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
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another: from a set of erratic individual data points to a simpler description of the
key features of the data.
Statistics teaches us that the more times we repeat our measurements, the better
and more refined the conclusions we can draw from them. Given many repetitions,
it becomes possible to describe our data in terms of variables that summarize
the features that matter: the mean value of the measured variable, taken over
the set of data points; the magnitude of the noise (the standard deviation of the
set of data points); the likely error in our estimate of the mean value (the standard
error of the mean); and, for specialists, the details of the probability distribution
describing the likelihood that an individual measurement will yield a given value.
For all these things, statistics provides recipes and quantitative formulas that biologists
must understand if they are to make rigorous conclusions on the basis of
variable results.
Summary
Quantitative mathematical analysis can provide a powerful extra dimension in our
understanding of cell regulation and function. Cell regulatory systems often depend
on macromolecular interactions, and mathematical analysis of the dynamics of
these interactions can unveil important insights into the importance of binding
affinities and protein stability in the generation of transcriptional or other signals.
Regulatory systems often employ network motifs that generate useful behaviors:
a rapid negative feedback loop dampens the response to input signals; a delayed
negative feedback loop creates a biochemical oscillator; positive feedback yields a
system that alternates between two stable states; and feed-forward motifs provide
systems that generate transient signal pulses or respond only to sustained inputs.
The dynamic behavior of these network motifs can be dissected in detail with deterministic
and stochastic mathematical modeling.
What we don’t know
• Many of the tools that revolutionized
DNA technology were discovered by
scientists studying basic biological
problems that had no obvious
applications. What are the best
strategies to ensure that such crucially
important technologies will continue to
be discovered?
• As the cost of DNA sequencing
decreases and the amount of
sequence data accumulates, how
are we going to keep track of and
meaningfully analyze this vast amount
of information? What new questions
will this information allow us to answer?
• Can we develop tools to analyze
each of the post-transcriptional
modifications on the proteins in living
cells, so as to follow all of their
changes in real time?
• Can we develop mathematical
models to accurately describe the
enormous complexity of cellular
networks and to predict undiscovered
components and mechanisms?
Problems
Which statements are true? Explain why or why not.
8–1 Because a monoclonal antibody recognizes a specific
antigenic site (epitope), it binds only to the specific
protein against which it was made.
8–2 Given the inexorable march of technology, it
seems inevitable that the sensitivity of detection of molecules
will ultimately be pushed beyond the yoctomole
level (10 –24 mole).
8–3 If each cycle of PCR doubles the amount of DNA
synthesized in the previous cycle, then 10 cycles will give a
10 3 -fold amplification, 20 cycles will give a 10 6 -fold amplification,
and 30 cycles will give a 10 9 -fold amplification.
8–4 To judge the biological importance of an interaction
between protein A and protein B, we need to know
quantitative details about their concentrations, affinities,
and kinetic behaviors.
8–5 The rate of change in the concentration of any
molecular species X is given by the balance between its
rate of appearance and its rate of disappearance.
8–6 After a sudden increase in transcription, a protein
with a slow rate of degradation will reach a new steady
state level more quickly than a protein with a rapid rate of
degradation.
Discuss the following problems.
8–7 A common step in the isolation of cells from a
sample of animal tissue is to treat the tissue with trypsin,
collagenase, and EDTA. Why is such a treatment necessary,
and what does each component accomplish? And
why does this treatment not kill the cells?
8–8 Tropomyosin, at 93 kd, sediments at 2.6S, whereas
the 65-kd protein, hemoglobin, sediments at 4.3S. (The
sedimentation coefficient S is a linear measure of the rate
of sedimentation.) These two proteins are drawn to scale
in Figure Q8–1. How is it that the bigger protein sediments
more slowly than the smaller one? Can you think of an
analogy from everyday experience that might help you
with this problem?
hemoglobin
Figure Q8–1 Scale models of tropomyosin
and hemoglobin (Problem 8–8).
tropomyosin