Information Technology Reference
In-Depth Information
ADDING AUTOREPRESSION An operator that binds the output protein may
be added to the promoter/operator region to accomplish autorepression. The
simulated transfer functions shown above are not balanced because they are
more sensitive to fluctuations in low input signals versus fluctuations in high
input signals. Autorepression reduces the maximum output protein synthesis
rate and therefore reduces some of the asymmetry in the signal sensitivities.
Figure 4.19e illustrates the effect of adding autorepression on
, the coopera-
tive binding stage of inversion. For low levels of the input protein repressor,
the promoter is active and transcribes the output protein. This output protein
binds to the operator of its own promoter, and therefore there is always some
concentration of inactive/bound promoter,
C
ρ
A
. High levels of input repressor
increase
ρ
A
until saturation.
Functional Composition of Transfer Functions
In biocircuit design, the engineer creates a genetic logic circuit using a small set
of basic gates and a database of biochemical reaction kinetic rates. The kinetics
database contains transfer-curve measurements obtained using the mechanism
described in chapter 7. Given transfer-curve measurements, the engineer pre-
dicts the behavior of complex circuits through the functional composition of
behavioral data describing only the basic components. For example, figures 4.17
and 4.21 show the predicted steady-state behavior of circuits with two inverters
based on the transfer curves of the constituent inverters.
Without autorepression, the transfer function of an inverter is determined
by the input mRNA,
φ
A
, RBS, input protein
A
, operator, promoter, and out-
put mRNA,
φ
Z
, but not by the output protein
Z
. This means that the relation
φ
Z
=
I
1
(
φ
A
)
does not depend on
Z
. Therefore, gate couplings are indepen-
dent of the output protein. To predict the transfer function of two gates in a
series,
φ
Y
=
I
2
(
φ
Z
)
connected to
φ
Z
=
I
1
(
φ
A
)
, the database only needs to
contain
∗=
I
2
(
φ
Z
)
and
∗=
I
1
(
φ
A
)
, where
∗
denotes any protein. If the
inversion uses autorepression, then the relation
φ
Z
=
I
3
(
φ
A
)
also depends on
the characteristics of
Z
. To compute the transfer function of a gates coupling
φ
Y
φ
A
)
, the database must specifically include
the transfer functions of the input/output protein pairs
Y/Z
and
Z/A
and their
associated mRNA.
Using the transfer-curve measurements, the efficacy of a particular transfer
function in implementing the digital abstraction is evaluated in terms of factors
such as gain and noise margins. The transfer function of inverters in a series
is the functional composition of their respective transfer functions. A series of
inverters is then also evaluated in terms of gain and noise margins. Because the
transfer functions are different for each inverter, the gates must be matched. In
addition, the matching process must also evaluate the gain and noise margins
=
I
4
(
φ
Z
)
connected to
φ
Z
=
I
3
(
