Single-molecule Stretching Method For Lateral And Normal AFM Levers Calibration

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1 Single-molecule Stretching Method For Lateral And Normal AFM Levers Calibration Maciej Dendzik 1,, Andrzej Kulik, Fabrizio Benedetti, Piotr E. Marszalek 3 and Giovanni Dietler 1 Centre for Nanometer-Scale Science and Advanced Materials (NANOSAM), Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, Kraków, Poland Laboratoire de Physique de la Matière Vivante, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH Lausanne, Switzerland 3 Department of Mechanical Engineering and Materials Science, Center for Biologically Inspired Materials and Material Systems, Duke University, Durham NC 7708, USA andrzej.kulik@epfl.ch Abstract A novel method for quantitative eral force measurements (LFM) calibration has been developed. Using a single-molecule spectroscopy approach it is possible to calibrate the AFM levers for both eral and al spring constant with a single image scan. Moreover, our method does not involve tip modifications. Dextran molecules were chosen for testing our calibration procedure due to their characteristic peau feature in the force-elongation curve that enables an easy identification of single-molecule stretching events. Using a non-standard (tilted) geometry of AFM scanning, it is possible to observe different components of the stretching force on both al and eral force signals. These signals can be further compared to the values obtained by standard (al) spectroscopic measurements. The values of the al spring constant obtained with our method are in good agreement with the results obtained from the method exploiting the energy equipartition theorem. The statistical analysis shows that the approach proposed in our paper gives reproducible results of the eral sensitivity with a reive standard deviation less than 15%. 1. Introduction Atomic force microscopy (AFM) [1] is an invaluable tool in nano-physical and biological studies due to its ability to measure ultralow forces. Typically, vertical deflections of the AFM cantilever are measured and converted into al forces. In addition, twisting of the cantilever can be measured to determine eral forces (LFM) [], which for example, may be reed to friction. Friction on the nanoscale plays a crucial role in the design of nanoelectromechanical systems (NEMS) [3] and is therefore a subject of extensive research. LFM measurements on self-assembled monolayers (SAMs) are also of significance [4]. 1

2 Lateral force measurements are particularly appealing in biological research. For example, microbial cells are often exposed to shear force fields in their natural environment, which can be emued in LFM measurements. The ability to work in physiological and aqueous environments enables LFM experiments under nearly in vivo conditions [5-7]. However, quantitative LFM measurements are still difficult [8, 9] due to the lack of reliable and simple procedures for calibration of the eral spring constant of the AFM cantilever. The available methods of calibration have different drawbacks. Theoretical calcuions based on the shape of the cantilever require that the geometrical dimensions of the cantilever, which are difficult to obtain, to be precisely known. Some of the calibration methods require specialized equipment and are rather difficult to perform [10-17]. Currently the most promising method seems to be wedge approach [8] and it s er improvements [10]. The base of those methods is scanning a wedged surface of known tilt. By comparison of topography and eral signals the eral sensitivity is estimated. Lateral signal obtained while using wedge calibration seems to be very noisy and proper data analysis requires application of specialized algorithms. Our method is based on a completely different idea of making spectroscopic stretching of single molecules. This approach does not require any other specialized specimen, is easy to use and in some applications calibration could be done on the same, measured sample. Several articles [18] stress that a simple eral force AFM calibration procedure, which would be widely accepted, is warranted. This work attempts to reach this goal, and thus alleviates the limitations of the current methods. The main idea of our method involves performing single molecule spectroscopic eral force measurements and compare them with al spectroscopic data on the same molecular system. Due to very robust force spectrograms and ease of sample preparation, a polysaccharide dextran was chosen for our measurements. However, in principle, any sticky surface could be used for calibration of eral forces. Apart from its calibration application, this work also shows that it is possible to make single molecule stretching measurements with LFM, which could be of value in molecular recognition studies [19].. Materials and methods AFM calibration was conducted using dextran molecules (100kDa, Sigma) adsorbed to glass. The glass cover slips were treated with air plasma (Harrick Plasma cleaner PDC-3G) with a pressure of 1000 mtorr. The treatment was carried out using the lowest available power on our plasma cleaner for five minutes. Immediately after the plasma treatment, we deposited 45 µl of 5 % w/w of dextran water solution on the cover slip. The sample was allowed to dry. After ca. 0 hours, samples were heavily rinsed using approximately 00 ml of ultrapure water and blown dry with air. The AFM pulling measurements were made in distilled water.

