Genetic Process Engineering - Cellular Computing - page 49

signal

L C T

ψ Α φ Α ρ Α ψ Ζ

cooperative
binding

translation transcription

input
mRNA

input
protein

repression output

mRNA

input
protein

mRNA

T

L

“gain”

+ + =

ψ Ζ

ρ Α ψ Ζ

φ Α

0 1

0 1 0 1 0 1

ψ Α φ Α ρ Α ψ Α

+ + =

scale input “clean” signal invert signal digital inversion

Figure 4.4 Functional composition of the inversion stages: the translation stage maps
input mRNA levels ( ψ A ) to input protein levels ( φ A ), the cooperative binding stage
maps input protein levels to bound operator levels ( ρ A ), and the transcription stage
maps bound operator levels to output mRNA levels ( ψ Z ). The degradation of the
mRNA and protein molecules is represented with the electrical ground symbol. The
degradation of mRNA is part of the translation stage, while the degradation of pro-
teins is part of the cooperative binding stage. The graphs illustrate the steady-state
relationships for each of these stages and the overall inversion function that results
from combining these stages.

maximal, additional repressor molecules have no noticeable effect. The purpose
for this stage is to provide signal restoration: as a result of this stage, the analog
input signal better approximates its digital meaning.
In the last stage, RNA polymerase transcribes the structural gene and inverts
the signal. Let

ψ Z denote the mRNA concentration for the output signal Z .
Then, in the steady-state relation T (transcription stage) between ψ Z and ρ A ,

ψ Z decreases monotonically as ρ A increases. With no repression, transcription

proceeds at maximum pace (i.e., maximum level of

ψ Z ). Any increase in re-
pression activity results in a decrease in transcription activity, and hence the
inversion of the signal.
As illustrated in Figure 4.4, the functional combination I of the above stages
achieves digital inversion:

ψ Z = I ( ψ A ) = T ◦ C ◦ L ( ψ A ).

I is the transfer function of the inverter.

Intracellular Logic Circuits

Biochemical inverters are the building blocks for constructing intracellular logic
circuits. First, most protein-coding sequences can be successfully fused to any