Deriving analytic positive steady states of biochemical reaction networks with non-trivial independent decompositions

2023. 05. 09. 17:15
Bryan Fernandez

The long-term behaviors of biochemical systems are usually described by their steady states. Deriving these states directly for complex networks arising from real-world applications, however, is often challenging. Recent work has consequently focused on network-based approaches. Specifically, biochemical reaction networks are transformed into weakly reversible and deficiency zero generalized networks, which allows the derivation of their positive steady states. Identifying this transformation, however, can be challenging for large and complex networks. In this talk, we discuss how to decompose reaction networks into their finest independent subnetworks, i.e., decomposition with the maximum number of subnetworks. After such decomposition, we transform the subnetworks to derive the steady states of each subnetwork. Stitching these solutions together leads to the positive steady states of the original network. To facilitate this process, we present a computational package, COMPILES (COMPutIng anaLytic stEady States). With COMPILES, we can easily test the absence of bistability of a CRISPRi toggle switch model, which was previously investigated via a tremendous number of numerical simulations and within a limited range of parameters. Furthermore, COMPILES can be used to identify absolute concentration robustness (ACR), the property of a system that maintains the concentration of particular species at a steady state regardless of any initial concentrations. Specifically, our approach completely identifies all the species with and without ACR in a complex insulin model.

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