The relation between indel length and functional divergence A - - PowerPoint PPT Presentation

The relation between indel length and functional divergence

A formal study Alexander Schönhuth

Raheleh Salari, Fereydoun Hormozdiari, Artem Cherkasov, Cenk Sahinalp

Computational Biology Lab School of Computing Science Simon Fraser University, Canada Division of Infectious Diseases Faculty of Medicine University of British Columbia

September 17, 2008

Guideline

Goals and Motivation

• Develop computational solutions to identify truly

evolutionary insertions and deletions (indels) in alignments.

Goals and Motivation

• Develop computational solutions to identify truly

evolutionary insertions and deletions (indels) in alignments.

• Examine whether significant indels are correlated to

more severe functional divergence between homologous proteins.

• Improved assessment of functional similarity of

homologous proteins.

Indel Facts

Evolutionary processes behind insertions and deletions are not well understood. Truely evolutionary distributions of indel length:

• Mixtures of exponentials [Qian

and Goldstein, 2003], [Pang et. al, 2005]

• Zipfian distribution [Chang and

Benner, 2004]

Indel Facts

Evolutionary processes behind insertions and deletions are not well understood. Truely evolutionary distributions of indel length:

• Mixtures of exponentials [Qian

and Goldstein, 2003], [Pang et. al, 2005]

• Zipfian distribution [Chang and

Benner, 2004] Classical alignment procedures with affine gap penalties:

• Geometric distribution.

Indel Facts

Evolutionary processes behind insertions and deletions are not well understood. Truely evolutionary distributions of indel length:

• Mixtures of exponentials [Qian

and Goldstein, 2003], [Pang et. al, 2005]

• Zipfian distribution [Chang and

Benner, 2004] Classical alignment procedures with affine gap penalties:

• Geometric distribution.

Moreover, from small-scale studies:

• Indels often occur in the proteins’

loop regions and cause significant structural changes [Fechteler et al., 1995]

• Indels occur in disease-causing

mutational hot spots [Kondrashov et al., 2004]

• Thanks to the structural changes:

novel approaches to antibacterial drug design [Cherkasov et al. 2005, 2006], [Nandan et al. 2007]

Basic Idea and Workflow

Large-scale correlation study on indel occurrence and functional similarity for paralogous proteins.

• 1. Compute all paralogous protein

pairs in an organism.

• 2. Collect “indel” and “non-indel”

pairs.

• 3. Compare functional similarity of

“indel” and “non-indel” protein pairs.

Basic Idea and Workflow

Large-scale correlation study on indel occurrence and functional similarity for paralogous proteins.

• 1. Compute all paralogous protein

pairs in an organism.

• 2. Collect “indel” and “non-indel”

pairs.

• 3. Compare functional similarity of

“indel” and “non-indel” protein pairs.

• 1. Interesting organism and

sound, but efficient alignment method needed.

Basic Idea and Workflow

Large-scale correlation study on indel occurrence and functional similarity for paralogous proteins.

• 1. Compute all paralogous protein

pairs in an organism.

• 2. Collect “indel” and “non-indel”

pairs.

• 3. Compare functional similarity of

“indel” and “non-indel” protein pairs.

• 1. Interesting organism and

sound, but efficient alignment method needed.

• 2. How to identify true indels?

Idea: Identify alignments that contain statistically significant indels, neglect “alignment noise”. Sound indel statistics needed.

Basic Idea and Workflow

Large-scale correlation study on indel occurrence and functional similarity for paralogous proteins.

• 1. Compute all paralogous protein

pairs in an organism.

• 2. Collect “indel” and “non-indel”

pairs.

• 3. Compare functional similarity of

“indel” and “non-indel” protein pairs.

• 1. Interesting organism and

sound, but efficient alignment method needed.

• 2. How to identify true indels?

Idea: Identify alignments that contain statistically significant indels, neglect “alignment noise”. Sound indel statistics needed.

• 3. Definition of functional

similarity needed.

Data and Methods

Organism: E.coli K12

• E.coli K12 is a well known organism.
• In prokaryotes: horizontal gene transfer, insertion of genetic

material from other prokaryotic organisms.

• In bacteria: genomic islands, regions that accumulate inserted

genetic material.

• Novel classes of antibacterial drug targets needed.

