14 July 2010
Manoj Gopalkrishnan
School of Technology and Computer Science
Tata Institute of Fundamental Research
Mumbai, India
It is a common expectation in chemistry that a chemical transformation which takes place in the presence of a catalyst must also take place in its absence, though perhaps at a much slower rate. A reaction network will be called "saturated" if it satisfies such an expectation. I propose a mathematical definition for saturated networks and show that the associated dynamical systems have no boundary equilibria in positive stoichiometric classes, and are therefore permanent. This result is independent of the specific rates, and generalizes previous results for complete networks by Gnacadja, atomic event-systems by Adleman et al. and constructive networks by Shinar et al. I require no assumption of complex balance or deficiency restrictions. The question of permanence for weakly-reversible reaction networks remains a long-standing open problem.