25/05/2004 evolution/phylogeny/pattern recognition bioinformatics master course bioinformatics data...
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25/05/2004
Evolution/Phylogeny/Pattern recognition
Bioinformatics Master Course
Bioinformatics Data Analysis and Tools
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PatternsSome are easy some are not
• Knitting patterns
• Cooking recipes
• Pictures (dot plots)
• Colour patterns
• Maps
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Example of algorithm reuse: Data clustering
• Many biological data analysis problems can be formulated as clustering problems– microarray gene expression data analysis– identification of regulatory binding sites (similarly, splice
junction sites, translation start sites, ......)– (yeast) two-hybrid data analysis (for inference of protein
complexes)– phylogenetic tree clustering (for inference of horizontally
transferred genes)– protein domain identification– identification of structural motifs– prediction reliability assessment of protein structures– NMR peak assignments – ......
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Data Clustering Problems
• Clustering: partition a data set into clusters so that data points of the same cluster are “similar” and points of different clusters are “dissimilar”
• cluster identification -- identifying clusters with significantly different features than the background
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Application Examples
• Regulatory binding site identification: CRP (CAP) binding site
• Two hybrid data analysis Gene expression data analysis
Are all solvable by the same algorithm!
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Other Application Examples
• Phylogenetic tree clustering analysis (Evolutionary trees)
• Protein sidechain packing prediction
• Assessment of prediction reliability of protein structures
• Protein secondary structures
• Protein domain prediction
• NMR peak assignments
• ……
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Multivariate statistics – Cluster analysis
Dendrogram
Scores
Similaritymatrix
5×5
12345
C1 C2 C3 C4 C5 C6 ..
Raw table
Similarity criterion
Cluster criterion
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Human Evolution
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Comparing sequences - Similarity Score -
Many properties can be used:
• Nucleotide or amino acid composition
• Isoelectric point
• Molecular weight
• Morphological characters
• But: molecular evolution through sequence alignment
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Multivariate statistics – Cluster analysisNow for sequences
Phylogenetic tree
Scores
Similaritymatrix
5×5
Multiple sequence alignment
12345
Similarity criterion
