which approximately explains the width of our measurements.
which approximately explains the width of our measurements.
We also measured the lengths of the origami structures on the TEM images. Histograms of the length distributions display a gaussian shape (figure xxx). For increasing concentrations of spermine, the length decreases steadily (figure yyy, for raw data see this file: [[Image:TEM length measurements raw data.xlsx]]). Surprisingly, for rising concentrations of ethidium bromide, the length decreases as well, although addition of ethidium bromide is known to increase the length of a simple double stranded DNA. It seems, that origami structures respond in another manner then single helices. <br>
[[Image:Control length histo gaussian.png |390px|center|thumb|Fig. xxx: Length distribution of theU negative control, with a gaussian fit, histogram based on 256 particles]]<br>
[[Image:Etbr length.png|375px|right|thumb|Fig. xxx a: Gaussian fits of length distributions of ethidium bromide concentration series]]
[[Image:Spermine length.png|375px|left|thumb|Fig. xxx b: Gaussian fits of length distributions of spermine concentration series]]
The U structure was folded using the 15_65 ramp. This ramp was the fastest of the tested ones and also led to proper folded origamis as shown in figure 1. There is only one major band visible in the agarose gel, indicating that no significant amounts of byproducts (like dimers) have been formed. The results of the slower ramps 2D_H3_ML and 5D_H3_ML yielded similar results as the 15_65 ramp.
Most of the structures from the major band were folded correctly, which was proven by TEM images (figure 2).
The purification of the structures was tried both with an agarose gel and with an Amicon size exclusion filter (molecular weight cutoff: 100kDa). According to general experience, the yield of purification via agarose gel is approximately 2 nM. The yield of the filter purification was definitively higher, since unexpected weak dilutions led to appropriate concentrations for TEM and fluorescence microscope. Therefore we estimate the yield to be roughly 10 nM.
TEM Image Analysis
When we inspected the structure in the TEM, we saw a spread of the arms in the uprightly orientated structures (figure 1). The magnitude of this spread seemed to be correlated to the amount of DNA binding molecules in solution.
Side view of BM2 without DNA-binders.
Side view of BM2 with one EtBr molecule every 7bp.
The angles between the arms were measured with different concentrations of DNA binders. The widths of the angle distributions could be explained by thermal fluctuations. We assumed to find a peak shift of the angles dependend on the added DNA binder concentration.
The peaks for the tested DNA binding molecules DAPI, ethidium bromide and spermine as well as the negative control and the positive control (intrinsically twisted) are displayed in table 1.
'''Table 1: '''
Spermine 0.42 µM
Spermine 1.34 µM
EtBr 0.69 µM
EtBr 0.74 µM
EtBr 2.27 µM
EtBr 2.4 µM
DAPI 432 nM
DAPI 144 nM
!!!Include ausagekräfitge Bilder von gespreizten U's, eine reihe control, andere twisted control!!!
Fig. 1: The class averages of pure structures (left) and a structure with an internal twist, induced by additional base pairs (right). A spread of the arms in the twisted structure is clearly visible.
The values in the above mentioned table 1 come from the following histograms:
Distribution of Angles
The measured angles are distributed in a gaussian manner around an angle φ0 with a width σ. The distribution of angles in the control has two populations. One where the two arms are exactly above each other which leads to very small angles and one where the slightly twisted arms are pulled down to the surface at the adheration to the grid and therefore is pushed to the side and repelled from the lower arm. This leads to the distribution around an finite angle. Further more we measured a structure with an internally induced twist by including additional base pairs in each helix (these additional base pairs lead to a net torque in each helix and therefore a macroscopic deformation of the structure) which lead to a distribution of the angles around a much higher angle. The population around zero is maybe due to deformed structures which had no second arm and couldn't be excluded. This results in many angles around zero. The other population around the finite angle is now the more spread structure. This angle is shifted to higher values by approximately a factor of 2 because of the induced twist. So in principle this way of measuring the deformation of our structure in dependence of induced stress works.
The width of our measured angles can be explained by the following mechanism:
when the grids for TEM are prepared, the structures are able to fluctuate around a certain mean position which - in our case - corresponds to φ0. So when the structures adhere to the carbon film of the grid and stain is added, they are fixed in one actual position. Since this fluctuation can be described by a Boltzmann distribution, we can easily calculate a theoretical value for the width of our angle measurements with some assumptions (for more details, please see: Thermal fluctuation of the arms).
So we get a theoretical prediction of
which approximately explains the width of our measurements.
The theory determines the torsion for these particular φ-values to ° and °. This corresponds to a torsion of 5° per base-pair in the base.
We also measured the lengths of the origami structures on the TEM images. Histograms of the length distributions display a gaussian shape (figure xxx). For increasing concentrations of spermine, the length decreases steadily (figure yyy, for raw data see this file: Image:TEM length measurements raw data.xlsx). Surprisingly, for rising concentrations of ethidium bromide, the length decreases as well, although addition of ethidium bromide is known to increase the length of a simple double stranded DNA. It seems, that origami structures respond in another manner then single helices.
