Comparative Genomics: Sequence, Structure, and Networks. Bonnie Berger MIT

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1 Comparative Genomics: Sequence, Structure, and Networks Bonnie Berger MIT

2 Comparative Genomics Look at the same kind of data across species with the hope that areas of high correlation correspond to functional parts or modules of the genome.

3 Biology in One Slide Protein Function

4 Comparative Genomics of DNA Protein Function

5 Multiple Species Comparison Look at multiple species simultaneously

6 Application to Regulatory Motif Discovery S. cer S. par S. mik S. bay Evaluate conservation within: Gal4 Controls (1) All intergenic regions 22% 5% (2) Intergenic : coding (3) Upstream : downstream 4:1 1:3 12:1 1:1 A signature for regulatory motifs

7 Result Highlights [Kellis, Patterson, Birren, Berger*, Lander* (2004). RECOMB, ; J. Comp Biol special issue, 11:2-3, ; Kellis et al. Nature (2003)] Identify gene correspondence across species for > 90% of genes in Yeast. 99.9% sensitivity and 99% specificity on 4000 known genes. Refine boundaries of hundreds of genes (5700 genes total). Identify most previously known and 41 novel regulatory motifs. Genome-wide, unbiased search. No previous knowledge necessary.

8 Comparative Genomics of RNA Protein Function

9 RNA Secondary Structure Detection Problem: Identify biologically significant RNA secondary structure. Challenge: Any given single sequence will have a plausible secondary structure. A-U G-C G-U Hairpin Loops Stems Bulge loop Interior loops Multi-branched loop

10 Compensatory Mutations Given K orthologous aligned RNA sequences: If i th and j th positions are base-paired in many organisms, then their nucleotides must covary.

11 Compensatory Mutations Given K orthologous aligned RNA sequences: If i th and j th positions are base-paired in many organisms, then their nucleotides must covary.

12 Approaches to Secondary Structure Detection Statistical Stochastic context free grammars for 2- species comparison (QRNA) Machine learning (RNAGenie) Our approach: statistical significance across multiple species (MSARi) Homology Train on a particular RNA secondary structure and try to predict that structure

13 Result Highlights [Coventry, Kleitman, Berger (2004), PNAS] Identifies RNA secondary structure with 90% sensitivity at 98% specificity. no previous knowledge necessary Used to identify functionally significant RNA secondary structure in mrna. Can be used to scan multiple genomes for RNA secondary structure. Benchmarks: QRNA 19.8% sensitivity at 98% specificity ddbrna 68% sensitivity at 97.7% specificity

14 Comparative Genomics of Proteins Protein Function

15 Protein Structure: The Protein Folding Problem Given an amino acid sequence, e.g., MDPNCSCAAAGDSCTCANSCTCLACKCTSCK, how will it fold in 3D? Proteins must fold to function Some diseases are caused by misfolding e.g., mad cow disease

16 Protein Folding by Comparative Modeling Similar protein sequences similar structures Use known structures to predict a new one About 40,000 protein structures have been solved using experimental techniques and stored in the Protein Data Bank (PDB) ; ~1000 are unique structural folds Same structural folds Different structural folds

17 Protein Threading Query Sequence: DRVYIHPFADRVYIHPFA The Best Match Threading = Match between a string and a 3D object

18 Result Highlights Result Highlights RAPTOR: threading as Linear-Programming (Jinbo Xu) {0,1}, 1 ] [, ] [,.. ), )(, (, ] [, ],, [ ), )(, (, ],, [ ), )(, (, ), )(, ( ), )(, (,, = = = + = k j l i l i i D l l i i k j R l k j l i k j l j i R k k j l i l i k j l i k j l i l i l i y x x j D k y x D i l y x s t y b x a E Minimize Structural Template 9 T N L A K Y E T L Input Sequence RAPTOR was the best performing algorithm at CAFASP, a worldwide competition

19 Threading Protein Complexes A B RGPPQLIK EGAATQY DBLRAP DBLRAP is our extension of RAPTOR for joint homology modeling of two structures (PSB 06) Extend LP formulation to score interfaces between two structures as well DBLRAP was able to predict interactions for 8% of proteins in the yeast genome (c.f. 5% previously)

20 Structure Alignment

21 Protein Structure Alignment Problem: find the optimal alignment between two protein structures

22 Contact Map Alignment Goal: find maximum common subgraph contact distance Du (5Å 7.5Å)

23 State of Art: Contact Map Alignment History: more than 20 years, many programs based on heuristic algorithms NP-hard and hard to approximate if being measured by Maximum Common Subgraph (Goldman, Papadimitriou & Istrail, FOCS 99) Lagrangian relaxation (Caprara & Lancia, Recomb 2002) Integer programming (Caprara et al, JCB 2004)

24 Tree-Decomposition for Protein Structure Alignment Method: tree-decomposition of one protein structure into small pieces to exploit the geometric characteristics of a structure Results: there is a poly-time approximation algorithm (PTAS) to find an alignment at least (1-1/k) of the best. Its time complexity is: O( k 2 tw= O(( poly( N) Δ D D l ) 3 k 2 tw ) /( 6 ε Dc ) ) Δ = (1 + ε) 3 ( D D c l ) 3 The parameters D, Dc and Dl are small constants, so is D/Dl. Therefore, this problem admits a PTAS, the best that we can achieve since this problem is NP-hard.

