a Agonist (the triangle) binding to receptor activates a G protein, , which in turn activates an effector protein, . For simplicity, the G protein is always bound to the receptor, and we show explicitly neither G and G nor the deactivation of the G protein. b The G pathway. The effector protein is the isoform of phospholipase C. When activated, PLC cleaves the phospholipid PIP into membrane-bound DAG and cytosolic IP. High IP concentrations cause the release of calcium ions from the endoplasmic reticulum. PKC when bound by calcium is recruited to the membrane by DAG and becomes activated. c The G pathway. The effector protein is adenylyl cyclase which synthesizes cAMP from ATP when activated. d The increased concentrations of cytosolic cAMP activate PKA by binding to its inhibitory domain.

a A bifurcation diagram for calcium as a function of activated PLC when activated AC is at 0.25 M. Symbols are the same as Fig. 2. Example time courses show oscillations in both calcium and cAMP when activated PLC is at 2.1 M or 4.5 M. The frequency of the oscillations increases with activated PLC and a phase lag appears between cAMP and calcium. b The frequency of the cAMP and calcium oscillations as a function of both activated AC and PLC concentrations. A region where the system has two stable steady-states is shaded black. c The amplitude of the calcium oscillations for the same range of activated AC and PLC. d The amplitude of the cAMP oscillations. We model only global levels of second messengers. Local changes at distinct sub-cellular sites may be much higher.

a A bifurcation diagram for the G pathway showing the nature of the calcium response for differing concentrations of activated PLC. Thin lines indicate a stable steady-state concentration of calcium; thick lines indicate that calcium concentrations oscillate. The upper thick line marks the maximum concentration that calcium reaches during one oscillation; the lower thick line marks the minimum concentration reached. Dotted lines indicate unstable attractors and red squares show bifurcation points. The label HB indicates a Hopf bifurcation; LP indicates a saddle-node bifurcation. The frequency of calcium oscillations ranges from effectively zero Hz when the concentration of PKC is near 0.65 M and to approximately 0.12 Hz (a period of around 8 s) when the concentration of PKC is near 2.4 M. Example time courses of calcium concentration illustrating the appearance and disappearance of oscillations are shown at different points in the bifurcation diagram: at activated PLC concentrations of 0.3 M, 0.9 M, 2.0 M, and 2.5 M. b A bifurcation diagram for the G pathway showing stable steady-state concentrations of activated PKA for differing concentrations of activated AC. cAMP concentrations behave similarly and appear linear for the AC concentrations shown. In the example time course at 0.15 M concentration of activated AC, activated PKA increases monotonically with time while agonists are present. The concentration of cAMP behaves similarly.

a A bifurcation diagram for calcium as a function of activated PLC when activated AC is at 0.17 M. Symbols are the same as Fig. 2. PD indicates a period-doubling bifurcation. Example time courses of calcium and cAMP are shown when activated PLC is at 0.2 M, 0.28 M, 0.31 M, and 0.36 M. Bursting oscillations appear for intermediate activated PLC concentrations. The amplitude of the oscillations increases and decreases as activated PLC increases, and oscillations gradually disappear. b The frequency of the cAMP and calcium oscillations as a function of both activated AC and PLC concentrations. c The amplitude of the calcium oscillations. d The amplitude of the cAMP oscillations.