Fig. xxx: Length distribution of theU negative control, with a gaussian fit, histogram based on 256 particles
Fig. xxx a: Gaussian fits of length distributions of ethidium bromide concentration series
Fig. xxx b: Gaussian fits of length distributions of spermine concentration series
FRET Bulk Measurements
For first tests, a simple 18 bp DNA double helix with Atto 550 ddCTP at the one end and Atto 647N ddUTP at the other end was examined.
The idea to perform bulk measurements based on FRET using a photospectrometer and a real time PCR was unsuccessful.
The photospectrometer is not sensitive enough to handle Atto dyes at concentrations below 10 nM (peaks were not visible at all).
The real time PCR, which is more sensitive, still did not deliver trustworthy data when using 50 µl samples with 10 nM Atto dyes. It could be shown that the reproducibility of the real time PCR setup was poor with deviations of up to 40 % between identical samples (figure 1) . To assure the identity of the samples a 100 µl stock was divided into two 50 µl samples. Based on these results no experiments with theU structure were performed at all with this device as the concentration of theU structure is lower than the concentration of the here test structure.
Figure 1: FRET efficiency Spermine and FRET efficiency EtBr
To handle the issue with the small concentrations further experiments were done with a fluorescence microscope.
FRET at the Fluorescence Microscope
We designed the structure in such a way that a small change of angle in the base, which is a 30 helix bundle in a honey comb lattice, is amplified by the two arms, which are both 10 helix bundles and therefore should twist as well. To measure the change in twist and angle two fluorophores were attached to the two arms so that a deformation should cause a change in distance between them. We chose a donor and an acceptor fluorophore, namely Atto 550 and Atto 647N, so a change in distance between them leads to a change in FRET-efficiency.
In order to immobilize our structure standing upright on the coverslide we used neutravidin and biotinylated oligos complementary to staples at the base of our structure, which is a common way to immobilize DNA origamis on surfaces.
The fluorescence microscope has three lasers with different wavelenghts (blue:473nm, green: 532nm, red: 640nm). We only used the red and the green one because of the dyes we attached to our “U”.
For the measurement we used alternating-laser excitation of single molecules (ALEX) with an excitation length of 0.05 sec.
Depending on the background we decided to use the microscope either in epifluorescence or in TIRF modus.
The analysis program is a matlab script which searches for spots in the red and the green movie and plots the intensities over time to identify bleaching events. Only those plots where the acceptor bleaches first and the donor bleaches afterwards are useful to calculate the FRET-efficiency.
Fig: Example of an intensity over time plot of the acceptor and donor
The graph shows the intensities of the donor and the acceptor and in addition the intensity of the FRET-events. As one can see the intensity of the donor rises as soon as the acceptor bleaches. After some while the donor bleaches too. From that the FRET-efficiency can be calculated.
We at first measured the FRET-efficiencies for the BM14 structure without any intercalator or groove binder as a control and afterward we measured the same structure with 4.8µM spermine. We plotted the FRET-efficiencies in the following histograms.
It is obvious that we actually measured FRET, though the low yield of FRET-events that were found by the matlab script does not allow to draw any conclusions because of the low statistics. This could mean that there are not all of the staples were labeled correctly so that there are structures that only contain one fluorophore or even none.
Yet the fact that there actually were FRET-events makes it worth to keep on elaborating these measurements.
Fluorescence Tracking at the Fluorescence Microscope
Besides FRET-measurements we also applied another approach to investigate the deformation of the structure where we determine the distance between the fluorophores and thereby get the distance of the two arms by directly comparing two images. At first we excite the Atto 550 dye and observe at its characteristic wavelength and then excite the Atto 647N dye and observe at its characteristic wavelength.
For the analysis with the homemade matlab script at first we had to calibrate the cameras.
Then the matlab script searches for spots in the green and the red picture and fits in an gaussian. The peaks from the green picture then are transfered into the red picture. When there is a matching red spot for the a green spot the distance between them is calculated.
We did those measurements for a control and for two different concentrations of spermin.
Though quantitative evidence is a bit tricky because of the calibration and the fact that one pixel of the pictures equals 101.03nm a qualitative evidence can be see in a shift in distance from the control to higher concentrations of spermin of approximately nm. This shows that in principle it is possible to detect a structure deformation of our biosensor.
Now that we knew this approach principally works, we decided to take pictures at the fluorescence microscope in epifluorescence of a control (the structure immobilized on the surface) and with two different spermine concentrations (1 spermine every 7 bases (1.34 µM spermine) and 1 spermine every 21 bases (0.42 µM spermine)). Every picture was illuminated for 1 sec with the green laser for the green channel and then with the red laser for the red channel for the same time. The graph below now shows the histograms of the distribution of the distance between the maxima of the fitted gaussians in the green and red channel.
