Single Biomolecule Imaging with Frequency and Force Modulation in

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2007, 111, 2125-2129 Published on Web 02/10/2007

Single Biomolecule Imaging with Frequency and Force Modulation in Tapping-Mode Atomic Force Microscopy Santiago D. Solares* Department of Mechanical Engineering, UniVersity of Maryland, College Park, Maryland 20742 ReceiVed: January 4, 2007; In Final Form: January 31, 2007

A new intermittent-contact atomic force microscopy (AFM) mode (frequency and force modulation AFM, FFM-AFM) has been recently proposed to characterize soft samples. This method uses excitation force frequency and amplitude modulation to eliminate bistability and reduce the tip-sample forces. This letter describes theoretical modeling of FFM-AFM applied to a single bacteriorhodopsin molecule on a substrate, showing that its cross section can be measured without damage, in contrast to conventional tapping-mode AFM. Speculations are made regarding nonideal conditions and the ability of FFM-AFM to perform quantitative nanoelasticity measurements.

Since its invention,1 atomic force microscopy (AFM) has found a wide range of applications in many areas of nanotechnology. Currently, it is used to study surfaces, nanoparticles, biological samples, carbon nanotubes, etc. with a variety of tip designs,2-7 which can be functionalized to obtain information about the sample’s chemical properties8-19 in addition to its geometry and mechanical properties. Among the various applications of AFM, biomolecule imaging20-32 is one of the most challenging. These challenges derive primarily from the fact that soft biosystems can be damaged and even destroyed by the relatively high tip-sample forces that emerge during imaging. Biological samples can be imaged with AFM in contact mode (CM-AFM),20-22 whereby the tip slides laterally, always in contact with the sample, to reproduce its topography; in amplitude modulation tapping mode (AM-AFM),23-29 whereby the tip continuously oscillates at a relatively large amplitude over the sample and is in intermittent contact with it; and less frequently in noncontact frequency modulation mode (FMAFM),30-32 whereby the tip oscillates at a very small amplitude above the surface without making contact with it. Each of these modes has its own advantages and challenges. CM-AFM is advantageous in the sense that it guides the tip along the actual “skin” of the sample but can in some instances be limited to relatively blunt tipssdepending on sample stiffnesssthat can distribute the force over a larger area of the sample and to very low tip-sample forces (typically on the order of 0.1-0.5 nN)20 and can in many cases damage the sample due to the lateral forces exerted by the tip, especially for weakly immobilized structures.23 AM-AFM, the most common mode of AFM, is relatively simple and can achieve high resolution for a wide variety of samples but is subject to imaging bistability, whereby two imaging solutions can emerge for a single set of parameters, and to relatively high tip-sample repulsive forces that often destroy the softest biological samples.2 Finally, FM-AFM can provide high resolution without sample damage, but since the * E-mail: [email protected].

10.1021/jp070067+ CCC: $37.00

tip is never in contact with the sample, this method can suffer from imaging artifacts such as tip broadening,33,34 does not provide information about the elastic properties of the sample, and is generally unable to accurately characterize samples containing deep crevices on the surface. Recently a new intermittent-contact imaging mode was proposed, which combines existing knowledge from AM-AFM and FM-AFM to eliminate imaging bistability and limit the magnitude of the repulsive tip-sample interaction forces. This method, frequency and force modulation AFM (FFM-AFM),35,36 has been discussed in detail in previous publications, but briefly, it consists of a tapping mode in which the cantilever is continuously excited at its variable effectiVe resonant frequency, similar to the self-excited oscillators used in FM-AFM,37,38 to prevent bistability.2 Additionally, the effectiVe resonant frequency is controlled to always remain below the free resonant frequency through the modulation of the excitation force amplitude (Figure 1). Since increases in the effective resonant frequency are caused by repulsiVe tip-sample interactions,2 limiting the effective resonant frequency is equivalent to limiting the magnitude of the repulsive forces. The FFM-AFM algorithm (Figure 1) shows that if the effective frequency increases above the free resonant frequency, the controller reduces the amplitude of the excitation force in order to reduce the tip penetration into the repulsive part of the potential. This causes the effective frequency to decrease. If the effective frequency decreases below the free resonant frequency, the controller increases the amplitude of the excitation force to ensure that the tip reaches the repulsive part of the tip-sample interaction potential (i.e., to ensure that the tip “touches” the sample), thus increasing the effective frequency. Reference 36 presents numerical simulations illustrating the application of FFM-AFM to calculate the crosssectional scan of a carbon nanotube sample resting on a silicon surface. The calculations demonstrate reduced tip penetration and repulsive forces with respect to conventional AM-AFM. This letter discusses the application of FFM-AFM to the cross-sectional profile measurement of a single bacteriorhodop© 2007 American Chemical Society

