title: Finding the positive feedback loops underlying multi-stationarity.
abstract: BACKGROUND
  Bistability is ubiquitous in biological systems. For example, bistability is found in many reaction networks that involve the control and execution of important biological functions, such as signaling processes. Positive feedback loops, composed of species and reactions, are necessary for bistability, and generally for multi-stationarity, to occur. These loops are therefore often used to illustrate and pinpoint the parts of a multi-stationary network that are relevant ('responsible') for the observed multi-stationarity. However positive feedback loops are generally abundant in reaction networks but not all of them are important for understanding the network's dynamics.
  
  
  RESULTS
  We present an automated procedure to determine the relevant positive feedback loops of a multi-stationary reaction network. The procedure only reports the loops that are relevant for multi-stationarity (that is, when broken multi-stationarity disappears) and not all positive feedback loops of the network. We show that the relevant positive feedback loops must be understood in the context of the network (one loop might be relevant for one network, but cannot create multi-stationarity in another). Finally, we demonstrate the procedure by applying it to several examples of signaling processes, including a ubiquitination and an apoptosis network, and to models extracted from the Biomodels database. The procedure is implemented in Maple.
  
  
  CONCLUSIONS
  We have developed and implemented an automated procedure to find relevant positive feedback loops in reaction networks. The results of the procedure are useful for interpretation and summary of the network's dynamics.
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark. efeliu@math.ku.dk.
authors.forename: Elisenda
authors.initials: E
authors.lastname: Feliu
authors.affiliation: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark. wiuf@math.ku.dk.
authors.forename: Carsten
authors.initials: C
authors.lastname: Wiuf
mesh_terms: D017209:Apoptosis; D019295:Computational Biology / Q000379:methods*; D025461:Feedback, Physiological; D007700:Kinetics; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D010766:Phosphorylation; D063150:Polycomb Repressive Complex 1 / Q000378:metabolism; D015398:Signal Transduction; D054875:Ubiquitination
chemical_list: D063150:Polycomb Repressive Complex 1