Reduction of chemical systems by delayed quasi-steady state assumptions

Mathematical analysis of mass action models of large complex chemi-cal systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of this technique we propose delayed quasi-steady state assumptions (D-QSSA) which yield systems of delay differential equa-tions. We define the approximation based on D-QSSA and prove the corre-sponding error estimate showing the accuracy of this approximation. Then we define a class of well mixed chemical systems and formulate assumptions enabling the application of D-QSSA. We also apply the D-QSSA to a model of Hes1 expression to illustrate the improved accuracy of the D-QSSA with respect to the standard quasi-steady state assumptions