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

524 Chapter 8: Analyzing Cells, Molecules, and Systems
between randomly moving molecules, with each event resulting in changes in the
number of molecular species by integer amounts. The amplified effect of fluctuations
in a molecular reactant, or the compounded effects of fluctuations across
many molecular reactants, often accumulates as an observable phenotype. This
can endow a cell with individuality and generate non-genetic cell-to-cell variability
in a population.
Non-genetic variability can be studied in the laboratory by single-cell measurements
of fluorescent proteins expressed from genes under the control of a specific
promoter. Live cells can be mounted on a slide and viewed through a fluorescence
microscope, revealing the striking variability in protein expression levels (Figure
8–87). Another approach is to use flow cytometry, which works by streaming a
dilute suspension of cells past an illuminator and measuring the fluorescence of
individual cells as they flow past the detector (see Figure 8–2). Fluorescence values
can be used to build histograms that reveal the variability in a process across a
population of cells, with a broad histogram indicating higher variability.
Several Computational Approaches Can Be Used to Model the
Reactions in Cells
We have focused primarily on the use of ordinary differential equations to model
the dynamics of simple regulatory circuits. These models are called deterministic,
because they do not incorporate stochastic variability and will always produce
the same result from a specific set of parameters. As we have seen, such models
can provide useful insights, particularly in the detailed mechanistic analysis of
small regulatory circuits. However, other types of computational approaches are
also needed to comprehend the great complexity of cell behavior. Stochastic models,
for example, attempt to account for the very important problem of random
variability in molecular networks. These models do not provide deterministic predictions
about the behavior of molecules; instead, they incorporate random variation
into molecule numbers and interactions, and the purpose of these models
is to obtain a better understanding of the probability that a system will exist in a
certain state over time.
Numerous other modeling strategies have been or are being developed. Boolean
networks are used for the qualitative analysis of complex gene regulatory
networks containing large numbers of interacting components. In these models,
each molecule is a node that can exist in either the active or inactive state, thereby
affecting the state of the nodes it is linked to. Models of this sort provide insights
into the flow of information through a network, and they were useful in helping
us understand the complex gene regulatory network that controls the early development
of the sea urchin (see Figure 7–43). Boolean networks therefore reduce
complex networks to a highly simplified (and potentially inaccurate) form. At the
other extreme are agent-based simulations, in which thousands of molecules (or
“agents”) in a system are modeled individually, and their probable behaviors and
interactions with each other over time are calculated on the basis of predicted
physical and chemical behaviors, often while taking stochastic variation into
account. Agent-based approaches are computationally demanding but have the
potential to generate highly lifelike simulations of real biological systems.
Figure 8–87 Different levels of gene
expression in individual cells within a
population of E. coli bacteria. For this
experiment, two different reporter proteins
(one fluorescing green, the other red),
controlled by a copy of the same promoter,
have been introduced into all of the
bacteria. Some cells express only one gene
copy, and so appear either red or green,
while others express both gene copies,
and so appear yellow. This experiment
reveals variable levels of fluorescence,
indicating variable levels of gene expression
within an apparently uniform population of
cells. (From
MBoC6
M.B. Elowitz
m8.75/8.88
et al., Science
297:1183–1186, 2002. With permission
from AAAS.)
Statistical Methods Are Critical For the Analysis of Biological Data
Dynamics, differential equations, and theoretical modeling are not the be-all and
end-all of mathematics. Other branches of the subject are no less important for
biologists. Statistics—the mathematics of probabilistic processes and noisy datasets—is
an inescapable part of every biologist’s life.
This is true in two main ways. First, imperfect measurement devices and other
errors generate experimental noise in our data. Second, all cell-biological processes
depend on the stochastic behavior of individual molecules, as we just discussed,
and this results in biological noise in our results. How, in the face of all
this noise, do we come to conclusions about the truth of hypotheses? The answer
is statistical analysis, which shows how to move from one level of description to