85, 2746.

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Figure 12. Two-dimensional PSD of the postinsertion protegrin image. Table 1. RMS Roughness Results after Wavelet Denoising

RMS roughness of original image (nm) RMS roughness of base structure (nm)

before protegrin insertion

after protegrin insertion

0.0044 0.0042

0.0055 0.0034

in supported lipid bilayers due to polypeptide insertion were found to be 11 and 22 nm in diameter. The presence of holes causes the reduction of lipid bilayer fluctuations due to the line tension caused by the holes in the lipid bilayer. Wavelet analysis can be a powerful technique for analysis of surface images in that it can be used to perform quantitative analysis of features identified by frequency analysis of the images. Appendix A

Figure 14. Schematic for distance calculation.

rotated so that the ridges are parallel to either the x- or the y-direction. The schematic in Figure 14 illustrates the rotation of the image. In Figure 14, d1 and d2 are the actual distances of interest and y and x are the known quantities. To determine d1 or d2, the image must be rotated by an angle θ, which is to be determined. The equations for calculating d1 or d2 for a given value of θ and known values of x and y are

d1 )

y1 sin(θ)

d2 )

y2 sin(90 - θ)

(B1)

y1 ) y - y 2

(B2)

where

Figure 13. Magnification of hemicylindrical SDS surface micelles on a SAM on gold. The image is obtained in water with the SDS bulk concentration equal to 100 mM.

Appendix B To obtain the peak-to-peak distance between the ridges of the hemicylinders in Figure 5a, the image needs to be

y2 )

x tan(θ) - y tan2(θ) - 1

To determine the angle θ for rotating the image, the above equations are iterated over θ until d1 is minimized. In this case, the values of d1 and θ are 6.0 nm and 20.5° and the x-axis is orthogonal to the ridges of the admicelles. LA048753C

Using Wavelets To Analyze AFM Images of Thin Films: Surface

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