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, 105 (6), 1913-8

Emergent Decision-Making in Biological Signal Transduction Networks

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Emergent Decision-Making in Biological Signal Transduction Networks

Tomás Helikar et al. Proc Natl Acad Sci U S A.

Abstract

The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow simulation and dynamical analysis. Exposing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in that the network performed sharp, nonfuzzy classifications even in the face of added noise, a hallmark of real-world decision-making.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
The Boolean model of signal transduction and method of simulation. The actual connection graph of the 130-node Boolean model is shown inside the cell. The inputs are external to the cell and the outputs are nodes that are part of the network and thus inside the cell. The four nonstress output nodes were selected on the basis of their role in regulating other major cellular functions, as indicated. The stress outputs are the two stress-activated protein kinases SAPK and p38. As a demonstration of how simulations are performed, four random inputs are applied to the network, indicated as runs 1–4. These inputs are stress-limited because the stress inputs are limited to values between 0% and 5% ON, whereas the nonstress inputs are random values between 0% and 100% ON. After the application of each of the inputs, the network is iterated until it reaches a cycle, and the percentage ON of each output is calculated. This results in four corresponding individual outputs, shown at the bottom. The global outputs are the combination of all four individual outputs and are represented by conversion to a ternary string (shown on the bottom right) based on the ranges described in the text.
Fig. 2.
Fig. 2.
Qualitative, individual input–output relationships in the Boolean model of signal transduction. (A) Positive relationship between EGF and Akt (25). (B) Positive relationship between EGF and Erk (34). (C) EGF dependence on Integrin stimulation by extracellular matrix (ECM) proteins for Erk stimulation (27). (D) Low-level stimulation of Erk by high levels of ECM (36). (E) Hormonal stimulators (alpha_s_lig) of G-associated GPCR activation of adenylate cyclase (AC) (37, 38). (F) GPCR activation of Erk. (39) (G) GPCR stimulation of Erk depends on transactivation of the EGFR (40). (H and I) Activation of the stress-associated MAPK's SAPK and p38 by stress (33, 34). (J and K) Activation of Rac and Cdc42 by ECM (28). (L) Activating mutations of known protooncogenes such as Ras result in growth factor-independent activation of Erk (41). Note that the references refer to classical, qualitative input–output relationships (not necessarily quantitative dose–response curves), and the dose–response curves presented here are intended to demonstrate how the Boolean model qualitatively reproduces the referenced input–output relationships over a range of inputs.
Fig. 3.
Fig. 3.
Scatter plots of all input vectors associated with the first 15 global outputs of Table 1. (A) The inputs associated with the 15 most common outputs are plotted in three dimensions by using principle component analysis (PCA, see Materials and Methods). All 9,389 inputs plotted together, with each input colored according to which of the 15 outputs it is associated. It appears that all inputs associated with a given output (indicated by the color) are clustered. (B) To verify that the model uniquely clusters inputs based on associated outputs, selected colored clusters in A are plotted on separate axes so the separation of each cluster is visible. For example, the 2,346 input values associated with the output 1000 (shown as black points) are clustered with little overlap with input values associated with outputs 2000 and 1011, as shown in the first plot. Taken together, these results show that the Boolean signal transduction model divides the input space into distinct equivalence classes that are associated with biologically appropriate global outputs.

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