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 signalling 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 subsequent interpretation of the network's dynamics.
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.
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.Comment: 16 pages, 4 figure