Molecular Biology of the Cell by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morgan, Martin Raff, Keith Roberts, Peter Walter by by Bruce Alberts, Alexander Johnson, Julian Lewis, David Morg

MATHEMATICAL ANALYSIS OF CELL FUNCTIONS
521
(A)
(B)
A
A1
R
A2
GENE
A
R
GENE
GENE
OFF OFF OFF
GENE
A1
This example illustrates an AND NOT logic function (A and not R) (see Figure
8–83A). Maximal activation of this gene is accomplished when [A] is high and [R]
is zero. However, intermediate levels of gene activation are also possible depending
on the levels of A and R and also on the binding affinities of [A] and [R] for their
respective sites (that is, K A and K R ). When K A » K R , even a small concentration of
[A] is capable of overcoming repression by R. Conversely, if K A « K R , then much
more [A] is needed to activate the gene (Figure 8–84B and C).
Many other logic functions can govern combinatorial gene regulation. For
example, an AND logic gate results when two activators, A1 and A2, are both
required for a gene to be transcribed (Figures 8–83B and 8–84D). In E. coli cells,
the AraJ gene controls some aspects of arabinose sugar metabolism: its expression
requires two transcription regulators, one activated by arabinose and the
other activated by the small
MBoC6
molecule
n8.613/8.84
cAMP (Figure 8–84E).
A
A2 A1 A2
A1
GENE
GENE
R
A
R
A2
GENE
OFF OFF ON
OFF
AND logic
ON
AND NOT logic
GENE
Figure 8–83 Combinatorial control of
gene expression. There are many ways in
which gene expression can be controlled
by two transcription regulators. To define
precisely the relationship between the two
inputs and the gene expression output, a
regulatory circuit is often described as a
specific type of logic gate, a term borrowed
from electronic circuit design. A simple
example is the OR logic gate (not shown
here), in which a gene is controlled by two
transcription activators, and one or the
other can activate gene expression. (A) In
a system with an activator A and repressor
R, if transcription is turned on only when A
is bound and R is not, then the result is an
AND NOT logic gate. We saw an example
of this logic in Chapter 7 (Figure 7–15).
(B) An AND gate results when two
transcription activators, A1 and A2, are
both required to turn on a gene.
K A [A]
fraction of A bound = 1 + KA [A]
(A)
concentration of R
(B)
concentration of A1
(D)
fraction of R not bound =
K A > K R
concentration of A
.
concentration of A2
1
1 + K R [R]
K A [A] 1 K A [A]
P(A,R) = =
1 + K A [A] 1 + K R [R] 1 + K A [A] + K R [R] + K A K R [A][R]
concentration of R
(C)
cAMP (mM)
(E)
20
6
1
K A < K R
concentration of A
EXPERIMENTAL VALUES
0.02 1.3 43
arabinose (mM)
Figure 8–84 How the quantitative output of
a gene depends on both its combinatorial
logic and the affinities of transcription
regulators. (A) In a combinatorial gene
regulatory system like that illustrated in Figure
8–83A, the fraction of promoters bound by
activator A and not bound by repressor R are
each determined as shown here. The product
of these probabilities provides the probability,
P(A, R), that a gene promoter is active.
(B–E) In these four panels, red indicates
high gene expression and blue indicates low
gene expression. (B) and (C) depict gene
expression from the system described
in panel (A). The two panels demonstrate
how the system behaves when the relative
affinities of the two transcription regulators
change as indicated above each panel.
(D) Gene expression in a case where the
gene turns on only at high levels of both
activating inputs (A1 and A2), as shown in
Figure 8–83B. (E) Experimental data showing
measured expression of a gene in E. coli
that is combinatorially regulated by two
inputs: arabinose and cAMP. Note the close
resemblance to panel (D). (E, adapted from
S. Kaplan et al., Mol. Cell 29:786–792, 2008.)