BLAST & Genome assembly

BLAST Genome assembly Conclusion

BLAST & Genome assembly

Solon P. Pissis Tomas Flouri

Heidelberg Institute for Theoretical Studies

May 15, 2014


1 BLASTWhat is BLAST?The algorithm

2 Genome assemblyDe novo assemblyMapping assembly

3 ConclusionOverview


Contents

1 BLAST

2 Genome assembly

De novo assemblyMapping assembly

3 Conclusion


What is BLAST?

What is BLAST?

One of the most widely used algorithms in Bioinformatics


What is BLAST?

What is BLAST?


Purpose: Query large databases for similar sequences


What is BLAST?

What is BLAST?



“Google for molecular biology”


What is BLAST?

What is BLAST?



“Google for molecular biology”

Publicly available under:http://blast.st-va.ncbi.nlm.nih.gov/Blast.cgi

http://blast.st-va.ncbi.nlm.nih.gov/Blast.cgi


What is BLAST?

BLAST: a set of programs

Basic Local Alignment Search Tool is a set of programs forfast and approximate comparison of biological sequences.


What is BLAST?


Basic Local Alignment Search Tool is a set of programs forfast and approximate comparison of biological sequences.In particular, BLAST is useful for the comparison between aquery sequence and a library or database of sequences, inorder to identify library sequences that resemble the querysequence above a certain threshold.


What is BLAST?


Basic Local Alignment Search Tool is a set of programs forfast and approximate comparison of biological sequences.In particular, BLAST is useful for the comparison between aquery sequence and a library or database of sequences, inorder to identify library sequences that resemble the querysequence above a certain threshold.The five traditional BLAST implementations are:


What is BLAST?



BLASTN: both the database and the query are nucleotidesequences


What is BLAST?



BLASTN: both the database and the query are nucleotidesequencesBLASTP: both the database and the query are proteinsequences


What is BLAST?



BLASTN: both the database and the query are nucleotidesequencesBLASTP: both the database and the query are proteinsequencesBLASTX: the database are protein sequences and the query isnucleotide translated into protein sequence


What is BLAST?



BLASTN: both the database and the query are nucleotidesequencesBLASTP: both the database and the query are proteinsequencesBLASTX: the database are protein sequences and the query isnucleotide translated into protein sequenceTBLASTN: the database are nucleotide translated into proteinsequence and the query is a protein sequence


What is BLAST?



BLASTN: both the database and the query are nucleotidesequencesBLASTP: both the database and the query are proteinsequencesBLASTX: the database are protein sequences and the query isnucleotide translated into protein sequenceTBLASTN: the database are nucleotide translated into proteinsequence and the query is a protein sequenceTBLASTX: both the database and the query are nucleotidetranslated into protein sequences


The algorithm

The algorithm

“Why not Smith-Waterman algorithm?”


The algorithm

The algorithm


Smith-Waterman algorithm computes the optimal (maximumscoring) local alignment between two sequences.


The algorithm

The algorithm



In biological applications, we usually need to infer thestatistically significant alignments very fast.


The algorithm

The algorithm




BLAST does not explore the entire search space (DP matrix)but it minimizes the search space for efficiency...


The algorithm

The algorithm





...at the cost of sensitivity


The algorithm

The algorithm






It uses three layers of rules to sequentially identify refinepotential high scoring pairs (HSPs).


The algorithm

The algorithm







These heuristics layers—seeding, extension, andevaluation—form a stepwise refinement procedure.


The algorithm

The algorithm







These heuristics layers—seeding, extension, andevaluation—form a stepwise refinement procedure.

Allows for sampling the entire search space without wastingtime on dissimilar regions.


The algorithm

The algorithm: seeding

BLAST assumes that significant alignments have commonsubwords (substrings or factors) of a fixed-length W .


The algorithm



It first determines the locations of all the common exactmatching substrings which are called word hits.


The algorithm




Only those regions with word hits will be used as alignmentseeds.


The algorithm





In this way BLAST ingores a large fraction of search space.


The algorithm






The neighborhood of a subword contains the word itself andall other words whose score is ≤ T when compared via thesubstitution matrix to the subword.


