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

510 Chapter 8: Analyzing Cells, Molecules, and Systems
assess the biological impact of any interaction in the cell, we need to know in
precise terms how the molecules interact, how they catalyze reactions, and, most
importantly, how the behaviors of the molecules change over time. If a cartoon
shows that protein A activates protein B, for example, we cannot judge the importance
of this relationship without quantitative details about the concentrations,
affinities, and kinetic behaviors of proteins A and B.
Let us begin by defining two different types of regulatory interaction in our
cartoons: one designating inhibition and the other designating activation. If the
protein product of gene X is a transcription repressor that inhibits the expression
of gene Z, we depict the relationship as a red bar-headed line ( ) drawn between
genes X and Z (Figure 8–71). If the protein product of gene Y is a transcription
activator that induces the expression of gene Z, then a green arrow ( ) is drawn
between genes Y and Z.
The regulation of one gene’s expression by another is more complicated than
a single arrow connecting them, and a complete understanding of this regulation
requires that we tease apart the underlying biochemical processes. Figure 8–72A
sketches some of the biochemical steps in the activation of gene expression by a
transcription activator. A gene encoding the activator, designated as gene A, will
produce its product, protein A, via an RNA intermediate. This protein A will then
bind to p X , the regulatory promoter of gene X, to form the complex A:p X . Once the
A:p X complex forms, it stimulates the production of an RNA transcript that is subsequently
translated to produce protein X.
We will focus here on the binding interaction that lies at the heart of this regulatory
system: the interaction between protein A and the promoter p X . Any molecule
of protein A that is bound to p X can also dissociate from it. The steps represented
by the green activation arrow in Figure 8–72A include both the binding of
A to p X and the dissociation of the complex A:p X to re-form A and p X , as illustrated
GENE X
GENE Z
GENE Y
GENE Z
Figure 8–71 Diagrams that summarize
biochemical relationships. Here, a simple
cartoon indicates MBoC6 that n8.600/8.72 gene X represses
gene Z (left) whereas gene Y activates gene
Z (right).
SUDDEN
ACTIVATING
INPUT
A + p X
k on
A:p X
k off
GENE A
DNA
rate of complex formation = k on [A][p X ]
RNA
rate of complex dissociation = k off [A:p X ]
(A)
A
A
promoter
(p X )
transcription
activator protein
GENE X
X
DNA
RNA
protein
(B)
at steady state:
k on [A][p X ] = k off [A:p X ]
k
[A:p X ] = on
[A][p X ] = K[A][p X ] Equation 8–1
k off
(C)
[p T X ] = [p X ] + [A:p X ]
substituting [p X ] from the above equation into
Equation 8–1 yields:
[A:p X ] = K[A]([p T X ] – [A:p X ])
[A:p X ](1 + K[A]) = K[A][p T X ]
K[A]
[A:p X ] = [pT
X ]
1 + K[A]
(D)
(E)
Equation 8–2
[A:p
bound fraction = X ] K[A] =
Equation 8–3
[p T
X ] 1 + K[A]
Figure 8–72 A simple transcriptional
interaction. (A) Genes A and X each
produce a protein, with the product of
gene A serving as a transcription activator
to stimulate expression of gene X. As
indicated by the green arrow, stimulation
depends in part on the binding of protein
A to the promoter region of gene X,
designated as p X . (B) The binding of protein
A to the gene promoter is determined
by the concentrations of the two binding
partners (denoted as [A] and [p X ], in units
of mol/liter, or M), the association rate
constant k on (in units of sec –1 M –1 ), and
the dissociation rate constant k off (in units
of sec –1 ). (C) At steady state, the rates of
association and dissociation are equal, and
the concentration of the bound complex is
determined by Equation 8–1, in which the
two rate constants are combined in the
equilibrium constant K. (D) Equation 8–2
can be derived to calculate the steadystate
concentration of bound complex at a
known total concentration of the promoter
[p X
T ]. (E) Rearrangement of Equation
8–2 yields Equation 8–3, which allows
calculation of the fraction of promoter p X
that is occupied by protein A.