Deconvoluting the effect of the Tip

In scanning probe microscopy techniques the image obtained is by definition a convo- lution of the tip and the sample topography. This can lead to an artefactual repre- sentation of the sample topography. This can partly be corrected for, for example to obtain the correct chiral angles in the structure of carbon nanotubes by STM [247]. A similar process can be applied to AFM images of DNA.

Figure 3.6 is a schematic of the tip passing over a DNA molecule, viewed along the s-axis. This illustrates that the measured tip position qtip yields an overestimate of

Figure 3.6: A schematic showing the AFM tip of radius R at different positions with respect to a cylindrical molecule of radius r (viewed as cross section).

the q-coordinate qDNA of the DNA surface, except when the tip is directly above the

DNA. The AFM measurement thus yields an overestimate of the DNA width, which also results in an overestimation of the chiral angle of DNA. This obviously depends on the tip radius, as has also been shown in simulations of DNA imaging by AFM [69]. We can deconvolute the tip effect from the data in this case using a geometric transfor- mation. To do this, we first estimate the molecular radius from the DNA height in the AFM topography, and estimate the tip radius based on the full-width half maximum width of the (averaged) height profile across the DNA. With these two radii, the AFM images can be corrected for the finite size of the tip via the following procedure. For our calculations we assume a cylindrical molecule and a spherical AFM tip (with radii defined as r and R, respectively; as shown in figure 3.6. The lateral position of the point of contact between a sample and tip (qDNA) relates to the lateral position of

the tip (qtip, i.e., the measured position in an AFM experiment) via equation 3.2.

qDNA =

qtip

1 + R/r, (3.2)

In our experiments, r was estimated from accurate, low-force measurements of the maximum height of the molecule (= 2r), and R from its measured full-width half maximum (_{≡ 2q}tip,1/2):

R = (qtip,1/2)

2_{− r}2

2r . (3.3)

Here, qtip,1/2 was determined from a fit with a Gaussian peak function (since more

complicated and accurate descriptions of the cross-sectional profile did not lead to significantly different results). Using Equation 3.2, straightened nucleic acid AFM

images in sqz coordinates were thus corrected for the effects of tip convolution. Coordinates with q∗

tip> 2

√

rR were excluded from the analysis, as these correspond to positions where the tip is expected to be in contact with the substrate, and not with the DNA any more. Consequently, the DNA surface is only probed over a width of 2q∗

DNA = 4

√

rR/(1 + R/r) ≤ 2r. In other words, though tips with larger sizes yield a wider appearance of the plasmid, they will probe a narrower part of the molecular surface. Using similar geometrical arguments, one may calculate a corrected height zDNA≥ ztip, where ztip refers to the very end of the tip. However, unlike the correction

of the lateral dimension q, this height correction in our experiments was not significant compared to the noise, and therefore was not pursued any further.

As outlined above, this procedure includes an estimate of the tip radius from the DNA width, which can also be verified by comparing the corrected chiral angle of the DNA to the DNA crystal structure, and which can be useful for calibration purposes in general. For the higher-quality images of DNA secondary structure, tip radii are found to be close to 1 nm. This is below nominal manufacturers’ specifications, as shown in table 2.1.

Visualisation of DNA Secondary

Structure

Atomic Force Microscopy (AFM) allows imaging of single molecules at high resolution under near-physiological conditions. Recently it has been shown that by finely tuning imaging techniques and sample preparation, it is possible to visualise the double helix structure of DNA in solution. Here a method is presented to image DNA at _{∼1 nm} resolution. This allows for the visualisation of the double helix secondary structure of DNA and variations therein by precise control of the applied force during imaging. In addition the convolution of the tip and the sample in the topographic image is analysed and accounted for, resulting in accurate structural parameters for DNA at the single molecule level.

4.1

Introduction

DNA is one of the extensively studied biological molecules, due in part to its signif- icance, and in part to its iconic structure. The double helix secondary structure of the DNA polymer is a key element for the storage of our genetic information, and for our understanding of how our cells, grow, replicate and die. DNA is a long linear polymer whose structural properties and interactions with proteins have been tradi- tionally elucidated by Electron Microscope (EM) and X-ray diffraction techniques. The disadvantage of these techniques is that they rely on ensemble averaging or ordered molecules. AFM allows the imaging of single molecules under physiological conditions, and can monitor these over time, providing information on conformational dynamics in addition to structure at nanometre resolution.

topology, dynamics, and interactions continue to be examined. B-DNA, the Watson- Crick form of DNA, is the most commonly occurring form of DNA under physiological conditions. The structure of B-DNA has been elucidated by X-ray crystallography, as described in chapter 1. B-DNA exhibits a right-handed helix with a helical repeat (pitch) of ∼3.6 nm, with major and minor grooves of widths ∼2.2 nm and ∼1.2 nm respectively. A space-filling representation of the structure of B-DNA was generated from PDB file 1BNA [11] and rendered using Chimera [10] and is shown in figure 4.1.

Figure 4.1: A space filling representation of B-DNA, annotated with the pitch, major and minor groove values, rendered using Chimera [10] from the PDB file 1BNA [11]. AFM is exquisitely suited to study DNA structure under conditions that are hard to study in methods that rely on ensemble-averaging: In the presence of supercoiling and in aqueous solutions. This may thus allow to elucidate the interplay between supercoiling, protein binding, and secondary structure. An important step to such studies would be the development of robust methods for visualising the DNA double helix structure and its variations, in particular since the vast majority of DNA images in the AFM literature so far show DNA molecules as featureless strands [230], [248]. There are some early exceptions where the secondary structure of DNA was imaged by DNA through manipulation of the sample preparation. In 1995, Mou et al. resolved the pitch of B-DNA as a periodic modulation of 3.4 ± 0.4 nm [116]. In their study, DNA was adsorbed onto the surface of a cationic supported lipid bilayer, deposited on a mica substrate. The pitch of the DNA was only observed when the DNA strands were densely and uniformly packed on the bilayer surface, and not where bilayers were populated by individual isolated DNA strands. The researchers concluded that close packing limited the movement of the molecules. The resolution obtained on DNA thus depends on the degree of adhesion and immobilisation of the DNA molecules on the substrate.

Only recently have developments in AFM technology resulted in the visualisation of both strands of the DNA double helix [69], [70], showing a tilted, double-banded struc- ture repeating along the molecule. Here we show a method by which commercial instru- mentation can be used to image the secondary structure of DNA plasmids, adsorbed on a mica surface, to obtain relevant structural information, allowing us to visualise structural variations in the secondary structure of DNA, at the single molecule level.