25 Biological Applications of Tree Decomposition Sidechain packing (Xu & Berger, Recomb 05, JACM 06) Protein threading (Xu, Jiao, & Berger, CSB 05) Network motif search (Dost et al, Recomb 07) RNA secondary structure alignment (Song et al, CSB 05) De novo sequencing (Liu et al, PSB 06) Protein structure alignment (Xu, Jiao, & Berger, Recomb 06, JCB 06; Xu, CDC 07)

26 Comparative Genomics of Networks Protein Function

27 Why understanding function-level differences is important Increased complexity (function) is not explained simply by variations in gene (or protein) count Estimated Number of Genes Estimated Number of Proteins Numbers from

28 Protein-Protein Interactions (PPIs( PPIs) Often, proteins interact with other proteins to perform their functions Many cellular activities are a result of protein interactions MAPK Signaling Cascade Image from: /mapkmap2.html

29 Modeling PPIs Traditional perspective: low-throughput, structural New perspective: high-throughput, network-based G-protein complex GDP GDP Gγ Gα Gα Gβ Gβ Gγ Traditional perspective Image from New systems-level perspective

30 Protein-Protein Interaction (PPI) Network X + Y =? Yeast 2-Hybrid method Cusick et al. Hum Med Gen, 05 Yeast PPI Network

31 Motivation behind Network Comparison Compare PPI networks at the species level Transfer annotation from one species to another More feasible, cheaper and easier than in humans Error detection Compute functional orthologs Functional orthologs: proteins which perform the same function across species

32 The Problem Given two protein-protein interaction networks, find for a piece of one network, something that has a comparative structure in the other network Our approach: match neighborhood topologies

33 Algorithm: IsoRank a1 a2 a4 a5 a7 a3 a8 a6 b3 b2 b5 b4 b7 b9 b1 b6 b8 Sequence similarity a5 b7 2.1 a5 b9 1.5 a3 b2 3.4 a5 a5 a5 a5 a3 a3 b7 b1 b3 b9 b1 b6 1e-2 2e-8 1e-7 1e-4 5e-4 3e-9 Functional similarity for each possible node pairing

34 Functional Similarity Score: Intuition Compute pairwise scores R ij : a1 a2 a3 a4 a5 R a5,b1 =? b1 b2 b5 b3 b4 Goal: high R ij i and j are a good match Intuition: i and j are a good match if their sequences align and their neighbors are a good match

35 Computing R ij Combine both sequence and network data network similarity R ij = (1-α)E E ij ij +αn ij functional similarity sequence similarity

36 Simple Case: α=1 (no E ij ) R ij =N ij. a1 a2 R ij a3 R ij depends on neighborhoods of i and j R= N= N 1 1 N v R ij ij uv u N ( ui ) Nv ( Ni )( v j) N ( j) ( N) ( u) ( N) ( v) a4 = N(a) is the set of neighbors of a a5 1, b4 a 2, b3 u 1 R = R a 2 3 R uv b1 b2 b5 b3 a1 a2 b3 b4 b4

37 Simple case: α=1 (no E ij ) R ij =N ij. R ij R ij depends on neighborhoods of i and j = N ij = u N ( i) v N ( j) ( ) ( ) N N(a) is the set of neighbors of a a1 b1 b2 a2 a3 b5 b3 b4 a4 a5 R a 2, b2 a1 1 = R R 3 1 a2 a3 u a1, b1 a3, b1 1 N v R uv 1 + R R 3 3 a1, b3 b1 b2 a3, b3 b3

38 Example: Computed R ij values a4 R a1 a2 a3 a5 b1 b2 b3 b4 b5 a a b1 b5 a a b2 b3 a b4 Empty cell indicates R ij = 0

39 Example: Computed R ij values a4 R a1 a2 a3 a5 b1 b2 b3 b4 b5 a a b1 b5 a a b2 b3 a b4 Empty cell indicates R ij = 0

40 Example: Computed R ij values a4 R a1 a2 a3 a5 b1 b2 b3 b4 b5 a a b1 b5 a a b2 b3 a b4 Empty cell indicates R ij = 0

41 Capturing non-local effects? p R pr =8.12e-3 r R pq =8.64e-3 q The algorithm can resolve between p-r vs. p-q

42 Computing R: an eigenvalue problem The equations for R describe an eigenvalue problem A[ ij ][ R uv ] = = AR N ( u 1 ) N ( v ) R is the principal eigenvector of A size ( A ) = N 1 N 2 N 1 N 2 N1 = # nodes in Graph 1 N2 = # nodes in Graph 2 A is about 10 8 x10 8 when aligning yeast and fly networks However, both A and R are very sparse We use the Power method to efficiently compute R Extension to weighted edges is straightforward

