The classical Michaelis-Menten approximation for the reversible enzyme-substrate reaction is a perfect example of the use of the quasi-steady state (QSS) approximation. This approximation is very useful for modeling various biological phenomena that entail different time scales. The quasi-steady state assumption (QSSA) often leads to valuable insights into the dynamics of the biological system when the pertinent mathematical model is difficult to handle analytically, and it frequently facilitates numerical integration of systems involving differential equations. However, this assumption should not be used indiscriminately and the parameter domains wherein the QSSA constitutes a valid approximation should be thoroughly characterized. In the present talk, I will present extensions to the standard QSSA (sQSSA) and criteria for assessing their validity. The relevance of the various types of QSSA to enzyme kinetics will be illustrated via a Michaelis-Menten-type model for the autocatalytic enzyme prostaglandin H synthesis. Mathematical models for immunological interactions and population dynamics that can benefit from the application of some type of QSSA will also be discussed
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