Basic Data Structures for

Graph based Visualization and Analysis of Metabolic Networks

Jan Griebsch & Arno Buchner & Hanjo Täubig

Lehrstuhl für Effiziente AlgorithmenProf. E.W. Mayr

Institut für Informatik, TU München

BFAM Workshop16.-17.01.2004

Outline

• Application Requirements

• Related Work

Graph Concepts

Existing Software

• Conclusions for Data Models

• A Test Case

User-defined Requirement Profile

• Work with (metabolic) networks including up to several 1000 nodes (reactions, substrates) Store arbitrary context information for each node Search for/filter/extract enzymes, metabolites,

pathways/subnetworks according to user-defined criteria

• Visualization of such networks Support expand / contract meta-/nodes

• Enable the use of graph algorithms efficiently

• Accommodate abstractions such as clusters of nodes

Compound Graphs

Definition A compound graph C = (G,D) consists of a graph G = (V,EG) and a directed acyclic graph D=(V,ED) that share the same set of nodes.

[Sugiyama and Misue 1991]

Clustered Graphs

Definition A clustered graph C = (G, T) consists of a base graph G and a rooted tree T, such that the leaves of T are exactly the vertices of G.

[Eades and Feng, 1996]

Graph Views Concept

Definition Let G = (VG,EG) be the base graph. The hierarchy is defined by the tree T = (VT,ET), with the leaves L(T) = VG. A view is defined as a subset of VT that induces a partition of VG.

[Buchsbaum and Westbrook 2000]

Existing Graph Software

Software/Libraries

LEDA, Boost, GTL no concept of hierarchies

Wilmascope, GVF Clusters no concept of views

Graph Class DiagramExample: WilmaScope

Data + id : Integer+ name : String

<<constructor>> + Data (id: int)<<constructor>> + Data (id: int, name : String)<<getter>> + getID () : Integer<<setter>> + setName (name: String) : void

GraphElement + data : Data

+ redraw () : void+ toString () : String

GraphNode # edges : (Vector)

<<constructor>> + GraphNode (data : Data )<<getter>> + getEdgesIterator () : Iterator+ addEdge (edge : Edge) : void+ removeEdge (edge: Edge) : void

Edge + startNode : GraphNode+ endNode : GraphNode+ directed : boolean = false

<<constructor>> + Edge (data : Data)<<setter>> + setStartNode (node : GraphNode) : void<<setter>> + setEndNode (node : GraphNode) : void

ClusterNode - members : Vector- internalEdges : Vector

<<constructor>> ~ClusterNode (id : int)<<getter>> + getNodes () : Vector+ containsNode : boolean+ addNode (node : GraphNode) : void+ removeNode (node : GraphNode) :void+ addInternalEdge (edge : Edge) : void

Graph # clusters : Vector# nodes : Vector# edges : Vector

<<constructor>> + Graph ()<<getter>> + getNodes () : Vector<<getter>> + getParentClusters (node : GraphNode) : Vector+ containsNode : boolean+ addNode (node : GraphNode) : void+ removeNode (node : GraphNode) : void+ addEdge (edge : Edge) : void+ removeEdge (edge : Edge) : void+ createCluster (clusteredNodes : Vector) : ClusterNode

GraphControl + id : Integer+ name : String

<<constructor>> : + Data (id: int)<<constructor>> : + Data (id: int, name: String)<<getter>> : + getID () : Integer<<setter>> : + setName (name: String) : void

Biochemical Visualisation and Analysis Framework for Metabolic Networks (BVAM)

Graph

GUIGeneral User Interface

GraphAnalysis

Tools

Data Exchange Layer

Moses(CCC Group)

GraphVisualisation

Tools

DatasourcesBioPathDatabase(CCC)

KEGG

WIT

BRENDA

Graph

Class Diagram

GraphElement

Node Relation

Edge

Graph

HierarchyView

GraphElement

# PropertyMap : HashMap

+ GraphElement()+ add_attribute(keytype, valuetype)+ remove_attribute(keytype)+ has_attribute(keytype) : bool+ get_value(keytype) : value

