
&
I
G
, &m and &
O
of the regulatory protein degradation rate
I
x
i
, immature
and mature reporter protein degradation rates
I
x
3
and
I
G
, maturation
rate m and dilution rate µ due to cell growth, respectively.
iv) Defi ne an explicit cost function
2
0
() ( (,) ())
1, 2 for low-pass and hosgh-pass filter
f
u
issiri
Jf E G fu G u du
i
=−
=
∫
high-pass filter
(7.6)
where f
i
denotes the combination
{}
123
,,,pR pR pR I
of promoter-RBS set
{}
123
,,pR pR pR
with an inducer concentration I;
(,)
ss i
Gfu
and
()
ri
Gu
are the estimated and desired steady-state fl uorescence levels under
the specifi c combination f
i
with input concentration u, respectively;
pR
1
, pR
2
, and pR
3
repr ...