Inducing sustained oscillations in mass action kinetic networks of a certain class

Engineering a synthetic oscillator requires an oscillatory model which can be implemented into practice. Some required conditions for a successful practical implementation include the robustness of the oscillation under realistic parameter values and the accessibility to the variables that need to be manipulated. For a particular class of theoretical oscillators derived from mass action kinetic models, oscillations appear provided that some of the concentrations are kept constant at given values. This condition is not trivially accomplished in practice. In this work we provide two different realizations of kinetic networks leading to the desired limit cycle oscillation: a mass action kinetic system with constant inflow and outflow for some of the species, and a stirred tank reactor configuration with some entrapped species where the nonchemical effect of keeping some concentrations constant is achieved by manipulating some accessible variables. The results, together with the robustness of the approach and the conditions for further practical implementation are discussed and illustrated through the well known Brusselator example.