Ca²⁺-Dependent PP1 Activity via Protein Signaling Cascade and Phosphorylated CaMKII Subunit Concentration Steady-States

<div><p>(A) Phosphorylation and dephosphorylation rate of inhibitor 1 as functions of the calcium concentration: the red line shows the calcineurin activity dephosphorylating inhibitor 1, <i>v</i>_CaN(<i>C</i>), as a function of calcium, and the blue line shows the PKA activity leading to phosphorylation of I1, <i>v</i>_PKA(<i>C</i>). Both rates are given by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030221#pcbi-0030221-e009" target="_blank">Equation 9</a>, in which the calcium/calmodulin complex concentration, <i>C</i>, is in equilibrium with the present calcium concentration. The total calmodulin concentration is Ca<i>M</i>₀ = 0.1 μM. The vertical thin full line depicts the position of the calcium resting concentration in all panels.</p><p>(B) Bistable region, PP1 activity, and I1P steady-state concentration in the PP1–Ca²⁺ plane: the full lines correspond to a total CaMKII concentration of <i>CaMKII</i>₀ = 16.67 μM, whereas dashed lines correspond to <i>CaMKII</i>₀ = 8.33 μM. The full red lines mark the positions of the left-hand (line above) and right-hand (line below) boundaries of the bistable region (red shaded region between both lines) with respect to the PP1 activity for <i>CaM</i>₀ = 0.1 μM. The purple and the green full lines show the calcium-dependent steady-state of the PP1 activity, (<i>k</i>₁₂ · <i>D</i>), and I1P concentration, <i>I</i>, respectively, given by the rates shown in (A). The numbered points 1, 2, 3, and 4 at the intersections of the PP1 steady-state with the full red lines give the locations of the boundaries (saddle-node bifurcation points) of the bistable regions. The dashed red and purple lines depict the boundaries of the bistable region and the steady-state PP1 activity, respectively, for the case <i>CaMKII</i>₀ = 8.33 μM (see text).</p><p>(C) Steady-states of the phosphorylated CaMKII subunit concentration (<i>S</i>_active) as a function of calcium: full lines characterize stable steady-states whereas dashed lines mark unstable steady-states. Steady-states for <i>CaMKII</i>₀ = 16.67 μM are shown in blue and for <i>CaMKII</i>₀ = 8.33 μM in green. Red shaded areas depict regions of bistability for the <i>CaMKII</i>₀ = 16.67 μM case, i.e., three steady-states (two stable and one unstable steady-state) exist for a given calcium concentration. Bifurcation points are numbered as in (B). The cross (diamond) marks the position of the UP (DOWN) state at resting calcium concentration for the <i>CaMKII</i>₀ = 16.67 μM case (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030221#pcbi-0030221-t001" target="_blank">Table 1</a> and text for parameters, <i>k</i>_CaN = 18 1/s).</p>