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Human -KITVVGVGAVGMACAISILMKDLADELALVDVIEDKLKGEMMDLQHGSLFLRTPKIVSGKDYNVTANSKLVIITAGARQ Chicken -KISVVGVGAVGMACAISILMKDLADELTLVDVVEDKLKGEMMDLQHGSLFLKTPKITSGKDYSVTAHSKLVIVTAGARQ Dogfish –KITVVGVGAVGMACAISILMKDLADEVALVDVMEDKLKGEMMDLQHGSLFLHTAKIVSGKDYSVSAGSKLVVITAGARQLamprey SKVTIVGVGQVGMAAAISVLLRDLADELALVDVVEDRLKGEMMDLLHGSLFLKTAKIVADKDYSVTAGSRLVVVTAGARQ Barley TKISVIGAGNVGMAIAQTILTQNLADEIALVDALPDKLRGEALDLQHAAAFLPRVRI-SGTDAAVTKNSDLVIVTAGARQ Maizey casei -KVILVGDGAVGSSYAYAMVLQGIAQEIGIVDIFKDKTKGDAIDLSNALPFTSPKKIYSA-EYSDAKDADLVVITAGAPQ Bacillus TKVSVIGAGNVGMAIAQTILTRDLADEIALVDAVPDKLRGEMLDLQHAAAFLPRTRLVSGTDMSVTRGSDLVIVTAGARQ Lacto__ste -RVVVIGAGFVGASYVFALMNQGIADEIVLIDANESKAIGDAMDFNHGKVFAPKPVDIWHGDYDDCRDADLVVICAGANQ Lacto_plant QKVVLVGDGAVGSSYAFAMAQQGIAEEFVIVDVVKDRTKGDALDLEDAQAFTAPKKIYSG-EYSDCKDADLVVITAGAPQ Therma_mari MKIGIVGLGRVGSSTAFALLMKGFAREMVLIDVDKKRAEGDALDLIHGTPFTRRANIYAG-DYADLKGSDVVIVAAGVPQ Bifido -KLAVIGAGAVGSTLAFAAAQRGIAREIVLEDIAKERVEAEVLDMQHGSSFYPTVSIDGSDDPEICRDADMVVITAGPRQ Thermus_aqua MKVGIVGSGFVGSATAYALVLQGVAREVVLVDLDRKLAQAHAEDILHATPFAHPVWVRSGW-YEDLEGARVVIVAAGVAQ Mycoplasma -KIALIGAGNVGNSFLYAAMNQGLASEYGIIDINPDFADGNAFDFEDASASLPFPISVSRYEYKDLKDADFIVITAGRPQ
Lactate dehydrogenase multiple alignment
Distance Matrix 1 2 3 4 5 6 7 8 9 10 11 12 13 1 Human 0.000 0.112 0.128 0.202 0.378 0.346 0.530 0.551 0.512 0.524 0.528 0.635 0.637 2 Chicken 0.112 0.000 0.155 0.214 0.382 0.348 0.538 0.569 0.516 0.524 0.524 0.631 0.651 3 Dogfish 0.128 0.155 0.000 0.196 0.389 0.337 0.522 0.567 0.516 0.512 0.524 0.600 0.655 4 Lamprey 0.202 0.214 0.196 0.000 0.426 0.356 0.553 0.589 0.544 0.503 0.544 0.616 0.669 5 Barley 0.378 0.382 0.389 0.426 0.000 0.171 0.536 0.565 0.526 0.547 0.516 0.629 0.575 6 Maizey 0.346 0.348 0.337 0.356 0.171 0.000 0.557 0.563 0.538 0.555 0.518 0.643 0.587 7 Lacto_casei 0.530 0.538 0.522 0.553 0.536 0.557 0.000 0.518 0.208 0.445 0.561 0.526 0.501 8 Bacillus_stea 0.551 0.569 0.567 0.589 0.565 0.563 0.518 0.000 0.477 0.536 0.536 0.598 0.495 9 Lacto_plant 0.512 0.516 0.516 0.544 0.526 0.538 0.208 0.477 0.000 0.433 0.489 0.563 0.485 10 Therma_mari 0.524 0.524 0.512 0.503 0.547 0.555 0.445 0.536 0.433 0.000 0.532 0.405 0.598 11 Bifido 0.528 0.524 0.524 0.544 0.516 0.518 0.561 0.536 0.489 0.532 0.000 0.604 0.614 12 Thermus_aqua 0.635 0.631 0.600 0.616 0.629 0.643 0.526 0.598 0.563 0.405 0.604 0.000 0.641 13 Mycoplasma 0.637 0.651 0.655 0.669 0.575 0.587 0.501 0.495 0.485 0.598 0.614 0.641 0.000
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Multivariate statistics – Cluster analysis
Dendrogram/tree
Scores
Similaritymatrix
5×5
12345
C1 C2 C3 C4 C5 C6 ..
Data table
Similarity criterion
Cluster criterion
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Multivariate statistics – Cluster analysis
Why do it?• Finding a true typology• Model fitting• Prediction based on groups• Hypothesis testing• Data exploration• Data reduction• Hypothesis generation But you can never prove a
classification/typology!
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Cluster analysis – data normalisation/weighting
12345
C1 C2 C3 C4 C5 C6 ..
Raw table
Normalisation criterion
12345
C1 C2 C3 C4 C5 C6 ..
Normalised table
Column normalisation x/max
Column range normalise (x-min)/(max-min)
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Cluster analysis – (dis)similarity matrix
Scores
Similaritymatrix
5×5
12345
C1 C2 C3 C4 C5 C6 ..
