Images taken of paired helical filaments (PHF) using atomic force microscopy (AFM) have shown the apparent existence of both left and right-handed filaments. Computational simulations of the images obtainable have been carried out to explain these findings and to confirm them as instrumental artifacts. When carried out using ideal spherical tips, the images of the structures are distorted in their lateral dimensions but retain their helicity. The fine structure of the sample is often lost for tips which are slightly oblong, resulting in beaded structures. In some instances, the image distortion is such that the handedness of the structures appears to change. These findings illustrate the applicability or lack thereof to determine the helicity of a sample using the atomic force microscope.

Introduction

The atomic force microscope is one of the general class of instruments known as scanning probe microscopes which has found tremendous use in biology, largely due to its ability to image non-conductive samples under fluids. The AFM is increasingly being used to elucidate these three dimensional structures (for recent reviews, see Firtel and Beveridge, 1995; Yang and Shao, 1995; Lal and John, 1994).

Over the past few years, several papers have reportedly imaged the helicity of various biological structures. For the most part, the reported helicity is merely a repetition of local maxima with periodicity identical to that predicted for models or other forms of microscopy (Kirby et al., 1995). To date, only a few papers have suggested that true helicity of the structures, DNA in two such cases, can be seen in the AFM images (Hansma et al., 1995; Mou et al., 1995). In the latter paper, it was stated "...that the handedness is better resolved when the DNA strand is parallel with the fast scan direction", which was attributed to the fact that "..instrumental drift is more noticeable in the slow scan direction."

Helen Hansma (1995), in her review of the AFM study of acetan by Kirby et al. (1995), pointed out some of the difficulties in obtaining helicity using the AFM, namely the problem with imperfect tips leading to misleading image artifacts and the effect of tip convolution. In their paper which introduced the deconvolution algorithm termed envelope reconstruction, Keller and Franke (1993) presented real and simulated AFM images of F-actin. Although it was stated that electron microscopy and X-ray diffraction show F-actin to be a right-handed double helix, the images and simulations presented were of left-handed helical structure, with no discussion of the discrepancy. Keller later wrote that "..calculated images showed that F-actin appears left handed only if the actin filament is itself left handed; right-handed filaments invariably give rise to right handed conformations...image reconstructions helped to confirm that F-actin can, depending on the preparation conditions, adopt either left- or right-handed helical conformations" (Bustamante et al., 1994). For their reconstructions, the authors used parabolic tip shapes.

Previous calculations by Franke and Keller (1993) suggest that the AFM tip must be 0.5 nm in radius to access the major grove in DNA in order that the helicity can be revealed. Our ongoing investigations of paired helical filaments using the atomic force microscope (Pollanen et al., 1994ab, 1995, 1997) should not be hampered greatly by tip convolution since the periodicity of these structures is 80 nanometers and therefore, easily accessible by standard tip. On one occasion, we had fortuitously imaged both left- and right-handed structures but, as will be shown, the apparent handedness was subsequently dismissed as a tip artifact.

This chapter sets out to study how the use of a slightly skewed tip can affect the quality of the images obtained for a helical structure. It is the goal of these efforts to show the instances when such reversal of conformation can occur. The ideal helical structure of PHF is considered.

Methods

PHF Preparation

The preparation procedure has been presented elsewhere (Pollanen et al., 1997) using a modification of the Greenberg and Davies method (1990) as described by Ksiezak-Reding et al. (1992).

Atomic Force Microscopy

The filamentous material, as prepared above, was suspended in water and deposited onto freshly cleaved mica. The AFM images were obtained using a Nanoscope II atomic force microscope (Digital Instruments, Santa Clara, CA). This was equipped with a D scanner which provides a maximum viewing of a 16 by 16 micron area. Triangular cantilevers with integrated square pyramidal tips, (Digital Instruments) made of silicon nitride with force constants of 0.58 N/m were used. Forces were approximately 100 nN during imaging which was always carried out in ambient conditions. Proportional and integral gain settings were set high, typically 2 and 3, respectively. No electronic filtering, other than the deconvolution algorithm mentioned in the next section, was used during or after imaging. All data presented here was obtained in the height mode at scanning frequencies of approximately 2 Hz. Concurrent images taken in the force mode, which provides a measure of the cantilever deflection from the setpoint, indicated negligible variations. All images were taken with no electronic rotation, that is, the fast scan direction was from right to left with the sample oriented as shown in the figures which follow. The pictures presented here are false colored: higher data points are brightly colored while lower points are darker.

