Team:Warwick/Modelling5
Sexaleaquadrantal Plasmatio
Concept and Use
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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:
For the cubes megastructure 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 megastructure 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.
SIZING OF THE 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.
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.
From reading various papers, such as this one 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.
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.
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).
And finally the image shows how the more tetrahedrons are used to construct the structure, the smoother the resulting sphere will be.