43 = ) ( ) ( ) ( ) ( 1 i N u j N v ij R uv v N u N R A Random Walk Interpretation A Random Walk Interpretation Tensor Product: G 1 x G 2 r p s v j q i u G 1 G 2 ) ( ) ( 1 v N u N ) ( ) ( 1 j N i N r,s r,j r,v u,s u,j u,v i,s i,j i,v

44 General Case: 0 α 1 Let B ij = sequence similarity score between i (from graph #1) and j from (graph #2) E ij = B ij / B 1 R = (1 α R 0 = αar 1 ) E + α AR

45 Complex Case: Multiple Networks 1 R 3 #1 #3 1 R 2 2 R 3 #2

46 Results: Yeast-Fly Global Alignment # of edges in the common subgraph: 1420 Implies about 5% overlap! Why so low? PPI data currently is noisy and low-coverage # of edges in the largest component: 35 The value of α used: 0.6 Provided best overall agreement with previous gene correspondence predictions

47 Various Topologies Are Found Existing local alignment methods (PathBlast; Kelley et al.) often find only specific topologies

48 Role of α: why the dip?

49 Robustness to Error in PPI data a1 a2 a4 a1 a2 a4 a5 a7 a5 a7 a11 a8 a3 a10 a9 a6 a11 a8 a3 a9 a10 a6

50 Robustness to Error in PPI data True curve somewhere around here

51 Functional Orthologs Genes that perform similar functions functional orthologs vs plain old orthologs distinguish between orthologs and paralogs Bandyopadhyay et al. [Genome Res. 06] Use local network alignment results Then use a MRF to partially resolve ambiguities We compared our results with theirs

52 Functional Orthologs: IsoRank Pairwise Alignment Predictions Protein Functional Ortholog IsoRank Bandyopadhyay et al. Gid8 CG6617 CG % CG Gpa1 Goα47a Goα47a 41% Giα65a --- Kap104 Trn Trn 41% CG % CG18617 Vph1 Vph1 43% Stv1 48% Egd1 Bic Bcd 47%

53 Results: Multiple Network Alignment Size of networks human (36387 PPIs), yeast (31899 PPIs), fly (25831 PPIs), worm (4573 PPIs) and mouse (255 PPIs) # of edges in the common subgraph with Isorank 1663 PPIs aligned in at least 2 species 157 PPIs aligned in at least 3 species Comparison with NCBI s Homologene 509 PPIs in at least 2 species 40 PPIs in at least 3 species INPARANOID ( PPIs in at least 2 species

54 Multiple Network Alignment: Functional Orthologs Coverage of known genes Out of 86,932 proteins in five species Isorank: 59,539 have at least one mapping INPARANOID: 55,000; 66% overlap with ours Homologene: 33,434 Functional coherence Isorank INPARANOID Homologene

55 Theoretical Considerations Limitation: K-regular graphs, i.e., what if all the nodes have the same degree? Convergence guarantee: number of iterations of the power method scales as log(1/α)

56 Biological Applications of Isorank Pairwise network alignment (Singh, Xu & Berger, Recomb 07, SODA 08) Multiple network alignment (Singh, Xu & Berger, PSB 08) Multiple RNA secondary and tertiary structure alignment Multiple protein structure alignment

57 Related Work on (Pairwise( Pairwise) Network Alignment PathBlast: Kelly et al. Use sequence similarity to shortlist possible pairs of matching nodes Search for conserved topologies like pathways and hub-and-spokes Koyuturk et al. Like PathBlast, but with a more sophisticated objective function that models gene deletion etc. Graemlin: Batzoglou et al. First uses sequence data to generate matching pairs of seed subgraphs and then heuristically grows the seed matches in search of a specific topology

58 Open Issues How can traditional graph-theoretic algorithms be extended to handle noise and incomplete data in biology?

59 Acknowledgments Sequence Genomics Manolis Kellis, Eric Lander, Nick Patterson RNA Secondary Structure Alex Coventry, Dan Kleitman Protein Structure Jinbo Xu, Rohit Singh PPI Network Alignment Rohit Singh, Jinbo Xu Thanks also to: Michael Baym Gopal Ramachandran Leonid Chindelevitch Michael Schnall-Levin Chris Bakal, HMS & CSAIL Lenore Cowen, Tufts