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

516 Chapter 8: Analyzing Cells, Molecules, and Systems
concentration of protein R
time
WITH
FEEDBACK
the behavior of A and R over time for any value of the input. As before, we plug in
values for the parameters (β R , τ R , etc.) and then use a computer to determine the
MBoC6 n8.606/8.78
values of [A] and [R] as a function of time after a sudden input activates gene A.
The results reveal several important properties of negative feedback. First,
rather surprisingly, negative feedback increases the speed of the response to the
activating input. As shown in Figure 8–76C, the system with negative feedback
reaches its new steady state faster than the system with no feedback.
Second, negative feedback is useful for protecting cells from perturbations
that continuously arise in the cell’s internal environment—due either to random
variations in the birth and death of molecules or to fluctuations in environmental
variables such as temperature and nutritional supplies. Let us imagine, for example,
that β A , the transcription rate constant for gene A, fluctuates by 25% of its
value and ask whether and how much the levels of protein R are affected. The
results, shown in Figure 8–77, reveal that a change in β A causes a smaller change
in the steady-state value of R when the network has negative feedback.
concentration of protein R
time
NO
FEEDBACK
Figure 8–77 The effect of fluctuations
in kinetic rate constants on a system
with negative feedback compared to
one without feedback. The plot at left
represents the levels of protein R after a
sudden activating stimulus, according to
the regulatory scheme in Figure 8–76A and
determined by the solution of Equation set
8–8 (see Figure 8–76B). A perturbation was
induced by changing β A from 4 M/min (red
line) to 3 M/min (blue line). The plot at right
shows the results when negative feedback
was removed. The system with negative
feedback deviates less from its normal
operation as β changes than does the
system with no feedback. Notice that, as
in Figure 8–76C, the system with negative
feedback also reaches its steady state
more rapidly.
Delayed Negative Feedback Can Induce Oscillations
A beautiful thing happens when a negative feedback loop contains some delay
mechanism that slows the feedback signal through the loop: rather than generating
a new stable state as in a rapid negative feedback loop, a delayed loop generates
pulses, or oscillations, in the levels of its components. This can be seen,
for example, if the number of components in a negative feedback loop increases,
which leads to delays in the amount of time required for the cycle of signals to be
completed. Figure 8–78 compares the behavior of two network motifs—one with
a three-stage and one with a five-stage negative feedback loop. Using the same
kinetic parameters at each stage in the two loops, one finds that stable oscillations
arise in the longer loop, while in the shorter loop the same parameters lead to
relatively rapid convergence to a stable steady state.
Changes in the parameters of a delayed negative feedback loop—binding
affinities, transcription rates, or protein stabilities, for example—can change the
amplitude and period of the oscillations, providing a remarkably versatile mechanism
for generating all sorts of oscillators that can be used for various purposes
in the cell. Indeed, many naturally occurring oscillators, including the calcium
oscillators described in Chapter 15 and the cell-cycle network described in Chapter
17, use delayed negative feedback as the basis for biologically important oscillations.
Not all of the oscillations observed in cells are thought to have a function,
however. Oscillations become inevitable in a highly complex, multicomponent
biochemical pathway like glycolysis, due simply to the large number of feedback
loops that appear to be required for its regulation.
DNA Binding By a Repressor or an Activator Can Be Cooperative
We have focused thus far on the binding of a single transcription regulator to a
single site in a gene promoter. Many promoters, however, contain multiple adjacent
binding sites for the same transcription regulator, and it is not uncommon for
these regulators to interact with each other on the DNA to form dimers or larger
oligomers. These interactions can result in a cooperative form of DNA binding,