1 / 46

Gene regulatory networks

Gene duplication models and reconstruction of gene regulatory network evolution from network structure Juris Viksna, David Gilbert Riga, IMCS, 10.02.2006. Gene regulatory networks. Yeast network:. [J.Rung,T.Schlitt,A.Brazma,K.Freivalds,J.Vilo Bioinformatics 18 S2 (ECCB), 202-210 ].

saul
Télécharger la présentation

Gene regulatory networks

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Gene duplication models and reconstruction of gene regulatory network evolution from network structure Juris Viksna, David Gilbert Riga, IMCS, 10.02.2006

  2. Gene regulatory networks Yeast network: [J.Rung,T.Schlitt,A.Brazma,K.Freivalds,J.Vilo Bioinformatics 18 S2 (ECCB), 202-210 ]

  3. Gene regulatory networks • Directed graph • Graph vertices correspond to • genes • An edge from gene A to B • means that gene B is (directly) • regulated by gene A

  4. Properties of gene networks (1) • Believed to be scale-free (vertex degrees • satisfy so-called power law): • N(k) – number of vertices with degree k • N(k)  k

  5. Properties of gene networks (1) [F.Chung,L.Lu,T.Dewey,D.Gallas JCB 10, 677-687] N(k)  k

  6. Properties of gene networks (2) • Believed to have a noticeable modularity • i - vertex • ki - number of neighbours for vertex i • ki - number of direct links between these • ki neighbours • Clustering coefficient (for vertex i): • Ci= 2ni/ki(ki1)

  7. Properties of gene networks (2) • Clustering coefficient (for vertex i): • Ci= 2ni/ki(ki1) [E.Ravasz,A.Somera,D.Mongru,Z.Oltvai,A.Barabasi Science 297, 1551-1555]

  8. Network evolution models (1) • networks expand continuously by the addition of new vertices, • (ii) new vertices attach preferentially to sites that are already well connected. • A model based on these two ingredients reproduces the observed stationary scale-free distributions. [A.Barabasi, R.Albert Science 286, 509-512]

  9. Network evolution models (2) "Hierarchical" model Sample hierarchical networks (scale-free and modular) [E.Ravasz,A.Somera,D.Mongru,Z.Oltvai,A.Barabasi Science 297, 1551-1555]

  10. Network evolution models (3) "Duplication" model Scale-free with b < 2 for ½ < p < 1 [F.Chung,L.Lu,T.Dewey,D.Gallas JCB 10, 677-687]

  11. Network evolution models (4)

  12. Network evolution models (M1) M1

  13. M1, p = 0.1, 5000 vertices   4.5

  14. M1, p = 0.01, 5000 vertices   3

  15. M1, p=0.05, d=0.2, 5000 vertices

  16. M1, p=0.05, d=0.2, 5000 vertices   2.5

  17. Network evolution models (M1) M1 V E 20 40 50 200 100 700 500 15000 1000 50000 5000 800000

  18. Network evolution models (M2) A A genome evolution X X' X X'

  19. Network evolution models (M2) A X X' A genome evolution or X X' A X X'

  20. Network evolution models (M2) M2

  21. M2, p = 0.1, 20000 vertices

  22. M2, p = 0.1, 20000 vertices   1

  23. Network evolution models (M2) M2 V E 20 40 50 80 100 150 500 700 1000 1500 5000 7000

  24. Evolution graphs k+2 vertices two types of edges: - for swappable events (black) - for dependent events (grey)

  25. Evolution graphs

  26. Evolution graphs Initial graph G Numbered vertices correspond to evolution steps and are marked by the vertices duplicated in the corresponding steps Intermediate graphs between G and G' correspond to cuts of evolution graph (G and G' can also be obtained in this way) Graph G' obtained from G after k (in this example k=6) evolution steps

  27. Evolution graphs – some questions Equivalence Decide whether 2 given evolution graphs are equivalent Irreducible networks – networks that can’t be obtained from simpler networks by evolution graph Uniqueness of evolution Is it possible that D(G1,E1)= D(G2,E2) for two different irreducible networks G1 and G2?

  28. "Reverse engineering" problems E Reconstruct: Given: G' G

  29. "Reverse engineering" problem (1) (Assuming either model M1 or M2.) Reconstruction of evolution graph For a given network N’ find an irreducible network N, the sequence of duplication events D1,...,Dm and the corresponding evolution tree, such that N’=D(N,E).

  30. "Reverse engineering" problem (2) (Assuming either model M1 or M2.) Reconstruction of duplication event For a given network N’ find a network N and a duplication event D, such that N’=D(N).

  31. "Reverse engineering" problem (3) (Assuming either model M1 or M2.) Reconstruction of the largest duplication event For a given network N’ find a network N with the smallest possible number of genes and a duplication event D, such that N’=D(N).

  32. "Reverse engineering" - complexity For a given network N’ find a network N with the smallest possible number of genes and a duplication event D, such that N’=D(N). • at least as hard as graph isomorphism problem • likely NP-hard (maximum clique for reconstruction • graphs) • reconstruction graphs are much smaller than • networks • still might be practically solvable for random graphs • of reasonable size (few tens of thousands of vertices).

  33. Algorithm – stage 1 Partition G' vertices into orbits Can be done e.g. with nauty package One can try to use some property p which is more simple to compute than automorphisms and is such that p(G1)=p(G2) for isomorphic graphs G1 and G2.

  34. Reconstruction graphs Vertices correspond to non-singleton orbits Two types of edges: - (1) have to participate in the same duplication event (solid) - (2) can not participate in the same duplication event (dotted)

  35. Algorithm – stage 2 Find reconstruction graph

  36. Algorithm – stage 3 Find the largest independent set (according to type 2 edges) in reconstruction graph

  37. Algorithm – stage 4 - if all selected orbits contain just 2 nodes, we are practically done - otherwise we have to find a pair of (largest) sets of vertices from selected orbits, which correspond to duplication event [currently exhaustive search]

  38. Algorithm Evolution graph can be reconstructed by repeated use of Largest duplication event

  39. Algorithm - efficiency - using nauty we can deal with networks with < 200 genes - for larger graphs one can use heuristics to compute orbits - vertex/edge counts at different DFS levels seems to work quite well - likely to find a large part of duplication event - for <200 vertices often gives the exact result

  40. Algorithm – Model 2 General case – check automorphisms for all k-tuples of vertices A serious problem even for k=2 However, large components are duplicated not that often Previous algorithm could be used to find "large" part of duplicated genes Still an open problem Also, a question about good heuristics

  41. Model 2 – Component sizes Model M2 550 vertices 132 duplications

  42. Model 2 – Component sizes Constructing random network with 20000 genes: Component sizes#of events 1 177008 2 342 3 97 4 49 5 37 6 18 7 13 8 10 10,11,14 4 9,12,13,15,27 3 16,24 2 17,18,21,22,31,27 1

  43. Experiments with yeast network 6270 genes 106 regulators

  44. Experiments with yeast network p=0.0001 E=106 V=216

  45. Experiments with yeast network 277 pairs of duplication candidates were discovered Few "real": COS5 and COS8, YLR460C and YNL134L All 5962 genes were compared all-v-all using SW Normalized compression score: ssearch_score(P1,P2)/min{length(P1),length(P2)} Scores for the found duplication pairs were compared with average values

  46. Experiments with yeast network Observed distances vs average, all non-adjacent gene pairs

More Related