Genomics Sequencing tech Sequencing tech: next generation What do - - PowerPoint PPT Presentation

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Genomics Sequencing tech Sequencing tech: next generation What do - - PowerPoint PPT Presentation

Jan 02, 2023 463 likes •863 views

Genomics Sequencing tech Sequencing tech: next generation What do we get from sequencing? How to analyze these reads? Mutation identification: Mapping Cancer Heart Disease Brain Disease Genome projects: Assembly Use sequencing for other

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Genomics

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Sequencing tech

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Sequencing tech: next generation

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What do we get from sequencing?

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How to analyze these reads?

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Cancer Heart Disease Brain Disease

Mutation identification: Mapping

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Genome projects: Assembly

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Use sequencing for other types of data

X-seq technology

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RNA-seq

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Assembly

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Assembly

Computational Challenge: assemble individual short fragments (reads) into a single genomic sequence (“superstring”)

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Problem: Given a set of strings, find a shortest string that contains all of them Input: Strings s1, s2,…., sn Output: A string s that contains all strings s1, s2, …., sn as substrings, such that the length of s is minimized

Shortest common superstring

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Shortest common superstring

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Any ideas?

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Directed Graph

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Overlap Graph

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Example

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Shortest common superstring problem is hard

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Shortest common superstring problem is hard

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Is there a better or more feasible way?

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Matching a superstring to a set of short reads

Assume we have a set S of reads with length k (k-mers) Goal: Find a string that can be exactly split in to set S.

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Overlap graph approach

Assume we have a set S of reads with length k (k-mers) Goal: Find a string that can be exactly split in to set S.

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Overlap graph approach is hard

Assume we have a set S of reads with length k (k-mers) Goal: Find a string that can be exactly split in to set S.

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There is an alternative way

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De Bruijn Graph

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De Bruijn Graph

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What is the goal now?

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AT GT CG CA GC TG GG Path visited every EDGE once

Overlap graph vs De Bruijn graph

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MultiEdge

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MultiGraph

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Some definitions

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Eulerian walk/path

zero or

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Eulerian walk/path

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Proof? Algorithm?

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  • a. Start with an arbitrary

vertex v and form an arbitrary cycle with unused edges until a dead end is reached. Since the graph is Eulerian this dead end is necessarily the starting point, i.e., vertex v.

Assume all nodes are balanced

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  • b. If cycle from (a) is not an

Eulerian cycle, it must contain a vertex w, which has untraversed edges. Perform step (a) again, using vertex w as the starting point. Once again, we will end up in the starting vertex w.

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  • c. Combine the cycles from

(a) and (b) into a single cycle and iterate step (b).

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  • A vertex v is semibalanced if

| in-degree(v) - out-degree(v)| = 1

  • If a graph has an Eulerian path starting from s and

ending at t, then all its vertices are balanced with the possible exception of s and t

  • Add an edge between two semibalanced vertices:

now all vertices should be balanced (assuming there was an Eulerian path to begin with). Find the Eulerian cycle, and remove the edge you had added. You now have the Eulerian path you wanted.

Eulerian path