Singular perturbation theory for open enzyme reaction networks.

The main goal of this paper is to present some results of singular perturbation theory on infinite time intervals justifying the application of the well-known pseudo-steady-state hypothesis for general open enzyme reaction networks. A condition on the input/output function, which allows us to write a suitable reduced system associated with the original complete system, is discussed. The type of convergence between the solutions of the two systems, out of the initial boundary layer, is studied, in relation to the asymptotic behaviour of the degenerate system. We will consider mainly the common cases where the degenerate system has: either (1) an asymptotically (Lyapunov) stable fixed point or (2) an asymptotically orbitally stable periodic solution. Owing to the generality of the results, they can also be applied to several other problems.