Finding the positive feedback loops underlying multi-stationarity

TL;DR

This paper introduces an automated method to identify the specific positive feedback loops responsible for multi-stationarity in biological reaction networks, aiding interpretation of complex signaling dynamics.

Contribution

The authors develop and implement a procedure that isolates relevant feedback loops linked to multi-stationarity, improving understanding of network dynamics beyond all existing loops.

Findings

The procedure successfully identifies key feedback loops in biological networks.

Application to signaling and biomodels demonstrates its practical utility.

Relevant loops vary depending on the network context.

Abstract

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.