Computing Large-Scale Alignments on a Multi ... - Semantic Scholar

Computing Large-Scale Alignments on a Multi-Cluster Chunxi Chen and Bertil Schmidt

Contents • • • • • •

Motivation Smith-Waterman Algorithm Multi-Cluster Platform Parallelization Performance Evaluation Conclusions

Motivation Growth of GeneBank

Base Pairs of DNA (in billions)

30 25 20 15 10 5 0 1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

Year

• Genetic sequence databases are growing exponentially • Growth rate will continue, since multiple concurrent genome projects have begun with more to come

Motivation • Discovered sequences are analyzed by comparison with sequence databases • Complexity of sequence comparison is proportional to the product of query size times database size • ⇒ Analysis too slow on sequential computers • There are two approaches: – Heuristics, e.g. BLAST, but the more efficient the heuristics, the worse the quality of the results – Parallel Processing, get high quality results in reasonable time

Motivation • Number of completely sequenced genomes: – 105 microbial, 10 Eukaryotic – ~ 10 nearly completed eukaryotic genomes – > 300 genome projects planned or underway (http://www.nslijgenetics.org/seq/)

• Closely related genomes – Eukaryotic example: C. elegans and C. briggsae – Prokaryotic example: E. coli K12 and O157:H7

• What’s Common and What’s Unique – Identify unique & important proteins in pathogens as targets – Identify Genes and Predict Function based on Synteny – Susceptibility to disease (SNPs)

Sequence Alignment • Several algorithms: BLAST, FastA, Smith-Waterman Slower

SmithWaterman

Search Speed

FastA BLAST

Faster Lower

Data Quality

Higher

Smith-Waterman Algorithm • Optimal local alignment of two sequences • Performs an exhaustive search for the optimal local alignment – Complexity O(n×m) for sequence lengths n and m

• Based on the 'dynamic programming' (DP) algorithm – Fill the DP matrix using a substitution (mutation) matrix – Find the maximal value (score) in the matrix – Trace back from the score until a 0 value is reached

Smith-Waterman Algorithm • Aligning S1 and S2 of length l1 and l2 using Recurrences:

⎧0 ⎪ E (i, j ) ⎪ H (i, j ) = max ⎨ ,1 ≤ i ≤ l1, 1 ≤ j ≤ l 2 ⎪ F (i, j ) ⎪⎩ H (i − 1, j − 1) + Sbt ( S1i , S 2 j ) ⎧ H (i, j − 1) − α ⎧ H (i − 1, j ) − α E (i , j ) = max ⎨ , F (i , j ) = max ⎨ E ( i , j 1 ) β − − H (0, j ) = F (0, j ) = 0 ⎩ ⎩ F (i − 1, j ) − β H (i,0) = E (i,0) = 0

• Calculate three possible ways to extend the alignment – by one AminoAcid (AA) in each sequence – by one AA in the first sequence and align it with a gap in the second – by one AA in the second sequence and align it with a gap in the first

Smith-Waterman Algorithm Align S1=ATCTCGTATGATG S2=GTCTATCAC ⎧2 if ( x = y) Sbt( x, y) = ⎨ ⎩− 1 else

α=1, β=1

∅ G T C T A T C A C

∅ A

T

C

T

C G T

A

T G A

0 0 0 0 0 2 1 0 2 1

0 0 2 1 2 2 4 3 2 1

0 00 1 4 3 2 3 6 5 4

0 0 2 3 6 5 4 5 5 4

0 0 1 4 5 5 4 6 5 7

0 0 3 3 4 7 5 5 7 6

0 0 2 2 5 6 9 8 7 6

0 0 0 0 0 0 0 0 0 0

⎧0 ⎪ H (i − 1, j ) − 1 ⎪ H (i, j ) = max ⎨ ⎪ H (i, j − 1) − 1 ⎪⎩ H (i − 1, j − 1) + Sbt ( S1i , S 2 j )

0 2 1 3 4 4 4 5 5 6

0 1 4 3 5 4 6 5 4 5

T G

0 0 0 2 1 0 1 1 3 1 0 2 4 3 2 5 6 5 8 7 8 8 7 7 7 10 10 9 6 9 9

0 2 2 2 1 4 7 7 8 8

ATCTCGTATGATG GTC −TATCAC

Smith-Waterman Algorithm • Aligning two sequences of length N and M – Time Complexity: O(N×M) – Memory Complexity: O(N×M)

• Example – aligning m. pneumoniae (816,394 nucleotides) and m. genitalium (580,074 nucleotides) – around 500-G Cells in the Similarity Matrix

Computing Maximal Score in Linear Space Idea: Store only one row in Similarity Matrix

