Team:Warwick/Modelling5
Sexaleaquadrantal Plasmatio
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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Cube Construction
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.
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.
Method:
The method is outlined in detail in this paper .
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.
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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Sizing of Structure
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.
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.
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.
To find the minimum size of the arms we used the following excel spreadsheet:
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).
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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Manufacture of the structure
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.
The link to the paper is here.
The desired structure is illustrated below:
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Problems with this model
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.