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Figure 1. Controls scheme for FFM-AFM (from ref 36). The controls system obtains the instantaneous effective frequency, oscillation amplitude, and phase angle from the real-time tip position signal. It continuously adjusts the excitation force frequency to match the instantaneous effective frequency and varies the excitation force amplitude to ensure that the cantilever is oscillating at the highest possible amplitude while its frequency remains at the free resonant frequency.35,36 The sample height is calculated as the fixed cantilever rest position minus the instantaneous oscillating amplitude (i.e., sample height ) Zc - A) as the cantilever travels horizontally scanning the sample. Q is the cantilever’s quality factor, and k is its harmonic force constant.

Figure 2. Atomistic model of a 2.4-nm triple-walled carbon nanotube AFM tip (composed of three individual 18,18-, 13,13-, and 8,8-singlewalled carbon nanotubes) tapping on a molecule of bacteriorhodopsin, resting on a Si(100)-OH surface in vacuum: (a) side view of the probe approaching the sample; (b) side view of the probe at the point of maximum sample compression in FFM-AFM imaging mode; (c) top view showing the ten horizontal tip positions (yellow marks) at which force curves were constructed to calculate the sample’s cross-sectional scan (the images correspond to the fifth scan point from the top). The arrow shows the direction in which the image was constructed.

sin molecule (an important benchmark in biomolecular AFM imaging)21,22 using a 2.4-nm-diameter triple-walled carbon nanotube tip (TWNT, composed of three individual 18,18-, 13,13-, and 8,8-single-walled carbon nanotubes) within molecular and classical simulations, performed with previously reported methods35,36,39 (note that this system is significantly more challenging to image with AFM than those consisting of densely packed biomolecules,20-23 where the presence of neighbors increases the vertical stiffness of each individual molecule by reducing its lateral deformation). To construct the cross-sectional scan, tip-sample interaction force curves were calculated for

the tip tapping at ten different points above the biomolecule as indicated in Figure 2. To prevent lateral sliding of the sample, eight of its atoms closest to the surface were kept fixed during the approach of the tip. Molecular simulations were conducted with parameters from the Dreiding40 force field using the NAMD41 software. Atomic charges were calculated using the charge equilibration (QEQ)42 scheme, prior to equilibrating the samples through 300 ps of molecular dynamics at temperatures ranging from 75 to 300 K and 35 000 steps of geometry optimization. The accurate simulation of the cantilever motion in AM-AFM using a point-mass damped harmonic oscillator

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Figure 3. Tip-sample force curves for the 2.4-nm-diameter triple-walled carbon nanotube tapping on the bare Si(100)-OH surface, corresponding to scan point no. 1 in Figure 2c (a), and directly on the bacteriorhodopsin molecule, corresponding to scan point no. 5 (b). The square denotes the largest repulsive force that occurs during each oscillation in conventional AM-AFM when the tip is tapping on the substrate. The circles give the maximum forces that take place in FFM-AFM imaging. Figure 3b does not show a square indicating the maximum tip-sample force for AM-AFM because its value is beyond the region of sample destruction, where the tip-sample forces behave erratically. Note that the vertical scales are significantly different in both graphs.

TABLE 1: AFM Imaging Parameters Used for Numerical Simulations cantilever force constant, k cantilever free resonant frequency, νo cantilever quality factor, Q frequency setpoint (FFM-AFM) free oscillation amplitude (AM-AFM) amplitude setpoint (AM-AFM) excitation force amplitude (AM-AFM)

40 N/m 300 kHz 150 300 kHz (same as νo) 10 nm 9 nm 2.67 nN

model has been extensively treated and demonstrated in the AFM literature.2,43,44 The corresponding equation of motion is the following:

m

d2z(Zc,t) dt2

ωo dz(Zc,t) + Fts(zts) + Q dt Fo cos(ωt) (1)