The algorithm







We may adjust T to control the size of theneighborhood—affecting speed and sensitivity.


The algorithm







We may adjust T to control the size of theneighborhood—affecting speed and sensitivity.

Hence, the interplay between W , T , and the substitutionmatrix is critical!!!


The algorithm

The algorithm: extension


The algorithm


Once the search space is seeded, alignments can be generatedby starting from the individual seeds.


The algorithm



BLAST extends a longer alignment between the query and thedatabase sequence in the left and right direction of the word.


The algorithm




It only searches a subset of the space, so it needs amechanism to know when to stop the extension procedure.


The algorithm





It uses a threshold X representing how much the score isallowed to drop off since the last maximum.


The algorithm






The extension is stopped as soon as the sum score decreasesby more than X when compared with the highest valueobtained during the extension process.


The algorithm







The alignment is trimmed back to the maximum score.


The algorithm







The alignment is trimmed back to the maximum score.

It is generally a good idea to use a large value for X , whichreduces the risk of premature termination.


The algorithm

The algorithm: evaluation

Once seeds have been extended in both directions to createalignments, these alignments are evaluated (post-processed)to determine if they are statistically significant.


The algorithm



The significant alignments are termed HSPs (High ScoringPairs).


The algorithm




At the simplest level we can use an optional alignment scorethreshold (cut-off) S—empirically determined—to sort thealignments into low and high scoring.


The algorithm




At the simplest level we can use an optional alignment scorethreshold (cut-off) S—empirically determined—to sort thealignments into low and high scoring.

By examining the distribution of the alignment scores modeledby comparing random sequences, S can be determined suchthat its value is large enough to guarantee the significance ofthe remaining HSPs.


The algorithm


BLAST next assesses the statistical significance of each HSPscore by using a so called expect value or E-value.


The algorithm



It computes the probability p of observing a score S equal toor grater than score x by exploiting the Gumbel extreme valuedistribution (GEDV).


The algorithm




It is shown that the distribution of Smith-Waterman localalignment scores between two random sequences followsGEDV.


The algorithm





The computation of p is based on statistical parametersdepending upon the substitution matrix, the gap penalties,and the problem size.


The algorithm





The computation of p is based on statistical parametersdepending upon the substitution matrix, the gap penalties,and the problem size.

The expect value E (computed by p) of a database match isthe expected number of times that a random sequence wouldobtain a score S higher than x by chance.


Contents

1 BLAST

2 Genome assembly


3 Conclusion


Genome assembly: DNA sequencing

ATTAGCATAC...


Genome assembly

Genome assembly is the process of taking a huge number ofDNA sequences and putting them back together to create arepresentation of the genome from which the DNA originated.


Genome assembly


De novo: assembling short reads to createfull-length—sometimes novel—sequences.


Genome assembly



Mapping: assembling reads by aligning them against anexisting reference sequence—building a sequence that issimilar but not necessarily identical to the reference.


Genome assembly




Genome assembly is generally a very difficult computationalproblem, and since 2005, probably, one of the hottests inBioinformatics.


Genome assembly




Genome assembly is generally a very difficult computationalproblem, and since 2005, probably, one of the hottests inBioinformatics.

In terms of time and space complexity, de novo assembly isorders of magnitude slower and more memory intensive thanmapping assembly.


Contents

1 BLAST

2 Genome assembly


3 Conclusion


De novo assembly: what is it?


De novo assembly


De novo assembly is a hierarchical data structure that mapsthe sequence data to a putative reconstruction of the target.


De novo assembly



It groups reads into contigs and contigs into scaffolds.


De novo assembly




Contigs provide a multiple sequence alignment of reads plusthe consensus sequence.


De novo assembly





Scaffolds define the contig order and orientation and the sizesof the gaps between contigs using mate pairs (paired-end)information.


De novo assembly






Assemblies are measured by the size and accuracy of theircontigs and scaffolds.


De novo assembly







Assembling a genome using many short NGS reads requires adifferent approach than the methods developed for the fewerbut longer reads produced by Sanger sequencing.


De novo assembly







Assembling a genome using many short NGS reads requires adifferent approach than the methods developed for the fewerbut longer reads produced by Sanger sequencing.