Raw table
Similarity criterion
Di,j = (k | xik – xjk|r)1/r Minkowski metrics
r = 2 Euclidean distancer = 1 City block distance
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Cluster analysis – Clustering criteria
Dendrogram (tree)
Scores
Similaritymatrix
5×5
Cluster criterion
Single linkage - Nearest neighbour
Complete linkage – Furthest neighbour
Group averaging – UPGMA
Ward
Neighbour joining – global measure
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Cluster analysis – Clustering criteria
1. Start with N clusters of 1 object each
2. Apply clustering distance criterion iteratively until you have 1 cluster of N objects
3. Most interesting clustering somewhere in between
Dendrogram (tree)
distance
N clusters1 cluster
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
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Single linkage clustering (nearest neighbour)
Char 1
Char 2
Distance from point to cluster is defined as the smallest distance between that point and any point in the cluster
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Cluster analysis – Ward’s clustering criterion
Per cluster: calculate Error Sum of Squares (ESS)
ESS = x2 – (x)2/n
calculate minimum increase of ESS
Suppose:
Obj Val c l u s t e r i n g ESS
1 1 1 2 3 4 5 0
2 2 1 2 3 4 5 0.5
3 7 1 2 3 4 5 2.5
4 9 1 2 3 4 5 13.1
5 12 1 2 3 4 5 86.8
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Multivariate statistics – Cluster analysis
Phylogenetic tree
Scores
Similaritymatrix
5×5
12345
C1 C2 C3 C4 C5 C6 ..
Data table
Similarity criterion
Cluster criterion
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Multivariate statistics – Cluster analysis
Scores
5×5
12345
C1 C2 C3 C4 C5 C6
Similarity criterion
Cluster criterion
Scores
6×6
Cluster criterion
Make two-way ordered
table using dendrograms
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Multivariate statistics – Principal Component Analysis (PCA)
12345
C1 C2 C3 C4 C5 C6 Similarity Criterion:Correlations
6×6
Calculate eigenvectors with greatest eigenvalues:
•Linear combinations
•Orthogonal
Correlations
Project datapoints ontonew axes (eigenvectors)
12
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“Nothing in Biology makes sense except in the light of evolution” (Theodosius Dobzhansky (1900-1975))
“Nothing in bioinformatics makes sense except in the light of Biology”
Bioinformatics
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Evolution
• Most of bioinformatics is comparative biology
• Comparative biology is based upon evolutionary relationships between compared entities
• Evolutionary relationships are normally depicted in a phylogenetic tree
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Where can phylogeny be used
• For example, finding out about orthology versus paralogy
• Predicting secondary structure of RNA
• Studying host-parasite relationships
• Mapping cell-bound receptors onto their binding ligands
• Multiple sequence alignment (e.g. Clustal)
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Phylogenetic tree (unrooted)
human
mousefugu
Drosophila
edge
internal node
leaf
OTU – Observed taxonomic unit
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Phylogenetic tree (unrooted)
human
mousefugu
Drosophila
root
edge
internal node
leaf
OTU – Observed taxonomic unit
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Phylogenetic tree (rooted)
human
mouse
fuguDrosophila
root
edge
internal node (ancestor)
leaf
OTU – Observed taxonomic unit
time
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How to root a tree
• Outgroup – place root between distant sequence and rest group
• Midpoint – place root at midpoint of longest path (sum of branches between any two OTUs)
• Gene duplication – place root between paralogous gene copies
f
D
m
h D f m h
f
D
m
h D f m h
f-
h-
f-
h- f- h- f- h-
5
32
1
1
4
1
2
13
1
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Combinatoric explosion
# sequences # unrooted # rooted trees trees
2 1 13 1 34 3 155 15 1056 105 9457 945 10,3958 10,395 135,1359 135,135 2,027,02510 2,027,025 34,459,425
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Tree distances
human x
mouse 6 x
fugu 7 3 x
Drosophila 14 10 9 x
human
mouse
fugu
Drosophila
5
1
1
2
6human
mouse
fuguDrosophila
Evolutionary (sequence distance) = sequence dissimilarity
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Phylogeny methods
• Parsimony – fewest number of evolutionary events (mutations) – relatively often fails to reconstruct correct phylogeny
• Distance based – pairwise distances
• Maximum likelihood – L = Pr[Data|Tree]
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Parsimony & DistanceSequences 1 2 3 4 5 6 7Drosophila t t a t t a a fugu a a t t t a a mouse a a a a a t a human a a a a a a t
human x
mouse 2 x
fugu 3 4 x
Drosophila 5 5 3 x
human
mouse
fuguDrosophila
Drosophila
fugu
mouse
human
12
3 7
64 5
Drosophila
fugu
mouse
human
2
11
12
parsimony
distance
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Maximum likelihood
• If data=alignment, hypothesis = tree, and under a given evolutionary model,
maximum likelihood selects the hypothesis (tree) that maximises the observed data
• Extremely time consuming method
• We also can test the relative fit to the tree of different models (Huelsenbeck & Rannala, 1997)
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Bayesian methods
• Calculates the posterior probability of a tree (Huelsenbeck et al., 2001) –- probability that tree is true tree given evolutionary model
• Most computer intensive technique• Feasible thanks to Markov chain Monte Carlo
(MCMC) numerical technique for integrating over probability distributions
• Gives confidence number (posterior probability) per node
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Distance methods: fastest
• Clustering criterion using a distance matrix
• Distance matrix filled with alignment scores (sequence identity, alignment scores, E-values, etc.)
