http://creativecommons.org/licenses/by-sa/2.0/

CIS786, Lecture 6

Usman Roshan

Some of the slides are based upon material by David Wishart of University of Alberta and Ron Shamirof Tel Aviv University

Previously…

Iterated local search: Recursive-Iterative-DCM3

Local optimum

Output of Recursive-DCM3

Recursive-DCM3

Local search

Local search

13921 Proteobacteria rRNA

How to run Rec-I-DCM3 then?

• Unanswered question: what about better TNT heuristics? Can Rec-I-DCM3 improve upon them?

• Rec-I-DCM3 improves upon default TNT but we don’t know what happens for better TNT heuristics.

• Therefore, for a large-scale analysis figure out best settings of the software (e.g. TNT or PAUP*) on the dataset and then use it in conjunction with Rec-I-DCM3 with various subset sizes

Maximum likelihood

Maximum likelihood

• Four problems– Given data, tree, edge lengths, and ancestral

states find likelihood of tree: polynomial time– Given data, tree and edge lengths find

likelihood of tree: polynomial time dynamic programming

– Given data and tree, find likelihood: unknown complexity

– Given data find tree with best likelihood: unknown complexity

Sequential RAxML

Compute randomized parsimony starting treewith dnapars from PHYLIP

Apply exhaustive subtree rearrangements

Iterate while tree improves

Subtree Rearrangements

ST5

ST2

ST6ST4

ST3

ST1

Need to optimize all branches ?

Idea: Lazy Subtree Rearrangements

ST5

ST2

ST6

ST4

ST3

ST1

Idea: Lazy Subtree Rearrangements

ST5

ST2

ST6

ST4

ST3

ST1

Comparison across all datasets

Dataset size Improvement as %

Steps improvement

Max p Avg p

2025 (ARB) -0.002% -6 0.56 0.36

2415 Bininda-Emonds

0.004% 23 0.48 0.2

6673 (RG) 1.251% 6877 1 0.29

7769 (RG) 2.338% 13290 1 0.33

8780 (ARB) 0.03% 270 0.55 0.23

Parallel Rec-I-DCM3

Local optimum

Output of DCM3

Recursive-DCM3Local

search

Local search

(1) Solve subproblems in parallel

(2) Merge subtrees in the proper subtree order

Use parallel RAxMLdeveloped by Duand Stamatakis

P-Rec-I-DCM3 vs Rec-I-DCM3Dataset Parallel LH Sequential

LHImprovement in steps

Improvement (as a %)

500 rbcL (Zilla) -99945 -99967 22 0.022%

2560 rbcL (Kallersjo)

-354944 -355088 144 0.041%

4114 16s Actinobacteria (RDP)

-383108 -383524 416 0.11%

6281 ssu rRNA Eukaryotes (ERNA)

-1270379 -1270785 406 0.032%

6458 16s Firmicutes Bacteria (RDP)

-900875 -902077 1202 0.13%

7769 rRNA 3-dom+2org (Gutell)

-540334 -541019 685 0.13%

Parallel performance limits

• Performance appears sub-optimal because of significant load imbalance caused by different subproblem sizes

• Optimal speedup=(total subproblem time)/(minimum time)

• Dataset 3– 19 subproblems of which 3 require

at least 5K seconds (max is 5569 seconds)

– Optimal speedup: 37353/5569=6.71

• Dataset 6– 43 subproblems of which longest

takes 12164 seconds– Optimal speedup:

63620/12164=5.23

Dataset 3

4

8

16

1.9

5.5

6.7

2.6

5

5.7

2.2

5.3

6.2

Dataset 6

4

8

16

3.2

4.8

5.4

1.95

2.5

2.8

2.2

3

3.3

Processors Base Global Overall

Summary of last time

• Rec-I-DCM3 in detail

• Rec-I-DCM3(TNT)

• Maximum likelihood (ML) problem

• RAxML for solving ML

• Rec-I-DCM3(RAxML)

• Parallel Rec-I-DCM3(RAxML)

Sequencing SuccessesT7 bacteriophagecompleted in 198339,937 bp, 59 coded proteins

Escherichia colicompleted in 19984,639,221 bp, 4293 ORFs

Sacchoromyces cerevisaecompleted in 199612,069,252 bp, 5800 genes

Sequencing SuccessesCaenorhabditis eleganscompleted in 199895,078,296 bp, 19,099 genes

Drosophila melanogastercompleted in 2000116,117,226 bp, 13,601 genes

Homo sapienscompleted in 20033,201,762,515 bp, 31,780 genes

Genomes to Date• 8 vertebrates (human, mouse, rat, fugu, zebrafish)• 3 plants (arabadopsis, rice, poplar)• 2 insects (fruit fly, mosquito)• 2 nematodes (C. elegans, C. briggsae)• 1 sea squirt• 4 parasites (plasmodium, guillardia)• 4 fungi (S. cerevisae, S. pombe)• 200+ bacteria and archebacteria• 2000+ viruses

So what do we do with all this sequence data?