There are two basic algorithmic approaches for de novoassembly: overlap graphs and de Bruijn graphs.


De novo assembly

De novo assembly algorithms: Overlap graphs

Figure: Colored nucleotides indicate overlaps between reads


De novo assembly


Compute all pair-wise overlaps between the reads and capturethis information in a graph.


De novo assembly



Each node in the graph corresponds to a read, and an edgedenotes an overlap between two reads.


De novo assembly




The overlap graph is used to compute an arrangement ofreads and a consensus sequence of contigs.


De novo assembly





This method works best when there is a small number ofreads with significant overlap.


De novo assembly





This method works best when there is a small number ofreads with significant overlap.

Some NGS assemblers use overlap graphs, but this traditionalapproach is computationally intensive: even a de novoassembly of small-sized genomes needs millions of reads,making the overlap graph extremely large.


De novo assembly


Walking along a Hamiltonian cycle (each vertex once) byfollowing the edges in numerical order allows one toreconstruct the genome by combining alignments betweensuccessive reads.


De novo assembly


This method, however, although simple is computationallyextremely expensive.


De novo assembly


A million reads will require a trillion pairwise alignments.


De novo assembly


A million reads will require a trillion pairwise alignments.

There is no known efficient algorithm for finding aHamiltonian cycle.


De novo assembly

De novo assembly algorithms: de Bruijn graphs

Figure: The trick is to construct the de Brujin graph by representing allk-mer prefixes and suffixes as nodes and then drawing edges thatrepresent k-mers having a particular prefix and suffix


De novo assembly


Most NGS assemblers use de Bruijn graphs.


De novo assembly



De Bruijn graphs reduce the computational effort by breakingreads into smaller sequences of DNA, called k-mers, where theparameter k denotes the length in bases of these sequences.


De novo assembly




The de Bruijn graph captures overlaps of length k − 1between these k-mers and not between the actual reads.


De novo assembly





By reducing the entire data set down to k-mer overlaps the deBruijn graph reduces redundancy in short-read data sets(same k-mers are represented by a unique node in the graph).


De novo assembly






The most efficient k-mer size for a particular assembly isdetermined by the read length as well as the error rate; k hassignificant influence on the quality of the assembly.


De novo assembly






The most efficient k-mer size for a particular assembly isdetermined by the read length as well as the error rate; k hassignificant influence on the quality of the assembly.

Another attractive property of de Bruijn graphs is that repeatsin the genome can be collapsed in the graph and do not leadto many spurious overlaps.


De novo assembly



De novo assembly


Finding an Eulerian cycle (visit each edge once) allows one toreconstruct the genome by forming an alignment in whicheach succesive k-mer (from successive edges) is shifted by oneposition.


De novo assembly



De novo assembly


Hence we avoid the computationally expensive task of findinga Hamiltonian cycle.


De novo assembly



De novo assembly


As we visit all edges of the de Brujin graph, which representall possible k-mers we can spell out a candidate genome; foreach edge we traverse, we record the first nucleotide of thek-mer assigned to that edge.


De novo assembly

De novo assembly: a note for Computer Scientists

A simple formulation of the de novo assembly problem as anoptimization problem phrases the problem as a classicalproblem of algorithms on strings: the Shortest CommonSuperstring (SCS) problem.


De novo assembly



Input: strings s1, s2, . . . , sk , where si ∈ Σ∗.


De novo assembly




Output: the shortest string s containing each si as a factor.


De novo assembly





e.g. given s1 = abaab, s2 = baba, s3 = aabbb, ands4 = bbab, we want to output s = bbabaabbb.


De novo assembly





e.g. given s1 = abaab, s2 = baba, s3 = aabbb, ands4 = bbab, we want to output s = bbabaabbb.

SCS problem is shown to be NP-complete! (via the TravelingSalesman problem)


Mapping assembly

Contents

1 BLAST

2 Genome assembly


3 Conclusion


Mapping assembly

Mapping assembly: what is it?

ATTAGCATAC...~3GB

Depth 10 * 3GB = 30GB


Mapping assembly


Hundreds of millions of short reads (dozens or hundreds ofGigabytes) must be mapped (aligned) against a reference sequence(3Gb for human).