3 The calibration procedure was performed on the Park AFM (XE-10) with two types of Olympus triangular cantilevers (TR400PSA) having a theoretical spring constant of k1 [ N / m] k [ N m] = and = 8 /, respectively. The tilt scans were made using the software parameter slope, which enabled us to control the tilt angle β in the range from.5 to.5. The Z feedback parameter was set to zero during scanning. The set point and the scanning size were adjusted in order to observe the moment when the tip detaches from the surface (trace) or enters into contact with the surface (retrace) (see Figure 1) with typical values of scan size of 1µ m and load force set point 1 nn. Scanning was conducted at a eral speed in the range of 0.7 µm / s. The obtained results were independent of the scanning speed for that regime. Figure 1. Schematic representation of the AFM tilted scanning with rectangular cantilever. First the lever is scanned from the right to the left on a sloped trajectory (trace) and then from left to right following the same path (retrace). Using this simple procedure we were able to capture force spectrograms of single dextran molecules. The force-extension curves of dextran display a characteristic and distinct change of the slope at a force of approximately 700 pn [0], which is interpreted in terms of a forced conformational transition of the glucose monomers from their chair-like to a boat-like structure [1]. This transition at 700 pn is independent of the pulling speed [0, ]. This characteristic behavior is exploited here in the tilted molecular stretching measurements (see Figure (a-b)). The eral and al components of the pulling force were measured on the eral and vertical signal channel, respectively. The β angle could be accurately calcued from z detector signal data. 3

4 Figure. (a) Schematic of the AFM molecular stretching. (b) Schematic of the AFM tilted stretching used during measurements on Dextran. In this way we were able to observe simultaneously both components of the known force and calibrate both eral and al sensitivity. Moreover, as long as the al sensitivity is known, one can estimate eral sensitivity from the geometrical reions of both components. Tilt scanning may not be available in older microscopes, however it could be replaced using a tilted specimen. 3. Results and discussion Our al force spectroscopy AFM measurements of dextran showed the characteristic peau feature in the force-extension curve starting at the force Fstart 837(5) [ pn ] 1047 ( 38)[ pn ] Fstop 4 = and ending at the force = (see Figure 3 (a)). The beginning and end points of the peau were found as the inflection points of the force curve and were averaged over 10 measurements. For better accuracy of finding the peau feature, the numerical derivative was calcued from spectroscopy data using the Savitsky-Golay method. With the same AFM setup, laser alignment, and feedback turned off, the slope scanning was then performed. We were able to observe both eral and al components of the force on the eral and vertical signals. From Figure b) we can see that: F = F cos β (1) eral F = F sin β () al In the regime of small deflections of the cantilever we can assume Hooke s law and the linear response of the photodiode to cantilever s motion which, for both components, gives us: Fal, eral = kαs (3) Where α is photo detector sensitivity of units [ α ] = m / V, k the spring constant, and S the signal in [ S] = V. From the obtained data we were able to identify the characteristic peau feature. The angle β was calcued from z detector displacement data in the proper regime (see Figure 3 (d)). Slope parameter

5 of the fitted line corresponds to tanβ. Typically, for the range of distance ~100 nm it is possible to obtain excellent linear fit to z detector displacement data (Pearson s r better than 0.999). This approach results in estimation of tanβ with a reive standard deviation smaller than 1%. a).0 Dextran's spectroscopy b) 1.0 Force (nn) Vertical Signal (V) Contact@x=303 nm Peau@x=35 nm d) Z detector displacement (nm) Extension (nm) x=60 nm x=380 nm The force peau was not always observed in eral force measurements. However, this is not necessary for the LFM calibration as we are observing the components of the same force (as in (1) 5 c) Lateral force Signal (V) Contact@x=303 nm Peau@x=35 nm Figure 3. (a) Dextran s vertical spectroscopy. (b) Vertical signal channel during slope scanning with AFM. Distance refer to scanner movement in the fast-scan direction. (c) Lateral force signal channel during slope scanning with AFM. The curves (b) and (c) are recorded simultaneously. One can see that both vertical and eral signals are exactly correed. (d) z detector displacement refers to scanner movement in the direction perpendicular to the scanning plane. The fitted line on the relevant range (between 60 nm and 380 nm) was used to calcue the angle β. For each scanning line, the end of the peau was measured in the same manner as in classical, vertical spectroscopic measurements. The corresponding z detector displacement data were used to measure the angle. In this way we were able to calibrate both al and eral AFM cantilever deflections. The averaged value obtained (30 measurements) of the al spring constant was in good agreement with the value obtained from the energy equipartition theorem [3]. The starting and ending points of the force peau of both al and eral force curves were at the same positions (indicated on Figure 3 (b) and Figure 3 (c)). This result shows that we were truly observing both al and eral components of the stretching force of dextran molecules.

6 and ()). If the AFM is calibrated for al force measurement, we can take the ratio of both al and eral component and use it for the LFM calibration: S kα = kα ctgβ [ V / N ] (4) S The same data can be extracted from experiments using the pull-off events between the tip and any kind of adhesive substrates. In particular, for some applications LFM calibrations can be done on the measured sample which would reduce the risk of contamination of the sample. As shown in the Figure 4, there is a distinct event visible only on the retraction curve on both eral and al signals, clearly correed. This event shows us the response of the detector due to stretching of a dextran s molecule. The minimum of the signal is at the same position both for the eral and the al signal. One can take those minimum values of the signal for calcuing the ratio S / S to avoid searching for the end of the peau and this will easily automatize the calcuions. a) 6-0. b) 1.0 S (V) x=31.3 nm Trace Retrace S (V) x=31.3 nm Trace Retrace Figure 4. (a) Trace and retrace of the vertical signal channel during slope scanning. (b) Trace and retrace of the same scan line as in (a) for eral signal channel during slope scanning. ( Si3N 4 triangular cantilever with [ N m] k = 138(01) / ). From only one or two AFM images (51x51) taken in the slope mode it is possible to obtain more than 150 curves showing the expected behavior. Typical eral AFM image, together with crosssections along marked lines, is presented in the Figure 5 (a-b). The distribution of 173 ratios S / S for Si 3 N 4 triangular cantilever with spring constant [ N m] k = 534(0) / is shown in Figure 6. This statistical analysis gave us S / S = 3.8(0.6) with the reive standard deviation amounting to 8%. Analogical analysis of the results obtained with 3 4 Si N triangular cantilever with k 138(01) [ N / m] significant difference in distribution character and standard deviation. = shows no 6

