  Mathematical models are increasingly being used to understand complex
biochemical systems, to analyze experimental data and make predictions about
unobserved quantities. However, we rarely know how robust our conclusions are
with respect to the choice and uncertainties of the model. Using algebraic
techniques we study systematically the effects of intermediate, or transient,
species in biochemical systems and provide a simple, yet rigorous mathematical
classification of all models obtained from a core model by including
intermediates. Main examples include enzymatic and post-translational
modification systems, where intermediates often are considered insignificant
and neglected in a model, or they are not included because we are unaware of
their existence. All possible models obtained from the core model are
classified into a finite number of classes. Each class is defined by a
mathematically simple canonical model that characterizes crucial dynamical
properties, such as mono- and multistationarity and stability of steady states,
of all models in the class. We show that if the core model does not have
conservation laws, then the introduction of intermediates does not change the
steady-state concentrations of the species in the core model, after suitable
matching of parameters. Importantly, our results provide guidelines to the
modeler in choosing between models and in distinguishing their properties.
Further, our work provides a formal way of comparing models that share a common
skeleton.
