In Section 4, as an application of elementary reaction processes, we consider solving the ODE system that arises from the PWN of molecule concentration dynamics in ECM degradation.
In PWN, in addition to the simple dimerization of monomers, there are polymerizations of higher complexes.
The PWN of association or dissociation of these complexes are shown in Figure 3.
Now, according to the binding rules discussed above, we have the following three associations or dissociations in the PWN:
For reactions (I)-(III), there are twelve molecules in the PWN in Figure 3: a, b, c, ab, bc, cc, abc, bcc, abcc, bccb, abccb, and abccba.
In order to obtain the correct ODEs, it is necessary to extract the appropriate doubling rules for the reaction coefficients in the PWN. We will explain it in the next subsection.
In addition, upon being clarified the model behaviors we notice the most important pathways in the PWN. They are three parts producing [[xi].sub.91112] (association parts just before the three blue boxes in Figure 5).
Thus, the initial "mass" continues to exist in the PWN with its components changing to dimer, trimer, tetramer, ...: at every moment, such dimer, trimer, ..., and hexamer contained in the unit variables coexist.
That is, the PWN system is settled so as to continue to produce [X.sub.9] as much as possible at every moment.