Figure 5
From: Regulation of cytoplasmic polyadenylation can generate a bistable switch
Steady state solution characteristics of molecular loop with respect to CPEB1 activation parameter k 5 . The parametric steady state solution characteristics are developed through an approximate analytical solution (a, c) and numerical/analytical bifurcation diagrams (b, d). The approximate analytical solution is developed through graphing equation 6, whereas the numerical/analytical bifurcation diagrams are developed through tracking the steady state behavior of all three models with respect to k5. Two different set of parameters are compared. For first set of parameters the approximate solution and numerical/analytical bifurcation diagrams from three alternative models converge to same upper, stable steady state solution branch (a, b). For the second set of parameters the approximate solution and numerical/analytical bifurcation diagrams from three alternative models does not converge to same upper, stable steady state and solution branch (c, d). The approximate analytical solution for first set of parameters (a) is located at two different values of rate constant k5 (The dotted red curve "1" represent k5 = 0.0072 μM-1.s-1, second dotted red curve "2" represent k5 = 0.0001 μM-1 .s-1 ). This method locates the upper stable steady state at XT = 95, while the lower and unstable steady state are at XT = 0.0001 and XT = 9.4 when k5 is set at 0.0072μM-1 .s-1 (curve "1"). As k5 is decreased to 0.0001 new solution is located at XT = 70 (upper stable steady state), XT = 0.0001 (lower stable steady state) and XT = 16 (unstable steady state). The numerical and analytical bifurcation diagrams for first set of parameters (b) are developed through tracking the steady state behavior of all three models with respect to k5. The three bifurcation diagrams are exactly matching with each other for the entire range of activation parameter (dotted blue line represent the bifurcation diagram based on full model, whereas solid blue lines represent the bifurcation diagrams based on reduced three differential equation and a single equation model). The approximate analytical solution for second set of parameters (c) is also located at two different values of rate constant k5 (The dotted red curve "1" represent k 5 = 0.0072 μM-1.s-1, second dotted red curve "2" represent k5 = 0.0001 μM-1.s-1). The numerical and analytical bifurcation diagrams for second set of parameters (d) are developed through tracking the steady state behavior of all three models with respect to k5. Full model bifurcation diagram does not match with reduced and single equation model.