NANO LETTERS
Surface Imaging by Self-Propelled Nanoscale Probes
2002 Vol. 2, No. 2 113-116
Henry Hess,† John Clemmens,† Jonathon Howard,‡,§ and Viola Vogel*,† Department of Bioengineering and Department of Physiology and Biophysics, UniVersity of Washington, Seattle, Washington 98195 Received October 16, 2001; Revised Manuscript Received November 19, 2001
ABSTRACT A new approach to image microscopic surface properties is introduced. Information about surface properties such as topography is obtained by repeated acquisition of an optical signal from a large number of microscopic, self-propelled probes moving on random paths across a surface. These self-propelled probes sample the surface in a statistical process in contrast to the deterministic, linear sampling performed by a scanning probe microscope. This method is experimentally demonstrated using microtubules as probes, which are moved by the motor protein kinesin.
The development of scanning probe techniques by Binnig et al. revolutionized the imaging of surface properties. Starting with scanning tunneling microscopy (STM)1 a multitude of related scanning techniques have since been introduced. Atomic force microscopy (AFM)2 was proven to be especially versatile in probing different surface properties, such as topography, tribology, or chemistry. In AFM, a cantilevered tip is scanned across a surface, whereby the interaction of the surface with the tip causes a displacement in the z-direction or a tilt of the cantilever, which is detected by optical means. The acquisition time is drastically reduced if a large number of probes are employed in parallel, and consequently probes with multiple cantilevered tips have been constructed.3 However, a user-controlled and predetermined movement of the tips characterizes all these techniques. An alternative approach is to replace the tip of a macroscopic cantilever with an autonomous, self-propelled probe “robot” of microscopic dimensions, which moves across the surface in a random path. We can then derive information about the surface simply by tracking the robot, provided that its position can be detected accurately and that its path or the detected signal is sensitive to surface properties. By following a large number of probe robots simultaneously, the acquisition speed can be drastically increased. Conceptually this procedure is similar to mathematical Monte Carlo techniques utilizing random sampling to calculate, for instance, definite integrals.4 * Corresponding author: Department of Bioengineering, University of Washington, Box 352125, Seattle, WA 98195. Fax: (206) 685-4434. E-mail:
[email protected]. † Department of Bioengineering. ‡ Department of Physiology and Biophysics. § Present address: Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany. 10.1021/nl015647b CCC: $22.00 Published on Web 12/14/2001
© 2002 American Chemical Society
Several advantages of the proposed method may be pointed out. The large number of probes increases fault tolerance, since the defect of many probes only reduces the acquisition speed. The absence of a physical connection between probes and detection devices would allow the probes to explore internal surfaces provided the signal and position of the probes can still be detected. Finally, a mixture of different types of probes could detect different surface properties simultaneously. Limitations arise from the underlying assumption of ergodicity for the probe paths, ensuring that equally accessible spots are visited with equal probability and requiring sufficient equilibration of the initial probe distribution. Here we experimentally demonstrate the feasibility of this statistical approach to surface imaging using a particular probe robot and a suitable detection method. The proposed probe robots are fluorescent microtubules moving across a surface coated with the motor protein kinesin. The rhodaminelabeled microtubules with a diameter of 24 nm and an average length of 1.5 µm bind to the kinesin motors on the surface and appear as bright rods under the fluorescence microscope. This so-called gliding motility assay has been originally developed to study motor proteins in vitro.5,6 In the presence of ATP the adsorbed kinesin motor proteins translate the microtubules across the surface with a velocity of up to 800 nm/s. The positions of several hundred microtubules are simultaneously recorded using a fluorescence microscope and a CCD camera. Previous experiments have shown that surface topography influences the path of an individual microtubule, since the stiff microtubules (persistence length 5 mm7) avoid climbing steep walls.8 That effect has been exploited to guide microtubules in 1 µm deep channels.9 The elevated surfaces are therefore much less
Figure 1. Fluorescently labeled microtubules are moved by the motor protein kinesin homogeneously adsorbed to a polyurethane (PU) surface coated with casein. Microtubules are guided around elevated regions (1 µm high) of the PU surface since they resist a sharper turn upward due to their significant stiffness. This makes the plateaus less accessible.
