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Understanding the bacterial stringent response using reachability analysis of hybrid systems. (English) Zbl 1135.93334

Alur, Rajeev (ed.) et al., Hybrid systems: computation and control. 7th international workshop, HSCC 2004, Philadelphia, PA, USA, March 25–27, 2004. Proceedings. Berlin: Springer (ISBN 3-540-21259-0/pbk). Lecture Notes in Computer Science 2993, 111-125 (2004).
Summary: 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.
For the entire collection see [Zbl 1046.93002].

MSC:

93C10 Nonlinear systems in control theory
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
93A30 Mathematical modelling of systems (MSC2010)
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