) -kz(Zc,t) - m

where z(Zc,t) is the instantaneous tip position with respect to its equilibrium rest position (Zc), k the harmonic force constant for the displacement of the tip with respect to its equilibrium rest position, m the AFM cantilever’s effective mass, ωo ) 2πνo ) (k/m)1/2 is the free resonant angular velocity (νo is the free resonant frequency), Q the quality factor, zts the instantaneous tip position with respect to the sample, Fts(zts) is the Vertical component of the tip-sample interaction force (i.e., force curves such as those shown in Figure 3), and Fo cos(ωt) is the oscillating driving force applied to the cantilever. FFM-AFM can also be modeled with eq 1, but with the continuous adjustment of the excitation force amplitude and frequency as described in Figure 1.35,36 Table 1 summarizes the parameters used in the simulations (note that with FFM-AFM there are no special restrictions on the cantilever parameters). Simulations with other parameters were also performed, and those reported here are representative of the results obtained in all cases. Figure 3 shows the tip-sample interaction force curves calculated for the TWNT tip tapping directly on the rhodopsin molecule (scan point no. 5; see Figure 2) and on the Si(100)OH surface (scan point no. 1), as well as the maximum forces that occur in AM-AFM and FFM-AFM imaging modes. As the graphs show, the repulsive portion of the tip-sample force is steeper, higher, and more regular for the Si(100)-OH surface than for the rhodopsin molecule (note that the vertical axis scales are significantly different in both graphs). The curves indicate that the bare surface is able to withstand relatively high tip-

Figure 4. Bacteriorhodopsin molecule compressed by the triple-walled carbon nanotube tip to 2/3 of its initial height at scan point no. 5 (see Figure 2). Despite significant horizontal and vertical deformation, Figure 3b shows that the repulsive tip-sample forces remain below 3 nN. The repulsive forces in conventional tapping-mode AFM are on the order of tens of nanonewtons and are able to compress the molecule well beyond the state of deformation shown here, causing irreversible changes in its structure.

sample interaction forces, as opposed to the bacteriorhodopsin molecule, which is only able to withstand repulsive forces on the order of ∼2.6 nN before being destroyed by the tip. Since in AM-AFM, the repulsive forces are typically on the order of tens of nanonewtons, a cantilever oscillating in tapping mode with fixed excitation force amplitude will penetrate beyond the point of sample damage. Indeed, the simulations show that the maximum tip-sample force that occurs in AM-AFM for the tip tapping on the Si(100)-OH surface is ∼12.9 nN with an amplitude setpoint equal to 90% of the free oscillation amplitude (Figure 3a), which is much higher than the maximum tipsample forces needed to destroy the protein (Figure 3b). Figure 4, shows the molecule after the tip has compressed it to 2/3 of its initial height during the construction of the tip-sample force curve. Significant deformation is evident, even though the repulsive tip-sample forces have not reached 3 nN (Figure 3b). In contrast, the repulsive tip-sample forces that emerge with FFM-AFM are below ∼3.1 nN for the tip tapping on the Si(100)-OH surface and below ∼0.6 nN for the tip tapping directly on the bacteriorhodopsin molecule, resulting in a measured sample height of ∼2.9 nm (for scan point no. 5).

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Figure 5. Calculated cross-sectional scan of the bacteriorhodopsin molecule. The lines above and below the image indicate the location of the sample skin (tip-sample interaction potential well) and the tip positions below which irreversible changes occur (damage region), respectively. The sample compression was below ∼0.3 nm, and the maximum tip-sample forces were below ∼0.7 nN throughout the scan. The calculation shows that no excessive tip penetration took place. Note that the image width is approximately equal to the sample width plus the probe width.6,39

