Difference between revisions of "Team:Warwick/Modelling5"

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<br>Solutions for the smallest diameter circles into which ‘n’ unit-diameter circles (taken to have a relative diameter of 1) can be packed are shown in the table above. Considering the shape of the megastructure, and looking at it at any angle as a 2-D shape, it becomes apparent that the most appropriate model to use is the model for 4 circles packed within a larger circle.
 
<br>Solutions for the smallest diameter circles into which ‘n’ unit-diameter circles (taken to have a relative diameter of 1) can be packed are shown in the table above. Considering the shape of the megastructure, and looking at it at any angle as a 2-D shape, it becomes apparent that the most appropriate model to use is the model for 4 circles packed within a larger circle.
  
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<br>This graph shows the exponential increase of the number of tetrahedrons needed to bond various amounts of E.coli cells to the surface of the formed structure. Due to our time period and budget it would seem a lot better to use a smaller value of E.coli cells to be bonded (<50) to minimise the DNA sequencing.
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<br>To find the minimum size of the arms we used the following excel spreadsheet:
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<img src="https://static.igem.org/mediawiki/2015/c/c9/Structure_size_spreadsheet.png" align="middle">
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<p style="float: right;"><img src="https://static.igem.org/mediawiki/2015/8/85/WarwickGraphofsizeincrease.png" align="right" height="480px" width="720px" border="1px"></p>
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<p>Using the relative diameter of a circle with 4 circles of unit diameter packed into it as tightly as possible, we find the radius of the structure by taking away two unit diameters from the larger diameter and dividing that value by two ([2.41421-2]/2). However this only gives us the radius of the structure relative the diameter of the whole structure. To find the radius of the structure in metres, we multiplied the relative radius by the radius of an end of an E-coli cell (0.5x10-6 x 0.207105).  
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<br>If we wanted to bond different zinc fingers to the outside of the structure we would add different binding sites to the tetrahedrons. So each tetrahedron would have, for example 4 different types of zinc finger binding site, each repeated to increase the number of bonded cells. You would also need to change the proportion of binding sites if they have different binding constants. For example if a zinc finger had a binding constant half that of another then you would have to double the number of binding sites for that zinc finger (if you wanted the same number of zinc fingers for each type).
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<br>And finally the image shows how the more tetrahedrons are used to construct the structure, the smoother the resulting sphere will be.
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<br> Once we have the radius of the structure in metres, we can easily find the total width of the structure (double the radius). We can also find the width and radius of the structure in base pairs by dividing the values in metres by the distance between two base pairs (34 x 10-10m) To find the length and width of the structure in cube/zinc finger combinations, we can divide their values in metres by (26.6 x 10-9m). Our calculations gave us a value of 2.07 x 10-7 m for the width of the entire structure
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<img src="https://static.igem.org/mediawiki/2015/3/3e/WarwickSphereys.png" height="300px" width="500px" class="pics" alt="">
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<div class="fifteen columns noleftmargin">
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<h5 class="sidebartitle">Sizing of Structure</h5> 
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<p> For this shape to be manufactured, manual assembly will be needed. The way in which the cubes will be bound is illustrated by this picture. However due to the size of each cube, there will be significantly less zinc finger binding to each cube than in the picture.
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<p><img src="https://static.igem.org/mediawiki/2015/d/d0/Zinc_finger_diagram.png" align="middle">
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</p>
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<p> The link to the paper is <a href= "http://www.nature.com/nature/journal/v350/n6319/abs/350631a0.html">here</a>. </p>
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Revision as of 14:11, 19 August 2015

Warwick iGEM 2015

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