Figure 5. System identification of CaMKII and PP1 activities in the bi-directional turning response.

(A) The schematic drawing depicting the regulation of CaMKII and PP1, which up- and down-regulate the effector X, respectively, in the growth cone model. (B) Simulation of the multi-phasic bi-directional turning response by a mathematical model where the parameters were identified by the reverse engineering approach (solid red line). Points and error bars represent the experimental results (the same as in Fig. 3B). Goodness of fitting was evaluated by the Pearson’s chi-square test (p = 0.78), indicating no significant difference. (C) Reverse-engineered dose-responses of CaMKII (Red line) and PP1 (blue line) to the total cAMP:cGMP concentration (cNMP). The dose-responses were normalized. The blue line is the sum of CaN- and Calpain-dependent PP1 (blue dashed and dotted lines). The estimated parameter values are listed in Methods. (D) Contributions of the activator (A; CaMKII) and the inhibitor (I; PP1) to growth cone turning (black line in (B)) depending on the cNMP level. Attractive and repulsive influences of the activator and inhibitor are represented by red and blue solid lines, respectively, which correspond to the first and second terms in Equation (1). The PP1-induced repulsion (blue solid line) is given by the sum of the CaN- and Calpain- dependent factors (dashed and dotted blue lines, respectively).