In this paper we model coupled genetic and metabolic networks as hybrid systems. The vector fields are multi - affine, i.e., have only product - type nonlinearities to accommodate chemical reactions, and are defined in rectangular invariants, whose facets correspond to changes in the behavior of a gene or enzyme. For such systems, we showed that reachability and safety verification problems can be formulated and solved (conservatively) in an elegant and computationally inexpensive way, based on the fact that multi-affine functions on rectangular regions of the space are determined at the vertices. Using these techniques, we study the stringent response system, which is the transition of bacterial organisms from growth phase to a metabolically suppressed phase when subjected to an environment with limited nutrients.
|Title of host publication||Hybrid Systems : Computation and Control ; Proceedings 7th International Workshop HSCC2004, Philadelphia PA, USA, March 25-27, 2004|
|Editors||R. Alur, G.J. Pappas|
|Place of Publication||Berlin|
|Publication status||Published - 2004|
|Name||Lecture Notes in Computer Science|