Affiliations: La.M.I UMR 8042, CNRS & Université
d'Évry, Boulevard François Mitterrand, 91025 Évry
cedex-France. {arichard,comet,bernot}@lami.univ-evry.fr
Note: [] Address for correspondence: La.M.I UMR 8042, CNRS &
Université d'Évry, Boulevard François Mitterrand, 91025
Évry cedex-France
Abstract: In the field of biological regulation, models extracted from
experimental works are usually complex networks comprising intertwined feedback
circuits. The overall behavior is difficult to grasp and the development of
formal methods is needed in order to model and simulate biological regulatory
networks. To model the behavior of such systems, R. Thomas and coworkers
developed a qualitative approach in which the dynamics is described by a state
transition system. Even if all steady states of the system can be detected in
this formalism, some of them, the singular ones, are not formally included in
the transition system. Consequently, temporal properties in which singular
states have to be described, cannot be checked against the transition system.
However, steady singular states play an essential role in the dynamics since
they can induce homeostasis or multistationnarity and sometimes are associated
to biological phenotypes. These observations motivated our interest for developing an
extension of Thomas formalism in which all singular states are represented,
allowing us to check temporal properties concerning singular states. We easily
demonstrate in our formalism the previously demonstrated theorems giving the
conditions for the steadiness of singular states. We also prove that our
formalism is coherent with the Thomas one since all paths of the Thomas
transition system are preserved in our one, which in addition includes singular
states.
Keywords: biological networks, feedback circuits, singular states, steady states
