Computing quasi-steady state reductions

There is a systematic approach to the computation of quasi-steady state reductions, employing the classical theory of Tikhonov and Fenichel, rather than the commonly used ad-hoc method. In the present paper we discuss the relevant case that the local slow manifold (in the asymptotic limit) is a vector subspace, give closed-form expressions for the reduction and compare these to the ones obtained by the customary method. As it turns out, investment of more theory pays off in the form of simpler reduced systems. Applications include a number of standard models for reactions in biochemistry, for which the reductions are extended to the fully reversible setting. In a short final section we illustrate by example that a QSS assumption may be erroneous if the hypotheses for Tikhonov’s theorem are not satisfied.