7 b).0 Lateral force Signal (V) A B C Figure 5. (a) Lateral AFM image with three different lines denoted as A, B and C. (b) Cross-sections of (a) along lines A, B and C. Figure 6. Histogram of the ratio al-eral signal for 173 results. S / S = 3.8(0.6). The distribution of S / S seems to be al, so the usage of average as the expected value estimator is justified. Most of the obtained sets of data, when standardized, fulfills the standard statistical tests (Anderson-Darling, Kolmogorov-Smirnov, D'Agostino-Pearson) at the 5% significance level. The analysis using quantile-quantile plot (Figure 7) also confirms this hypothesis. 7

8 Figure 7. Quantile- quantile plot for 157 standardized S /S results. Red dashed line shows standard al quantiles. Figure 7 clearly shows the linear character of q-q plot, especially in the range [ 1;1 ] of standard al quantiles. Deviation from linearity outside this range are due to data processing. By a careful choice of the data selection criteria, those deviations can be even further minimized. Proposed method enables finding only the product of eral spring constant and eral photo detector sensitivity ( k α ) instead of both of those values independently. This, however, does not limit the usage of our method as long as the calibration and measurements are performed at the same equipment. From equation (4) one can derive the combined standard uncertainty formula: ( k ) k ( S / S ) α α ctgβ = kα k α S / S ctgβ The uncertainties connected with al photo detector sensitivity as well as uncertainty of ctgβ are marginal and does not contribute significantly to the combined uncertainty. We assume that reive uncertainty connected with this contribution is no greater than 5%. With uncertainty of al spring constant k and uncertainty of signals ratio S / S both at the level of 10% we estimate the overall uncertainty of eral calibration as less than 15%. (5) 4. Conclusions In summary, this paper shows an easy and fast method of calibrating AFM levers for eral force measurements with an accuracy better than 15%. This idea of calibration is completely different 8

9 than previous attempts and proves that molecular spectroscopic measurements can be taken using LFM mode, which in some applications may be desired. The presented method does not require using any additional devices or modification of the tip. The statistical analysis shows that calibration measurements are very reproducible, with small standard deviation. Single scan should deliver sufficient amount of information to calibrate LFM properly. Acknowledgements PEM is supported by the National Science Foundation grant MCB References [1] Binnig G, Quate C F and Gerber C 1986 Phys. Rev. Lett [] Mate M C, McClelland G M, Erlandsson R and Chiang S 1987 Phys. Rev. Lett [3] Singh R A, Satyanarayana N, Kustandi T S and Sinha S K 011 J. Phys. D-Appl. Phys. 44 [4] Sasaki K, Koike Y, Azehara H, Hokari H and Fujihira M 1998 Applied Physics A: Materials Science & Processing [5] Han L, Dean D, Ortiz C and Grodzinsky A J 007 Biophysical Journal [6] Lekka M, Kulik A J, Jeney S, Raczkowska J, Lekki J, Budkowski A and Forro L 005 Journal of Chemical Physics 13 [7] Sotres J, Barrantes A and Arnebrant T 011 Langmuir [8] Ogletree D F, Carpick R W and Salmeron M 1996 Rev. Sci. Instrum [9] Neumeister J and Ducker W 1994 Rev. Sci. Instrum [10] Varenberg M, Etsion I and Halperin G 003 Rev. Sci. Instrum [11] Tocha E, Song J, Schonherr H and Vancso G J 007 Langmuir [1] Tocha E, Schonherr H and Vancso G 006 Langmuir [13] Stiernstedt J, Rutland M W and Attard P 005 Rev. Sci. Instrum [14] Ruan J A and Bhushan B 1994 Journal of Tribology [15] Carpick R and Salmeron M 1997 Chem. Rev [16] Cannara R J, Eglin M and Carpick R W 006 Rev. Sci. Instrum. 77 [17] Asay D B and Kim S H 006 Rev. Sci. Instrum [18] Wright C J and Armstrong I 006 Surf. Interface Anal [19] Papastavrou G and Akari S 1999 Nanotechnology [0] Rief M, Oesterhelt F, Heymann B and Gaub H E 1997 Science [1] Marszalek P E, Oberhauser A F, Pang Y P and Fernandez J M 1998 Nature [] Rief M, Fernandez J M and Gaub H E 1998 Phys. Rev. Lett [3] Florin E L, Rief M, Lehmann H, Ludwig M, Dornmair C, Moy V T and Gaub H E 1995 Biosens. Bioelectron