Similarity Matrix

• Compute maximal score in similarity matrix • Computing the path (traceback) requires additional computation

Traceback in Linear Space start point max point Optimal midpoint

N/8 N/4 3N/8

i*=N/2 5N/8 3N/4 7N/8

Similarity Matrix

Finding Near-Optimal NonOverlapping Alignments

• •

C=0

C=1

C=2

C=3

C=4

C=5

C=6

C=7

C=8

C=9

C=10

C=11

C=12

C=13

∅

A

T

C

T

C

G

T

A

T

G

A

T

G

R=0

∅

0

0

0

0

0

0

0

0

0

0

0

0

0

0

R=1

G

0

0

0

0

0

0

2

1

0

0

2

1

0

2

R=2

T

0

0

2

1

2

1

1

4

3

2

1

1

3

2

R=3

C

0

0

1

4

3

4

3

3

3

2

1

0

2

2

R=4

T

0

0

2

3

6

5

4

5

4

5

4

3

2

1

R=5

A

0

2

2

2

5

5

4

4

7

6

5

6

5

4

R=6

T

0

1

4

3

4

4

4

6

5

9

8

7

8

7

R=7

C

0

0

3

6

5

6

5

5

5

8

8

7

7

7

R=8

A

0

2

2

5

5

5

5

4

7

7

7

10

9

8

R=9

C

0

1

1

4

4

7

6

5

6

6

6

9

9

8

Aligning Determine k highest scores with different alignment start points. Use divide-conquer algorithm k times to determine the actual alignments.

Multi-Cluster Platform Parallel and Distributed Processing Lab in NTU (PDP)

1Gbps Myrinet

1Gbps Myrinet

BioInformatics Research Center in NTU (BIRC)

30Mbps bandwidth 0

1

Head node

• High performance at low cost • Geographically distributed • Different Bandwidths

Head node

1

0

Multi-Cluster Programming Environment MPICH-GLOBUS2 control node of cluster1

control node of cluster2

MPICH-G2 process

node n

node n-1

MPICH process

MPICH process

sharing memory

sharing memory

MPICH process

MPICH process

MPICH Cluster1

MPICH-G2 Layer

MPICH-G2 process

node n-1

MPICH process

MPICH

internet

Cluster2

node n

MPICH process

MPICH Layer

Parallelization on Multi-Cluster • Wavefront Computation of DP matrix

Sequence Y

P0

P1

P2

Sequence X

Parallelization on Multi-Cluster • Divide-and-Conquer traceback computation • Define special columns (SC’s) as the last columns of the parts of the similarity matrix allocated to each processor, except the last processor • Identify the intersection of an optimal path with the special columns SC1 1 P0

SC2 2 P1

SC3 3 P2

P3

Optimal Path

Performance Evaluation • Using MPICH in PDP and BIRC to check the performance of every cluster 8 7

Ideal Speedup PDP BIRC

Speedup

6 5 4 3 2 1 0 0

1

2

3

4

5

6

Number of processors

7

8

Performance Evaluation • Speedups on two the clusters in PDP for aligning two sequences of length 100,000 Ideal Speedup Two Clusters in PDP

10

Speedup

8

6

4

2

0 0

2

4

6

Number of Processors

8

10

Performance Evaluation • Speedups on the PDP and BIRC clusters for aligning two sequences of length 100,000 20

Ideal Speedup PDP+BIRC

18 16 14

Speedup

12 10 8 6 4 2 0 0

2

4

6

8

10

12

14

Number of Processors

16

18

20

Performance Evaluation • Quality of Alignment Results • Comparison to results of MUMmer – Assumes two sequences are closely-related (highly similar) – Can align two bacterial genomes under 1 minute – Uses Suffix Tree to find Maximal Unique Matches – Maximal Unique Match (MUM) Definition: • A subsequence that occurs in two exactly matching copies, once in each input sequence, and that can not be extended in either direction – Key idea: significant long MUM is certainly to be part of the global alignment

Can you find the MUM?

Performance Evaluation • Quality of Alignment Results • Align mitochondrial genomes of Human and Drosophila (not very related) 20000

20000

16000

Drosophila mitochondrial

Drosophila mitochondrial

MUMmer

Our System

16000

12000

8000

4000

0

12000

8000

4000

0 0

4000

8000

12000

Human mitochondrial

16000

0

4000

8000

12000

Human mitochondrial

16000

Conclusion and Future Work • Presented how alignment of long DNA sequences based Dynamic Programming and Divide-andConquer can be efficiently parallelized on a MultiCluster Architecture • Investigating which other applications can benefit from this type of computing power • Investigating different bandwidths levels