Estudios sobre las acciones colectivas de la MANE en Colombia, años 2011 a

Persistence length,P, was measured in two different ways. In most cases it was possible to confine the nanotubes to 2D (see Preparation of Samples, above). The persistence length was then determined by extracting the end-to-end distance,R, and contour length,L, from fluorescence images of several different nanotubes (N> 4) in many distinct conformations (hUi =23) and fitting the data to the 2D Kratky-Porod model:

hR2i= 4P L1−2P e−L/2P/L (3.15) Each point on the hR2_{i versus L plot was derived from a set of U conformations observed}

for a single DNA nanotube. A complete data set for a given tube type consisted of N

such points. Uncertainty in the persistence length thus determined was estimated using a bootstrap method: From every set ofU confomations of a given nanotube, k conformations were selected at random with replacement (thus a particular conformation might be picked twice or not at all). The average end-to-end distance of the selected conformations,hR2i(k), was computed. This value typically differed only slightly from the end-to-end distance,

hR2_{i(n), of the “original” set. A least-squares fit of the Kratky-Porod model to a plot of}

hR2i(k) versus L was performed and, accordingly, resulted in a slightly different estimate of the persistence length. For each type of nanotube, this process was repeated 1000 times using randomly selected sets of the same size as the original (that is, k =U). The resulting persistence length estimates were normally distributed about the one derived from the original data set and their standard deviation was taken as the uncertainty (67% confidence interval) in the measurement.

It was not possible to confine the 6HB+2 (parallel) nanotube (in which six out of eight sticky ends were at the same Z position along the helical axis) to 2D, so a different approach to estimating persistence lengths was taken. Movies containing several hundreds of frames were taken as a freely diffusing nanotube was manually tracked in the focal plane of a microscope. All independent images of a given nanotube were aligned according to their centers of mass and added together to generate a single composite image of the nanotube. The intensity profile along a straight line through the center of mass of the composite image fit well to a normalized Gaussian distribution, the standard deviation, σ, of which was taken as a measure of the nanotubes radius of gyration (RG). The contour length (L) was measured from the most extended conformation observed. These parameters were related to the persistence length (P) of the nanotube using the following two equations: RG = nν_P/(6)1/2 _{and L = nP, where ν = 0.6 for a 3D self-avoiding random walk. The}

average persistence length of the 6HB+2 nanotube design estimated in this manner was 0.78± 0.1µm, based on analysis of two different nanotubes using 400 independent images of each.

Chapter 4

Curved and Twisted DNA

Nanotubes

Curved and twisted filaments such as bacterial flagella [37] and FtsZ filaments [54] consti- tute an important class in biological systems with interesting mechanical properties. It has been suggested that such filaments can be described theoretically by a helical worm like chain (HWLC) model [53, 113]. However direct experimental verification of this model is difficult because model parameters such as filament stiffness or equilibrium curvature are not easily varied in biological filaments.

DNA nanotubes may serve as ideal model filaments of HWLC theory because of the ability to program curvature and twist. This programming has been achieved by targeted deletion and insertion of base pairs in DNA origami structures [17, 32] and tiled DNA nano rings [115]. In addition, straight and untwisted DNA nanotubes have been decorated with curved and twisted (helical) patterns of gold nano particles to demonstrate the fascinating optical properties of chiral nano structures [46].

Here, we describe methods for the construction of twisted, (un-curved) DNA nanotubes, which do not rely on generating torsion within individual DNA helices by introducing over- or under- twist. Instead twist is generated by folding a sheet of DNA helices into a tube with a defined edge offset (sections 4.1.1, 4.1.2). Tube formation and tube twist are studied by temperature-controlled UV absorbance experiments, fluorescence microscopy and atomic force microscopy (AFM).

Next we demonstrate the construction of curved (un-twisted) DNA nanotubes, which form rings with narrow size distribution (section 4.2.1). This is achieved by applying the principle of targeted deletion and insertion of base pairs. We show that the same method yields writhe-shaped nanotubes when the twist is non-zero and characterize their curvature and twist (section 4.2.2). We further show that changes in salt conditions can also induce writhe shape in (unwrithed) DNA nanotubes and discuss the underlying reasons.

Finally we given an outlook on how DNA nano-rings may serve as a template to con- struct lipid-DNA assemblies and show that DNA rings are stable under vesicle preparation conditions (extrusion), can be densely decorated with cholesterol “anchors” and be imaged by Stochastic Optical Reconstruction Microscopy (STORM) under solution conditions.

4.1

Intrinsically Supertwisted DNA Nanotubes

In chapter 2 we showed that based on their sequence design, HX-tubes can form with different amounts of supertwist. However, direct visualization of AuNP decorated tubes by TEM revealed that only the lowest accessible supertwist state was populated. Consistently calculation of the folding energy showed that higher supertwist states are energetically less favorable and thus much less likely to form.

In this section we present two designs to force a specific supertwist state by 1) repro- gramming the assembly pathway (section 4.1.1) and 2) increasing the number of single stranded tiles per sequence repeat unit (section 4.1.2). We term both versions HX-ST tubes, where HX refers to the type of strand cross-overs in the tubes (“half-cross-overs”) and ST denotes that they form with specific super twist.