Biomod/2011/TUM/TNT/Results: Difference between revisions

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DNA binders were added in such concentrations, that a previously calculated fraction of binding sites should be occupied [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/LabbookA/Calculation_of_intercalator_concentrations (see here for calculation)].  
DNA binders were added in such concentrations to theU, that a previously calculated fraction of binding sites should be occupied [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/LabbookA/Calculation_of_intercalator_concentrations (see here for calculation)].  
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 spermine, ethidium bromide and DAPI as well as the negative control and the positive control (intrinsically twisted) are displayed in table 1.
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 spermine, ethidium bromide and DAPI as well as the negative control and the positive control (intrinsically twisted due to additional base pairs) are displayed in table 1.


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The values in table 1 are based on the following histograms:  
The values in table 1 are based on the following histograms (figure 4):  


[[Image:Negative control gaussian.png|390px]]
[[Image:Negative control gaussian.png|390px]]
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[[Image:DAPI 7 histo gaussian.png|390px]]
[[Image:DAPI 7 histo gaussian.png|390px]]


The measured angles are distributed in a gaussian manner around an angle <math> \phi_0 </math> with a width <math> \sigma </math>. 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 two arms are considerably spread. This leads to the distribution around an finite angle. The width of this distribution is in good agreement with the calculated [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/Project/Theory#Fluctuation_of_the_measured_angles thermal fluctuations]. <br>
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 two arms are considerably spread. This leads to a gaussian distribution around an finite angle. The width of this distribution is in good agreement with the calculated [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/Project/Theory#Fluctuation_of_the_measured_angles thermal fluctuations], which yield deviation of ca. 4.4°. <br>
Furthermore 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 positive control with an internally induced twist by 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) displays much higher angles. The population around zero is maybe due to deformed structures which had no second arm and could not be excluded. This results in many angles around zero. The other population around the finite angle is now the more spread structure. Here the angle of the positive control 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. <br>
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> \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: [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/Methods/Data_Analysis Thermal fluctuation of the arms]).
So we get a theoretical prediction of <br/>
<math> \sigma = 4.4^{\circ} </math> <br/>
which approximately explains the width of our measurements.


<h2>Including Base-Twist Theory</h2>
<h2>Including Base-Twist Theory</h2>

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