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inducer binds to the repressor and changes the conformation of the repressor.
The conformation change prevents the repressor from binding to the operator
and allows RNAp to transcribe the gene, yielding a high output.
The IMPLIES gate has the same three biochemical stages as the inverter:
translation, cooperative binding, and transcription. The inducer concentration
levels affect the cooperative binding stage
C , which now has two inputs. Let
υ A
denote the inducer concentration level, let
φ A denote the concentration level
of the input mRNA, and let
φ Z denote the concentration level of the output
mRNA. Here, the repression activity
ρ A resulting from the cooperative binding
ρ A = C ( φ A , υ A ) , depends nonlinearly on the level of the repressor and
on the level of the inducer. The binding affinities of the active repressor to the
operator, and of the inducer molecule to the repressor, determine the shape of
C . The transfer function I of the IMPLIES logic gate is the mapping:
ψ Z = I ( ψ A ) = T C υ A , L ( ψ A ) .
stage,
The two gate inputs are not interchangeable. The input and output repres-
sors can be connected to any other circuit component, but the inducer input
is an intercellular signal and is specifically coupled to the input repressor. As
with the different inverter signals, before building a circuit the designer should
experimentally check for unintended interactions between a specific inducer,
other repressors, and other inducers. Any set of noninterfering repressor/inducer
pairs can then serve as a library of potential signals for constructing intercellular
circuits.
The AND Gate
The AND gate allows cells to detect incoming messages from other cells. Fig-
ure 4.8 illustrates the biochemical reactions, the logic symbol, and the truth
table for an intercellular gate that implements the AND logic function. Here,
RNAp normally has a low affinity for the promoter, and basal transcription is
correspondingly small. Therefore, in the absence of the activator and inducer
inputs, the output is low. If the activator is present but the inducer is not present,
the activator has a low affinity for the promoter and does not bind to it. In this
case, the output is still low. Finally, if the inducer and the activator are both
present, the inducer binds to the activator. The newly formed bond changes the
conformation of the activator and allows the activator/inducer complex to bind
to the operator. In turn, the activator/inducer complex helps recruit RNAp to
the promoter and initiate transcription, yielding a high output. Often, a dimeric
form of the activator is necessary for complex formation.
Similar to the biochemical stages of the NOT and IMPLIES gates, the AND
gate stages include translation, cooperative binding, and transcription. The first
stage, translation, is similar in all three cases. For the AND gate, the following
cooperative binding stage C
maps the activator protein
φ A and inducer
υ A
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