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Review
. 2009 Feb 27;284(9):5451-5.
doi: 10.1074/jbc.R800056200. Epub 2008 Oct 20.

Insights Into the Organization of Biochemical Regulatory Networks Using Graph Theory Analyses

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Free PMC article
Review

Insights Into the Organization of Biochemical Regulatory Networks Using Graph Theory Analyses

Avi Ma'ayan. J Biol Chem. .
Free PMC article

Abstract

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.

Figures

FIGURE 1.
FIGURE 1.
Schematics representing properties of cell signaling networks identified using the graph theory. A, the connectivity distribution of networks fits a power law (straight line on a log-log plot). B, networks consist of party and date hubs, where multiple colors represent different locations and times. C, hubs are either multisite or single-site. D, there are many pathways from some receptors to some effectors and few from most receptors to most effectors. E, signals from many receptors are converging into few cytosolic components and then fanning out to regulate many transcription factors in a “bow-tie” structure. F, the bifan motif is shown. G, negative feedback loops are more often observed in loops that include receptors; positive feedback loops are more common a few steps downstream from receptors. H, feed-forward loops are mostly coherent (positive) where negative and less regulated outgoing hubs are used to shut off signals. I, positive feedback loops are more abundant than negative feedback loops and are highly nested.
FIGURE 2.
FIGURE 2.
Example of network motifs within cell signaling networks. PFBL, positive feedback loop; NFBL, negative feedback loop; PFFL, positive feed-forward loop; NFFL, negative feed-forward loop; CaM, calmodulin; CaN, calcineurin; AC1, adenylyl cyclase I; AA, arachidonic acid; B2AR, β2-adrenergic receptor; I1, inhibitor-1; PKA, protein kinase A; PKC, protein kinase C; PP1, protein phosphatase-1; MAPK, mitogen-activated protein kinase; PLA2, phospholipase A2; CaMKII, Ca2+/calmodulin-dependent kinase II. Gray arrows represent the components in these motifs that signal to other biomolecules that are not part of the motif.

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