DNA Sequencing. Overview

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1 BINF 3350, Genomics and Bioinformatics DNA Sequencing Young-Rae Cho Associate Professor Department of Computer Science Baylor University Overview Backgrounds Eulerian Cycles Problem Hamiltonian Cycles Problem Fragment Assembly for Genome Reconstruction 1

2 Genome Sequencing (1) Genome The entire set of genes A genome can be represented as a book written in an alphabet containing only 4 letters, called nucleotides: A, T, C, and G A human genome has roughly 3 billion nucleotides...ctgatgatggactacgctactactgctagctgtattacgatcagctaccacatcgtagctacgatgcattagcaagctatcgatcgatcgatcgatt ATCTACGATCGATCGATCGATCACTATACGAGCTACTACGTACGTACGATCGCGGGACTATTATCGACTACAGATAAAACATGCTAGTACAACAGTATAC ATAGCTGCGGGATACGATTAGCTAATAGCTGACGATATATAGCCGAGCGGCTACGATGATGCTAGCTGTACAGCTGATGATCTAGCTATCGATGCGATCG ATGCGCGAGTGCGATCGATCACTTCGAGCTAGCTGATCGATCGATGCTAGCTAGCTGACTGATCATGGCGTTAGCTAGCTAGCTGATCGTCGATCGTACG TAGCTGATTACGATCGTCCGATCGTGCTATGACGTACGAGGCGGCTACGTAGCATGCTAGCTGACTGATGTAGCTAGCTATACGATACTATATATTCGAT CGATTTATTACCATGACTGACGCGCATCGCTGTACACGTACTAGCTGATCGATGCTAGTCGATCGATCGATCATGTTATATATCGCGGCGCATCGATCGA CTGCTCGATTATCGATACGTCGATCGCTGTATATACGTCTTTATAGCTAGGAGCATAGCGACGCGCTATCGATCGATCGTCTAGTCGACTGATCGTACTA GCTGACGCTGACGACTAGCTAGCTATCGACGATCGTAGTGCGATTACTAGCTAGGATCCTACTGTACGTCAGTCAGTCTGATCGATAGCGAGGAAAGCGA GACTGATCGTTCTCTAGATGTAGCTGATGTGACTACTATACTACTGGCAGCGATCGGGA... Genome Sequencing Process of determining the sequence of nucleotides that make up a genome. Genome Sequencing (2) Features of Human Genomes Different people have slightly different genomes All humans share 99.9% of the same genetic code. The 0.1% difference accounts for height, eye color, high cholesterol susceptibility, etc. CTGATGATGGACTACGCTACTACTGCTAGCTGTATTACGA TCAGCTACCACATCGTAGCTACGATGCATTAGCAAGCTAT CGATCGATCGATCGATTATCTACGATCGATCGATCGATCA CTATACGAGCTACTACGTACGTACGATCGCGGGACTATTA TCGACTACAGATAAAACATGCTAGTACAACAGTATACATA GCTGCGGGATACGATTAGCTAATAGCTGACGATATCCGAT CTGATGATGGACTACGCTACTACTGCTAGCTGTATTACGA TCAGCTACAACATCGTAGCTACGATGCATTAGCAAGCTAT CGATCGATCGATCGATTATCTACGATCGATCGATCGATCA CTATACGAGCTACTACGTACGTACGATCGCGTGACTATTA TCGACTACAGATGAAACATGCTAGTACAACAGTATACATA GCTGCGGGATACGATTAGCTAATAGCTGACGATATCCGAT 2

3 Types of Genome Sequencing Species Sequencing Determine the consensus genome of an entire species Compare various species (e.g. human and chimpanzee) to understand how their genes function Reveal evolutionary relationships between species Determine the genetic makeup of our evolutionary ancestors Individual Sequencing Determine how an individual differs from its species Unearth the genetic basis of many diseases Forensics applications Brief History of Genome Sequencing (1) Late 1970s First independent sequencing methods were developed by Walter Gilbert and Frederick Sanger - They share the Nobel Prize in Chemistry in Still, their sequencing methods were too expensive for large genomes (with a $1 per nucleotide cost, it would cost $3 billion to sequence the human genome.) 3

4 Brief History of Genome Sequencing (2) 1990s High-throughput methods were used for Human Genome Project - The draft of the human genome was simultaneously completed by the Human Genome Project Consortium (a public project) and Celera Genomics (a private firm) in s Advanced next-generation sequencing techniques were introduced with dramatic cost-down Many mammalian genomes have been sequenced Problem of Genome Sequencing Ideal Situation When we read a book, we can read the entire book one letter at a time from the beginning to the end Real Problem However, modern sequencing machines cannot read an entire genome one nucleotide at a time from beginning to end. They can only shred the genome and read the short pieces. Identify very short fragments of DNA, called reads No idea which genomic positions these reads come from Have to figure out how to put the reads back together to assemble a genome 4

5 Process of Genome Sequencing (1) (Step 1) Read Generation Experimental technique Generate many reads from multiple copies of the same genome (Step 2) Fragment Assembly Computational technique Use the reads to algorithmically put the genome back together Process of Genome Sequencing (2) Multiple (Unsequenced) Genome Copies Reads Read Generation Sequenced Genome Fragment Assembly GGCATGCGTCAGAAACTATCATAGCTAGATCGTACGTAGCC 5

6 Overview Backgrounds Eulerian Cycles Problem Hamiltonian Cycles Problem Fragment Assembly for Genome Reconstruction Königsberg Bridges Problem Königsberg Bridges Problem The people of Königsberg, Prussia, wondered if they could walk through the city, cross each bridge exactly once, and return where they started 6

