Laplacian Dynamics and Kron Reduction in Species-Reaction Graphs of Chemical Reaction Networks
Gasparyan, M.; Bhalla, U. S.; Radulescu, O.; Rao, S.
Show abstract
We present a method for modeling the dynamics of enzymatic chemical reaction networks using species-reaction graphs. These bipartite graphs contain two sets of vertices, one representing species and the other representing reactions, connected by directed edges that indicate relationships between them. Our approach starts by assigning appropriate edge weights to the bipartite graph, which are then used to compute the weighted graph Laplacian. This Laplacian allows us to reformulate the standard system of ordinary differential equations governing the network dynamics, emphasizing the flow of information - such as influences or dependencies between species and reactions - throughout the chemical reaction network considered as causal network. As an application of this framework, we introduce a novel model reduction technique based on the Kron reduction of the weighted Laplacian matrix associated with the species-reaction graphs. Our systematic approach involves identifying nodes for deletion while preserving the bipartite structure, followed by constructing the Kron-reduced model. To demonstrate the effectiveness of our method, we apply it to complex biochemical networks, showing how model simplification facilitates analysis and interpretation of these systems.
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