Biology Reference
In-Depth Information
As in many situations, the information of gene regulatory pathway and mechanism is not available
and one needs to take recourse to more approximate models. In this sense, the discrete model will be
favorable.
Diffusion transportation
Most of the models deal with the amount of metabolites in a cell. In the simplest case, we may be able
to assume that the cell is a “well-mixed pool”, i.e., the amount of metabolites, enzymes, etc. is uniform
across the cell. In many situations, however, concentration gradients exist which will affect the local rate
of biochemical reactions, in particular for large systems and different compartments, we must consider
explicitly the effect of diffusion or transportation.
In general, if concentration gradients exist within the spatial scale of interest it is highly likely that
diffusion will have an impact on the modeling results, unless the gradients change so slowly that they can
be considered stationary compared to the timescale of interest. A growing number of modeling studies
[Markram
et al.
, 1998; Naraghi and Neher, 1997] have emphasized the important effects of diffusion on
molecular interactions. Moreover, many bioprocesses take place in different compartments in a cell. For
instance, glycolysis conducts in cyotoplasma while TCA in mitochondria. Membranes play an important
role to separate these bioprocesses and meanwhile maintain the normal transportation of metabolites
inside and outside of them. In addition, signal transduction also occurs across the membranes.
So far, in order to model a metabolic network, not only all effect of metabolites and reaction behaviors
but different compartments should be considered. Diffusion, facilitated diffusion and active transport
could be the very important physical effects in the models. We will focus on the membrane transportation.
The rate of penetration of a metabolite across a membrane is related to the concentration gradient by
Fick's Law of Diffusion:
Rate of penetration
J
=
D
d
[
S
]
dx
Dβ
Δ
x
−
[
S
]
in
)
where [S]
out
and [S]
in
are concentrations of metabolite outside and inside the membrane, respectively;
D
denotes the diffusion coefficient (
D
decreases with the size of the metabolite);
A
is the area of
membrane (the greater it is, the more metabolite that can pass);
β
is the partition coefficient (
β
increases
with increasing solubility) and
dx
is the membrane thickness (the greater the thickness, the slower the
rate). Usually,
D
Δ
x
is called the permeability constant, a constant for a given substance moving through
a given membrane.
In carried systems, the carrier exhibit saturation kinetics, so that “Michaelis-Menten equation” formula
might be used to describe such a process where low
K
m
means a high rate of “affinity and transport”, and
high
K
m
a low “affinity and transport” rate. Some metabolites and/or signals (hormones) may modify
carriers and change
K
m
.
V
max
is related to “carrier mobility”, the total number of carriers present.
·
A
·
β
·
=
·
A
·
([
S
]
out
Petri net modeling algorithm
Modeling algorithm and analysis of hybrid Petri nets can be done by the following procedures:
Draft network construction
Normally, a Petri net model is built manually by drawing places, transitions and arcs with mouse
events. Fortunately, The XML based Petri net interchange format standardization which consists of a
Petri net markup language (PNML) and a set of document type definitions (DTD) or XSL Schema is
coming into being and intended to be applied. Several Petri net tools such as PNK, Renew, Design/CPN
