Graphs and the Dynamics of Biochemical Networks
Graphs and the Dynamics of Biochemical Networks
This chapter describes two approaches, one based on bipartite graphs and Petri net concepts, and another based on decompositions into order-preserving subsystems. It addresses the basic formalism used for modeling biochemical networks. It reviews some results that use bipartite graphs, and specifically Petri nets. It postulates a quasi-steady-state reduction principle (QSSRP) and asks the question, for what types of components is the QSSRP a valid mathematical tool? It presents a (partial) answer to this question, after introducing monotone systems. This chapter shows that the QSSRP has been recently validated using tools from synthetic biology.
Keywords: bipartite graphs, Petri net concepts, decompositions, biochemical networks, quasi-steady-state reduction principle, monotone systems, synthetic biology
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