Analyzing fixed points of intracellular regulation networks with interrelated feedback topology.
BACKGROUND
Modeling the dynamics of intracellular regulation networks by systems of ordinary differential equations has become a standard method in systems biology, and it has been shown that the behavior of these networks is often tightly connected to the network topology. We have recently introduced the circuit-breaking algorithm, a method that uses the network topology to construct a one-dimensional circuit-characteristic of the system. It was shown that this characteristic can be used for an efficient calculation of the system's fixed points.


RESULTS
Here we extend previous work and show several connections between the circuit-characteristic and the stability of fixed points. In particular, we derive a sufficient condition on the characteristic for a fixed point to be unstable for certain graph structures and demonstrate that the characteristic does not contain the information to decide whether a fixed point is asymptotically stable. All statements are illustrated on biological network models.


CONCLUSIONS
Single feedback circuits and their role for complex dynamic behavior of biological networks have extensively been investigated, but a transfer of most of these concepts to more complex topologies is difficult. In this context, our algorithm is a powerful new approach for the analysis of regulation networks that goes beyond single isolated feedback circuits.
Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9, Germany. nicole.radde@ist.uni-stuttgart.de
Nicole
N
Radde
D000465:Algorithms; D002454:Cell Differentiation; D003196:Computer Graphics; D004926:Escherichia coli / Q000378:metabolism; D029968:Escherichia coli Proteins / Q000378:metabolism; D025461:Feedback, Physiological; D006412:Hematopoietic Stem Cells / Q000166:cytology; D042541:Intracellular Space / Q000378:metabolism*; D008954:Models, Biological; D012097:Repressor Proteins / Q000378:metabolism; D014364:Tryptophan / Q000378:metabolism
D029968:Escherichia coli Proteins; D012097:Repressor Proteins; D014364:Tryptophan