MAPS OF DNA AND INTERVAL GRAPHS by Akshita Gurram.
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Transcript of MAPS OF DNA AND INTERVAL GRAPHS by Akshita Gurram.
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MAPS OF DNA AND INTERVAL GRAPHS
by Akshita Gurram
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OUTLINE
• Problem Statement• Graph Construction• Depicting the Graph Problem• NP-hard problem• Special Properties• Graph Solution
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Problem Statement
• Shear DNA into millions of small fragments.
• These fragments are known as “clones”.
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Problem statement
• The sequence of the clones remains unknown.
• The relative order of the probes is identified in clones.
• The sequence of the probes is known in advance
y x z w
Probes
Clones
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Problem Statement
• The main goal of mapping of DNA is
to reconstruct the relative positions
of clones along the original DNA.
• This problem has much in common
with interval graphs and consecutive
1s property of incidence matrices.
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Graph Construction
• Assume that the clones overlap when the
probes sequence matches with each other.
• By sequencing the clones accordingly with the
probes,the original DNA is obtained back.
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Graph Construction
• Consider the clones a,b,c,d,e and let the adjacency matrix tells which pairs of clones overlap in a DNA.
a b c d e a 0 1 0 1 0 b 1 0 1 1 0 c 0 1 0 1 1 d 1 1 1 0 0 e 0 0 1 0 0
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Graph construction• This problem of finding whether pairs of
clones overlap in a long DNA strand can be modeled by an interval graph.
• Let G be a graph with vertices corresponding to clones and edges corresponding to overlapping pairs of clones.
b
a
d
c e
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Relation to a graph problem
• The problem in graphical terms can be defined
as vertices represent clones and two vertices
are adjacent if and only if the clones overlap.
• From the graph we construct a set of intervals
on the real line corresponding to probes using
which the clones were sequenced.
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Graph problem
• Interval model for the given problem is
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An NP-Hard Problem
• The proper sequence of the clones is hard to
determine without the probes.
• The problem is solvable in polynomial time on
interval graphs that is NP-hard.
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Special Properties
The properties that define interval graphs:
The graph should not contain cycles formed by more than
3 vertices in a graph.
• It is chordal and its compliment G is a comparability graph.
• It contains no induced C4 and G is transitively orientable.
• It is chordal and contains no asteroidal triple.
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Graph Solution
• From the interval graph we get the sequencing order of the clones with following intervals:
a: (1,4) b: (2,8) c: (5,10) d: (3,6) e: (7,9)
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Comments
• Interval graphs are extensively used
in bioinformatics.
• It is difficult to determine the clones
sequence without the help of probes
order.
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References
• Golumbic, M. C. (1980). Algorithmic
graph theory and graphs. New York:
Academic Press.
• Graph algorithms in bioinformatics.
http://sydney.edu.au/engineering/it/~
mcharles/teaching/compx456/slides/L07_Gra
phsDNAseq.pdf
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References
• Michael S.Waterman and Jerrold R.Griggs-
Interval graphs and maps of DNA.
http://
link.springer.com/article/10.1007%2FBF02460022
• http://www.powershow.com/view/80865-MTVlN/
Physical_Mapping_of_DNA_powerpoint_ppt_present
ation
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Thank You!!
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Any Queries??