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Figure 2 | BMC Systems Biology

Figure 2

From: Regulation of cytoplasmic polyadenylation can generate a bistable switch

Figure 2

The approximate analytical solution of αCaMKII-CPEB1 molecular loop. It is obtained through graphically locating all the steady state solutions of single differential equation 1. This equation describes the rate of change of total concentration of αCaMKII (XT) and its functional relation between the new synthesis and degradation of CaMKII. The steady state form of equation 1 is transformed into two functions F (XT) and G (XT). The function F (XT) (solid blue curve) basically represents the net αCaMKII degradation, whereas the modified function G'(XT) = G [g (XT)] (dotted red curve) represent the net generation of αCaMKII. (a) This analytical solution is developed by setting all parameters as described in table 1. Graphs of both functions intersect at three locations which are characterized as steady state solutions of equation 1 and provide the approximate analytical solution. The upper steady state solution is located at XT = 95, while the unstable solution is located at XT = 9.4, and lower steady state solution at XT = 0.0001. (b) The effect of degradation rate on analytical solution. Four different degradation rates are selected λ = 0.00006 s- (solid blue line #1, bistable system), λ, = 0.0001 s-1 (solid blue line #2 bistable system), λ = 0.0003 s-1(solid blue line #3 bistable system) and λ = 0.0006 s-1 (solid blue line #4 mono-stable system). (c) The effect of CPEB1 activation parameter k5 on analytical solution. Four different values of CPEB1 activation are selected k5 = 0.00001μM-1.s-1 (dotted red line #1, mono-stable system), k5 = 0.00006μM-1.s-1 (dotted red line #2 bistable system), k5 = 0.0001μM-1.s-1 (dotted red line #3 bistable system) and λ = 0.0072 μM-1s-1 (dotted red line #4 bistable system).

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