FIGURE 2.
A simple network consisting of two parallel cascades with cross talk. The network consists of two pathways, X and Y. Pathway X has three components (x0, x1, and x2); component x0 is input signal itself, or is activated in manner that is strictly proportional to the input signal. (Because the input signal can have any shape, x0 can abstractly represent any upstream component, e.g., a receptor, a G-protein, a kinase, etc.) The parameters a1 and a2 are activation rate constants, and 
and 
are deactivation, or decay, rate constants. For example, a1 is the rate constant for the activation of x1 by x0, and 
is the rate constant for the deactivation of x1. (B) Outputs of this network in response to X signaling (that is, X input) and Y signaling. Signal x0 does not lead to the production of y2, because none of the components of X can activate or inhibit components of Y. Thus, the specificity of X with respect to Y and fidelity of Y with respect to X are complete (see text for definitions). In contrast, y1 (which might be a kinase of pathway Y) weakly activates x2 (which might be a transcription factor for pathway X), at a rate characterized by the “leak constant”, hleak. Thus, the specificity of Y and the fidelity of X are finite functions of hleak and other key parameters of the network. In particular, in the text it is shown that network specificity is proportional to 1/hleak. (C) Depiction of the ratios equal to the specificity of pathway Y and the fidelity of pathway X.