Biology Reference
In-Depth Information
FIGURE 8.8
Hypergraph for system (8.19).
Some immediate questions regarding our software arise. In particular, can the
software deal with hypergraphs? And if so, how will we represent hypergraphs as
input for
ExPA
? It turns out that
ExPA
handles everything beautifully. In fact, because
ExPA
does its analysis on the stoichiometric matrix, all the program requires is the
stoichiometry of the biochemical process. And so in order to have
ExPA
find the
extreme paths of this process, all we need to do is enter internal fluxes in the obvious
way. For example,
r
1
will be given as in Table
8.2
.
Exercise 8.24.
Create an input file for
ExPA
which represents Figure
8.8
.Listthe
extreme paths given by the program and explain in laymen's terms why your answer
makes sense.
Exercise 8.25.
Write down the stoichiometric matrix for (
8.19
) and explain how
your input file for
ExPA
relates to this matrix.
Now let's look at something a little more complex. Consider the following abstract
biochemical process:
⎧
⎨
A
−→
B
+
C
,
D
−→
E
+
F
,
B
+
E
−→
G
,
C
+
E
−→
H
,
(8.21)
⎩
F
−→
I
,
H
+
I
−→
J
+
K
,
G
+
J
−→
L
.
Suppose that
A
and
D
are system inputs, while
I
K
, and
L
are system outputs.
Exercise 8.26.
Draw a hypergraph representation for (
8.21
).
,
J
,
Exercise 8.27.
Using only the hypergraph or representation (
8.21
), see if you can
find the proper inputs to create one molecule of
J
as an output. Is it possible? What
about
n
molecules of
J
?
Exercise 8.28.
Use
ExPA
to find the extreme paths of the system, making sure
that your input file fully represents (
8.21
). Explain carefully why these are the
only
extreme paths for the system using either the biochemical representation (
8.21
), your
hypergraph representation, or both.
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