The structure of MESSI biological systems. We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many post-translational modification networks are MESSI systems. For example: the motifs in [Feliu and Wiuf (2012a)], sequential distributive and processive multisite phosphorylation networks, most of the examples in [Angeli et al. (2007)], phosphorylation cascades, two component systems as in [Kothamachu et al. (2015)], the bacterial EnvZ/OmpR network in [Shinar and Feinberg (2010)], and all linear networks. We show that, under mass-action kinetics, MESSI systems are conservative. We simplify the study of steady states of these systems by explicit elimination of intermediate complexes and we give conditions to ensure an explicit rational parametrization of the variety of steady states (inspired by [Feliu and Wiuf (2013a, 2013b), Thomson and Gunawardena (2009)]). We define an important subclass of MESSI systems with toric steady states [Pérez Millán et al. (2012)] and we give for MESSI systems with toric steady states an easy algorithm to determine the capacity for multistationarity. In this case, the algorithm provides rate constants for which multistationarity takes place, based on the theory of oriented matroids.

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Feliu, Elisenda; Kaihnsa, Nidhi; de Wolff, Timo; Yürük, Oğuzhan: The kinetic space of multistationarity in dual phosphorylation (2022)
  2. Dickenstein, Alicia: Families of polynomials in the study of biochemical reaction networks (2021)
  3. Grigoriev, Dima; Iosif, Alexandru; Rahkooy, Hamid; Sturm, Thomas; Weber, Andreas: Efficiently and effectively recognizing toricity of steady state varieties (2021)
  4. Lichtblau, Daniel: Symbolic analysis of multiple steady states in a MAPK chemical reaction network (2021)
  5. Rahkooy, Hamid; Sturm, Thomas: Parametric toricity of steady state varieties of reaction networks (2021)
  6. Rahkooy, Hamid; Sturm, Thomas: Testing binomiality of chemical reaction networks using comprehensive Gröbner systems (2021)
  7. Tang, Xiaoxian; Wang, Jie: Bistability of sequestration networks (2021)
  8. Torres, Angélica; Feliu, Elisenda: Symbolic proof of bistability in reaction networks (2021)
  9. Bradford, Russell; Davenport, James H.; England, Matthew; Errami, Hassan; Gerdt, Vladimir; Grigoriev, Dima; Hoyt, Charles; Košta, Marek; Radulescu, Ovidiu; Sturm, Thomas; Weber, Andreas: Identifying the parametric occurrence of multiple steady states for some biological networks (2020)
  10. Gross, Elizabeth; Harrington, Heather; Meshkat, Nicolette; Shiu, Anne: Joining and decomposing reaction networks (2020)
  11. Barabanschikov, Alexander; Gunawardena, Jeremy: Monostationarity and multistationarity in tree networks of Goldbeter-Koshland loops (2019)
  12. Conradi, Carsten; Iosif, Alexandru; Kahle, Thomas: Multistationarity in the space of total concentrations for systems that admit a monomial parametrization (2019)
  13. Conradi, Carsten; Mincheva, Maya; Shiu, Anne: Emergence of oscillations in a mixed-mechanism phosphorylation system (2019)
  14. Dickenstein, Alicia: Algebra and geometry in the study of enzymatic cascades (2019)
  15. Dickenstein, Alicia; Millán, Mercedes Pérez; Shiu, Anne; Tang, Xiaoxian: Multistationarity in structured reaction networks (2019)
  16. Feliu, Elisenda: Sign-sensitivities for reaction networks: an algebraic approach (2019)
  17. Giaroli, Magalí; Bihan, Frédéric; Dickenstein, Alicia: Regions of multistationarity in cascades of Goldbeter-Koshland loops (2019)
  18. Jeronimo, Gabriela; Pérez Millán, Mercedes; Solernó, Pablo: Identifiability from a few species for a class of biochemical reaction networks (2019)
  19. Johnston, Matthew D.; Müller, Stefan; Pantea, Casian: A deficiency-based approach to parametrizing positive equilibria of biochemical reaction systems (2019)
  20. Sadeghimanesh, AmirHosein; Feliu, Elisenda: The multistationarity structure of networks with intermediates and a binomial core network (2019)

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