Mapping assembly



Definition

Given a text t of length n, where t ∈ Σ+, Σ = {A,C,G,T}, a set

{p1, p2, . . . , pr } of patterns, each of length m < n, where pi ∈ Σ+,

for all 1 ≤ i ≤ r , and an integer e < m, find all the factors of t,which are at Hamming distance less than, or equal to, e from pi .


Mapping assembly



Definition

Given a text t of length n, where t ∈ Σ+, Σ = {A,C,G,T}, a set

{p1, p2, . . . , pr } of patterns, each of length m < n, where pi ∈ Σ+,

for all 1 ≤ i ≤ r , and an integer e < m, find all the factors of t,which are at Hamming distance less than, or equal to, e from pi .

where Σ+ denotes the set of all the strings on the alphabet Σ

except the empty string ε.


Mapping assembly

Mapping assembly: algorithms

The most straightforward way of finding all the occurrences ofa read, if no gap is allowed, consists in sliding the read alongthe genome sequence and noting the positions where thereexists a match.


Mapping assembly



Unfortunately, although conceptually simple, this algorithmhas a huge complexity.


Mapping assembly




When gaps are allowed, one has to resort to traditionaldynamic programming algorithms, such as theNeedleman-Wunsch algorithm.


Mapping assembly





Unfortunately, the complexity becomes even larger.


Mapping assembly






Therefore, to be efficient, all the methods must rely on somesort of pre-processing.


Mapping assembly






Therefore, to be efficient, all the methods must rely on somesort of pre-processing.

i.e. index the genome to provide a direct and fast access to itssubstrings of a given size, using either hashing-based indexesor Burrows-Wheeler-transform-based indexes.


Mapping assembly

Mapping assembly algorithms: hashing

Store the positions of the k-mers in an array of linked lists,using a value of k significantly less than the read size, sayk = 9.


Mapping assembly



In terms of space, the problem is tractable since there are, atmost, 49

= 262144 different 9-mers in the genome.


Mapping assembly





Select a k-mer for each read (a good choice is the leftmostpart, because the quality is better) and map it to the genomeusing the hashing procedure—the seed.


Mapping assembly






For each possible hit, the procedure would then try to mapthe rest (extend) of the read to the genome (possibly allowingerrors, in a Needleman-Wunsch-like algorithm).


Mapping assembly







This two-steps strategy is called seed and extend.


Mapping assembly







This two-steps strategy is called seed and extend.

Drawback is that seeds are usually highly repeated in thereference genome: huge linked lists!


Mapping assembly


A better approach is to divide each read into q equally-longnon-overlapping substrings.


Mapping assembly



Suppose that one allows for e mismatches.


Mapping assembly




At least q − e out of the q substrings can be mapped exactly(in the worst case, the e errors are located in e differentsubstrings, thus leaving q − e substrings without error).


Mapping assembly





The above follows immediately from the pigeon-hole principleand is known as the filtering or partitioning into exactmatches strategy.


Mapping assembly






The q − e substrings that exactly match the genomeconstitute an anchor.


Mapping assembly







There exist( q

q−e

)

possible anchor combinations of the qfragments of a read that we have to check and also extend.


Mapping assembly







There exist( q

q−e

)

possible anchor combinations of the qfragments of a read that we have to check and also extend.

In practice, for the seed part, we use q = 4 and e = 2:( q

q−e

)

= 6 combinations.


Mapping assembly

Mapping assembly algorithms: BWT

Burrows-Wheeler Transform (BWT) (Burrows and Wheeler,1994) is an algorithm used in data compression applicationssuch as bzip2.


Mapping assembly



It can be applied to create a permanent index of the referencesequence, which may be re-used across mapping runs.


Mapping assembly




Consider the n × n matrix in which each row contains adifferent cyclic rotation of the original text of length n.


Mapping assembly




Consider the n × n matrix in which each row contains adifferent cyclic rotation of the original text of length n.Sort the rows lexicographically.


Mapping assembly




Consider the n × n matrix in which each row contains adifferent cyclic rotation of the original text of length n.Sort the rows lexicographically.BWT is the rightmost column in the sorted matrix.


