期刊
PROCEEDINGS OF THE IEEE
卷 96, 期 8, 页码 1281-1291出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JPROC.2008.925474
关键词
biochemical reaction networks; multigraph; multistability; oscillations; pattern formation; positive feedback
We represent interactions among biochemical species using a directed multigraph, which is a generalization of a more commonly used digraph. we show that network properties that are known to lead to multistability or oscillations, such as the existence of a positive feedback cycle, can be generalized to critical subnetworks that can contain several cycles. we also derive corresponding graph-theoretic conditions for pattern formation for the respective reaction-diffusion models. We present as an example a model for cell cycle and apoptosis along with bifurcation diagrams and sample solutions that confirm the predictions obtained with the help of the multigraph, network conditions.
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