Graph

#adj : List<Edge>#nodes : List<Node>

+ Graph()+ add_node(Node)+ add_edge(Node, Node)+ remove_node(Node)+ remove_edge(Edge)

View

+ view(hierarchy&)+ expand(node)+ collapse(node)

Hierarchy

+ hierarchy(Graph&)+ add_node(Node)+ remove_node(Node)+ father_edge() : Edge+ son_edges() : edge_iterator+ is_predecessor(Node, Node) : bool+ induced_edge(Node, Node) : bool

Class Diagram

GraphElement

Node Relation

Edge

Graph

HierarchyView

How could arbitrary many hierarchies and views be modelled ?

Observer PatternView and Hierarchy are updated through callbacks [Raitner, 2003].

Class Diagram

GraphElement

Node Relation

Edge

Graph

Hierarchy View

ObservedGraph

+ ObservedGraph()+ add(Observer&)+ remove(Observer&)

Observer

+ Observer(ObservedGraph&)+ add_node_handler(Node)+ remove_node_handler(Node)+ add_edge(Node, Node)+ remove_edge(Edge)

1 1..*

Space Time Trade-offs

• Induced edges are calculated when needed No redundant information Expand/contract worst case: O(|EG|+ |VG|) Quick edit operations on the base graph

• Induced edges are stored[Buchsbaum and Westbrook, 2000] Expand/contract in optimal time Space required: O(|EG|D2) Updates of the base graph are more complicated and

need O(D2) expected time

• Is there a good compromise ?

Example: Constructing Hierarchies on Metabolic Networks

• Motivation Explore properties of hierarchies on metabolic networks Test prototype implementations Study the question to what extend metabolic networks can be

said to be composed of distinct sub- and sub-subnetworks(Betweenness centrality could also be used for detecting key reactions/enzymes)

• Previous work Large-scale organization of metabolic networks

[Jeong et al., 2000] The small world inside large metabolic networks

[Fell and Wagner, 2001] Exploring the pathway structure of metabolism

[Schuster et al., 2002] Subnetwork hierarchies of biochemical networks

[Holme et al., 2002] Hierarchical analysis of dependency in metabolic networks

[Gagneur et al., 2003]

Example: Constructing Hierarchies on Metabolic Networks

• Data BioPath Database, Computer Chemie Centrum, Prof. Gasteiger

• Decomposition successively delete nodes according to a global centrality

measure

through passing paths shortest of number (r)

paths shortest of number total

substrates of set the

reaction a

Definition

with

rmm

mm

M

r

Mm mMm

rB mm

mmC

tys CentraliBetweennes

\

)(

Example: Constructing Hierarchies on Metabolic Networks• Deleted Metabolites

Metabolite Betweeness

PROTON (5.31227e+06)WATER (5.2434e+06)ATP (3.04506e+06)NAD (2.03219e+06)NADP (reduced) (2.26506e+06)COENZYME A (1.75499e+06)NADP (1.83248e+06)NAD (reduced) (2.23032e+06)PYROPHOSPHATE (2.04188e+06)ADP (2.08268e+06)CARBON DIOXIDE (1.89917e+06)PHOSPHATE (with GTP) (2.16805e+06)L-GLUTAMATE (1.78612e+06)ACETYL-COENZYME A (1.71162e+06)AMP (1.9995e+06)PYRUVATE (1.29878e+06)GLYCINE (1.31198e+06)AMMONIA (1.18789e+06)2-OXOGLUTARATE (1.19791e+06)PHOSPHATE (protonated) (1.14856e+06)FAD (linked with enzyme) (1.2225e+06)OXALOACETATE (1.55343e+06)

SUCCINYL-COENZYME A FORMATE L-SERINEL-METHIONINEUTPGLYCERALDEHYDE 3-PHOSPHATE UDPPALMITOYL-ENZYME

Initial Graph: 3548 Nodes 8956 Edges

Example: Constructing Hierarchies on Metabolic Networks

Screenshots

Graph including all Biopath reactions (Random Layout with LEDA)

