title: A method to identify important dynamical states in Boolean models of regulatory networks: application to regulation of stomata closure by ABA in A. thaliana.
abstract: BACKGROUND
  We introduce a method to analyze the states of regulatory Boolean models that identifies important network states and their biological influence on the global network dynamics. It consists in (1) finding the states of the network that are most frequently visited and (2) the identification of variable and frozen nodes of the network. The method, along with a simulation that includes random features, is applied to the study of stomata closure by abscisic acid (ABA) in A. thaliana proposed by Albert and coworkers.
  
  
  RESULTS
  We find that for the case of study, that the dynamics of wild and mutant networks have just two states that are highly visited in their space of states and about a third of all nodes of the wild network are variable while the rest remain frozen in True or False states. This high number of frozen elements explains the low cardinality of the space of states of the wild network. Similar results are observed in the mutant networks. The application of the method allowed us to explain how wild and mutants behave dynamically in the SS and determined an essential feature of the activation of the closure node (representing stomata closure), i.e. its synchronization with the AnionEm node (representing anion efflux at the plasma membrane). The dynamics of this synchronization explains the efficiency reached by the wild and each of the mutant networks.
  
  
  CONCLUSIONS
  For the biological problem analyzed, our method allows determining how wild and mutant networks differ 'phenotypically'. It shows that the different efficiencies of stomata closure reached among the simulated wild and mutant networks follow from a dynamical behavior of two nodes that are always synchronized. Additionally, we predict that the involvement of the anion efflux at the plasma membrane is crucial for the plant response to ABA.
  
  
  BACKGROUND
  The algorithm used in the simulations is available upon request.
authors.affiliation: Departamento de Física, Universidade Federal de Santa Maria, Santa Maria (UFSM), RS, Brasil.
authors.forename: Cristhian A
authors.initials: CA
authors.lastname: Bugs
authors.forename: Giovani R
authors.initials: GR
authors.lastname: Librelotto
authors.forename: José C M
authors.initials: JC
authors.lastname: Mombach
mesh_terms: D000040:Abscisic Acid / Q000378:metabolism*; D000465:Algorithms; D017360:Arabidopsis / Q000235:genetics / Q000378:metabolism*; D053263:Gene Regulatory Networks; D008962:Models, Theoretical; D009154:Mutation
chemical_list: D000040:Abscisic Acid