MESSI swMATH ID: 33875 Software Authors: Mercedes Pérez Millán, Alicia Dickenstein Description: 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. Homepage: https://arxiv.org/abs/1612.08763 Related Software: REDLOG; QEPCAD; Maple; Binomials.m2; DAISY; Mathematica; crntwin; CoNtRol; SINGULAR; SIAN; Bertini; MapleBinomials; GNU parallel; RAGlib; parest_dae; NumericalAlgebraicGeometry; ProjectionCAD; Paramotopy; RegularChains; PHCpack Cited in: 23 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year The structure of MESSI biological systems. Zbl 1395.92071Pérez Millán, Mercedes; Dickenstein, Alicia 2018 all top 5 Cited by 42 Authors 5 Dickenstein, Alicia M. 5 Feliu, Elisenda 4 Sturm, Thomas 3 Millán, Mercedes Pérez 3 Rahkooy, Hamid 3 Shiu, Anne 2 Conradi, Carsten 2 Grigor’ev, Dmitriĭ Yur’evich 2 Iosif, Alexandru 2 Sadeghimanesh, AmirHosein 2 Tang, Xiaoxian 2 Weber, Andreas Günter 1 Barabanschikov, Alexander 1 Bihan, Frédéric 1 Bradford, Russell J. 1 Craciun, Gheorghe 1 Davenport, James Harold 1 de Wolff, Timo 1 Deshpande, Abhishek 1 England, Matthew 1 Errami, Hassan 1 Gerdt, Vladimir Petrovich 1 Giaroli, Magalí 1 Gross, Elizabeth 1 Gunawardena, Jeremy 1 Harrington, Heather A. 1 Hoyt, Charles Tapley 1 Jeronimo, Gabriela 1 Johnston, Matthew D. 1 Kahle, Thomas 1 Kaihnsa, Nidhi 1 Košta, Marek 1 Lichtblau, Daniel A. 1 Meshkat, Nicolette 1 Mincheva, Maya 1 Müller, Stefan 1 Pantea, Casian Alexandru 1 Radulescu, Ovidiu 1 Solernó, Pablo 1 Torres, Angélica 1 Wang, Jie 1 Yürük, Oğuzhan all top 5 Cited in 9 Serials 7 Bulletin of Mathematical Biology 3 Journal of Mathematical Biology 2 Journal of Symbolic Computation 2 SIAM Journal on Applied Dynamical Systems 1 Advances in Applied Mathematics 1 Journal of Dynamics and Differential Equations 1 Discrete and Continuous Dynamical Systems. Series B 1 Mathematical Biosciences and Engineering 1 Mathematics in Computer Science all top 5 Cited in 10 Fields 21 Biology and other natural sciences (92-XX) 7 Commutative algebra (13-XX) 4 Algebraic geometry (14-XX) 4 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Field theory and polynomials (12-XX) 1 Convex and discrete geometry (52-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year