Mapping assembly





If the text has several repeating substrings, then the BWT willhave several places where a single character is repeated;e.g. BWT(mississippi) = pssmipissii.


Mapping assembly





If the text has several repeating substrings, then the BWT willhave several places where a single character is repeated;e.g. BWT(mississippi) = pssmipissii.

The remarkable thing about the BWT is that it isreversible—allowing the original text to be re-generated onlyfrom the last column!


Mapping assembly


mississippi

imississipp

pimississip

ppimississi

ippimississ

sippimissis

ssippimissi

issippimiss

sissippimis

ssissippimi

ississippim

Table: n × n matrix of the cyclic rotations of mississippi


Mapping assembly


Prefix of n − 1 letters nth letter (BWT)

imississip p

ippimissis s

issippimis s

ississippi m

mississipp i

pimississi p

ppimississ i

sippimissi s

sissippimi s

ssippimiss i

ssissippim i

Table: n × n lexicographically sorted matrix of the cyclic rotations ofmississippi


Mapping assembly


There exists a direct relationship between the BWT and thesuffix array—an efficient indexing data structure from whichwe may obtain directly the BWT.


Mapping assembly



The amount of storage that we need to store the BWT,however, is significantly smaller than that suffix array.


Mapping assembly




An increasing number of algorithms is developed to searchthese compressed full-text indexes for permitting fastsubstring queries; the most well-known is the FM-index(Ferragina and Manzini, 2000).


Mapping assembly





It can be used to efficiently find the number of occurrences ofa pattern within the compressed text, as well as to locate theposition of each occurrence.


Mapping assembly






Both the query time and storage space requirements aresublinear with respect to the size of the input data.


Mapping assembly






Both the query time and storage space requirements aresublinear with respect to the size of the input data.

Most recent mapping tools are based on such BWT indexes.


Mapping assembly

Mapping assembly algorithms: some experiments

Table: Mapping 25, 000, 000 64 bp-long simulated reads to the humanchromosome 6 (166, 880, 988 bp)

Programme Total time Reads alignedIndexing Mapping

SOAP2 5m10s 28m25s 22,699,605REAL -q 0 0m00s 26m43s 22,509,708Bowtie 7m35s 49m11s 21,594,916REAL -q 1 0m00s 31m54s 22,519,739

All programmes were run with 48 bp-long seed, with at most two

mismatches in the seed, and reported best hits only.


Contents

1 BLAST

2 Genome assembly


3 Conclusion


Overview

Overview

Recent technological advances have dramatically improvednext-generation sequencing throughput and quality.


Overview

Overview


In parallel with the technological improvements that haveincreased the throughput of the next-generation short-readsequencers, many algorithmic advances have been made.


Overview

Overview



BLAST: a set of programs for the comparison of biologicalsequences.


Overview

Overview




Genome assembly: taking a huge number of DNA sequencesand putting them back together to create a representation ofthe genome from which the DNA originated.


Overview

Overview





De novo assembly: assembling short reads to createfull-length—sometimes novel—sequences.


Overview

Overview





De novo assembly: assembling short reads to createfull-length—sometimes novel—sequences.

Mapping assembly: assembling reads by aligning them againstan existing reference sequence—building a sequence that issimilar but not necessarily identical to the reference.


Overview

Want to know more?

A very nice online course:

“Bioinformatics Algorithms (Part 1)”by Phillip E. C. Compeau, Nikolay Vyahhi, Pavel Pevzner

https://class.coursera.org/bioinformatics-001

https://class.coursera.org/bioinformatics-001


Overview

S. F. Altschul, W. Gish, W. Miller, E. W. Myers, and D. J.Lipman.Basic Local Alignment Search Tool.Journal of Molecular Biology, 215(3):403–410, 1990.

M. Burrows and D. J. Wheeler.A block-sorting lossless data compression algorithm.Technical Report SRC-RR-124, Standord Univeristy, 1994.

J. C. Dohm, C. Lottaz, T. Borodina, and H. Himmelbauer.SHARCGS, a fast and highly accurate short-read assemblyalgorithm for de novo genomic sequencing.Genome Res, 17(11):1697–1706, November 2007.

