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comparison of the predicted and observed circuit behavior indicates that these
models are not complete, they represent a necessary step in the device science of
cells, and continued efforts may provide insights into the complex functioning
of natural genetic circuits. There are excellent reviews of cell modeling efforts
[28, 36, 49, 70, 79, 83, 96].
At least for the near term, the modeling of genetic circuits is likely to differ
somewhat from that found in the physical sciences, where models are based
on fundamental concepts and contain a large number of parameters that can be
individually measured [79]. However, the successful efforts to generate robust
and predictive models of semiconductor devices and circuits can offer insights
that may accelerate the development of analogous models for genetic circuits.
It has been suggested that there is an element of convergent evolution between
complex engineered devices and biological systems [23], and a rich history of
electronic system design may provide clues for understanding gene network
topology. A complete treatment of this material is beyond the scope of this
chapter, but consider the following example.
Several strategies for analyzing or simulating the stochastic properties of
genetic circuits have been reported [9, 47, 71, 78, 83, 102, 105]. Most often the
results are given as signal-to-noise ratio, noise strength, stability parameters, or
a time history of molecular concentration. Lost or hidden within such results are
the frequency domain features of the noise, which are important as noise cas-
cades through subsequent circuits. Maintaining the frequency domain features
is especially important in autoregulated gene circuits analysis, as feedback im-
pacts both magnitude and frequency composition of the noise [95]. A complete
analysis requires that the frequency composition of the noise be preserved.
Recently we adapted frequency domain techniques borrowed from elec-
tronic circuit analysis that use the loop transmission concept to elucidate the
noise performance of autoregulated (i.e., negative feedback) genetic circuits
(Figure 5.8) while maintaining critical frequency information [95]. The loop
transmission, T , is the transfer function around the loop and may be thought of
as a measure of the resistance of the feedback loop to variation. T is calculated
by introducing a perturbation (
) at any point within the circuit (e.g., a small
change in transcription rate) and determining the response (
) that returns to the
same point (e.g., a reactionary change in transcription rate). T(f) is given by
ρ
ρ
(f )/
(f ) , and the feedback is negative if T( 0 ) is negative (i.e., has a phase of
±
180). For the autoregulated gene circuit in Figure 5.8b, T(f) is given by [95]
T( 0 )
T(f)
=
1
π f
γ R
1
+ i 2
π f
γ P
+ i f
f α
where b is the average number of proteins produced from each mRNA transcript,
α ( 0 ) is the feedback term from a linear approximation to the Hill repression
 
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