Image Processing and Simulation of Ideal Structural Models

The convolution simulations were carried out using MIDAS95D, a public domain program (http://www.chem.utoronto.ca) used to take into account the effect that the tip geometry has on the AFM images obtained. Details on this program are given elsewhere (Markiewicz and Goh, 1994, 1995 ab). All calculations were carried out to produce data files compatible with the Nanoscope II format, namely a 200x200 file size with the unique 2k header.

The core of the paired helical filament structure was modeled using the equation:

where the x, y, z co-ordinates are given in nanometers and the trigonometric functions are in radians. The positive and negative signs in the calculation of y are meant to imply that there are two filaments undulating directly opposite each other, while the same sign for the calculation of z indicates that, as it is applied to each, the filaments can be wound in a left or right-handed configuration. This produces the helical backbone consisting of two lines which appear intertwined about a central axis. Cylindrical structures of 7 nanometers radius are then constructed to be centered on these lines to give the filamentous structure. At this resolution, no substructure, which would indicate the presence of subunits, is evident; the two filamental structures are identical. The winding of the each filaments repeats every 160 nanometers, but as the two are identical, the overall structure has 80 nanometers periodicity and a 14 nanometers width. The construction of the ideal PHF structures and the modification of the AFM data files were carried out using a QBASIC program.

Results and Discussion

Figure 1 : Various AFM images of PHF at different orientations and magnifications, but only (a) shows left-handedness. each taken with different tips. All images shown the expected 80 nanometer periodicity.
During the initial course of our investigations into PHF, the serendipitous images led us to conclude that the structure was left-handed, as seen for the raw image given in Figure 1a. Further investigations relating to PHF were hampered by the fact that its helicity was not readily apparent from the images taken, but rather a bstructure was obtained. This was dismissed as being due to a tip artifact, since it could be seen that many of the images were more greatly distorted in their lateral dimensions than for the initial images, which would indicate that the radius of curvature at the apex of the tip was larger than before. The distortion in the lateral dimensions is a typical artifact of AFM images brought about by the convolution of the tip and sample (Allen et al., 1992). Repeated attempts at changing the AFM tip failed to produce an improvement in the images, as shown in Figure 1b-f.

Figure 2 : Images of a PHF preparation showing left-, right- and ambidextrous handedness (a, b, and c, respectively). All three images were taken with the same AFM tip.
Only on one subsequent occasion was the helicity apparent in the images obtained, as shown in Figures 2 and 3a. In this instance, straight structures of 80 nanometers periodicity were seen to have either left and right-handed helicity, as seen in Figures 2a and b, respectively. In addition to these, bent formations of PHF were imaged for the first time and these were found having both left and right handedness (Figures 2c and 3a).

Figure 3 : (a) A bent PHF sample, imaged using the same tip as in Figure 2, shows both left and right handedness as well as an indeterminate helicity. (b) Simulation of a bent, left handed PHF sample resembling (a) shows similar structure when convoluted with a 1:2 oblong tip, as does a similar right handed sample (c). Deconvolution of (a) using an oblong tip gives (d).
Contemplation on the overall results aided in deducing the apparent helicity as being a unique tip artifact. For those PHF structures or portions thereof lying such that they appear to be falling to the right it can be seen that images taken with this particular tip had a left-handed geometry (Figures 2a and 3a). Conversely, any structure which appears to be falling to the left appears to be right-handed (Figures 2b and 3a). In addition, any structure which lay parallel to the scan direction, that is, appears horizontally on the image, has an indistinct helicity, as seen for a portion of Figure 2c. It would therefore lead to the conclusion that, for this particular tip, the PHF structure could have either a left, right or indeterminate helicity depending on the orientation relative to the scan direction. Figure 3a illustrates all three such artifacts on a single structure.

The geometry of the tip used in Figures 2 and 3a is suggested by the extraneous debris imaged along with the PHF if one assumes the real shape of the debris to be spherical. The shape of the tip can often be inferred by the presence of a repetition of patterns in an image, or by the distortion produced on features of known shape. Figure 3a illustrates the indication of tip distortion for an image containing the bent PHF and other unknown structures. As discussed earlier, the immediate impression of the PHF is that it contains both left and right handed portions. The arrows given in Figure 3a show that the material other than PHF is oblong, all seemingly twice as long in the y direction compared to the x. If the material were indeed oblong, it is highly unlikely that such a large number of extraneous material would preferentially deposit in a vertical orientation, and so it can be assumed that this distortion is solely a result of the tip geometry. If the debris is assumed to be spherical, this would imply that it is the tip that is oblong with the x:y aspect ratio being 1:2.

