IDBA - A practical Iterative de Bruijn Graph De Novo Assembler

Transcription

1 IDBA - A practical Iterative de Bruijn Graph De Novo Assembler Speaker: Gabriele Capannini May 21, 2010

2 Introduction De Novo Assembly assembling reads together so that they form a new, previously unknown sequence. Ilumina and SOLiD high throughput sequencing technologies: fast and cheap, but more difficult to use with repeats or near-identical repeats. Main Existing Solutions String Graph vs de Bruijn Graph.

3 Existing Solutions & Techniques String Graph [1] Each read is represented by a vertex and there is a direct edge from vertex u to vertex v if the suffix of at least x nucleotides of read u is the same as the prefix of read v.

4 Existing Solutions & Techniques de Bruijn Graph [4] An n-dimensional de Bruijn graph of m symbols (s 1,..., s m) is a directed graph with m n vertices, consisting of all possible sequences of n symbols. The set of edges is: Uses: V = {(s 1,..., s 1, s 1), (s 1,..., s 1, s 2),..., (s m,..., s m, s m)} E = {((u 1,..., u n), (v 1,..., v n)) : u 2 = v 1,..., u n = v n 1}. Some grid network topologies are De Bruijn graphs [2]. The DHT protocol Koorde uses a De Bruijn graph [3]. In bioinformatics De Bruijn graphs are used for de novo assembly.

5 Existing Solutions & Techniques Velvet [5] Velvet algorithm manipulates de Bruijn graphs for genomic sequence assembly. Example:

6 Existing Solutions & Techniques Three major problems In general these techniques [5, 6, 1] are affected by: False Positive Vertices Errors in reads introduce false positive vertices which make both graphs bigger and consume more memory. Gap problem Due to non-uniform or low coverage 1, reads may not be sampled for every position in the genome. When all the reads covering consecutive k-mers are missing, we may have short dead-end paths larger k. Branching problem Those k-mers which connect with multiple k-mers due to repeat regions or erroneous reads introduce branches in the graph smaller k. 1 Coverage can be calculated from the length of the original genome (G), the number of reads(n), and the average read length(l) as N L G

7 Existing Solutions & Techniques Removing tips [5] A tip is a chain of nodes that is disconnected on one end. Tips to remove are recognized on the base of two criteria: lenght, a tip will only be removed if it is shorter than 2k, and minority count, at the node where the tip connects to the rest of the graph, the arc has a multiplicity inferior to at least one of the other arcs radiating out of that junction node.

8 Existing Solutions & Techniques Removing bubbles [5] Two paths that start and end at the same nodes and contain similar sequences, are defined a bubble. Whenever the SPT-visit encounters a previously visited node, it backtracks to find the closest common ancestor. If judged similar enough, the paths are merged. The path that reaches the end node first 2 is used as the consensus path. 2 According to the notion of distance, that considers the path-length and the related multiplicity

9 IDBA The algorithm IDBA iterates on a range of k values from k = k min to k = k max and maintains an accumulated de Bruijn graph H k at each step. 1: Filter out k min -mers appearing m times 2: Construct H kmin 3: for(k = k min ; k k max; k k + s) 4: Remove dead-ends with length < 2 k 5: Get all potential contigs 6: Remove reads represented by potential contigs 7: Construct H k+s 8: Remove dead-end with length < 2 k max 9: Merge bubbles 10: Connect potential contigs in H kmax using mate-pair information

10 IDBA The algorithm (cont.) 1: Filter out k min -mers appearing m times In the first step, H kmin is equivalent to the de Bruijn graph G kmin after deleting all vertices whose corresponding k-mers appear no more than m times in all reads. Theorem The probability that a k-mer v in the genome does not appear in H k when t length-l reads are uniformly sampled from a length-g genome with error rate e is at most P m i=1 `t i pi (1 p) t i where p = l k+1 g l+1 (1 e)k p = Pr(v is sampled in a read) Pr(read contains v is sampled) Pr(v is sampled read contains v is sampled) (g l + 1) 1 (l k + 1) (1 e) k where (g l + 1) is the number of possible length-l reads in the genome, (l k + 1) is the number of k-mers per length-l read, and (1 e) k is the probability to correctly read a k-mer.

11 IDBA The algorithm (cont.) 4, 8: Remove dead-end with length < 2 k max Removing tips Velvet [5] 5: Get all potential contigs 6: Remove reads represented by potential contigs 7: Construct H k+1 from H k 1 1 identifying maximal paths v 1... v p i.e. possible contigs of lenght k + p 1. removing all reads that are substring of a contig. (v i, v j ) H k v = v i v j H k+1

12 IDBA The algorithm (cont.) 9: Merge bubbles Removing bubbles Velvet [5] 10: Connect potential contigs in H kmax using mate-pair information Contigs merging ABySS [6] The paired-end information 3 is used to identify contigs that can be linked together. The reads are aligned to the contigs to create a set of linked contigs: two contigs are considered to be linked if at least p pairs join the contigs. A graph search is then performed to look for a single unique path. 3 It offers long-range positional information and simplifies de novo assembly

13 Some Results Test result on real Data Results of each algorithm for real data: Time Memory k Contigs Contigs Max Length IDBA 325s 310M Edena [1] 649s 632M Velvet [5] 150s 893M Abyss [6] 729s 923M Adding the paired-end information: Time Memory k Contigs Contigs Max Length IDBA 361s 310M Abyss [6] 3766s 936M

14 Literature Literature [1] David Hernandez, Patrice Francois, Laurent Farinelli, and Magne Osteras. De novo bacterial genome sequencing: Millions of very short reads assembled on a desktop computer. Genome Research, 18(5): , May [2] Ljiljana Spadavecchia. A network-based asynchronous architecture for cryptographic devices, [3] M. Kaashoek and D. Karger. Koorde: A simple degree-optimal distributed hash table, [4] Nicolaas Govert de Bruijn. A combinatorial problem, [5] Daniel R. Zerbino and Ewan Birney. Velvet: Algorithms for de novo short read assembly using de bruijn graphs. Genome Res., 18, March 2008.

15 Literature Literature (cont.) [6] Jared T Simpson, Kim Wong, Shaun D Jackman, and Jacqueline Schein. Abyss: a parallel assembler for short read sequence data. Genome Res, 19, 2009.

16 Backup Frames Question Theorem The probability that a k-mer v in the genome does not appear in H k when t length-l reads are uniformly sampled from a length-g genome with error rate e `t i is at most P m i=1 that v is sampled in a read. pi (1 p) t i where p = l k+1 (1 g l+1 e)k is the probability Given a error-free sampler (e = 0) able to get all genome in one read (l = g) the probability that a k-mer v appears in the length-g genome when the unique length-l read is sampled with no-error is p = l k+1 g l+1 (1 e)k = l k + 1.