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Materials and Methods
Network analysis
As outlined in the main text, the comprehensive map was analyzed for identifying core snetwork
structural
properties.
The
analysis
was
performed
using
Cytoscape
2.6.0
(http://www.cytoscape.org/) which allows the import of SBML files (Level 2 Version 1) which
was exported from CellDesigner 4.0.1 version of the maps. In order to compute the network
properties, the Cytoscape plugin NetworkAnalyzer 2.6.1 (http://med.bioinf.mpiinf.mpg.de/netanalyzer/) were employed which allows the computation of network parameters
like degree, path length and centrality indices (explained later). It may be noted here that
Cytoscape represents the reactions as nodes in the graph along with the molecules and the
analysis was performed on this Cytoscape-specific graph representation of the map. Analysis on
NetworkAnalyzer was performed on an undirected version of the graph and for completeness we
present the definition of the terms used in the analysis below:
Degree distributions: In undirected networks, the node degree of a node n is the number of
edges linked to n. A self-loop of a node is counted like two edges for the node degree (Maslov &
Sneppen, 2002). The node degree distribution gives the number of nodes with degree k for
different values of k.
Shortest paths: The length of the shortest path between two nodes n and m is L(n,m). The
shortest path length distribution gives the number of node pairs (n,m) with L(n,m) = k for k =
1,2,….. The path length distribution gives the frequency distribution of path length for all
possible (n,m) pairs.
Neighborhood connectivity: The connectivity of a node is the number of its neighbors. The
neighborhood connectivity of a node n is defined as the average connectivity of all neighbors of
n. The neighborhood connectivity distribution gives the average of the neighborhood
connectivities of all nodes n with k neighbors for k = 0,1,…. If the neighborhood connectivity
distribution is a decreasing function in k, edges between low connected and highly connected
nodes prevail in the network.
Closeness centrality: The closeness centrality Cc(n) of a node n is defined as the reciprocal of
the average shortest path length and is computed as follows:
Cc(n) = 1 / avg( L(n,m) ),
where L(n,m) is the length of the shortest path between two nodes n and m. The closeness
centrality of each node is a number between 0 and 1. NetworkAnalyzer computes the closeness
centrality of all nodes and plots it against the number of neighbors. The closeness centrality of
isolated nodes is equal to 0. Closeness centrality is a measure of how fast information spreads
from a given node to other reachable nodes in the network.
Comparative motif analysis: (1) Construct Cytoscape SIF models based on the Boolean Li
model, the dynamic Chen model (ODEs), and our comprehensive map. Determine an active state
for each protein (nodes) at first, and then adding interactions (edges) (for the Chen model and
our map). The interactions are classified into three types by the following way (only for the Chen
model): (a) activation if the corresponding Jacobian element is positive (>0), (b) inhibition if it is
negative (<0), or (c) none if it is constitutively equal to zero (==0).
(2) Count the numbers of two distinct motifs in each model (For details of the program used for
these analyses, see Supporting Data S10): (a) Counting feed-forward regulations. For each pair
connected by an edge (A->B), count the number of intermediating nodes directed in the same
way with the pair (node C such as A->C->B). Then, sum all the counts. (b) Counting feed-back
and mutual regulations (length 2 feed-backs). By using the algorithm by Johnson (Johnson,
1975), enumerate all elementary feed-back regulations (for details, see Supporting Data S10).
Then, normalize the number of loops with their length, and sum all the counts. The type of
regulations (feed-back activation or inhibition) can be distinguished when counting (see Table
3).
Reference
Maslov S, Sneppen K (2002) Specificity and stability in topology of protein networks. Science
296: 910-913.