Figure 4 : Computer simulations of the AFM images obtained for left handed PHF in various angular orientations (shown in the left column) convoluted using five tip geometries (shown in the top row).
To help explain the artifacts seen in the AFM images, numerous calculations were carried out simulating the convolution of various tip shapes with PHF. Figure 4 represents a summary of these for the left handed structures considered. The first column of Figure 4 shows the simulated PHF at different angular orientations. These are the ideal AFM images obtainable with an infinitely sharp, thin tip. The PHF is at angles of 90, 60, 45, 30, 0, -30, -45 and -60 degrees, with zero chosen as that where the PHF is oriented parallel to the fast scanning direction of the tip, that is, horizontally from right to left as seen in the images. The top row in Figure 4 shows the five tip geometries used for the convolution simulations. Two of the tips shown are grossly oblong, with the first being longer in the x direction than in y, while the other is longer in y. The length to width (x:y) ratio for the first tip is 2:1, where the dimension along the fast scanning direction is here denoted as the length (contrary to the notation that might otherwise be given for the image of the tip's cross section as shown in the upper row). The second tip shown is only slightly oblong, having a length to width ratio of 3:2. The central tip geometry represents an ideal sphere, that is, one with an aspect ratio of 1:1. The forth and fifth tips are of 2:3 and 1:2 aspect ratio, respectively, which means that they are identical to the first two tips if these latter tips were rotated by ninety degrees. All tips shown are 25 nanometers in radius, typical of some of the standard tips used in the AFM (Albrecht et al., 1990). For the oblong tips, the outermost portions of the structures are hemispheres of 25 nanometers radius joined by a cylindrical central portion with that same radius. As mentioned earlier, the PHF structures are modeled to be 14 nanometers in height, therefore the apex of the AFM tip is the only portion which interacts in these convolutions. The shape of the body of the tip has no influence on the resulting images and is therefore immaterial to this study.

By comparing the images of the ideal structures in the first column with those convoluted ones in the body of Figure 4, it can be seen that images representing the convolution of the various tips with the ideal PHF structure all show the stereotypical lateral broadening of the obtained image typically seen in AFM images. The unchanging contrast between the higher points at the crossover points on the PHF structures and the substrate indicates that the height of the structures relative to the background remains constant.

Many of the resulting convoluted images shown in Figure 4, such as those obtained with the spherical tip, retain the general features of the original PHF structure, namely, the periodicity is distinct and the left-handedness is immediately evident. This holds true for all images produced using the ideal spherical tip (the central column ) regardless of the orientation of the PHF relative to the scan direction.

The handedness of some structures becomes indistinguishable for some of the oblong tips and PHF, with the structures appearing as a string of beads rather than of twisting filaments. An example of this would be the product of PHF at -60 degrees imaged with a 2:3 tip.

Some distortions produced by oblong tips and PHF show the apparent reversal of handedness, such as the images with the PHF at a positive angle in the column for the 2:1 ratio tip, which appear right handed. The apparent change in handedness of the simulated images are most readily seen in those images made with this highly asymmetric tip, but right handedness is also suggested in those images where a slightly distorted tip was used.

Table 1 : A summary of the apparent handedness of the convoluted images given in Figures 4 and 6 for the various angles and tip geometries considered. L = distinctly left handed, l = moderately left, U = unknown handedness or beaded structure, r = moderately right, and R = distinctly right handed.

Tip	2:1		3:2		1:1		2:3			1:2
Original	Left	Right	Left	Right	Left	Right	Left	Right	Left		Right
90°	l	r	l	r	L	R	L	R	L		R
60°	R	R	R	R	L	R	L	L	L		L
45°	R	R	r	R	L	R	L	L	L		L
30°	R	R	U	R	L	R	L	L	L		L
0°	l	r	L	R	L	R	l	r	l		r
-30°	L	L	L	r	L	R	r	R	R		R
-45°	L	L	L	l	L	R	r	R	R		R
-60°	L	L	L	U	L	R	U	R	R		R

To help summarize the findings from the simulations shown in Figure 4, Table 1 was constructed showing the apparent conformations for the various tips and orientations. The assignments of the apparent helicity given in the Table are highly subjective and many of the classifications, particularly those where the structure is deemed moderately or of unknown handedness, can be debated. The important entries in Table 1 are those where the resulting AFM images have readily perceived handedness which may or may not reflect that of the true sample.

