Information Technology Reference
In-Depth Information
Table 4.3 Kinetic constants used in BioSPICE simulations.
k
dim(a)
8.333
k
rprs(a
2
)
66.67
k
dec(a)
0.5775
k
dec(ga
2
)
0.2887
k
sngl(a)
0.1667
k
dis(a
2
)
0.2
k
dec(a
2
)
0.5775
k
dec(ga
4
)
0.2887
k
dim(z)
8.333
k
rprs(a
4
)
333.3
k
dec(z)
0.5775
k
dec(mrna)
2.0
k
sngl(z)
0.1667
k
dis(a
4
)
0.25
k
dec(z
2
)
0.5775
k
xscribe
0.0001
k
xlate
0.03
The units for the first-order reactions are 100 sec
−
1
, and the units for the second order reactions are
µ
M
−
1
·
100 sec
−
1
.
The reactions proceed as follows: At first, no input mRNA or input protein
repressor are present. As a result,
P
Z
is active and RNAp transcribes the gene
into the output mRNA
Z
. The level of mRNA
Z
increases until it stabilizes when
the gene expression and decay reactions reach a balance. At this stage, the input
signal is low while the output signal is high.
Then, an externally imposed drive increases the input mRNA
A
, which rRNA
translates into the input repressor protein
A
. The protein begins to form dimers,
and these dimers bind to the promoter's free operators. The system quickly
reaches a state where each promoter is essentially completely bound by two
dimers. The almost total inactivation of the promoters occurs at a fairly low
concentration of the dimer
A
2
and indicates the strong repression efficiency
of the
cI
repressor that is used for this simulation. As a result of the promoter
inactivation, transcription stops, and the output mRNA
Z
decays to zero. At the
end of this stage, the input signal is high while the output signal is low.
Finally, the external drive of mRNA
A
stops, resulting in the decay of
mRNA
A
,
A
, and
A
2
. Slowly, the repressor dimers dissociate from the
P
Z
operators, and the level of the active promoter
P
Z
rises back to the original
level. This allows RNAp to resume transcription of
P
Z
, and the level of the
output mRNA
Z
rises again. At this stage, the input signal reverts to low, while
the output signal reverts to high.
The simulation shows that the gate switching time (measured in minutes
for this mechanism) is governed by the rate of recovery of
P
Z
. The limiting
rate is therefore the dissociation of bound repressor dimer
A
2
from
P
Z
. Fig-
ure 4.11 shows simulation results of how an engineered reduction in the repres-
sor binding coefficient improves the gate delay. Through simulations such as
this, BioSPICE offers insights into biocircuit design and ultimately motivates
laboratory experiments. For example, chapter 7 describes experimental results
of reducing the binding efficiency of
cI
to the
λ
promoter by mutating base
pairs in the O
R
1 region.
Simulations of Proof of Concept Circuits
This section describes BioSPICE simulation results of an RS latch and a ring
oscillator, two simple but interesting logic circuits built from the inverter model