accessible to the microtubules, which are bound to the recessed regions (Figure 1). In this situation, the path of the microtubules (acting as probes) is confined by the surface topography, and the positions of the microtubules at one time point correspond to a sample of the accessible regions. Repeated sampling gives an increasingly reliable estimate of the surface topography. The topography information can be represented in a binary format: a pixel is accessible (recessed) or inaccessible (elevated). Since we are mainly concerned in this paper with deriving how an image can be generated from randomly moving probes, we do not include how to to obtain height information (with a possible resolution of 0.2 µm) by acquiring images at different focus positions. While imaging a simple pattern of elevated and recessed regions is the most straightforward illustration of the method, other surface properties could potentially be imaged. The path of the probe robot might be sensitive to surface hydrophobicity or magnetization. Alternatively, the signal transmitted from the probe robot could depend on the presence of certain reagents. If, for instance, the probe is labeled with a pH sensitive dye, the local pH could be detected. Fluorescent resonant energy transfer between a donor on the surface and the probe could be used to selectively image the distribution of the donor on the surface. In the following, we will first discuss the general process of surface sampling, then the proof-of-principle experiment, and finally the possibility of extending the resolution of this approach to the nanometer scale. Regardless of the surface property of interest, the random movement of multiple probes covers the surface in a stochastic process rather than in the sequential, deterministic fashion of a scanning probe microscope. For each frame acquired, a pixel on the surface is visited by one of the probes 114
with a certain probability. In our experiment, two probes can visit the same pixel on the surface at the same time, since microtubules can cross each other without interaction. The landing of microtubules from an equilibrated solution ensures that the initial spatial distribution does not deviate too far from a uniform distribution and also that isolated accessible regions (e.g., the inside of a ring) of sufficient size are reached and imaged by probes. While the initial distribution of probes on the surface and the direction of movement are random, the distribution of probes is not necessarily independent from frame to frame, since the microtubules tend to move in straight lines on a plane surface. To estimate the required acquisition time, we will neglect this and treat each acquired frame as an independent sample of the surface. It is important to recognize that each accessible pixel has the same probability of being visited regardless of the shape of the accessible regions, since the probes resemble a gas filling a two-dimensional tank and thus assume a configuration of maximum entropy. The probability P that a pixel is visited at least once is given by P(K) ) 1 - (1 - p)K
(1)
with K being the number of samples, p ) N/n the probability that an accessible pixel is covered at a single sample, N the pixel covered by probes, and n the number of accessible pixels. The average number of visits to each pixel is given by Z ) pK ) NK/n, and the standard deviation of the number of visits is σ ) [Kp(1 - p)]1/2. The minimal time tmin between successive samples is related to the length l and velocity V of the probe by tmin > l/V, so that the probes have sufficient time to move to a new spot. In the experimental realization presented here, an 85 µm × 68 µm (636 × 510 pixels) image of the surface of a thin (20 µm) polyurethane (PU) film, patterned by replica molding10 with posts of 10 µm diameter and 1 µm height, was constructed. The PU film supported by a coverslip was the bottom surface of a 60 µm high flow cell. The inner surfaces of the flow cell were coated with casein before the kinesin motor proteins were adsorbed. The uniform surface chemistry of the PU surface leads to a constant surface density of adsorbed motor proteins. Then, the flow cell was filled with a solution containing microtubules, 1 mM ATP, and an antifade reagent (for detailed protocols see ref 9). Each microtubule binds to several kinesin motor proteins on the surface and starts its motion in a random direction. After the microtubules landed on the PU surface, 500 fluorescence images of the adsorbed microtubules are acquired in 5 s intervals using a CCD camera and an epifluorescence microscope (100× objective). Initially, approximately 600 microtubules with an average length of 1.5 µm were found on the surface, 80% of them moving with an average velocity of 250 nm/s, the others being fixed to one spot. These 600 microtubules covered 4% of the total surface when observed through the fluorescence microscope (18% of the total surface is inaccessible). Since extended exposure Nano Lett., Vol. 2, No. 2, 2002
Figure 2. Fluorescence microscopy image (100× objective, rhodamine dye, 100 ms exposure) of microtubules on surface patterned with 1 µm high posts (10 µm diameter). Microtubules located on top of the posts appear dim, since they are out of focus. The inset shows an AFM image of a post.
to the excitation light causes depolymerization of microtubules, the number of microtubules fell to 25% of the initial number after the acquisition of 500 frames within 2500 s. An example of a single image (frame 200) is shown in Figure 2. The detection of out-of-focus microtubules bound to the top of the posts shows that the elevated regions are not completely inaccessible due to microtubules binding from solution and occasional climbing of the walls from microtubules in the recessed regions. The acquired images were first thresholded to identify all microtubules. Thresholding also discriminates between outof-focus and in-focus microtubules. In a second step, stationary microtubules were excluded by subtracting from each frame the previous frame. This image analysis procedure distills the subset of microtubules, which are landing on the bottom surface, moving, and successfully guided. The resulting stack of binary images was then summed up to show which parts of the surface were visited by the microtubules (Figure 3). The pattern of circular posts can be clearly distinguished from the accessible area. The grainy appearance of the accessible area is due to the small number of visits to each pixel (six in average). By picking every second, fourth, eighth, etc. frame from the original stack of 500 images we can create stacks of 250, 125, 62, etc. frames with increasing time intervals between frames. The evolution of the image quality with the number of frames can be quantified by the increase in coverage of the accessible area defined as the percentage of pixels visited at least once (Figure 4). The agreement between observed and predicted (eq 1, p ) 0.02) coverage is good, when the 4-fold decrease of the number of microtubules in the course of the acquisition time is taken into account (p falls from 0.04 to 0.01). As 500 frames are acquired in 5 s intervals, the microtubules (length 1.5 µm) do not move fast enough (speed 0.25 µm/s) to reach a completely new position. Therefore, the average number of new visits per pixel does not double when 500 frames instead of 250 frames are analyzed. The time a probe needs to cross Nano Lett., Vol. 2, No. 2, 2002
Figure 3. Sum image of a surface patterned with circular posts of 10 µm diameter and 1 µm height. The posts cannot be climbed by microtubules moving on the surface between them. The position of several hundred microtubules moving with a velocity of 0.25 µm/s in random directions was detected every 5 s for 2500 s. After thresholding of the individual images and selecting for moving microtubules, all 500 frames were summed up.
