Biology Reference
In-Depth Information
Fig. 2. The
lac
operon: The enzyme
β
-galactosidase, produced by the
lacZ
gene, hydrolyzes lactose to glucose and galactose.
lacY
encodes the permease that brings lactose into the cell, and
lacA
encodes an acetylase that is believed to detoxify
thiogalactosides, which, along with lactose, are transported into cells by
lacY
. The “operator” lies within the “promoter”, and
the “CAP site” lies just upstream of the promoter.
Fig. 3. The HFPN representation of the control mechanism of the lac operon transcription switch. Only discrete elements are
used for representing the switching mechanism.
transitions. In addition, common formulas for biological reactions such as Michaelis-Menten's equation
can be modeled almost directly with assigning concentrations of substrate and product to continuous
places and the formula for the reaction of them to the continuous transition between these two places.
HFPN MODELING OF THE LAC OPERON GENE REGULATORY MECHANISM AND
GLYCOLYTIC PATHWAY
This section demonstrates how we can model the lac operon gene regulatory mechanism and glycolytic
pathway in
E. coli
with an HFPN. Biological facts used for constructing this model are described in
the biological literature [Alberts
et al.,
1994; Lewin, 1997; Watson
et al.,
1987]. The HFPN modeling
will start with a “transcription control switch” (Fig. 3), then it will be enhanced gradually by adding
“positive regulation” (Fig. 4), “negative regulation” (Fig. 5), and “hydrolyzing lactose to glucose and
galactose” (Fig. 7). This step-by-step explanation based on the well-known biological facts helps readers
to understand how HFPNs are created according to the biological knowledge.
All the parameters in the transitions of the HFPN model are summarized in Tables 1 and 2. In this
example, we shall show a rough guideline for usage of continuous and discrete transitions. In accordance
with the guideline below, readers can understand the modeling manner of biological pathway with HFPN
described in the subsections from “Transcription control switch” to “Hydrolyzing lactose to glucose and
galactose”. For the detail explanation about firing rules, refer to the paper [Matsuno
et al.,
2003b].
