This figure shows the modules that could be used to describe interactions between the growth factor and β-adrenergic receptor pathways. The growth factor signaling pathway is divided into two modules (the red box and the green box). Such modularity divides this pathway by their location within different subcellular regions. All members of the red box are functional at the plasma membrane while the members of the green box are cytoplasmic. At a functional level, the reactions in the red box specify how EGF binding to its receptor regulates activation of Ras while the reactions in the green box specify how the activated Ras regulates MAPK phosphorylation. The gray box provides a counter point to the organizational logic of the red and green boxes. Here the module spans reactions from the membrane to the cytoplasm, from the β-adrenergic receptor agonist isoproternol to the small G protein Rap1 in the cytoplasm. This modular arrangement provides a facile way of understanding how β-adrenergic receptor stimulation could inhibit or augment EGF activation of MAP-kinase. Comparison of Figures 1A and 1B are crucial for understanding the necessity of specifying the isoforms of the components within the modules to understand regulatory behavior. When the major isoform is C-Raf, the interactions between the EGF receptor pathway and β-adrenergic receptor pathway are antagonistic since Rap1 sequesters but does not activate C-Raf (Figure 1A). In contrast, B-Raf is activated both by Ras and Rap1. Here, the two pathways are additive or synergistic in activating MAP-kinase (Figure 1B).

Networking and activation of a positive feedback loop by norepi-nephrine acting through the α1- and α2- adrenergic receptor pathways.
When norepinephrine (NE) binds the α1 adrenergic receptor it activates the Gq pathway, leading to stimulation of the phospholipase C-β. This results in release of intracellular calcium and the activation of protein kinase C, which in turn can activate both Ras and Raf. When NE activates the α2-adrenergic receptor, which couples to the Gi/o pathway, release of Gβγ results in the activation of the Ras-MAPK pathway. Simultaneous activation of both pathways results in MAPK regulation of cytoplasmic phospholipase-A2 (cPLA2), which produces arachadonic acid (AA) that activates protein kinase C in the presence of basal levels of diacylglycerol (DAG). This sets up a positive feedback loop indicated by the circular arrow, resulting in sustained activation of MAP-kinase. Thus brief pulses of NE could lead to prolonged activation of MAP-kinase (MAPK) in cells where both α1 and α2 adrenergic receptors and other components of the network are present.

The solution to Equation B1 has the special property that its derivative (slope) at any given time is simply equal to the negative of its value multiplied by a proportional constant k