Paralogs

• Paralogous proteins (paralogs) can assume different functions in

the organism [Gerlt and Babbitt, 2000].

• Global alignments: Needleman-Wunsch algorithm with affine gap
• penalties. Tool: GGSEARCH [Pearson and Lipman, 1988]
• Paralogous pairs: E-value below 10−6, at least 50% sequence

and 20% sequence identity.

Paralogs

• Paralogous proteins (paralogs) can assume different functions in

the organism [Gerlt and Babbitt, 2000].

• Global alignments: Needleman-Wunsch algorithm with affine gap
• penalties. Tool: GGSEARCH [Pearson and Lipman, 1988]
• Paralogous pairs: E-value below 10−6, at least 50% sequence

and 20% sequence identity.

• Above 40% sequence identity: aligned proteins are structurally

similar [Rost, 1999].

• Between 20% and 40% sequence identity: Twilight zone,

structural similarity cannot straightforwardly be inferred.

GO based Computation of Functional Similarity

• Gene Ontology (GO):

Structured description of functional annotation.

• Three subcategories:
• Molecular Function
• Biological Process
• Cellular Component
• Organized as directed

acyclic graph (DAG).

GO based Computation of Functional Similarity

• Gene Ontology (GO):

Structured description of functional annotation.

• Three subcategories:
• Molecular Function
• Biological Process
• Cellular Component
• Organized as directed

acyclic graph (DAG).

• Proteins are identified with subsets of

nodes in a DAG.

• Protein similarity can be measured based
• n reasonable comparison of “subDAGs”.

GO based Computation of Functional Similarity

• Gene Ontology (GO):

Structured description of functional annotation.

• Three subcategories:
• Molecular Function
• Biological Process
• Cellular Component
• Organized as directed

acyclic graph (DAG).

• Proteins are identified with subsets of

nodes in a DAG.

• Protein similarity can be measured based
• n reasonable comparison of “subDAGs”.

Method of choice: Extension of the semantic similarity measure by [Resnik, 1999] to protein similarity, as described by [Schlicker, 2006], suggested by Francisco Couto and Daniel Faria.

Indel Statistics: Problem Definition

Definition

• If A is an alignment algorithm, let

LA(x, y) resp. IA(x, y) be the length of the alignment resp. the length of the largest indel in the alignment of x = x1...xm, y = y1...yn, as computed by A.

Indel Statistics: Problem Definition

Definition

• If A is an alignment algorithm, let

LA(x, y) resp. IA(x, y) be the length of the alignment resp. the length of the largest indel in the alignment of x = x1...xm, y = y1...yn, as computed by A.

Indel Statistics: Problem Definition

Definition

• If A is an alignment algorithm, let

LA(x, y) resp. IA(x, y) be the length of the alignment resp. the length of the largest indel in the alignment of x = x1...xm, y = y1...yn, as computed by A.

• If k is an integer, let

Pn,T(IA(x,y) ≥ k) := P(IA(x, y) ≥ k | LA(x, y) = n, (x, y) ∈ T) be the probability that the largest indel in the alignment of x and y ((x,y) drawn from a pool of pairs T such that LA(x, y) = n) is greater than k.

Problem Definition

Indel Length Probability (ILP) Problem Computation of the probabilities Pn,T(IA(x,y)≥k). Input: A pair of sequences (x, y), a pool T with (x, y) ∈ T, an alignment algorithm A and an integer k. Output: Pn,T(IA(x,y) ≥ k).

Remark

• Replacing IA(x, y) by SA(x, y), the score of an alignment of x and y is

the classical problem of score statistics.

• Exact solution for A the Smith-Waterman algorithm for ungapped local

alignments given by the Altschul-Dembo-Karlin statistics [Karlin and Altschul, 1990], [Dembo and Karlin, 1991].

Solution Strategy: Pair HMMs

1-q 1-q 1-2p q q p p

X Y M

Px y

i j

qxi

j

q y

End Begin

Pn,T (IA(x, y) ≥ k) correspond to probabilities that Viterbi paths contain a consecutive run of either ’X’ or ’Y’ states

• f length at least k. Hard problem!

Match Indel

q 2p 1-q 1-2p

Solution Strategy: Pair HMMs

1-q 1-q 1-2p q q p p

X Y M

Px y

i j

qxi

j

q y

End Begin

Pn,T (IA(x, y) ≥ k) correspond to probabilities that Viterbi paths contain a consecutive run of either ’X’ or ’Y’ states

• f length at least k. Hard problem!

