Finding the positive feedback loops underlying multi-stationarity

BMC Systems Biology

Carsten Wiuf¹  Elisenda Feliu¹ 

[1] Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, Copenhagen, Denmark

关键词: Reaction network;    Interaction graph;    Injectivity;    Feedback loop;    DSR-graph;    Bistability;   

Others  :  1210172
DOI  :  10.1186/s12918-015-0164-0

 received in 2014-10-26, accepted in 2015-04-20,  发布年份 2015

【 摘 要 】

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.

【 授权许可】

   
2015 Feliu and Wiuf; licensee BioMed Central.

【 图 表 】

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Figure 1.

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