Screenshots

Graph after deleting of 30 most central Metabolites (Spring embedded 3D Layout by LEDA)

Screenshot

Graph with Data from Citrate-CycleRandom Layout, manually changed

Future Work

• Implement graphical user interface

• Include more data sources

• Add chemical analysis abilities:Interact with MOSES, Prof. Gasteiger

• Visualization

Thanks

We want to thank

Prof. E. W. Mayr, Dr. Jens Ernst, Klaus Holzapfel and Moritz Maass for ideas and discussion and Hanjo Täubig for practical support.

References

[1] Buchsbaum, A. L. and Westbrook, J.R.. Maintaining Hierarchical Graph Views. 11th ACM-SIAM Symposium on Discrete Algorithms, 2000.

[2] Eades, P. and Feng, Q.W. Multilevel Visualization of clustered graphs.Proc. Graph Drawing, LNCS, Vol. 1190, 101-112, Springer Verlag

[3] Sugiyama, K. and Misue, K. Visualization of structural information: Automatic Drawing of Compound Digraphs.IEEE Trans. Systems, Man and Cybernetics, 21(4), 876-892.

[4] Brandes, U.A Faster Algorithm for Betweenness Centrality.Journal of Mathematical Sociology, 25(2): 163-177, 2001

[5] Gagneur, J., Jackson, D. B. and Casari, G.Hierarchical analysis of dependency in metabolic networks.Bioinformatics, Vol. 19, 2003

[6] Schuster, S. , Pfeiffer, T., Moldenhauer, F., Koch, I. And Dandekar, T.Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycloplasma pneumoniae

[7] Holme, P., Huss, M. and Jeong, H.Subnetwork hierarchies of biochemical pathways

[7] M. RaitnerA Library for Hierarchies, Graphs and Views

Visualization using Hierarchies

• Example taken from EcoCyc (http://ecocyc.org/) Useful for getting overview Limitations here: Only few levels and global change of

detail-level

Analysis using Hierarchies

Recent approaches:

• Holme et al., 2002 Detecting subnetwork hierarchies of biochemical

networks using the betweeness centrality of reactions

• Gagneur et al., 2003 Analysis of hierarchical dependencies of subnetworks

using connectivity ranking of metabolites

• Schuster et al. , 2003 Decomposition of the metabolic network using connectivity ranking for metabolites

Resulting Data model

Bipartite hierarchical Graph

Bipartite node structure for different representation of reactions and metabolites

Specific information can be labelled to the respective graph element (and used for analysis and visualization)

Graph specific algorithms can be implemented for calculation (pathway searches, statistics)

Biological concepts (pathways, cell compartments) can be modelled and visualized using hierarchical structures

Hierarchical clustering approaches with different criteria can be used for automated network decomposition

Wrapper Concept

“Tell_IDSets”

IDNameSet1, IDNameSet2, …

Wrapper

Datasource

Wrapper Concept

Edgeset<IDValue1, IDValue2, IDName1,IDName2> : Set

“Build( IDNameSet )”

Wrapper

Datasource

Wrapper Concept

“Tell_PropertySet ( IDName )”

PropertyName-Set

Wrapper

Datasource

Wrapper Concept

“Get_PropertySet( IDValueSet, PropertyName )”

Propertyset<IDValue, PropertyValue> : Set

Wrapper

Datasource

Graph Concepts and Software

• Definitions Clustered Graphs, [Eades and Feng, 1996] Compound Graphs, [Sugiyama and Misue 1991] Hierarchical Graph Views, [Buchsbaum and Westbrook

2000]

• Software/Libraries LEDA Boost GTL Wilmascope GVF HGV

Supported Graph Operations

• Navigation/View Expand a node Contract nodes

• StructureBase Graph Insert a new edge between two nodes s,t Delete an edge Insert a new node Delete a nodeHierarchy Insert a new step into the hierarchy Remove a step from the hierarchy