P. Ferragina and G. Manzini.Opportunistic data structures with applications.In IEEE, editor, Proceedings of the fourty-first annualSymposium on Foundations of Computer Science (FOCS2000), pages 390–398, USA, 2000. IEEE Computer Society.


Overview

R. D. Fleischmann, M. D. Adams, O. White, R. A. Clayton,E. F. Kirkness, A. R. Kerlavage, C. J. Bult, J. F. Tomb, B. A.Dougherty, and J. M. Merrick.Whole-genome random sequencing and assembly ofHaemophilus influenzae.Science, 269:496–512, 1995.

K. Frousios, C. S. Iliopoulos, L. Mouchard, S. P. Pissis, andG. Tischler.REAL: an efficient REad ALigner for next generationsequencing reads.In A. Zhang, M. Borodovsky, G. Ozsoyoglu, and A. R. Mikler,editors, Proceedings of the first ACM International Conferenceon Bioinformatics and Computational Biology (BCB 2011),pages 154–159, USA, 2010. ACM.

D. Hernandez, P. Francois, L. Farinelli, M. Osteras, andJ. Schrenzel.


Overview

De novo bacterial genome sequencing: millions of very shortreads assembled on a desktop computer.Genome Res, March 2008.

B. Langmead, C. Trapnell, M. Pop, and S. L. Salzberg.Ultrafast and memory-efficient alignment of short DNAsequences to the human genome.Genome biology, 10(3):R25+, 2009.

H. Li and R. Durbin.Fast and accurate short read alignment with Burrows-Wheelertransform.Bioinformatics, 25(14):1754–1760, 2009.

R. Li, C. Yu, Y. Li, T.-W. Lam, S.-M. Yiu, K. Kristiansen, andJ. Wang.SOAP2: an improved ultrafast tool for short read alignment.Bioinformatics, 25(16):1966–1967, 2009.


Overview

R. Li, H. Zhu, J. Ruan, W. Qian, X. Fang, Z. Shi, Y. Li, S. Li,G. Shan, K. Kristiansen, S. Li, H. Yang, J. Wang, andJ. Wang.De novo assembly of human genomes with massively parallelshort read sequencing.Genome Research, 20(2):265–272, 2010.

M. Margulies, M. Egholm, W. E. Altman, S. Attiya, J. S.Bader, L. A. Bemben, J. Berka, M. S. Braverman, Y.-J. Chen,Z. Chen, S. B. Dewell, L. Du, J. M. Fierro, X. V. Gomes, B. C.Godwin, W. He, S. Helgesen, C. H. Ho, G. P. Irzyk, S. C.Jando, M. L. I. Alenquer, T. P. Jarvie, K. B. Jirage, J.-B. Kim,J. R. Knight, J. R. Lanza, J. H. Leamon, S. M. Lefkowitz,M. Lei, J. Li, K. L. Lohman, H. Lu, V. B. Makhijani, K. E.McDade, M. P. McKenna, E. W. Myers, E. Nickerson, J. R.Nobile, R. Plant, B. P. Puc, M. T. Ronan, G. T. Roth, G. J.Sarkis, J. F. Simons, J. W. Simpson, M. Srinivasan, K. R.Tartaro, A. Tomasz, K. A. Vogt, G. A. Volkmer, S. H. Wang,


Overview

Y. Wang, M. P. Weiner, P. Yu, R. F. Begley, and J. M.Rothberg.Genome sequencing in microfabricated high-density picolitrereactors.Nature, 437(7057):376–380, 2005.

J. R. Miller, S. Koren, and G. Sutton.Assembly algorithms for next-generation sequencing data.Genomics, 95(6):315–327, 2010.

J. Shendure, G. J. Porreca, N. B. Reppas, X. Lin, J. P.McCutcheon, A. M. Rosenbaum, M. D. Wang, K. Zhang,R. D. Mitra, and G. M. Church.Accurate Multiplex Polony Sequencing of an Evolved BacterialGenome.Science, 309(5741):1728–1732, 2005.

J. R. ten Bosch and W. W. Grody.


Overview

Keeping up with the next generation : Massively parallelsequencing in clinical diagnostics.Journal of Molecular Diagnostics, 10(6):484–492, 2008.

BLAST & Genome assembly

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