Radde N. Analyzing fixed points of intracellular regulation networks with interrelated feedback topology.
BMC SYSTEMS BIOLOGY 2012;
6:57. [PMID:
22672785 PMCID:
PMC3771561 DOI:
10.1186/1752-0509-6-57]
[Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2011] [Accepted: 06/06/2012] [Indexed: 11/24/2022]
Abstract
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.
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