7 Solving Königsberg Bridges Problem Solution by Leonhard Euler Leonhard Euler developed an approach to answer this question, even for a city with a million islands, in 1735 Eulerian Cycles Eulerian Cycle A cycle that travels to each edge exactly once Eulerian Graph A graph containing an Eulerian cycle Eulerian graph? Eulerian graph? 7

8 Eulerian Cycles in a Directed Graph Balanced Graph indegree(v) = the number of edges leading into vertex v outdegree(v) = the number of edges leading out of v A graph is balanced if indegree(v) = outdegree(v) for every vertex v Eulerian Graph A directed graph is Eulerian if it is connected and balanced Example (1, 2) (2, 1) (0, 2) (1, 1) (1, 0) (1, 1) (2, 1) Eulerian Cycles in an Undirected Graph Eulerian Graph An undirected graph is Eulerian if it is a connected graph with every vertex of even degree Eulerian Cycles vs. Eulerian Path Eulerian cycle: every vertex must have even degree Eulerian path: two vertices must have odd degree, and others must have even degree 8

9 Overview Backgrounds Eulerian Cycles Problem Hamiltonian Cycles Problem Fragment Assembly for Genome Reconstruction Icosian Game Icosian Game William Hamilton designed a game consisting of a board representing 20 islands connected by bridges. He wanted to find a walk that visits every island exactly once and returns back where it started 9

10 Solving Icosian Game Solution? mathematicians still do not know how to solve this problem, even with a small number of islands Hamiltonian Cycles (1) Hamiltonian Cycle A cycle that visits each vertex exactly once Hamiltonian A graph containing a Hamiltonian cycle 14 Hamiltonian cycle? Hamiltonian path?

11 Hamiltonian Cycles (2) Examples of Hamiltonian Complete graph Algorithms to Solve Hamiltonian Cycles Problem Exhaustive algorithm is not efficient No one have found more efficient algorithm than the exhaustive search The HCP has been classified as NP-Complete Overview Backgrounds Eulerian Cycles Problem Hamiltonian Cycles Problem Fragment Assembly for Genome Reconstruction 11

12 Genome Reconstruction Process (1) Read sequencing (2) Creating all possible k-mers (substrings of length k) from reads (3) Assembly of k-mers Assumptions Reads are error-free Every k-mer occurring in the genome occurs exactly once A genome consists of a single circular-shaped chromosome Example Read: AGATCGAGTG 3-mers: AGA GAT ATC TCG CGA GAG AGT GTG Fragment Assembly by Hamiltonian Cycles (1) (Step 1) Creating vertex for every k-mer ATG CGT GGC AAT GTG TGG TGC CAA GCA GCG (Step 2) Connecting vertex v to vertex w with a directed edge if the suffix of v matches the prefix of w ATG CGT GGC AAT GTG TGG TGC CAA GCA GCG 12

13 Fragment Assembly by Hamiltonian Cycles (2) (Step 2) Continued ATG CGT GGC AAT GTG TGG TGC CAA GCA GCG Fragment Assembly by Hamiltonian Cycles (3) (Step 3) Searching Hamiltonian cycle ATG CGT GGC AAT GTG TGG TGC CAA GCA GCG ATG TGG GGC GCG CGT GTG TGC GCA CAA AAT ATG 13

14 Fragment Assembly by Hamiltonian Cycles (4) (Step 4) Constructing a genome Genome: ATG TGG GGC GCG CGT GTG TGC GCA CAA AAT ATG ATGGCGTGCAATG Problem? Fragment Assembly by Eulerian Cycles (1) (Step 1) Creating vertex for each distinct prefix and suffix of length (k-1) from k-mers k-mers: ATG, CGT, GGC, AAT, GTG, TGG, TGC, CAA, GCA, GCG GT CG GG AT TG GC CA AA 14

15 Fragment Assembly by Eulerian Cycles (2) (Step 2) Connecting vertex v to vertex w with a directed edge if there is a k-mer whose prefix is v and whose suffix is w k-mers: ATG, CGT, GGC, AAT, GTG, TGG, TGC, CAA, GCA, GCG GT CGT GG CG AT ATG TG GC CA AA Fragment Assembly by Eulerian Cycles (3) (Step 2) Continued GT CGT CG GTG TGG GG GGC GCG AT ATG TG TGC GC GCA CA AAT AA CAA De Bruijn graph 15

16 Fragment Assembly by Eulerian Cycles (4) (Step 3) Searching for Eulerian cycle GT CGT 5 CG GTG 6 TGG 2 GG 3 4 GGC GCG AT ATG 1 TG TGC GC GCA 7 8 CA AAT 10 AA 9 CAA ATG TGG GGC GCG CGT GTG TGC GCA CAA AAT ATG Algorithm to Search Eulerian Cycle Algorithm (1) Start with an arbitrary node (2) If there is an outgoing edge that does not disconnect the graph when it is removed, then select the edge and remove it (3) If there is no such an edge, then select a remaining edge and remove it (4) Repeat (2) and (3) until reaching the starting node Runtime? 16

17 Fragment Assembly by Eulerian Cycles (5) (Step 4) Constructing a genome Genome: Problem? Multiple genome candidates k-mer multiplicity, e.g., ATCGATCG ATG TGG GGC GCG CGT GTG TGC GCA CAA AAT ATG ATGGCGTGCAATG Solution? Questions? Lecture Slides are found on the Course Website, web.ecs.baylor.edu/faculty/cho/