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
523
SUDDEN
ACTIVATING
INPUT
A1
inactive
A1
pulsed input
prolonged input
A1 protein
A1
A1 protein
A2 protein
A2 protein
fast A1
binding
A1
A2
delayed A2
binding
protein X
output
GENE X
time
(A) (B) (C)
X
protein X
output
time
This arrangement, known as a coherent feed-forward motif, has the interesting
characteristics illustrated in Figure 8–86.
MBoC6
Imagine
n8.616/8.87
that two activators, A1 and
A2, are both required to initiate transcription of a gene. The input to the network
activates A1 directly, but only activates A2 through this A1 activation. Thus, for
a protein to be synthesized from this gene, long-term inputs are required that
allow both A1 and A2 to be produced in active form. Brief input pulses are either
ignored or produce small outputs. The requirement for a long input is important if
assurances about a signal are needed before a costly cellular program is triggered.
For example, glucose is the sugar on which E. coli cells grow best. Before cells trigger
arabinose metabolism in the example above, it might be beneficial to be sure
that glucose has been depleted (a sustained CAP pulse), rather than inducing the
arabinose program during a transient glucose fluctuation.
Figure 8–86 How a coherent feedforward
motif responds to various
inputs. (A) Diagram of a coherent feedforward
motif in which the transcription
activators A1 and A2 together activate
expression of gene X using the AND logic
of Figure 8–83B. (B) The response to a
brief input can be either weak (as shown) or
nonexistent. This allows the motif to ignore
random fluctuations in the concentration of
signaling molecules. (C) A prolonged input
produces a strong response that can turn
off rapidly.
The Same Network Can Behave Differently in Different Cells Due
to Stochastic Effects
Up to this point, we have assumed that all cells in a population produce identical
behaviors if they contain the same network. It is important, however, to account
for the fact that cells often show considerable individuality in their responses.
Consider a situation in which a single mother cell divides into two daughter cells
of equal volume. If the mother cell has only one molecule of a given protein, then
only one daughter will inherit it. The daughters, though genetically identical, are
already different. This variability is most pronounced for molecules that are present
in small numbers. Nevertheless, even when there are many copies of a particular
protein (or RNA), it is very unlikely that both daughter cells will end up with
exactly the same number of molecules.
This is just one illustration of a universal feature of cells: their behaviors are
often stochastic, meaning that they display variability in their protein content and
therefore exhibit variations in phenotypes. In addition to the asymmetric partitioning
of molecules following cell division, variability can originate from many
chemical reactions. Imagine, for example, that our mother cell contains a simple
gene regulatory circuit with a positive feedback loop like that shown in Figure
8–80B. Even if both daughter cells receive a copy of this circuit, including one
copy of the initial transcription activator protein, there will be variability in the
time required for promoter binding—and it will be statistically nearly impossible
for the genes in the two daughter cells to become activated at precisely the same
time. If the system is bistable and poised near a switching point, then variability
in the response might flip the switch in only one daughter cell. Two daughter cells
that were born identical can thereby acquire, by chance, a dramatic difference in
phenotype.
More generally, isogenic populations of cells grown in the same environment
display diversity in size, shape, cell-cycle position, and gene expression. These
differences arise because biochemical reactions require probabilistic collisions