Match Indel

q 2p 1-q 1-2p

• We write I for ’Indel’ and M for ’Match’.
• Let

Cn,k be the set of sequences over the alphabet M, I of length n that contain a consecutive I stretch of length at least k.

Solution Strategy: Pair HMMs

1-q 1-q 1-2p q q p p

X Y M

Px y

i j

qxi

j

q y

End Begin

Pn,T (IA(x, y) ≥ k) correspond to probabilities that Viterbi paths contain a consecutive run of either ’X’ or ’Y’ states

• f length at least k. Hard problem!

Match Indel

q 2p 1-q 1-2p

• We write I for ’Indel’ and M for ’Match’.
• Let

Cn,k be the set of sequences over the alphabet M, I of length n that contain a consecutive I stretch of length at least k. COMPUTATION OF Pn,T (IA(x, y) ≥ k): 1: Align all sequence pairs from T. 2: Infer p and q by training the pair HMM with the alignments. 3: n ← length of the alignment of x and y 4: Compute P(Cn,k), the probability that the Markov chain generates a sequence from Cn,k. 5: Output P(Cn,k) as an approximation for Pn,T (IA(x, y) ≥ k).

Computation of P(Cn,k): Naive Approach

• Consider first Bt,k , the set of sequences of the type (M is for ’Match’ and I for

’Indel’. Z can be both M or I): Z

1 ... Z t−1

I

t ...

I

t+k−1

Z

t+k ... Z n .

• It holds that

Cn,k =

n−k+1

[

t=1

Bt,k

Computation of P(Cn,k): Naive Approach

• Consider first Bt,k , the set of sequences of the type (M is for ’Match’ and I for

’Indel’. Z can be both M or I): Z

1 ... Z t−1

I

t ...

I

t+k−1

Z

t+k ... Z n .

• It holds that

Cn,k =

n−k+1

[

t=1

Bt,k

• However, proceeding by inclusion-exlusion

P(Cn,k) =

n−k+1

X

m=1

(−1)m+1 X

1≤t1<...<tm≤n−k+1

P(Bt1,k ∩ ... ∩ Btm,k) results in computation of

n−k+1

X

m=1

“n − k + 1 m ” = 2n−k+1 − 1 terms of the type P(Bt1,k ∩ ... ∩ Btm,k), hence computation of P(Cn,k) would be exponential in n.

Efficient Computation of P(Cn,k)

• Therefore, for 1 ≤ t ≤ n − k, consider Dt,k, the set of sequences of the type

Z

1 ... Z t−1

I

t ...

I

t+k−1

M

t+k

Z

t+k+1 ... Z n

Efficient Computation of P(Cn,k)

• Therefore, for 1 ≤ t ≤ n − k, consider Dt,k, the set of sequences of the type

Z

1 ... Z t−1

I

t ...

I

t+k−1

M

t+k

Z

t+k+1 ... Z n

• Here as well

Cn,k =

n−k+1

[

t=1

Dt,k where Dn−k+1,k := Bn−k+1,k as before.

• Inclusion-exclusion

P(Cn,k) =

n−k+1

X

m=1

(−1)m+1 X

1≤t1<...<tm≤n−k+1

P(Dt1,k ∩ ... ∩ Dtm,k) followed by noting that Dt,k ∩ Ds,k = ∅ for |t − s| ≤ k, thereby canceling a large number of terms of the type P(Dt1,k ∩ ... ∩ Dtm,k), and applying Markov chain theory allows to efficiently compute the P(Cn,k) in a dynamic programming approach, recursively in n.

Results

Inference of Markov Chain Parameters

• Paralogs were grouped into

ten different pools, according to their alignment similarity scores.

Match Indel

q 2p 1-q 1-2p

• Parameters 1 − 2p and q of

the respective ten different Markov chains were inferred.

Inference of Markov Chain Parameters

• Paralogs were grouped into

ten different pools, according to their alignment similarity scores.

Match Indel

q 2p 1-q 1-2p

• Parameters 1 − 2p and q of

the respective ten different Markov chains were inferred.

• Sim. (%)
• No. Al.

