Oscillations in Biochemical Reaction Networks Arising from Pairs of Subnetworks |
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Authors: | Maya Mincheva |
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Institution: | (1) Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada;(2) Present address: Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706-1388, USA |
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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. |
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