Figure 2

The theoretical model is capable of producing both uni-directional and multi-phasic bi-directional turning responses.

(A,C,E,G) Examples of activator and inhibitor activities in response to increasing guidance signal (intracellular Ca²⁺ in the case of the growth cone). Red and blue lines indicate the dose-responses of activator A and inhibitor I, respectively, to the guidance signal. The dose-response curves are given by Hill equations (Equations (8 and 9)). Parameter values are listed in Methods. (B,D,F,H) Turning responses (black lines) are calculated based on the dose-responses of activator and inhibitor, shown in (A,C,E,G) (see Methods). When the intracellular Ca²⁺ level is in the red and blue shaded regions, the growth cone exhibits attraction and repulsion, respectively. The turning response is given by the sum of the attractive factor (red dashed line: the first term in Equation (1)) and the repulsive factor (blue dashed line: the second term in Equation (1)). Each dashed line represents the ratio between the slope and amplitude of the dose-response curve in (B), (C), (E) or (G); e.g., the red dashed line in (B) was obtained from the slope (ΔA) and amplitude (A^*) of the red solid line in (A). Thus, the theoretical model is able to produce a simple uni-directional attraction (A,B) or repulsion (C,D), bi-phasic bi-directional turning response (E,F), and tri-phasic bi-directional turning response (G,H). These complex responses are primarily due to the nonlinear responses of the activator and inhibitor to the guidance signal, typically observed in (G).