1 − 2p q 95 - 100 26 0.999 0.846 90 - 95 40 0.996 0.665 85 - 90 49 0.994 0.614 80 - 85 62 0.989 0.652 75 - 80 102 0.987 0.632 70 - 75 186 0.983 0.619 65 - 70 345 0.975 0.642 60 - 65 709 0.969 0.667 55 - 60 1793 0.956 0.659 50 - 55 20317 0.935 0.638

Determination of Indel- and Non-Indel Pairs

• n length of the alignment, k maximal indel length, θI, θNI significance

levels

Determination of Indel- and Non-Indel Pairs

• n length of the alignment, k maximal indel length, θI, θNI significance

levels

• Indel (I) pairs

P(Cn,k) ≤ θI

• Non-Indel (NI) pairs

1 − P(Cn,k+1) ≤ θNI

• We found that

θI = 0.045, θNI = 0.25 yielded sufficiently good discrimination while keeping sufficient amounts

• f alignments.

The Twilight Zone: Function

• No. Alignments

GO Similarity T-test Identity I NI O I NI O I vs. O NI vs. O I vs. NI ≥ 20.0 841 647 4413 0.6724 0.7507 0.7069 3.6844 3.9313 4.9547 ≥ 25.0 468 314 2219 0.6871 0.7783 0.7356 4.1953 2.9257 4.4796 ≥ 30.0 183 159 1030 0.7347 0.8132 0.7736 2.0633 2.0135 2.6321 ≥ 35.0 75 98 546 0.7629 0.8515 0.8304 2.2001 0.9201 2.1015 ≥ 40.0 42 63 328 0.8522 0.8610 0.8796 0.7731

• 0.7300

0.1808

0.65 0.7 0.75 0.8 0.85 0.9 0.95 20 25 30 35 40 45

GO similarity: Function Identity

"Indels" "NonIndels" "Overall"

The Twilight Zone: Process

• No. Alignments

GO Similarity T-test Identity I NI O I NI O I vs. O NI vs. O I vs. NI ≥ 20.0 813 670 4500 0.5609 0.7521 0.6699 8.4619 6.2435 9.5150 ≥ 25.0 446 326 2235 0.5443 0.7602 0.6756 7.5987 4.4952 7.6959 ≥ 30.0 177 160 1030 0.6069 0.8030 0.7261 4.3747 3.1777 4.9147 ≥ 35.0 76 97 545 0.7140 0.8193 0.8053 2.3570 0.4757 1.9635 ≥ 40.0 45 62 333 0.8122 0.8372 0.8653 1.3118

• 0.8248

0.4209

0.5 0.6 0.7 0.8 0.9 1 20 25 30 35 40 45

GO similarity: Process Identity

"Indels" "NonIndels" "Overall"

The Twilight Zone: Component

• No. Alignments

GO Similarity T-test Identity I NI O I NI O I vs. O NI vs. O I vs. NI ≥ 20.0 542 381 2986 0.8625 0.9376 0.9139 4.7200 2.2012 4.4590 ≥ 25.0 281 182 1479 0.8644 0.9483 0.9208 3.9673 2.0667 3.9138 ≥ 30.0 123 106 750 0.8698 0.9746 0.9438 3.2578 2.6746 3.6899 ≥ 35.0 60 63 411 0.8390 0.9843 0.9472 2.9245 3.2622 3.3570 ≥ 40.0 36 39 257 0.8443 0.9746 0.9554 2.2478 1.2842 2.2405 ≥ 45.0 19 25 175 0.8832 0.9604 0.9689 1.3316

• 0.4529

1.0406

0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 20 25 30 35 40 45 50

GO similarity: Component Identity

"Indels" "NonIndels" "Overall"

Outlook

• Other organisms / orthologs.
• Extending and refining the statistical model (e.g. for local

alignments)

Outlook

• Other organisms / orthologs.
• Extending and refining the statistical model (e.g. for local

alignments)

• Indels vs. protein interactions
• Drug targets (from studying human-pathogen orthologs)

Acknowledgments

• Francisco Couto, Daniel Faria
• SFU Community Trust Endowment Fund:

“Bioinformatics for Combatting Infectious Diseases” Project

• Pacific Institute for the Mathematical Sciences
• Computational Biology Lab Members, SFU
• Michael Coons
• Peter Höfl

Thanks for the attention!