Mechanisms of Gene Regulation: Boolean Network Models of the Lactose Operon in Escherichia coli - Mathematical Concepts and Methods in Modern Biology - page 7

FIGURE 1.3
Schematic of the lac operon regulatory mechanism (from Santillan at al. [ 14 ]) Protein
LacY is a permease that transports external lactose into the cell. Protein LacZ polymerizes
into a homotetramer named -galactosidase. This enzyme transforms internal lactose

(Lac) to allolactose (Allo) or to glucose and galactose (Gal). It also converts allolactose
to glucose and galactose. Allolactose can bind to the repressor (R) inhibiting it. When
not bound by allolactose, R can bind to a specific site upstream of the operon structural
genes and thus prevent transcription initiation. External glucose inhibits the production of
cAMP that, when bound to the CRP protein (also known as CAP) to form the CAP-cAMP
complex, acts as an activator of the lac operon. External glucose also inhibits lactose
uptake by permease proteins. Reprinted from Biophysics Journal , Vol. 92, M. Santillan,
M. C. Mackey, and E. S. Zeron, Origin of bistability in the lac operon 3830 - 3842,
Copyright (2007), with permission from Elsevier.

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imply that when lactose is absent from the medium, the operon is off, and that when
lactose is present but glucose is not, the operon is on. We consider Boolean models
with various levels of complexity and compare the results. The material can be used as
a gentle entry into mathematical modeling, especially for students without Calculus
background (see Section 1.5 for more details).

1.3.1 Identifying the Model Variables and Parameters
The modeling process begins with careful examination of the major interactions and
components of the system, as depicted in Figure 1.3 , and with selecting the model
variables and parameters. The model variables are generally chosen to represent the
major dynamic elements of the system (quantities that change with time) while the
parameters correspond to static descriptors. Different decisions regarding the exclu-
sion or inclusion of any given component or part of the system will lead to differ-
ent models. The next step is to define a wiring diagram (sometimes also called a