Untangling the wires: a strategy to trace functional interactions in signaling and gene networks - PubMed (original) (raw)

Untangling the wires: a strategy to trace functional interactions in signaling and gene networks

Boris N Kholodenko et al. Proc Natl Acad Sci U S A. 2002.

Erratum in

Abstract

Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. However, current methodologies for analysis do not permit interpretation of the data in ways that unravel cellular networking. We propose a quantitative method for determining functional interactions in cellular signaling and gene networks. It can be used to explore cell systems at a mechanistic level or applied within a "modular" framework, which dramatically decreases the number of variables to be assayed. This method is based on a mathematical derivation that demonstrates how the topology and strength of network connections can be retrieved from experimentally measured network responses to successive perturbations of all modules. Importantly, our analysis can reveal functional interactions even when the components of the system are not all known. Under these circumstances, some connections retrieved by the analysis will not be direct but correspond to the interaction routes through unidentified elements. The method is tested and illustrated by using computer-generated responses of a modeled mitogen-activated protein kinase cascade and gene network.

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Figures

Figure 1

Figure 1

A three-module cascade (A) and a gene network (B). The question marks stand for unknown connections and additional network components (e.g., uncharacterized genes), which can influence and in turn be affected by the known components.

Figure 2

Figure 2

Kinetic scheme of the MAPK cascade. Feedback effects of MAPK on the rate of MKKK and MKK phosphorylation are shown schematically by dashed lines. MKKKK, MKKK kinase; P and PP, monophosphorylated and bisphosphorylated forms.

Figure 3

Figure 3

Kinetic scheme of a four-gene network. Arrows correspond to activation interactions, whereas lines with blunt ends represent inhibitions.

Figure 4

Figure 4

Global fractional responses obtained by simulating experimental perturbations to the MAPK cascade. Four global response matrices (Rp⋅100, designated by superscripts a–d) were generated by applying the following 12 parameter perturbations. a or b, 10 or 50% decrease, respectively, in: [Ras-GTP], perturbation to module 1; the catalytic activities of steps 5 and 6 (kformula image and kformula image; see Table 1, which is published as supporting information on the PNAS web site), module 2; kformula image and kformula image, module 3. c or d, 10 or 50% decrease, respectively, in: [Ras-GTP], module 1; the maximal activities of steps 7 and 8 (Vformula image and Vformula image; see Table 1), module 2; Vformula image and Vformula image, module 3.

Figure 5

Figure 5

Retrieved “experimental” interaction maps (A) and known “theoretical” interaction map (B). Four experimental local interaction matrices (r) were retrieved from the data shown in Fig. 4. The response coefficients marked by superscripts a–d correspond to perturbations indicated in the legend to Fig. 4.

Figure 6

Figure 6

Revealed interactions between MAPK cascade modules. Responses of every module to perturbations to each single module were measured, and intermodular connections were discovered and quantified by using Eqs. 8 and 10.

Figure 7

Figure 7

Global fractional responses obtained by simulating experimental perturbations to the gene network shown in Fig. 3. Two global response matrices (Rp⋅100, designated by superscripts a and b) were generated by applying the following eight parameter perturbations. a or b, 30% decrease or 50% increase, respectively, in: the maximal activity of the transcription rate vformula image (Vformula image; see Table 2, which is published as supporting information on the PNAS web site), perturbation to module 1; Vformula image, module 2; Vformula image, module 3; and Vformula image, module 4.

Figure 8

Figure 8

Retrieved experimental interaction maps (A) and known theoretical interaction map (B). Two experimental local interaction matrices (r) were retrieved from the data shown in Fig. 7. The response coefficients marked by superscript a and b correspond to perturbations indicated in the legend to Fig. 7.

Figure 9

Figure 9

Retrieved wiring for a three-gene network. Because gene 4 was an unknown component, (quasi)direct effects of gene 3 on genes 1 and 2 were revealed.

Figure 10

Figure 10

Interaction maps retrieved from incomplete data. Two experimental local interaction matrices (r) were retrieved from the global response matrix corresponding to the first three rows and columns of the matrices shown in Fig. 7. The response coefficients marked by superscripts a or b correspond to perturbations indicated in the legend to Fig. 7.

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