Figure 4. The coverage of the area accessible to probes (diamonds) rises fast with the number of frames analyzed as described by eq 1 (solid line, p ) 0.02). Smaller stacks of frames have been created by picking every second, fourth, eighth, etc. image of the original stack of 500 images. The time interval between two frames therefore doubles from 5 s (500 frames) to 10 s (250 frames) to 20 s (125 frames), etc. The average number of new visits per accessible pixel (circles) rises linearly with the number of frames until the time between two acquisitions falls from 10 s (250 frames) to 5 s (500 frames). The length of error bars is one standard deviation. As the signal-to-noise ratio (given by average number of visits divided by the standard deviation of the number of visits) rises, the images become less “grainy”.
the imaged region is roughly 10 times shorter than the acquisition time of 2500 s. Therefore, the probes constantly leave the field of view and are replaced several times by new probes entering the field of view. This reduces the contribution of a single trajectory, and increases the randomness of the sampling process. This experiment demonstrates that surface coverage by the self-propelled probes increases as predicted, that the sampling 115
frequency is limited by the size and velocity of the probes, and that a microscopic surface pattern can be imaged. In this example the lateral resolution is given by the apparent width of a microtubule of 0.3 µm, which is defined by the resolution limit of the microscope. It has to be emphasized, that this is not the limit of resolution for the described imaging technique, since the center position of the diffraction image of an isolated probe can be found with nanometer resolution, as has been demonstrated in singleparticle-tracking experiments.11 We can therefore find the centerline of the image of a microtubule with nanometer accuracy, which combined with the microtubule diameter of 24 nm would give us a resolution of < 50 nm. Even smaller synthetic probes with the ability to move freely on a surface may be constructed, based for instance on the “atomic scale cars” proposed by Porto et al.12 However, since the surface density of probes has to be kept low so that their diffraction images do not overlap, any improvement in lateral resolution requires a proportional increase in acquisition time and cannot be made up by increasing the number of probes. Stochastic sampling of a surface by a large number of independent, self-propelled probes is an alternative concept to scanning probe techniques. Its main advantages are that no macroscopic cantilever is needed to move the probes, enabling us to image internal surfaces, and that an overview of the surface properties is quickly generated, which becomes more detailed as sampling proceeds. The microscopic probes also do not have to be retrieved from the surface after imaging. Together with the absence of a physical connection between probe and detection system, this may be beneficial for the handling of contaminated samples.
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Extending the resolution to the nanoscale is in principle possible, since a probe itself can have nanometer dimensions. By employing microtubules moved by the motor protein kinesin across a patterned surface, we have demonstrated an experimental realization of the proposed concept. Acknowledgment. The project was funded by NASA grant NAG5-8784. J.C. thanks the Center for Nanotechnology at the University of Washington for support. H.H. was supported by the Alexander von Humboldt Foundation. References (1) Binnig, G.; Rohrer, H. Sci. Am. 1985, 253, 40-6. (2) Binnig, G.; Quate, C. F.; Gerber, C. Phys. ReV. Lett. 1986, 56, 9303. (3) Lutwyche, M.; Andreoli, C.; Binnig, G.; Brugger, J.; Drechsler, U.; Haberle, W.; Rohrer, H. Sens. Actuators, A 1999, A73, 89-94. (4) Evans, M.; Swartz, T. Approximating integrals Via Monte Carlo and deterministic methods; Oxford University Press: Oxford, New York, 2000. (5) Yanagida, T.; Nakase, M.; Nishiyama, K.; Oosawa, F. Nature 1984, 307, 58-60. (6) Howard, J.; Hunt, A. J.; Baek, S. Methods Cell Biol. 1993, 39, 13747. (7) Gittes, F.; Mickey, B.; Nettleton, J.; Howard, J. J. Cell Biol. 1993, 120, 923-934. (8) Stracke, P.; Bohm, K. J.; Burgold, J.; Schacht, H. J.; Unger, E. Nanotechnology 2000, 11, 52-6. (9) Hess, H.; Clemmens, J.; Qin, D.; Howard, J.; Vogel, V. Nano Lett. 2001, 1, 235-239. (10) Xia, Y. N.; Rogers, J. A.; Paul, K. E.; Whitesides, G. M. Chem. ReV. 1999, 99, 1823-1848. (11) Gelles, J.; Schnapp, B. J.; Sheetz, M. P. Nature 1988, 331, 450-3. (12) Porto, M.; Urbakh, M.; Klafter, J. Phys. ReV. Lett. 2000, 84, 6058-61.
NL015647B
Nano Lett., Vol. 2, No. 2, 2002
