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Article overview
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A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks | Rebekah Aduddell
; James Fairbanks
; Amit Kumar
; Pablo S. Ocal
; Evan Patterson
; Brandon T. Shapiro
; | Date: |
4 Jan 2023 | Abstract: | Regulatory networks depict promoting or inhibiting interactions between
molecules in a biochemical system. We introduce a category-theoretic formalism
for regulatory networks, using signed graphs to model the networks and signed
functors to describe occurrences of one network in another, especially
occurrences of network motifs. With this foundation, we establish functorial
mappings between regulatory networks and other mathematical models in
biochemistry. We construct a functor from reaction networks, modeled as Petri
nets with signed links, to regulatory networks, enabling us to precisely define
when a reaction network could be a physical mechanism underlying a regulatory
network. Turning to quantitative models, we associate a regulatory network with
a Lotka-Volterra system of differential equations, defining a functor from the
category of signed graphs to a category of parameterized dynamical systems. We
extend this result from closed to open systems, demonstrating that
Lotka-Volterra dynamics respects not only inclusions and collapsings of
regulatory networks, but also the process of building up complex regulatory
networks by gluing together simpler pieces. Formally, we use the theory of
structured cospans to produce a lax double functor from the double category of
open signed graphs to that of open parameterized dynamical systems. Throughout
the paper, we ground the categorical formalism in examples inspired by systems
biology. | Source: | arXiv, 2301.01445 | Services: | Forum | Review | PDF | Favorites |
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