NDLI: Oscillations in Biochemical Reaction Networks Arising from Pairs of Subnetworks

Content Provider	Springer Nature Link
Author	Mincheva, Maya
Copyright Year	2011
Abstract	Biochemical reaction models show a variety of dynamical behaviors, such as stable steady states, multistability, and oscillations. Biochemical reaction networks with generalized mass action kinetics are represented as directed bipartite graphs with nodes for species and reactions. The bipartite graph of a biochemical reaction network usually contains at least one cycle, i.e., a sequence of nodes and directed edges which starts and ends at the same species node. Cycles can be positive or negative, and it has been shown that oscillations can arise as a result of either a positive cycle or a negative cycle. In earlier work it was shown that oscillations associated with a positive cycle can arise from subnetworks with an odd number of positive cycles. In this article we formulate a similar graph-theoretic condition, which generalizes the negative cycle condition for oscillations. This new graph-theoretic condition for oscillations involves pairs of subnetworks with an even number of positive cycles. An example of a calcium reaction network with generalized mass action kinetics is discussed in detail.
Starting Page	2277
Ending Page	2304
Page Count	28
File Format	PDF
ISSN	00928240
Journal	Bulletin of Mathematical Biology
Volume Number	73
Issue Number	10
e-ISSN	15229602
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-01-22
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Biochemical and chemical reaction networks Bipartite graph Generalized mass action kinetics Oscillations Negative feedback cycle Mathematical and Computational Biology Cell Biology Life Sciences
Content Type	Text
Resource Type	Article
Subject	Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences

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