Biomod/2011/TUM/TNT/Results

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<h1>TEM Image Analysis</h1>
<h1>TEM Image Analysis</h1>
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<h2>Distribution of Angles</h2>
When we inspected the structure in the TEM, we saw a spread of the arms in the uprightly orientated structures (figure 3). The magnitude of this spread seemed to be correlated to the amount of DNA binding molecules.  
When we inspected the structure in the TEM, we saw a spread of the arms in the uprightly orientated structures (figure 3). The magnitude of this spread seemed to be correlated to the amount of DNA binding molecules.  
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The angles between the arms were measured with different concentrations of DNA binders. The widths of the angle distributions could be explained by [http://openwetware.org/wiki/Biomod/2011/TUM/TNT/Project/Theory#Fluctuation_of_the_measured_angles thermal fluctuations]. We assumed to find a peak shift of the angles dependend on the added DNA binder concentration.<br>
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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)].  
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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.
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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.
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<td>Spermine 0.42 µM</td><td>1019</td><td>8.7</td><td>3.8</td>
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<td>Spermine 0.42 µM (in average one molecule per 21bp)</td><td>1019</td><td>8.7</td><td>3.8</td>
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<td>Spermine 1.34 µM</td><td>1809</td><td>9.3</td> <td>4.5</td>
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<td>Spermine 1.34 µM (in average one molecule per 7bp)</td><td>1809</td><td>9.3</td> <td>4.5</td>
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<td>Spermine 6.7 µM</td><td>621</td><td>12.5</td> <td>4.5</td>
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<td>Spermine 6.7 µM (in average one molecule per 2bp)</td><td>621</td><td>12.5</td> <td>4.5</td>
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<td>Spermine 12.1 µM</td><td>1129</td><td>12.3</td> <td>2.5</td>
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<td>Spermine 12.1 µM (in average one molecule per 1.5bp)</td><td>1129</td><td>12.3</td> <td>2.5</td>
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<td>Ethidium bromide 0.74 µM</td><td>626</td><td>11.2</td> <td>3.3</td>
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<td>Ethidium bromide 0.74 µM (in average one molecule per 21bp)</td><td>626</td><td>11.2</td> <td>3.3</td>
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<td>Ethidium bromide 2.27 µM</td><td>652</td><td>8.6</td> <td>5.4</td>
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<td>Ethidium bromide 2.27 µM (in average one molecule per 7bp)</td><td>652</td><td>8.6</td> <td>5.4</td>
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<td>DAPI 144 nM</td><td>325</td><td>7.4</td> <td>3.2</td>
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<td>DAPI 144 nM (in average one molecule per 21bp)</td><td>325</td><td>7.4</td> <td>3.2</td>
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<td>DAPI 432 nM</td><td>375</td><td>6.0</td> <td>3.8</td>
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<td>DAPI 432 nM (in average one molecule per 7bp)</td><td>375</td><td>6.0</td> <td>3.8</td>
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<h2>Histograms</h2>
 
The values in the above mentioned table 1 come from the following histograms:  
The values in the above mentioned table 1 come from the following histograms:  
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[[Image:DAPI 7 histo gaussian.png|390px]]
[[Image:DAPI 7 histo gaussian.png|390px]]
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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>
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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.  
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<h2>Distribution of Angles</h2>
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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 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.  
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The width of our measured angles can be explained by the following mechanism:
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]).
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]).

Revision as of 21:23, 2 November 2011

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