Information Technology Reference
In-Depth Information
The model includes the components described in the second section of this
chapter in the following reactions: translation of the input protein from the
input mRNA (reactions 8-9), input protein dimerization and decay (reactions
10-13), cooperative binding of the input protein (reactions 14-19), transcription
(reaction 20), and degradation of the output mRNA (reaction 21).
To simulate an inverter, BioSPICE automatically converts the chemical
equations of this model to the system of ordinary differential equations in
Table 4.2. The system of differential equations includes an entry for each of
the molecular species involved in inversion: the input mRNA, mRNA
A
; the
input protein monomer,
A
; the dimeric form of the input repressor protein,
A
2
; the unbound promoter,
P
Z
; the promoter bound with one repressor protein
dimer,
P
Z
A
2
; the promoter bound with two repressor protein dimers,
P
Z
A
4
;
and the output mRNA, mRNA
Z
. Each differential equation describes the time-
domain behavior of a particular molecular species based on all the equations in
the biochemical model that include that particular molecule. For example, the
“
k
dim(a)
·
A
2
” term of differential Equation 17 is derived from model Equation 3,
while the “
−
k
sngl(a)
·
A
2
” term is derived from model Equation 4. Note that the
Table 4.2 Ordinary differential equations used to simulate a single inverter.
(15)
d(
mRNA
A
)
=
drive
mRNA
A
(t )
−
k
dec(mrna)
·
mRNA
A
d(A)
=
2
·
k
sngl(a)
·
A
2
−
k
dec(a)
·
A
+
k
xlate
·
rRNA
·
mRNA
A
−
2
·
k
dim(a)
·
A
2
(16)
d(A
2
)
=
k
dim(a)
·
A
2
−
k
sngl(a)
·
A
2
−
k
dec(a
2
)
·
A
2
−
k
rprs(a
2
)
·
P
Z
·
A
2
+
k
dis(a
2
)
·
P
Z
A
2
(17)
−
k
rprs(a
4
)
·
P
Z
A
2
·
A
2
+
k
dis(a
4
)
·
P
Z
A
4
(18)
d(P
Z
)
=
k
dis(a
2
)
·
P
Z
A
2
−
k
rprs(a
2
)
·
P
Z
·
A
2
+
k
dec(ga
2
)
·
P
Z
A
2
d(P
Z
A
2
)
=
k
rprs(a
2
)
·
P
Z
·
A
2
−
k
dis(a
2
)
·
P
Z
A
2
−
k
rprs(a
4
)
·
P
Z
A
2
·
A
2
(19)
+
k
dec(ga
4
)
·
P
Z
A
4
−
k
dec(ga
2
)
·
P
Z
A
2
+
k
dis(a
4
)
·
P
Z
A
4
(20)
d(P
Z
A
4
)
=
k
rprs(a
4
)
·
P
Z
A
2
·
A
2
−
k
dis(a
4
)
·
P
Z
A
4
−
k
dec(ga
4
)
·
P
Z
A
4
(21)
d(
mRNA
Z
)
=
k
xscribe
·
P
Z
·
RNA
p
−
k
dec(
mRNA
)
·
mRNA
Z
These equations are derived from the biochemical inversion model in Table 4.1.
