Metabolic Network Visualization Using Constraint Planar Graph Drawing Algorithm.

Transcription

1 Metabolic Network Visualization Using Constraint Planar Graph Drawing Algorithm. Romain Bourqui, Université Bordeaux I LaBRI In Collaboration with : David Auber (LaBRI), Vincent Lacroix (INRIA) and Fabien Jourdan (INRA)

2 Introduction Metabolic pathway : small subset of biochemical reactions that occur in a cell

3 Glycolysis and Gluconeogenesis pathways from KEGG [K]

4 Introduction Metabolic pathway : small subset of biochemical reactions that occur in a cell Metabolic network : integration of all metabolic pathways into a single network

5 Introduction Boehringer poster of the whole network

6 Introduction Metabolic pathway : small subset of biochemical reactions that occur in a cell Metabolic network : integration of all metabolic pathways into a single network Commonly used modeling : bipartite graph Substrates Reaction Substrates

7 Motivation Visualization of the occurrences of a given motif (set of reactions) in the whole metabolic network

8 Limitation of Classical approaches Valine and Alanine Biosynthesis pathways from Ecocyc sharing motif { , , , }

9 Motivation Visualization of the occurrences of a given motif (set of reactions) in the whole metabolic network : Shared by several pathways Global context of the network

10 Goals Automatic drawing of the whole metabolic network

11 Naive representation Escherichia coli Metabolic Network

12 Goals Automatic drawing of the whole metabolic network Taking into account the biochemical textbook drawing conventions

13 Goals Automatic drawing of the whole metabolic network Taking into account the biochemical textbook drawing conventions Taking into account metabolic pathways information

14 Graph drawing problems Due to textbook drawing conventions : Limitation of edge-edge crossing Limitation on the number of bends per edge Drawing topological structure (cycle and cascade representation) Due to metabolic pathways information : Nodes belonging to a common metabolic pathway have to be drawn close one to each other

15 Overview Clustering Independent Set Problem Cycle Search Drawing Induced Path Search Cluster Drawing Quotient Graph Drawing

16 Clustering Algorithm First pass : Second pass: Dependence Graph Independent set of metabolic pathways Longest cycles search Longest paths search Third pass : Longest cycles search into clusters

17 Clustering : first pass Dependence graph G=(V,E) : To each pathway p, it exists one and only one node v in V, For all u,v in V, it exists an edge (u,v) in G iff the corresponding pathways share at least one substrate/reaction.

18 Clustering : first pass Dependence Graph

19 Clustering : first pass Dependence graph G=(V,E) : To each pathway p, it exists one and only one node v in V, For all u,v in V, it exists an edge (u,v) in G iff the corresponding pathways share at least one substrate/reaction. Coloration using Welsh and Powell heuristic [WP67]

20 Clustering : first pass Coloration of Dependence Graph

21 Clustering : first pass For each colour class, we count the number of substrate and reaction of all pathways in it : suppose the class that maximizes it is class c We clusterize each pathway p of colour c into a cluster For each other pathway p : Let {u1,...,ur} be nodes only belonging to p We clusterize {u1,...,ur} into a cluster

22 Clustering : first pass step 1

23 Clustering : second pass Longest cycles detection while exists cycle Graph Longest cycle detection Longest cycle clustering DAG

24 Clustering : second pass Longest cycles detection while exists cycle Graph Longest cycle detection Longest cycle clustering DAG Longest paths detection : longest sequence of adjacent nodes of degree <= 2

25 Clustering : second pass step 1 step 2

26 Clustering : third pass For each cluster computed in step 1 : we search the longest cycles using the same method as in step 2

27 Clustering : third pass step 1 and 2 step 3

28 Drawing Algorithms Drawing clusters Hierarchical drawing [A01] Circular drawing Drawing quotient graph Mixed-Model of Gutwenger and Mutzel [GM98]

29 Drawing The Quotient Graph Planarization of quotient graph Mixed-Model of Gutwenger & Mutzel Edge routing

30 Planarization Several techniques : Augmentation : O(n4) added nodes Edges and/or nodes deletions

31 Planarization Several techniques : Augmentation : O(n4) added nodes Edges and/or nodes deletions Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar

32 Planarization Several techniques : Augmentation : O(n4) added nodes Edges and/or nodes deletions Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar

33 Planarization Several techniques : Augmentation : O(n4) added nodes Edge and/or node deletion Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar Addition of deleted edges

34 Planarization Several techniques : Augmentation : O(n4) added nodes Edge and/or node deletion Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar Addition of deleted edges

