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Science 309 (5737): 10781083
Copyright © 2005 by the American Association for the Advancement of Science
Formation of Regulatory Patterns During Signal Propagation in a Mammalian Cellular Network
Avi Ma'ayan^{1},
Sherry L. Jenkins^{1},
Susana Neves^{1},
Anthony Hasseldine^{1},
Elizabeth Grace^{1},
Benjamin DubinThaler^{3},
Narat J. Eungdamrong^{1},
Gehzi Weng^{1}^{*},
Prahlad T. Ram^{1}^{},
J. Jeremy Rice^{4},
Aaron Kershenbaum^{4},
Gustavo A. Stolovitzky^{4},
Robert D. Blitzer^{1}^{,2}, and
Ravi Iyengar^{1}^{}
^{1} Department of Pharmacology and Biological Chemistry Mount Sinai School of Medicine, New York, NY 10029, USA.
^{2} Department of Psychiatry, Mount Sinai School of Medicine, New York, NY 10029, USA.
^{3} Department of Biological Sciences, Columbia University, New York, NY 10029, USA.
^{4} Functional Genomics and Systems Biology, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA.

Fig. 1.. Assembly of a functionbased cellular network. (A) Block diagram of information flow from ligands to cellular machines. Nodes are associated with functional compartments. The counts of nodes are in parentheses. (B) Total links in subnetworks created in steps from ligands. The total number of links accumulated as a signal moves through the steps, downstream from various ligands, is compared. (C) Total number of three and fourcomponent feedback loops (positive and negative) in subnetworks with two to eight steps from Glu, NE, and BDNF. (D) Counts of positive and negative feedback loops in subnetworks from Glu (I), NE (II), and BDNF (III). The counts in the biological subnetworks (solid lines) are compared with the expected counts (dashed lines) developed using combinatorial probabilities for positive or negative feedback loops based on the number of total positive and negative links. **, P < .05; *, P < .08; binomial test. (E) Counts of three and fourcomponent feedforward motifs in subnetworks with two to eight steps from Glu, NE, and BDNF. (F) An abbreviated list of the motifs found in the fully connected network using the MFinder program (19). CN, cellular network; SN, shuffled networks; SNs were used as controls. Under SN, the mean and SD are given for motifs in 100 shuffled networks. See (15) for details.
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Fig. 2.. Characteristics of subnetworks from three ligands to CREB. Subnetworks were analyzed starting from three extracellular ligands—glutamate, NE, and BDNF (source nodes)—extending to the transcription factor CREB (target node). (A to C) Changes in the number of links with increasing number of steps to reach the effectors. The same analysis was done with shuffled networks. Only the directionality of the links that do not involve the ligands or the effectors was randomly swapped while preserving the connectivity. The resultant graphs for both the cellular network (CN) and the shuffled networks (SN) were curvefitted with Microsoft Excel. For all of the cellular subnetworks, the best fit function was linear (lin), R^{2} = 0.96 to 0.99. For all of the shuffled networks, the best fit was obtained with exponential or powerlaw functions (exp or pow), R^{2} = 0.96 to 0.99. (D) Counts of total three and fournode positive and negative feedback and feedforward loops in subnetworks when different maximum numbers of steps are specified between NE and CREB.
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Fig. 3.. Comparison of motifs and clustering in subnetworks upstream from two effectors, CREB and AMPAR. (A and B) Positive and negative feedback loops (FBL) and feedforward loops (FFL) in subnetworks as the network is extended by including more steps upstream of the effectors CREB or AMPAR. (C and D) Changes in clustering coefficient and grid coefficient in these subnetworks.
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Fig. 4.. Analysis of subnetworks with sequential incorporation of nodes with increasing connectivity. (A) Islands (isolated clusters of connected nodes) are plotted as a function of connectivity per node. A single network (one island) is formed when the nodes with 21 or fewer connections are included. All highly connected nodes starting at 19 links per node are shown. Single isolated nodes were not considered islands. (B to F) The number of motifs in the subnetworks created with nodes with different connectivity. Nodes that contribute disproportionately to the number of added motifs are listed next to the step they produce in the graph. (G) Counts of three and fourcomponent positive or negative feedback and feedforward loops are compared.
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Fig. 5.. Maps of the regulatory profiles within the cellular network. (A) Density of Information Processing (DIP), representing the concentration of all motifs (shown in pseudocolor, with red indicating high density) and their local interconnectedness relative to the network size, was computed for subnetworks activated by glutamate, NE, and BDNF using the equation , where M_{i} = FBL3_{i} + FBL4_{i} + FFL3_{i} + FFL4_{i} + BIFAN_{i}. M_{i} is the total number of feedback loops, feedforward loops, and bifan motifs; L_{i} is the total number of links; and i is the step. FBL3 and FBL4 are feedback loops of size 3 and 4, FFL3 and FFL4 are feedforward loops of size 3 and 4, and BIFAN are bifan motifs of size 4. GC is the grid coefficient representing interconnectedness for the motifs, computed for the subnetwork at step i. DIP is plotted as a signal propagates vectorially through the network, as indicated by the downward arrow. The width of the bar represents the number of links engaged. (B) Relative distribution of regulatory motifs between ligands and cellular machines. Motifs were placed between extracellular ligands and cellular machines using the equation where n is the size of the motif, CPLM is the characteristic path length from a node within the motif to all other nodes in the cellular machine, and CPLL is the characteristic path length from a node to all extracellular ligands. If a node is an extracellular ligand, CPLL = 0 for that node; if the node is in the plasma membrane, CPLL = 1. If a node belongs to a cellular machine, CPLM = 0 for that node. The counts of motifs were placed in 100 bins based on the computed MLI and normalized to the fraction of total motifs for each class of motifs. An MLI value of 0 represents location at the cellular machines where all the nodes that make up the motif are within the cellular machine; a value of 1.0 represents location at the ligand level. PFBL and NFBL, three and fournode positive and negative feedback loops, respectively; PFFL and NFFL, three and fournode positive and negative feedforward loops; SCAF, threenode scaffold motifs; BIFAN, fournode bifan motifs. See (15) for details.
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