Quasi-steady-state approximation for chemical reaction networks

Abstract

The parameter embedding leading to the quasi-steady-state approximation of Heinrich [9] is investigated within the theory of invariant manifolds of Fenichel [4] in order to clarify the essential assumptions needed for this reduction to a low dimensional system. In particular, the concept of pool-variables can be avoided in this generalized approach. Moreover, the dominating influence of the slow subnetwork over the complementary fast subnetwork is interpreted geometrically and in chemical terms and this can be seen as an “enslaving” of the fast subsystem by the slow subsystem. Finally, the results are applied to a system of slime mould communication [6, 7, 13] and to a maltose transport system [2, 3].