Reduction of chemical systems by delayed quasi-steady state assumptions

Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most com-mon reduction technique is based on quasi-steady state assumptions. To in-crease the accuracy of this technique we propose delayed quasi-steady state assumptions (D-QSSA) which yield systems of delay differential equations. We define the approximation based on D-QSSA, prove the corresponding error estimate, and show how it approximates the invariant manifold. Then we define a class of well mixed chemical systems and formulate assump-tions enabling the application of D-QSSA. We also apply the D-QSSA to a model of Hes1 expression and to a cell-cycle model to illustrate the im-proved accuracy of the D-QSSA with respect to the standard quasi-steady state assumptions