Lceture4_DNA_mapping

Lceture4_DNA_mapping - An Introduction to Bioinformatics...

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www.bioalgorithms.info An Introduction to Bioinformatics Algorithms DNA Mapping and Brute Force Algorithms
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Partial Restriction Digest The sample of DNA is exposed to the restriction enzyme for only a limited amount of time to prevent it from being cut at all restriction sites This experiment generates the set of all possible restriction fragments between every two (not necessarily consecutive) cuts This set of fragment sizes is used to determine the positions of the restriction sites in the DNA sequence
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Partial Digest Example Partial Digest results in the following 10 restriction fragments:
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Multiset of Restriction Fragments We assume that multiplicity of a fragment can be detected, i.e., the number of restriction fragments of the same length can be determined (e.g., by observing twice as much fluorescence intensity for a double fragment than for a single fragment) Multiset : {3, 5, 5 , 8, 9, 14, 14 , 17, 19, 22}
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Partial Digest Fundamentals the set of n integers representing the location of all cuts in the restriction map, including the start and end the multiset of integers representing lengths of each of the fragments produced from a partial digest the total number of cuts X : n : D X :
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info One More Partial Digest Example X 0 2 4 7 10 0 2 4 7 10 2 2 5 8 4 3 6 7 3 10 Representation of D X = {2, 2, 3, 3, 4, 5, 6, 7, 8, 10} as a two dimensional table, with elements of X = {0, 2, 4, 7, 10} along both the top and left side. The elements at ( i , j ) in the table is x j x i for 1 ! i < j ! n .
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Partial Digest Problem: Formulation Goal : Given all pairwise distances between points on a line, reconstruct the positions of those points Input: The multiset of pairwise distances L , containing n(n-1)/2 integers Output: A set X , of n integers, such that D X = L
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Lceture4_DNA_mapping - An Introduction to Bioinformatics...

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