  Mathematical analysis of mass action models of large complex chemical 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 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 assumptions 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 improved accuracy of the D-QSSA with respect
to the standard quasi-steady state assumptions.