Figure 2b confirms that the compression experienced by the sample in FFM-AFM is not excessive. Figure 5 shows the cross-sectional scan of the bacteriorhodopsin molecule calculated in FFM-AFM mode. The graph also indicates the position of the sample surface (location of the tip-sample potential well) and the profile below which irreversible structural changes can take place in the molecule (both the location of the potential well and the damage profile were obtained from the tip-sample interaction force curve). The image is slightly below the sample skin, indicating that some deformation takes place, but it is above the region where irreversible changes occur. The sample compression was below ∼0.3 nm, and the maximum tip-sample forces were below ∼0.7 nN throughout the scan. There is no excessive penetration on the sample edges. Note that the image is much wider than the sample because its width is equal to the width of the sample plus the width of the probe.6,39 Reference 35 discusses the mechanics of FFM-AFM and explains why it is able to limit the repulsive forces. The fundamental principle is that FFM-AFM requires the influence of the attractive tip-sample interaction forces to be approximately balanced by the influence of the repulsive forces. This requirement provides guidelines regarding the type of tipsample interaction force that is most desirable to characterize soft samples. First, since the attractive and repulsive interactions need to be balanced, one way to minimize the repulsive forces is to first minimize the attractiVe forces. This means using tips that can only experience small attractive forces with the surface. Carbon nanotubes fit this criterion best because of their hollow geometry, which allows them to get close to the sample with fewer atoms than solid conventional tips or nanowires. Even in the cases when small carbon nanotubes are difficult to use (e.g., in water, due to their hydrophobicity), smaller/thinner tips are preferred for the same reasons just discussed. Another important aspect to consider is the steepness of the repulsive portion of the tip-sample interaction force curve. It has previously been shown that lower imaging forces are obtained with force curves that are less steep.45 The simulations show that the same is true for FFM-AFM, partly due to the arguments presented in ref 45 in terms of the work necessary to stop the cantilever as it approaches the surface and also due to the fact that a less steep curve allows the region of negative tip-sample force gradient to influence the cantilever frequency over a longer distance with smaller forces, thus reaching the required balance with a lower

Letters repulsive force. A fortunate consequence of this last point is that the naturally less-steep force curves of soft samples result in even lower repulsive forces in FFM-AFM imaging with respect to hard samples (the steepness of the repulsive tipsample force curve is proportional to the sample hardness, so soft samples have curves that are less steep). Despite the fact that the calculations discussed here were performed in ideal conditions, it is possible to make general speculations about two of the important differences one might expect in humid air or liquid environments. On one hand, one would expect that the long-range tip-sample attractiVe forces are generally smaller in liquids because the tip is surrounded by the fluid at all times. According to the previous paragraph, this would result in lower repulsive forces being needed to balance the smaller attractive forces, which would be beneficial in the characterization of delicate samples. On the other hand, significant capillary forces can be present in humid air environments.46-48 In such cases, the liquid film can to some extent oppose the motion of the cantilever approaching the surface, thus making the sample appear slightly stiffer, but it can also cause tip-sample adhesion as the tip leaves the sample. Although there is not sufficient quantitative information in the literature to estimate the forces for a wide range of systems of interest, it seems that the adhesion forces can be quite significant, and hence, higher repulsive forces would be necessary to balance their effect in FFM-AFM. This would be detrimental with soft samples. Despite these useful generalizations, much theoretical work still remains to be done in the development of a unified FFM-AFM theory to relate quantitatiVely the effect of the critical process control parameters (e.g., cantilever frequency and force constant, quality factor, etc.) to the magnitudes of the forces that take place between the tip and the sample. Research is also needed with regards to other more practical aspects of the technique, such as imaging speed and controls sensitivity, before the method can be used successfully in experiments. Overall, the experimental implementation of FFM-AFM seems to offer significant potential benefits in the characterization of a wide range of biological samples currently outside of the scope of AFM. This would include not only samples that are too soft to be imaged, but perhaps, also samples with deep crevices or hollow geometries, such as the actin bundles found in epithelial cells,49,50 which one might be able to image very gently with high-aspect-ratio probes that can penetrate into the void spaces between the fibers. Additionally, since FFM-AFM in principle allows the user to set the upper limit of the effective frequency (currently set to νo in Figure 1), it should be possible to study the effect of different effective frequency values (and consequently different magnitudes of tip-sample repulsive forces) on sample deformation. Such a study could lead to methods for the systematic evaluation of stress-strain relationships of nanoscale samples under subnanoscale deformations, thus contributing to a more rigorous study of nanoelasticity. In summary, the concept of intermittent-contact-mode frequency and force modulation AFM (FFM-AFM) has been applied to calculate the cross-sectional scan of a single bacteriorhodopsin molecule within atomistic and classical simulations, showing that it may be capable of gently imaging soft biomolecules that are currently beyond the capabilities of tapping-mode atomic force microscopy. This added capability should be useful in the study of a great deal of applied problems in nanotechnology, especially those involving biomolecules and soft tissues, and also in fundamental research, such as in the development of a more rigorous nanoelasticity theory.

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