Figure 5 : Due to their symmetry, results given in Figure 4 for the convolution of left-handed PHF at -45( imaged with a 2:1 tip are identical to the PHF at 45( with a 1:2 tip.
The results given in Figure 4 show a rotational symmetry for the oblong tips selected and various PHF structures. Many of the convolution simulations shown here are geometrically equivalent since only hard body interactions were considered to produce them. Thus, the results for any of the PHF structures and tip geometries will be identical to those produced where both sample and tip are rotated by an equal amount. This is shown in Figure 5 for the PHF at -45 degrees and the 2:1 tip compared to the PHF at 45 degrees and the 1:2 tip.

Simulations similar to that for the left-handed PHF structure were also carried out for the right handed one. The results are given in Figure 6 and have been summarized alongside the left handed results in Table 1. From the Table is can be seen that the tip shape is the factor determining the overall handedness of the convoluted image: regardless of the PHF structure, many of the images are all left or all right handed depending on the PHF orientation relative to the tip. This holds particularly true for the highly oblong tips.

Figure 6 : Simulations similar to those in Figure 4, obtained instead for right handed PHF in various angular orientations (shown in the left column) convoluted using five tip geometries (shown in the top row).
The changes in handedness are vividly shown in Figure 7 for the left and right structures. When either is convoluted with the same 1:2 tip, both would appear to be twisting in the opposite direction. Again, this effect is largely due to the symmetry of the geometric configurations and the simple assumptions made in the convolution algorithm.

Figure 7 : The apparent change of handedness occurs for both left and right handed PHF (insets) depending on their positional orientation, as shown here when convoluted with the same 1:2 tip.
The inadvertent use of a highly distorted oblong tip might therefore explain the apparent change in handedness for the bent PHF structures imaged by the AFM shown in Figures 2 and 3a. Simulating the structure of a bent, left-handed PHF similar to that obtained by the AFM produces Figure 3b when convoluted with a 1:2 tip. Similarly, a right handed structure will also give analogous results when imaged with the same tip (Figure 3c). It can be seen that both these simulations have the same apparent change in handedness as was obtained with the AFM given in Figure 3a, although very minor differences exist, most noticeably on the perimeter of the convoluted images.

With the shape of the AFM tip being known or inferred, the images taken can be processed to reduce or eliminate it's contribution on the sample geometry. Simulations of the convolution and subsequent deconvolution of some of the images presented in Figure 6 shows that the sample's helicity can be restored, as shown in Figure 8 for some of the situations previously examined. For some of the reconstructed structures, the helicity is lost, such as with the PHF oriented at 0 degrees and processed with a 2:1 tip (and, according to the results given earlier, for that at 90 degrees with a 1:2 tip). This loss of helicity is due to the fact that during imaging the geometry of the tip precluded its penetration into the groove between the filaments which make up the PHF structure thus losing these finer details. Images which have lost these details can not be improved through deconvolution. It can be seen, though, that most other images are restored well enough to indicate the paired filaments of the original model structure.

By using the tip geometry inferred by the debris which appears alongside it, the PHF structure shown in Figure 3a can be deconvoluted. As a first attempt, a 1:2 tip geometry of 25 nm radius was used. Analysis of the cross-section along the main axis of the left portion of Figure 3a showed that the original maximal height was approximately 17 nm, whereas for the deconvoluted image this height was 15 nm. Such a reduction in the sample height upon deconvolution is most often an indication that the tip used was too large. By trial and error, an optimum tip radius of 20 nm with an aspect ratio of 1:2.5, or 2:5, was used. The result is given in Figure 3d. From this it can be seen that the debris is reduced in size and made somewhat spherical in shape. Also, the left portion of the PHF appears much like the left-handed models used. Unfortunately, the portions to the right of the image have no identifiable shape. It is unknown as to why these deformations persist: they may be a result of complexities occurring during the imaging process which the simulations could not account for.

Figure 8 : Deconvolution of some previously convoluted images of right handed PHF (shown in the left column) which were presented in Figure 6 show that the right handed helicity is restored for most images when similar tips are used (shown in the top row).

Conclusions

It has been shown here that the AFM images of PHF can appear to have different conformations dependent on the geometry of the tip and the relative angular orientation of the two. This might imply that the use of the AFM to determine the handedness of any helical sample, be it DNA, acetan, or other structures, can be erroneous depending on the geometry of the tip that is used.

The computer algorithms used here have assumed ideal imaging conditions, neglecting the lateral forces which are to be expected as the tip navigates within the groove between the filaments. Deformation, either of the tip, sample, or both, is yet another factor which might be prevalent during contact imaging as was used here. Future investigations into the finer structure of helical samples such as PHF might be better facilitated using modes of imaging which are less susceptible to the influences of lateral forces or deformation due to the high forces during imaging.

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