Restrict.Mapping - RestrictionMappingAlgorithms

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Restriction Mapping Algorithms In this presentation, we will give algorithms to reconstruct the ordering of segments produced from an unknown DNA sequence by using restriction enzymes. We will consider only partial restriction digest. These algorithms are not used in modern day biotechnology but the techniques illustrate the application of branch and bound techniques in mathematical biology and was a hot research topic in the 70s and 80s.
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Discovering Restriction Enzymes Hin dII first restriction enzyme–was discovered accidentally in 1970 while studying how the bacterium Haemophilus influenzae takes up DNA from the virus Recognizes and cuts DNA at sequences: GTGCAC GTTAAC
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Discovering Restriction Enzymes Werner Arber Daniel Nathans Hamilton Smith Werner Arber – discovered restriction enzymes Daniel Nathans pioneered the application of restriction for the construction of genetic maps Hamilton Smith showed that restriction enzyme cuts DNA in the middle of a specific sequence “My father has discovered a servant who serves as a pair of scissors. If a foreign king invades a bacterium, this servant can cut him in small fragments, but he does not do any harm to his own king. Clever people use the servant with the scissors to find out the secrets of the kings. For this reason my father received the Nobel Prize for the discovery of the servant with the scissors". Daniel Nathans’ daughter (from Nobel lecture)
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Recognition Sites of Restriction Enzymes Molecular Cell Biology, 4 th edition
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Full Restriction Digest Cutting DNA at each restriction site creates multiple restriction fragments : Is it possible to reconstruct the order of the fragments from the sizes of the fragments {3,5,5,9} ?
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Full Restriction Digest: Multiple Solutions Alternative ordering of restriction fragments: vs
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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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Partial Digest Example Partial Digest results in the following 10 restriction fragments:
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Multiset of Restriction Fragments We assume 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} 0 5 14 19 22
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Restrict.Mapping - RestrictionMappingAlgorithms

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