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The activation of matrix metalloproteinase 2 (MMP2) is a crucial event duringtumor metastasis and invasion, and this pathway network consists of 3 monomers.The pathway network of the activation obeys to a set of specified reactionrules. According to the rules, the individual molecules localize in aparticular order and symmetrically around a homodimer following the formationof that dimer. We generalized the homodimer pathway network obeying to similarreaction rules, by changing the number of monomers involved in this pathwayfrom 3 to N. At the previous work, we found the molecules in the pathwaynetwork are classified to some reaction groups. We derived the law of massconservation between the groups. Each group concentration converges to itsequilibrium solution. Using these results, we derive the concentrations of thecomplexes theoretically and reveal that each complex concentration converges toits equilibrium value. We can say the pathway network with homodimer symmetricform complexes is asymptotic stable and identify the regulator parameter of thetarget complex in the network. Our mathematical approach may help us understandthe mechanism of this type pathway network by knowing the backgroundmathematical laws which govern this type pathway network.

Mathematical modeling and analysis of the pathway network consisting of symmetrical complexes with N monomers, like the activation of MMP2