Information Technology Reference
In-Depth Information
Figure 4.17
The simulated transfer curve of the
λ
cI
/P(R) inverter, with the transfer
curve of two such inverters connected in series shown in the inset. Both graphs plot
φ
A
versus
φ
Z
.
(i.e., slope), determines how well the gate reduces noise from input to output.
For electronic digital circuits, the low and high signal ranges are typically the
same for all gates because the circuit is composed of transistors with identical
threshold voltages, spatially arranged. However, in biochemical digital circuits,
the gate components (e.g., proteins and promoters) have different characteristics
depending on their reaction kinetics. Therefore, the designer of biological digital
circuits must take explicit steps to ensure that the signal ranges for coupled gates
are matched appropriately, as described below.
Before discussing the rules for biochemical gate coupling, we introduce a
variation of the transfer function, the
transfer band
, that captures systematic
fluctuations in signal levels. It is especially important to consider fluctuations
in biological settings. Experiments in chapter 7 report signal fluctuations by a
factor of 10 for cells with the same genetic circuit grown under the same con-
ditions. The transfer band captures these fluctuatations with a region enclosed
by a pair of transfer functions, as shown in Figure 4.18.
I
min
is the function that
maps an input to the minimum corresponding observed output, and
I
max
is the
function that maps an input to the maximum corresponding observed output.
Let I
il
and I
ih
be the input thresholds. Then, the low and high gate matching
requirement from above is:
into
−→
min
(
I
il
),
I
max
(
0
)
[in low]
0
,
I
il
I
[out high]
into
−→
[in high]
I
ih
,
∞
0
,
I
max
(
I
ih
)
[out low]
Consider the case of two inverters, I and J, with J's output coupled to I's
input. Then, the coupling is correct if and only if:
