TABLE 4

Sensitivity of networks to signals: cascades, feedback, and feedforward networks

In a signaling cascade, the net sensitivity of the output D with respect to the input A at steady state equals the product of the sensitivities along the cascade (Kholodenko et al., 1997; Bruggeman et al., 2002), with A-to-D as concentrations of signaling proteins,
Embedded Image (9)
All these local sensitivities, each denoted by an "r", can be obtained from steady-state dose-response curves. When D feedbacks onto A, regardless of whether this is a positive or negative interaction, we obtain:
Embedded Image (10)
with Embedded Image as the feedback strength, it is <0 in case of negative feedback and >0 in case of positive feedback. The effect of negative feedback is that the sensitivity of the output D with respect to the input signal A is reduced. These equations lose their meaning when the feedback destabilizes the system. In the case of positive feedback, stability is guaranteed as long as the denominator remains positive. The positive feedback sensitizes the cascade for the signal when Embedded Image. When Embedded Image, the sensitivity becomes infinite and all-or-none response occurs associated with "bistability," which is a known response of signaling cascades. When feedbacks destabilize the system oscillations or bistability can occur as discussed in the main text.