Model predictions related to the factors affecting Erk activity.

(A) Graphical explanation of the numerical procedure. We consider two generic curves A and B with Hill coefficients nA and nB respectively. The shape of both curves depends on the value of a parameter p that can range from 0 to 1. On the left, the curves A and B are shown when the value of the parameter p is equal to 0.1. In this condition the difference of the two Hill coefficient nB-nA is large. In the middle, the curves A and B are shown when the value of the parameter p is equal to 0.9. In this condition the difference of the two Hill coefficient nB-nA is smaller. The right panel is the heatmap showing the differences between the Hill coefficients of curves A and B (nB-nA) computed for all values of p between 0 and 1. (B) Erk* values are more sensitive to S1 than to [FGF]. Heatmaps show the difference between the Hill coefficient of the curve Erk*(S1) and the Hill coefficient of the curve Erk*([FGF]). Hill coefficients obtained with default values of the parameters are 1.47 for Erk*([FGF]) and 2.39 for Erk*(S1). To compute Erk*([FGF]) we fixed the value of S1 = 0.3. In the two panels, S1 and S2 are related by Eq (12), which reflects the relation between the portions of cell surfaces exposed to FGF and to Ephrin, respectively. (C) Erk* values are more sensitive to S2 than to [ephrin]. Heatmaps show the difference between the Hill coefficient of the curve Erk*(S2) and the Hill coefficient of the curve Erk*([ephrin]). Hill coefficients obtained with default values of the parameters are 1.17 for Erk*([ephrin]) and 1.57 for Erk*(S2). To compute Erk*([ephrin]) we fixed the value of S1 = 0.3. In the two panels, S1 and S2 are related by Eq (12), which reflects the relation between the portions of cell surfaces exposed to FGF and to Ephrin, respectively. (D) The presence of ephrin increases the steepness of the relation between Erk* and S1. Heatmaps show the difference between the Hill coefficient of the curve Erk*(S1) computed in the presence of ephrin and the Hill coefficient of the curve Erk*(S1) computed in the absence of ephrin ([ephrin] = 0.001). The Hill coefficient obtained with standard values of the parameters for Erk*(S1) in the absence of ephrin is 1.85. (E) The presence of ephrin increases the steepness of the relation between Erk* and [FGF]. Heatmaps show the difference between the Hill coefficient of the curve Erk*([FGF]) computed in the presence of ephrin and the Hill coefficient of the curve Erk*([FGF]) computed in the absence of ephrin ([ephrin] = 0.001). The Hill coefficient obtained with standard values of the parameters for Erk*([FGF]) in the absence of ephrin is 1.42. To compute Erk*([FGF]) we fixed the value of S1 = 0.3. For all panels, the Hill coefficients were computed varying the values of the parameters from 0 to 1 (Kb, K1, K2, Vs, Vrg; left panels) or from 0 to 2000 (Ks, Krg, Kd, Ke; right panels). Values of the Hill coefficients were obtained by curve fitting. The standard values of the parameters (Table 1) are highlighted with black boxes.