Jonathan Kaptcianos e-mail: email@example.com advisor: Professor Jo Ellis-Monaghan. Graph Theory Aiding DNA Fragment Assembly. Work supported by the Vermont Genetics Network through NIH Grant Number P20 RR16462 from the INBR program of the National Center for Research Resources.
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Previous approaches for fragment assembly follow the “overlap-layout consensus” algorithm
Some components in Graph Theory, specifically Eulerian
Paths and de Bruijn Graphs, help us come to some
possible conclusions about the problem regarding
reassembled strands of DNA
eEulerian Circuits and Paths
Eulerian Circuit – visits each edge in a graph exactly once, and ends at the same vertex in which it started.
a-d-b-f-e-d-f-c-b-a is an Eulerian cycle in this particular graph
Eulerian Path – visits each edge in a graph exactly once.
a-b-c-d-e-f-g-c-h-f-i-j is an Eulerian trail in this particular graph
DNA Strands and de Bruijn Graphs
de Bruijn Graph – a directed graph with vertices that represent sequences of symbols from an alphabet, and edges that indicate where the sequence may overlap.
Example: The strand ATCGACTATAAGGCATCGAA
de Bruijn graph has “snippets” of length 4, vertices of length 3, and the directed edge between two vertices represent the 4 piece snippet.
(G,P) → (G1,P1) → (G2,P2) →…→ (Gk,Pk)
Here, P is consistent with Px,y1
Through a series of detachments and cuts, it is possible to transform a once tangled and overwhelming graph into a simplified, equivalent and more easily resolvable graph.
The Eulerian Superpath Approach on DNA Fragment Assembly doesn’t eliminate the discrepancies about the original construction of the Genome, but just makes it a little neater and easier to work with.