• Cluster criterion
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Phylogenetic tree by Distance methods (Clustering)
Phylogenetic tree
Scores
Similaritymatrix
5×5
Multiple alignment
12345
Similarity criterion
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Human -KITVVGVGAVGMACAISILMKDLADELALVDVIEDKLKGEMMDLQHGSLFLRTPKIVSGKDYNVTANSKLVIITAGARQ Chicken -KISVVGVGAVGMACAISILMKDLADELTLVDVVEDKLKGEMMDLQHGSLFLKTPKITSGKDYSVTAHSKLVIVTAGARQ Dogfish –KITVVGVGAVGMACAISILMKDLADEVALVDVMEDKLKGEMMDLQHGSLFLHTAKIVSGKDYSVSAGSKLVVITAGARQLamprey SKVTIVGVGQVGMAAAISVLLRDLADELALVDVVEDRLKGEMMDLLHGSLFLKTAKIVADKDYSVTAGSRLVVVTAGARQ Barley TKISVIGAGNVGMAIAQTILTQNLADEIALVDALPDKLRGEALDLQHAAAFLPRVRI-SGTDAAVTKNSDLVIVTAGARQ Maizey casei -KVILVGDGAVGSSYAYAMVLQGIAQEIGIVDIFKDKTKGDAIDLSNALPFTSPKKIYSA-EYSDAKDADLVVITAGAPQ Bacillus TKVSVIGAGNVGMAIAQTILTRDLADEIALVDAVPDKLRGEMLDLQHAAAFLPRTRLVSGTDMSVTRGSDLVIVTAGARQ Lacto__ste -RVVVIGAGFVGASYVFALMNQGIADEIVLIDANESKAIGDAMDFNHGKVFAPKPVDIWHGDYDDCRDADLVVICAGANQ Lacto_plant QKVVLVGDGAVGSSYAFAMAQQGIAEEFVIVDVVKDRTKGDALDLEDAQAFTAPKKIYSG-EYSDCKDADLVVITAGAPQ Therma_mari MKIGIVGLGRVGSSTAFALLMKGFAREMVLIDVDKKRAEGDALDLIHGTPFTRRANIYAG-DYADLKGSDVVIVAAGVPQ Bifido -KLAVIGAGAVGSTLAFAAAQRGIAREIVLEDIAKERVEAEVLDMQHGSSFYPTVSIDGSDDPEICRDADMVVITAGPRQ Thermus_aqua MKVGIVGSGFVGSATAYALVLQGVAREVVLVDLDRKLAQAHAEDILHATPFAHPVWVRSGW-YEDLEGARVVIVAAGVAQ Mycoplasma -KIALIGAGNVGNSFLYAAMNQGLASEYGIIDINPDFADGNAFDFEDASASLPFPISVSRYEYKDLKDADFIVITAGRPQ
Lactate dehydrogenase multiple alignment
Distance Matrix 1 2 3 4 5 6 7 8 9 10 11 12 13 1 Human 0.000 0.112 0.128 0.202 0.378 0.346 0.530 0.551 0.512 0.524 0.528 0.635 0.637 2 Chicken 0.112 0.000 0.155 0.214 0.382 0.348 0.538 0.569 0.516 0.524 0.524 0.631 0.651 3 Dogfish 0.128 0.155 0.000 0.196 0.389 0.337 0.522 0.567 0.516 0.512 0.524 0.600 0.655 4 Lamprey 0.202 0.214 0.196 0.000 0.426 0.356 0.553 0.589 0.544 0.503 0.544 0.616 0.669 5 Barley 0.378 0.382 0.389 0.426 0.000 0.171 0.536 0.565 0.526 0.547 0.516 0.629 0.575 6 Maizey 0.346 0.348 0.337 0.356 0.171 0.000 0.557 0.563 0.538 0.555 0.518 0.643 0.587 7 Lacto_casei 0.530 0.538 0.522 0.553 0.536 0.557 0.000 0.518 0.208 0.445 0.561 0.526 0.501 8 Bacillus_stea 0.551 0.569 0.567 0.589 0.565 0.563 0.518 0.000 0.477 0.536 0.536 0.598 0.495 9 Lacto_plant 0.512 0.516 0.516 0.544 0.526 0.538 0.208 0.477 0.000 0.433 0.489 0.563 0.485 10 Therma_mari 0.524 0.524 0.512 0.503 0.547 0.555 0.445 0.536 0.433 0.000 0.532 0.405 0.598 11 Bifido 0.528 0.524 0.524 0.544 0.516 0.518 0.561 0.536 0.489 0.532 0.000 0.604 0.614 12 Thermus_aqua 0.635 0.631 0.600 0.616 0.629 0.643 0.526 0.598 0.563 0.405 0.604 0.000 0.641 13 Mycoplasma 0.637 0.651 0.655 0.669 0.575 0.587 0.501 0.495 0.485 0.598 0.614 0.641 0.000