So what do we do with all So what do we do with all this sequence data?this sequence data?

Comparative bioinformatics

DNA Sequence Evolution

AAGACTT -3 mil yrs

-2 mil yrs

-1 mil yrs

today

AAGACTT

T_GACTTAAGGCTT

_GGGCTT TAGACCTT A_CACTT

ACCTT (Cat)

ACACTTC (Lion)

TAGCCCTTA (Monkey)

TAGGCCTT (Human)

GGCTT(Mouse)

T_GACTTAAGGCTT

AAGACTT

_GGGCTT TAGACCTT A_CACTT

AAGGCTT T_GACTT

AAGACTT

TAGGCCTT (Human)

TAGCCCTTA (Monkey)

A_C_CTT (Cat)

A_CACTTC (Lion)

_G_GCTT (Mouse)

_GGGCTT TAGACCTT A_CACTT

AAGGCTT T_GACTT

AAGACTT

Sequence alignments

They tell us about

• Function or activity of a new gene/protein

• Structure or shape of a new protein

• Location or preferred location of a protein

• Stability of a gene or protein

• Origin of a gene or protein

• Origin or phylogeny of an organelle

• Origin or phylogeny of an organism

• And more…

Pairwise alignment

• How to align two sequences?

Pairwise alignment

• How to align two sequences?How to align two sequences?• We use dynamic programming• Treat DNA sequences as strings over the

alphabet {A, C, G, T}

Pairwise alignment

Dynamic programming

Define V(i,j) to be the optimal pairwise alignment score between S1..i and T1..j (|S|=m, |T|=n)

Dynamic programming

Time and space complexity is O(mn)

Define V(i,j) to be the optimal pairwise alignment score between S1..i and T1..j (|S|=m, |T|=n)

Tabular computation of scores

Traceback to get alignment

Local alignment

Finding optimally aligned local regions

Local alignment

Database searching

• Suppose we have a set of 1,000,000 sequences

• You have a query sequence q and want to find the m closest ones in the database---that means 1,000,000 pairwise alignments!

• How to speed up pairwise alignments?

FASTA

• FASTA was the first software for quick searching of a database

• Introduced the idea of searching for k-mers

• Can be done quickly by preprocessing database

FASTA: combine high scoring hits into diagonal runs

BLAST

Key idea: search for k-mers (short matchig substrings) quickly by preprocessing the database.

BLAST

This key idea can also be used for speeding up pairwise alignments when doing multiple sequence alignments

Biologically realistic scoring matrices

• PAM and BLOSUM are most popular

• PAM was developed by Margaret Dayhoff and co-workers in 1978 by examining 1572 mutations between 71 families of closely related proteins

• BLOSUM is more recent and computed from blocks of sequences with sufficient similarity

PAM

• We need to compute the probability transition matrix M which defines the probability of amino acid i converting to j

• Examine a set of closely related sequences which are easy to align---for PAM 1572 mutations between 71 families

• Compute probabilities of change and background probabilities by simple counting

PAM• In this model the unit of evolution is the amount

of evolution that will change 1 in 100 amino acids on the average

The scoring matrix Sab is the ratio of Mab to pb

PAM Mij matrix (x10000)

Multiple sequence alignment

• “Two sequences whisper, multiple sequences shout out loud”---Arthur Lesk

• Computationally very hard---NP-hard

Formally…

Multiple sequence alignment

Unaligned sequences

GGCTT

TAGGCCTT

TAGCCCTTA

ACACTTC

ACTT

Aligned sequences

_G_ _ GCTT_

TAGGCCTT_

TAGCCCTTA

A_ _CACTTC

A_ _C_ CTT_ Conserved regions help us to identify functionality

Sum of pairs score

Sum of pairs score

• What is the sum of pairs score of this alignment?

Tree alignment score

Tree alignment score

Tree Alignment

TAGGCCTT (Human)

TAGCCCTTA (Monkey)

ACCTT (Cat)

ACACTTC (Lion)

GGCTT (Mouse)

Tree Alignment

TAGGCCTT_ (Human)

TAGCCCTTA (Monkey)

A__C_CTT_ (Cat)

A__CACTTC (Lion)

_G__GCTT_ (Mouse)

TAGGCCTT_ A__CACTT_

TGGGGCTT_

AGGGACTT_

0 2

2

11

3

3

2

Tree alignment score = 14

Tree Alignment---depends on tree

TAGGCCTT_ (Human)

TAGCCCTTA (Monkey)

A__C_CTT_ (Cat)

A__CACTTC (Lion)

_G__GCTT_ (Mouse)

TA_CCCTT_ TA_CCCTTA

TA_CCCTT_

TA_CCCTTA

2 3

1

41

0

4

0

Tree alignment score = 15 Switch monkey and cat

Profiles

• Before we see how to construct multiple alignments, how do we align two alignments?

