
62 Feedback Control in Systems Biology
kinetics, the responses a re overdamped and thus the possibility of overshoot
is completely pro hibited. Indeed, in the case of the Dictyostelium network,
the response cannot be under-damped for any combination of the kinetic
parameters. This can be seen by c onsidering the fact that
ζ =
k
12
+ k
14
2
√
k
12
k
14
≥ 1 ⇒ (k
12
+ k
14
)
2
≥ 4k
12
k
14
⇒ k
2
12
− 2k
12
k
14
+ k
2
14
≥ 0 ⇒ (k
12
− k
14
)
2
≥ 0
(2.70)
for all k
12
> 0 and k
14
> 0. Hence, the overdamped dynamical response
appears to stem from the network structure itself, rather tha n being dependent
on any particular values of the kinetic parameters. The step responses with
k
12
and k
14
perturb ...