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Fixed point characterization of biological networks with complex graph topology

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. In this talk I consider regulatory network models, which are differential equations with an underlying directed graph that illustrates dependencies among variables. I 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.

Type of Seminar:
IfA BISON Seminar
Prof Nicole Radde
Uni Stuttgart
Feb 01, 2011   13:30

Contact Person:

Elias August
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