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Cluster analysis – (dis)similarity matrix
Scores
Similaritymatrix
5×5
1
2
3
4
5
C1 C2 C3 C4 C5 C6 ..
Raw table
Similarity criterion
Di,j = (k | xik – xjk|r)1/r Minkowski metrics
r = 2 Euclidean distancer = 1 City block distance
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Cluster analysis – Clustering criteria
Phylogenetic tree
Scores
Similaritymatrix
5×5
Cluster criterion
Single linkage - Nearest neighbour
Complete linkage – Furthest neighbour
Group averaging – UPGMA
Ward
Neighbour joining – global measure
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Neighbour joining
• Global measure – keeps total branch length minimal, tends to produce a tree with minimal total branch length
• At each step, join two nodes such that distances are minimal (criterion of minimal evolution)
• Agglomerative algorithm
• Leads to unrooted tree
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Neighbour joining
xx
y
x
y
xy xy
x
(a) (b) (c)
(d) (e) (f)
At each step all possible ‘neighbour joinings’ are checked and the one corresponding to the minimal total tree length (calculated by adding all branch lengths) is taken.
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How to assess confidence in tree
• Bayesian method – time consuming– The Bayesian posterior probabilities (BPP) are assigned to
internal branches in consensus tree – Bayesian Markov chain Monte Carlo (MCMC) analytical software
such as MrBayes (Huelsenbeck and Ronquist, 2001) and BAMBE (Simon and Larget,1998) is now commonly used
– Uses all the data
• Distance method – bootstrap:– Select multiple alignment columns with replacement– Recalculate tree– Compare branches with original (target) tree– Repeat 100-1000 times, so calculate 100-1000 different trees– How often is branching (point between 3 nodes) preserved for
each internal node?– Uses samples of the data
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The Bootstrap
1 2 3 4 5 6 7 8 C C V K V I Y SM A V R L I F SM C L R L L F T
3 4 3 8 6 6 8 6 V K V S I I S IV R V S I I S IL R L T L L T L
1
2
3
1
2
3
Original
Scrambled
4
5
1
5
2x 3x
Non-supportive