Approximation of fast species in kinetic networks using non-negative polynomials

Kinetic models of reaction networks often feature sets of fast-reacting species. If the slow timescale is of interest these species can be assumed to be in equilibrium and using a lumping method a system of lower order is obtained. However, to obtain a reduction in the number of equations that represent the dynamics of the reaction network, an explicit representation of the equilibrium species is required. In many cases algebraic manipulations required to obtain an explicit form are prohibitive. This paper examines the use of constrained polynomial fitting techniques to obtain an approximation of the explicit form that is consistent with the physical constraints of the reaction network.