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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Many of these methods are being expanded to investigate gene function on a
genome-wide scale. The generation of mutant libraries in which every gene in an
organism has been systematically deleted, disrupted, or made controllable by the
experimenter provides invaluable tools for exploring the role of each gene in the
elaborate molecular collaboration that gives rise to life. Technologies such as RNAseq
and DNA microarrays can monitor the expression of tens of thousands of genes
simultaneously, providing detailed, comprehensive snapshots of the dynamic patterns
of gene expression that underlie complex cell processes.
MATHEMATICAL ANALYSIS OF CELL FUNCTIONS
Quantitative experiments combined with mathematical theory mark the beginning
of modern science. Galileo, Kepler, Newton, and their contemporaries did
more than set out some rules of mechanics and offer an explanation of the movements
of the planets around the Sun: they showed how a quantitative mathematical
approach could provide a depth and precision of understanding, at least for
physical systems, that had never before been dreamed to be possible.
What is it that gives mathematics this almost magical power to explain the natural
world, and why has mathematics played so much more important a part in
physical sciences than in biology? What do biologists need to know about mathematics?
Mathematics can be viewed as a tool for deriving logical consequences from
propositions. It differs from ordinary intuitive reasoning in its insistence on rigorous,
accurate logic and the precise treatment of quantitative information. If the
initial propositions are correct, then the deductions drawn from them by mathematics
will be true. The surprising power of mathematics comes from the length
of the chains of reasoning that rigorous logic and mathematical arguments make
possible, and from the unexpectedness of the conclusions that can be reached,
often revealing connections that one would not otherwise have guessed at. Reversing
the argument, mathematics provides a way to test experimental hypotheses: if
mathematical reasoning from a given hypothesis leads to a prediction that is not
true, then the hypothesis is not true.
Clearly, mathematics is not much use unless we can frame our ideas—our initial
hypotheses—about the given system in a precise, quantitative form. A mathematical
edifice raised on a rickety or—even worse—a vague or overcomplicated
set of propositions is likely to lead us astray. For mathematics to be useful, we
must focus our analysis on simple subsystems in which we can pick out key quantitative
parameters and frame well-defined hypotheses. This approach has been
used with great success in physics for centuries, but it has been less common in
biology. But times are changing, and more and more it is becoming possible for
biologists to exploit the power of quantitative mathematical analysis.
In this final section of our methods chapter, we do not attempt to teach readers
every way in which mathematics can be fruitfully applied to biological problems.
Rather, we simply aim to give a sense of what mathematics and quantitative
approaches can do for us in modern biology. We focus primarily on the important
principles that mathematics teaches us about the dynamics of molecular interactions,
and how mathematics can unveil surprising and useful features of complex
systems containing feedback. We will illustrate these principles using the regulation
of gene expression by transcription regulators like those discussed in Chapter
7. The same principles apply to the post-transcriptional regulatory systems that
govern cell signaling (Chapter 15), cell-cycle control (Chapter 17), and essentially
all cell processes.
Regulatory Networks Depend on Molecular Interactions
Cell function and regulation depend on transient interactions among thousands
of different macromolecules in the cell. We often summarize these interactions in
this book with schematic cartoons. These diagrams are useful, but a complete picture
requires a deeper, more quantitative level of understanding. To meaningfully