Ch08_GraphsDNAseq - An Introduction to Bioinformatics...

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www.bioalgorithms.info An Introduction to Bioinformatics Algorithms Graph Algorithms in Bioinformatics
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Outline Introduction to Graph Theory Eulerian & Hamiltonian Cycle Problems Benzer Experiment and Interal Graphs DNA Sequencing The Shortest Superstring & Traveling Salesman Problems Sequencing by Hybridization Fragment Assembly and Repeats in DNA Fragment Assembly Algorithms
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info The Bridge Obsession Problem Bridges of Königsberg Find a tour crossing every bridge just once Leonhard Euler, 1735
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Eulerian Cycle Problem Find a cycle that visits every edge exactly once Linear time More complicated Königsberg
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Hamiltonian Cycle Problem Find a cycle that visits every vertex exactly once NP – complete Game invented by Sir William Hamilton in 1857
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Mapping Problems to Graphs Arthur Cayley studied chemical structures of hydrocarbons in the mid-1800s He used trees (acyclic connected graphs) to enumerate structural isomers
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Beginning of Graph Theory in Biology Benzer’s work Developed deletion mapping “Proved” linearity of the gene Demonstrated internal structure of the gene Seymour Benzer, 1950s
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Viruses Attack Bacteria Normally bacteriophage T4 kills bacteria However if T4 is mutated (e.g., an important gene is deleted) it gets disable and looses an ability to kill bacteria Suppose the bacteria is infected with two different mutants each of which is disabled – would the bacteria still survive? Amazingly, a pair of disable viruses can kill a bacteria even if each of them is disabled. How can it be explained?
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Benzer’s Experiment Idea: infect bacteria with pairs of mutant T4 bacteriophage (virus) Each T4 mutant has an unknown interval deleted from its genome If the two intervals overlap: T4 pair is missing part of its genome and is disabled – bacteria survive If the two intervals do not overlap: T4 pair has its entire genome and is enabled – bacteria die
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Complementation between pairs of mutant T4 bacteriophages
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Benzer’s Experiment and Graphs Construct an interval graph : each T4 mutant is a vertex, place an edge between mutant pairs where bacteria survived (i.e., the deleted intervals in the pair of mutants overlap) Interval graph structure reveals whether DNA is linear or branched DNA
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Interval Graph: Linear Genes
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Interval Graph: Branched Genes
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An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Interval Graph: Comparison Linear genome Branched genome
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