Differential algebra and QSSA methods in biochemistry

Differential algebra is an algebraic theory for differential equations (ordinary or with partial derivatives, linear or non linear). It involves an elimination theory which is completely algorithmic since the mid 1990s. In addition to the numerous applications which have been developed in control theory for more than twenty years, it was recently shown that differential elimination makes algorithmic a rigorous quasi-steady state approximation method for generalized chemical reaction systems. This result was recently succesfully applied to model reduction problems in cellular modeling. This paper presents this recent advance in connection with a new MAPLE package (with new functionalities). This package is built over the BLAD libraries, which are LGPL-licensed open source, written in the C programming language.