Fixed point characterization of biological networks with complex graph topology
Open Access
- 8 September 2010
- journal article
- research article
- Published by Oxford University Press (OUP) in Bioinformatics
- Vol. 26 (22), 2874-2880
- https://doi.org/10.1093/bioinformatics/btq517
Abstract
Motivation: Feedback circuits are important motifs in biological networks and part of virtually all regulation processes that are needed for a reliable functioning of the cell. Mathematically, feedback is connected to complex behavior of the systems, which is often related to bifurcations of fixed points. Therefore, several approaches for the investigation of fixed points in biological networks have been developed in recent years. Many of them assume the fixed point coordinates to be known, and an efficient way to calculate the entire set of fixed points for interrelated feedback structures is highly desirable. Results: In this article, we consider regulatory network models, which are differential equations with an underlying directed graph that illustrates independencies among variables. We introduce the circuit-breaking algorithm (CBA), a method that constructs one-dimensional characteristics for these network models, which inherit important information about the system. In particular, fixed points are related to the zeros of these characteristics. The CBA operates on the graph topology, and results from graph theory are used in order to make calculations efficient. Our framework provides a general scheme for analyzing network models in terms of interrelated feedback circuits. The efficiency of the approach is demonstrated on a model for calcium oscillations based on experiments in hepatocytes, which consists of several interrelated feedback circuits. Contact:radde@ist.uni-stuttgart.de Supplementary information: Supplementary data are available at Bioinformatics online.This publication has 26 references indexed in Scilit:
- The Impact of Time Delays on the Robustness of Biological Oscillators and the Effect of Bifurcations on the Inverse ProblemEURASIP Journal on Bioinformatics and Systems Biology, 2009
- Design principles of biochemical oscillatorsNature Reviews Molecular Cell Biology, 2008
- Quantitative approaches to the study of bistability in the lac operon of Escherichia coliJournal of The Royal Society Interface, 2008
- Experimental design for efficient identification of gene regulatory networks using sparse Bayesian modelsBMC Systems Biology, 2007
- Bifurcation dynamics in lineage-commitment in bipotent progenitor cellsDevelopmental Biology, 2007
- Oscillation patterns in negative feedback loopsProceedings of the National Academy of Sciences of the United States of America, 2007
- Analytical results and feedback circuit analysis for simple chaotic flowsJournal of Physics A: General Physics, 2003
- A model of periodic oscillation for genetic regulatory systemsIEEE Transactions on Circuits and Systems I: Regular Papers, 2002
- A search strategy for the elementary cycles of a directed graphBIT Numerical Mathematics, 1976
- An efficient search algorithm to find the elementary circuits of a graphCommunications of the ACM, 1970