Fragments-based Model Reduction: Some Case Studies

Molecular biological models usually suffer from a dramatic combinatorial blow up. Indeed, proteins form complexes and can modify each others, which leads to the formation of a huge number of distinct chemical species (ie non-isomorphic connected components of proteins). Combinatorial complexity forbids an explicit description of the quantitative semantics (stochastic or differential), since the set of states is usually a vector space the dimension of which is the number of distinct chemical species. Model reduction aims at reducing this complexity by providing another grain of observation. Fragments-based reduction consists in computing a set (hopefully smaller than the set of chemical species) of pieces of chemical species, such that the evolution of the number (or concentration) of these pieces can be soundly described in self-consistent abstract quantitative semantics. In this paper, we provide several intuitive examples so as to give some intuition about why this approach may work; and why stochastic semantics are more difficult to abstract than differential semantics.