Biomod/2011/TUM/TNT/Results/Structure deformation

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Structure deformation

http://openwetware.org/index.php?title=Biomod/2011/TUM/TNT/Results/Structure_deformation&action=edit

Fluorescence measurements

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


FRET measurement

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 therefor 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 neutravedin and biotinylated oligos complementary to staples at the base of our structure, which is a common way to immobilize DNA origamis on surfaces.

To prepare the slides we used this procedure.


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. 

     ...    film einfügen?!?      ...

Depending on the background we decided to use the microscope either in epifluorescence or in TIRF modus.

The analysis program, is a matlab program 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 analysis of all movies is summarized in the following histogramms


.... Histogramme ...



Measurement of the distance between the two dyes on one structure




Fluorescence tracking at the fluorescence microscope


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.

<html> <center><font size=1>'''Table 1: '''</font> <table cellspacing="0" cellpadding="6" align="center"> <tr bgcolor="#f5f5f5" > <td><b></b></td><td><b>Number</b></td><td><b>Mean</b></td></td><td><b>Variance</b></td></td><td><b>SEM</b></td></td> </tr> <tr bgcolor="#f5f5f5"> <td>ctrl</td><td>715</td><td>9.312</td><td>4.830</td><td>0.180642978</td> </tr> <tr bgcolor="#f5f5f5"> <td>ctrl pretwisted</td><td>424</td><td>21.119</td><td>8.161</td><td>0.396347765</td> </tr> <tr bgcolor="#f5f5f5"> <td>Spermine 0.42 µM</td><td>1019</td><td>8.864</td><td>4.793</td><td>0.150157669</td> </tr> <tr bgcolor="#f5f5f5"> <td>Spermine 1.34 µM</td><td>1809</td><td>9.663</td> <td>5.759</td><td>0.1354099</td> </tr> <tr bgcolor="#f5f5f5"> <td>EtBr 0.69 µM</td><td>156</td><td>9.169</td> <td>5.036</td><td>0.403186678</td> </tr> <tr bgcolor="#f5f5f5"> <td>EtBr 0.74 µM</td><td>472</td><td>11.059</td> <td>5.577</td><td>0.256697629</td> </tr> <tr bgcolor="#f5f5f5"> <td>EtBr 2.27 µM</td><td>223</td><td>10.877</td> <td>5.531</td><td>0.370363066</td> </tr> <tr bgcolor="#f5f5f5"> <td>EtBr 2.4 µM</td><td>431</td><td>7.474</td> <td>7.839</td><td>0.377567259</td> </tr> <tr bgcolor="#f5f5f5"> <td>DAPI 432 nM</td><td>375</td><td>6.0277</td> <td>5.3736</td><td>0.277491511</td> </tr> <tr bgcolor="#f5f5f5"> <td>DAPI 144 nM</td><td>325</td><td>7.5568</td> <td>4.1349</td><td>0.229362984</td> </tr> </table> </center> </html> !!!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.

Histogramms

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 [math]\displaystyle{ \phi_0 }[/math] with a width [math]\displaystyle{ \sigma }[/math]. The distribution of angles in the control has two populations. One were the two arms are exactly above each other which leads to very small angles and one were 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 as one can see in fig. 2. 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 (see fig. 3). 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 [math]\displaystyle{ \phi_0 }[/math]. 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
[math]\displaystyle{ \sigma = 3.9^{\circ} }[/math]
which approximately explains the width of our measurements which can be seen in fig. 2 and 3.


File:Control with dblgauss.png
Fig. 2: Histogram of the structure without any twist or DNA binding molecule. The two populations were fitted with a sum of two gaussians with a width around [math]\displaystyle{ \phi_1 = ... }[/math] of [math]\displaystyle{ \sigma_1 = ... }[/math] and another width of [math]\displaystyle{ \sigma_2 = ... }[/math] around [math]\displaystyle{ \phi_2 = ... }[/math]. The total number of measured structures was n=... .

File:Control twist with gauss.png
Fig. 2: Histogram of the structure an internal induced twist. The population around the finite angle was fitted with a gaussian with a width around [math]\displaystyle{ \phi = ... }[/math] of [math]\displaystyle{ \sigma = ... }[/math]. The total number of measured structures was n=... . A shift to higher angles is clearly visible. 

.png|x400px]]

Fig. 4:

We then plotted a histogram of the mean angles versus the part of the structure occupied with DNA binders. We could clearly see a rise of the spread with rising concentration of DNA binding molecules in fig. 5. Since we had many particles, the error is relatively small compared to the values and we assumed our mean spread angle to be accurate.

TIRF?

Including base-twist theory

The measured angles φ for negative and positive control, [math]\displaystyle{ \phi_{neg} \approx 9 }[/math]° and [math]\displaystyle{ \phi_{pos} \approx 21 }[/math]°, can be related to a torsion α of the base according to the Theoretical considerations of the base twist:

[math]\displaystyle{ \frac{cos \alpha -1}{\alpha} = \frac{B L}{R (B - 2 L)} sin \frac{\phi}{2} }[/math]

The theory determines the torsion for these particular φ-values to [math]\displaystyle{ \alpha_{neg} \approx 33 }[/math]° and [math]\displaystyle{ \alpha_{pos} \approx 93 }[/math]°. This corresponds to a torsion of 5° per base-pair in the base.



Arm-twist:

  • TIRF-Auswertung (FRET)

Längenänderung:

  • TIRF-FRET (evtl. two-color-dist.?)
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