35 Planarization Several techniques : Augmentation : O(n4) added nodes Edge and/or node deletion Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar Addition of deleted edges

36 Planarization Several techniques : Augmentation : O(n4) added nodes Edge and/or node deletion Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar Addition of deleted edges

37 Planarization Several techniques : Augmentation : O(n4) added nodes Edge and/or node deletion Our heuristic : Deletion one by one of node of highest degree until the resulting graph is planar Addition of deleted edges

38 Mixed-Model Two main steps : Decomposition phase Recomposition phase : nodes/bends placement

39 Mixed-Model Two main steps : Decomposition phase Recomposition phase : nodes/bends placement One of the goals : substrates and/or reactions belonging to the same pathways have to be drawn in a small area We constraint the algorithm during the decomposition step

40 Mixed-Model : Decomposition Deletion of nodes on the external face

41 Mixed-Model : Decomposition Deletion of nodes on the external face

42 Mixed-Model : Decomposition Deletion of nodes on the external face

43 Mixed-Model : Decomposition Deletion of nodes on the external face

44 Mixed-Model : Decomposition Deletion of nodes on the external face

45 Mixed-Model : Decomposition Deletion of nodes on the external face

46 Mixed-Model : Decomposition Deletion of nodes on the external face

47 Mixed-Model : Decomposition Deletion of nodes on the external face

48 Mixed-Model : Decomposition Deletion of nodes on the external face

49 Mixed-Model : Decomposition Deletion of nodes on the external face

50 Mixed-Model : Decomposition Deletion of nodes on the external face

51 Mixed-Model : Decomposition Deletion of nodes on the external face

52 Mixed-Model : Reconstruction Nodes' placement on the external face

53 Mixed-Model : Reconstruction Deletion of nodes on the external face

54 Mixed-Model : Reconstruction Deletion of nodes on the external face

55 Mixed-Model : Reconstruction Deletion of nodes on the external face

56 Mixed-Model : Reconstruction Deletion of nodes on the external face

57 Mixed-Model : Reconstruction Deletion of nodes on the external face

58 Mixed-Model : Reconstruction Deletion of nodes on the external face

59 Mixed-Model : Reconstruction Deletion of nodes on the external face

60 Mixed-Model : Reconstruction Deletion of nodes on the external face

61 Mixed-Model : Reconstruction Deletion of nodes on the external face

62 Mixed-Model : Reconstruction Deletion of nodes on the external face

63 Mixed-Model : Reconstruction Deletion of nodes on the external face

64 Mixed-Model : Reconstruction Deletion of nodes on the external face

65 Results Escherichia coli Metabolic Network

66 Results Human Metabolic Network

67 Results Yeast Metabolic Network

68 Motif visualization Visualization of { , , , } in E. coli Metabolic Network

69 Future Works More efficient heuristics for ISP, Cycle Search Problem, planarization and edge routing Highlighting motifs using an area-aware version of the drawing algorithms Interactions : Semantic Anamorphosis ( fisheyes )...

70 Conclusion Graph drawing algorithm dedicated to the visualization of metabolic network Designed to follow textbook drawing conventions Allow to see all occurrences of a motifs in a metabolic network

71 Acknowledgments The authors would like to thank M.-F. Sagot for initiating this collaboration and L. Cottret for his work on extracting the data.

72 References [K] Minoru Kanehisa, Post-genome Informatics, 2000 [BR01] M. Becker and I. Rojas, A graph Layout Algorithm for Drawing Metabolic Pathways, Bioinformatics, 17: , 2001 [WP67] Welsh and Powell, An Upper Bound to the Chromatic Number of a Graph and its Application to TimeTabling, The Computer Journal, 10:85-86, 1967 [A01] D. Auber, Graph Drawing Software, chapter Tulip- A Huge Graph Visualization Framework, Springer-Verlag, 2003 [GM98] C. Gutwenger and P. Mutzel, Planar Polyline Drawing with Good Angular Resolution, Graph Drawing' 98 (Proc.), vol. 1547: , 1998 [LFS05] V. Lacroix, C. G. Fernandes and M.-F. Sagot, Reaction Motifs in Metabolic Network, Proceeding of 5tth Workshop on Algorithms for BioInformatics, Lecture Notes in Computer Science, 3692: , 2005

73 Clusters' hierarchy Connected graph Entire pathway Nodes belonging to one pathway Cycle Cycle Isolated node Isolated node Entire pathway Cycle Isolated node path Cycle Isolated node Isolated node Nodes belonging to one pathway Cycle Isolated node Cycle Isolated node Isolated node