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Unformatted text preview: nucleotides). by the 5’ 10mer of the sequence
representing vj . These oligonucleotides were then combined to form strands
¶3. encoding random paths through the graph. An (illegal) example path (v1 → with
They were generated at random and assigned to the vertices, but
vthe restriction depicted in Fig. them were too similar or complementary.
2 → v3 → v4 ) is that none of 5.4.
Fixed amounts (50 pmol) of each oligonucleotide were mixed together in
¶4. aEach vertex code can At the end of this catenationis assumed that a vi =
single ligation reaction. be considered a reaction, it of two 10mers: ai b i .
(I.e., ai is the 50 10mer and bi is the 30 10mer.) ¶5. Edges: Also represented by 20mers.
The edge from vertex i to vertex j is represented by
ei!j = bi aj , where vi = ai bi , and vj = aj bj .
4 https://en.wikipedia.org/wiki/Adleman, Leonard (accessed 20121104). B. FILTERING MODELS 233 ¶6. Paths: Paths are represented by using complements of the vertex
20mers to stitch together the edge 20mers.
(Of course, using the complements of the edges to stitch together the
vertices works as well.)
For example, a path 2 ! 3 ! 4 is represented:
e e z 2!3 { z 3!4 {
}
}
b 2 a3 b 3 a4
a3 b 3
 {z }
v3 ¶7. Initial and ﬁnal edges: Edges from vin and to vout have special
representations as 30mers:
ein!j = vin aj , where vj = aj bj ,
ei!out = bi vout , where vi = ai bi .
¶8. Note that the special representation of the initial and terminal edges
results in blunt ends for complete paths.
¶9. Therefore, for the n = 7 problems, candidate solutions were 140bp in
length.
There are n 1 edges, but the ﬁrst and last edges are 30mers.
He...
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 Fall '13
 BruceMacLennan

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