• Idea: summarize an alignment using its profile and align the two profiles

Profile alignment

Iterative alignment(heuristic for sum-of-pairs)

• Pick a random sequence from input set S• Do (n-1) pairwise alignments and align to

closest one t in S• Remove t from S and compute profile of

alignment• While sequences remaining in S

– Do |S| pairwise alignments and align to closest one t

– Remove t from S

Iterative alignment

• Once alignment is computed randomly divide it into two parts

• Compute profile of each sub-alignment and realign the profiles

• If sum-of-pairs of the new alignment is better than the previous then keep, otherwise continue with a different division until specified iteration limit

Progressive alignment

• Idea: perform profile alignments in the order dictated by a tree

• Given a guide-tree do a post-order search and align sequences in that order

• Widely used heuristic

• Can be used for solving tree alignment

Simultaneous alignment and phylogeny reconstruction

• Given unaligned sequences produce both alignment and phylogeny

• Known as the generalized tree alignment problem---MAX-SNP hard

• Iterative improvement heuristic:– Take starting tree– Modify it using say NNI, SPR, or TBR– Compute tree alignment score– If better then select tree otherwise continue until

reached a local minimum

Median alignment

• Idea: iterate over the phylogeny and align every triplet of sequences---takes o(m3) (in general for n sequences it takes O(2nmn) time

• Same profiles can be used as in progressive alignment

• Produces better tree alignment scores (as observed in experiments)

• Iteration continues for a specified limit

Popular alignment programs

• ClustalW: most popular, progressive alignment• MUSCLE: fast and accurate, progressive and

iterative combination• T-COFFEE: slow but accurate, consistency

based alignment (align sequences in multiple alignment to be close to the optimal pairwise alignment)

• PROBCONS: slow but highly accurate, probabilistic consistency progressive based scheme

• DIALIGN: very good for local alignments

MUSCLE

MUSCLE

MUSCLE

Profile sum-of-pairs score

Log expectation score used by MUSCLE

Evaluation of multiple sequence alignments

• Compare to benchmark “true” alignments

• Use simulation

• Measure conservation of an alignment

• Measure accuracy of phylogenetic trees

• How well does it align motifs?

• More…

BAliBASE

• Most popular benchmark of alignments

• Alignments are based upon structure

BAliBASE currently consists of 142 reference alignments, containing over 1000 sequences. Of the 200,000 residues in the database, 58% are defined within the core blocks. The remaining 42% are in ambiguous regions that cannot be reliably aligned. The alignments are divided into four hierarchical reference sets, reference 1 providing the basis for construction of the following sets. Each of the main sets may be further sub-divided into smaller groups, according to sequence length and percent similarity.

BAliBASE

• The sequences included in the database are selected from alignments in either the FSSP or HOMSTRAD structural databases, or from manually constructed structural alignments taken from the literature. When sufficient structures are not available, additional sequences are included from the HSSP database (Schneider et al., 1997). The VAST Web server (Madej, 1995) is used to confirm that the sequences in each alignment are structural neighbours and can be structurally superimposed. Functional sites are identified using the PDBsum database (Laskowski et al., 1997) and the alignments are manually verified and adjusted, in order to ensure that conserved residues are aligned as well as the secondary structure elements.

BAliBASE

• Reference 1 contains alignments of (less than 6) equi-distant sequences, ie. the percent identity between two sequences is within a specified range. All the sequences are of similar length, with no large insertions or extensions. Reference 2 aligns up to three "orphan" sequences (less than 25% identical) from reference 1 with a family of at least 15 closely related sequences. Reference 3 consists of up to 4 sub-groups, with less than 25% residue identity between sequences from different groups. The alignments are constructed by adding homologous family members to the more distantly related sequences in reference 1. Reference 4 is divided into two sub-categories containing alignments of up to 20 sequences including N/C-terminal extensions (up to 400 residues), and insertions (up to 100 residues).

Comparison of alignments on BAliBASE

Next time…

• Comparison of alignments under simulation

• Heuristics for simultaneous alignment and phylogeny reconstruction

• Comparison of alignments for motif detection---functional sites in proteins

• Performance of alignments for phylogeny reconstruction