Difference between revisions of "Team:Warwick/Modelling5"

 
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<h5 class="sidebartitle">Concept and Use</h5>
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<img src="images/settings.png" class="pics" alt=""> ADD DESCRIPTION...............................................................
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<h5 class="sidebartitle">Cube Construction</h5>
 
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<img src="https://static.igem.org/mediawiki/2015/b/b0/3D_cube_assembly.png" class="pics" alt=""> The aim of this model is to design a 3D, self-assembling structure which forms a shape which allows E-coli cells to be bonded to the outside. One of the shapes we decided to use is a geodesic sphere made up of multiple tetrahedron ‘bricks’. Tetrahedrons are the strongest 3D structure and would allow any sized scaffold to be made. A sphere is the best 3D structure as it has the largest surface area to volume ratio which will allow the largest number of E.coli cells to bond to it.
 
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<br>The first two images are how the tetrahedrons are made, using DNA origami. Our sequences will be designed so that each side will have DNA hairpins which bond to another side of a different tetrahedron. The last image is what the DNA origami structure will look like once it has been made.
 
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Each side of the tetrahedrons will have the binding sequences needed to bind the E.coli cells to the outside of the structure, so that it doesn’t matter where each tetrahedron goes.
 
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    <p>These images show how each side of the tetrahedron will have different hairpins. The red side will bond to the yellow side, and as you can see they can form many shapes.
 
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<br>Optimising the size of the tetrahedrons
 
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<br>The smaller the tetrahedrons the stronger they are and hence the stronger the resulting formed 3D structure will be. However by decreasing their size you increase the amount of DNA you need to construct it which adds complexity, takes more time and is more expensive. Therefore it is important to find a compromise between size and amount of DNA used.
 
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From reading various papers, such as <a href="http://www.hindawi.com/journals/jna/2011/360954/">this one</a> we determined the maximum size you could make was a tetrahedron with side lengths of 75nm. This size maximised stiffness and strength while minimising the amount of DNA.
 
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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>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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The tetrahedron construction model could only create sphere shaped 3D structures. The cells that bound to the outside couldn't be controlled as well as we hoped so we came up with a new model that could. This page discusses the use of cube shaped DNA to create a shape where the cells bonded to the outside could be chosen.
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<p>_______________________________________________________________________________________________________________________________________</p><h5>Cube Construction</h5>
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<p> One idea for a 3-D structure was, with the use of zinc fingers, small cubes of DNA (6 x 6 x 6nm) being bound together to form a megastructure large enough for E-coli cells (size: 2 x 0.5 x 0.5 µm) to bind to with reasonable rates of success. </p>
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<p> The first problem would be to form the cubes readily and make them stable enough to last for the combination processes. In 1991, a paper called ‘Synthesis from DNA of a molecule with the connectivity of a cube’ outlined a method to produce hollow DNA cubes using 10 Double stranded DNA sequences.
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<br> Method:
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<p> <img src="https://static.igem.org/mediawiki/2015/b/b0/3D_cube_assembly.png" align="middle">
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<p> The method is outlined in detail in<a href= "http://www.nature.com/nature/journal/v350/n6319/abs/350631a0.html"> this paper </a>. </p>
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<p> For the cube structure to be able to bind to the E-coli cells, each individual cube will have to have at least one stretch of sequence that the double ended zinc finger could bind to. The double ended zinc fingers that we have been working with have binding sites that are 9 base pairs (2.97 nm or 0.865385 of a DNA helix turn) long. So the zinc finger binding couldn’t be directly on the DNA strand because the zinc finger wouldn’t bind orthogonally to the edge of the cube, meaning that the structure formed would be extremely disordered and hence much less effective in binding E-coli cells.
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<br>  To get around this problem, secondary structures can be used to our advantage. By forcing the strands of DNA on the edges of the small cubes. This way there will be much more control on the orientations in which the small cubes. Each edge of the small cubes would be about 20 nucleotides (6.6nm) long. The secondary structure will be formed from one of the single strands of DNA and will have the zinc finger protein at the tip of it. The sequence needed to form this structure can be manufactured using mFold. To aid the manufacture of the structure, zinc finger binding site will only be incorporated on 5 sides of the cubes on the edge of the structure. This to try and reduce the probability of cubes binding in the wrong orientations and forming an undesired shape.
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<p>_______________________________________________________________________________________________________________________________________</p> <h5>Sizing of Structure</h5> 
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<p> Using geometry, it is possible to determine the minimum size that the megastructure needs to be that will allow all the E-coli cells to bind to it without blocking each other off. This can be done using the idea of circle packing.
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    <img src="https://static.igem.org/mediawiki/2015/e/e6/Ecoli_picture.png" align="middle">
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<p> As shown by the picture above, E-coli cells have rounded edges and a generally cylindrical shape. By considering the ends of each of the E-coli cells as perfect circles of the same size; the following model can be used find the minimum length of each ‘arm’ of the megastructure.
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<p> <img src="https://static.igem.org/mediawiki/2015/1/1b/4_Circles_picture.png" align="left" height="450px" width="450px" border="1px">
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<img src="https://static.igem.org/mediawiki/2015/b/b6/Table_of_relative_diameters.png" align="right" height="500px" width="480px" border="1px">
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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.
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<br>To find the minimum size of the arms we used the following excel spreadsheet:
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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> 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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<p>_______________________________________________________________________________________________________________________________________</p> <h5>Manufacture of the 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> 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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<p> The desired structure is illustrated below: </p>
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<p><img src="https://static.igem.org/mediawiki/2015/c/c5/Sexalea.png"> </p>
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<p>_______________________________________________________________________________________________________________________________________</p><h5>Problems with this model</h5> 
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<p> The sizes are only approximations and they assume that the E-coli cells bind orthogonally to each other. They also only estimate the smallest size the structure could be to allow 6 cells to bind to it. In reality the structure would probably have to be much larger. The largest problem is that this method requires a lot of manual assembly which may be very expensive.
 
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Latest revision as of 20:41, 17 September 2015

Warwick iGEM 2015

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