Fig: Histogram of the calculated distances of the arms for control (red), 0.42 µM spermine (blue) and 1.34 µM spermine (green)
As one can see the distributions look nearly the same for every concentration except for the control. This is due to the small number of points that were measured for this traces. Furthermore the values for each trace seam not to be distributed in a gaussian manner. This maybe underlies the electrostatic repulsion of the arms when the are in close vicinity. Also the distribution reaches to 120 nm. If our structure occupies this conformation the arms are spread very strong which leads to heavy deformations and defects. In addition this wide spread of the distribution also occurs in the control as well as in the two samples with a high concentration of DNA binding molecules. Possible reasons for this artifacts could be a misalignment of the pictures and not accurate enough determination of the spot since we want to measure spatial separations of in the regime of 5 nm which corresponds to a 20th of one single pixel on the detector. Also acquisition of uncorrelated spots which belong to different structures might be a problem which can be solved by higher dilution of avidin adaptors and therefor the structure on the slide. So one has to refine the setup and acquire more values for better statistics to get trustable values of a mean distance of the arms.
Origamis respond in another way than single DNA helices on local deformations
Spermine causes a positive twist (46°) of double stranded DNA, and additionally decreases the length of DNA (base step rise reduced from 0.34nm to 0.29nm; Tari et.al.). According to Salerno et.al., each bound molecule of ethidium bromide increases the length of a DNA double helix by 3.4nm, which is exactly the length of one base pair. Additionally, it induces a twist of -27°, in contrast to the +36° twist of one base pair.
Although both DNA binders induce length changes in opposite directions on DNA helices, both shorten the whole origami structure. The crosslinking between the helices in theU alters the type of deformation compared to an isolated double helix. One could assume that local changes in twist and length combine in an origami, causing a length change effect with all local deformations integrated.
Regarding the measured twist angles, for small concentrations no effects can be seen with spermine. Without spermine, as well with ca. 5% and 14% occupied binding sides, the angle remains ca. 9°. For higher occupations (50% and 67%), the angle increases to 12°. Additional data points will be needed to fit these findings, but we suggest that a cooperative behavior would be an appropriate explanation. Within DNA origamis, not only a single helices needs to be twisted, but large bundles of helices with many crosslinks. This makes the single helices more rigid, consequently hindering an induced fit of spermine molecules. Only higher concentrations could excert enough force to overcome the local restraints and induce a global twist.
To put these considerations in a nutshell, new theoretical approaches are needed to correlate effects on a single helix with effects on a huge system of interconnected helices.
Twisted positive control is good comparison for deformation by ethidium bromide
One approach to gain further insights and a solid experimental fundament for this goal was the investigation of an intrinsically twisted structure as positive control. In average every 21bp an additional base was inserted, resulting in global deformations that were easily observable in the TEM. Effects on length cannot be examined in this way, since the positive control needed a longer scaffold than the normal theU structure, but it is a good examination object for the angles between the arms. Ethidium bromide lends itself for a comparison, since both every bound ethidium bromide and every additional base cause comparable elongation and they differ only in the twist they cause on a double stranded DNA. Thus this effect can be examined isolated. Regarding our angle distributions from the TEM data, the mean global twist for one additional base every 21bp is 21°, compared to 11° induced by one molecule ethidium bromide every 21bp. One could argue that our method is error-prone due to the angle measurement by hand, but the width of the distributions is in good agreement with the calculated thermal fluctuations, so these data can be regarded as reliable. It will be necessary to check further DNA binders, but the direction of twist should be of high importance for the angle deformation. Positive twists add to the existing pitch, while the negative twist by ethidium bromide needs to work against the intrinsic direction of helical rotation. One needs to consider also that the direction of the total twist of the structure cannot be determined from the 2D projections analyzed in this study.
New practical methods and theories will be needed
Therefore, FRET measurements would be an appropriate method. Although we cannot present final results for FRET analyses, first single molecule analyses can be provided. For an optimization of the FRET studies, the origami structure needs some slight improvements. For this, we have laid a thorough fundament not only of experimental results, but also lots of theoretical considerations, which can explain flexibility and correlate observable (via TEM and / or fluorescence measurements: distances, angles) with unobservable (twists) structural changes.
On the experimental side, one could try to eliminate some uncertainties regarding the applied concentrations. We did some calculations to determine the fraction of occupied binding sites even at small concentrations, but as mentioned above, binding could be cooperative and for a proper testing of such a behavior, concentrations of bound DNA binders must be checked experimentally. This is very trying due to the small concentrations and the little fraction of compounds bound compared to those free in solution. We suggest to try some radiolabeled DNA binders, of which the bound fraction can be determined from radioassays.
Using this information, it should be possible to unravel deformation events step by step on even tinier levels. This not only allows for sophisticated understanding of the flexibility of origamis in response to varying triggers, thereby enabling the development of custom-made dynamic structures, but also helps elucidating the mechanic and maybe also mechanistic effects of DNA binders.
For this last goal, we have the vision of a characteristic plot for DNA binders based on the twist and length changes they cause. In the field of bioscience the Ramachandran plot is a nice way to show typical secondary structures of proteins. In this case we would plot twist against length (fig zzz).
fig. 1: Classifying DNA-binders by twist and length change