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Routes to Multiple Equilibria for Mass-Action Kinetic Systems

Antonio A. Alonso, Irene Otero-Muras, Manuel Pájaro
2018 Complexity  
In this work we explore two potential mechanisms inducing multiple equilibria for weakly reversible networks with mass-action kinetics.  ...  The study is performed on a class of polynomial dynamic systems that, under some mild assumptions, are able to accommodate in their state-space form weakly reversible mass-action kinetic networks.  ...  The central objective of this note is to identify the mechanisms leading to the emergence of multiple equilibria in mass-action kinetic systems.  ... 
doi:10.1155/2018/3912627 fatcat:p35rfzixyjbefkut3u6prbiepi

Feasible Equilibrium in Kinetic Systems**This work received partial financial support through grants PIE201230E042 and Salvador de Madariaga (PR2011-0363) and PIE 201230E042

Antonio A. Alonso, Irene Otero-Muras
2016 IFAC-PapersOnLine  
For deficiency one networks a saddlenode bifurcation with respect to mass inventory is the only route to multiplicity whereas for higher deficiencies alternative routes exist which may include pitchfork  ...  For deficiency one networks a saddlenode bifurcation with respect to mass inventory is the only route to multiplicity whereas for higher deficiencies alternative routes exist which may include pitchfork  ...  mass action law kinetic systems.  ... 
doi:10.1016/j.ifacol.2016.10.745 fatcat:ukzg5hm4fzhgznqbf6j32bklvu

Multiple Equilibria in Complex Chemical Reaction Networks: Semiopen Mass Action Systems

Gheorghe Craciun, Martin Feinberg
2010 SIAM Journal on Applied Mathematics  
In two earlier papers [1], [3] , we developed means to determine whether a given (mass action) chemical reaction network has the capacity to exhibit multiple positive steady states in the context of what  ...  In two earlier articles, we provided sufficient conditions on (mass action) reaction network structure for the preclusion of multiple positive steady states in the context of what chemical engineers call  ...  suppose also that the kinetics is mass action.  ... 
doi:10.1137/090756387 fatcat:sr37jqjxd5a4vaodf66co2lb5m

Page 594 of British Journal of Clinical Pharmacology Vol. 10, Issue 6 [page]

1980 British Journal of Clinical Pharmacology  
Any two drugs must have the same value for this system factor for an interaction to be considered.  ...  This equation has also been generalized to permit competition among multiple drugs to be represented.  ... 

A 3-In-1 Approach to Evaluate Gas Hydrate Inhibitors

Narendra Kumar, Niaz Bahar Chowdhury, Juan G. Beltran
2019 Energies  
By applying a temperature gradient during hydrate formation, it was possible to study multiple subcoolings with a single experiment.  ...  Tight, local temperature control produced highly repeatable crystal morphologies in constant temperature systems and in systems subject to fixed temperature gradients.  ...  Hydrate-liquid-vapor equilibria for the system water + NaCl (w NaCl = 5.44%) + CH 4 . Error bars correspond to standard uncertainty. Literature data are also shown [54] .  ... 
doi:10.3390/en12152921 fatcat:eqtonca3tbft3lr2zpzdeoyy6y

Homo-Oligomerisation in Signal Transduction: Dynamics, Homeostasis, Ultrasensitivity, Bistability

Daniel Koch
2020 Journal of Theoretical Biology  
If post-translational modifications are considered, however, conventional mass action kinetics lead to thermodynamic inconsistencies due to asymmetric combinatorial expansion of reaction routes.  ...  a novel motif for bistable modification reactions.  ...  I would like to thank Joseph Ng for the bioinformatic estimation of the fraction of oligomeric signalling proteins and an anonymous referee for constructive criticism.  ... 
doi:10.1016/j.jtbi.2020.110305 pmid:32437710 pmcid:PMC7327509 fatcat:fcqjw4tf4vhxtp3o7ayl5ny5ay

Identifying parameter regions for multistationarity

Carsten Conradi, Elisenda Feliu, Maya Mincheva, Carsten Wiuf, Philip K Maini
2017 PLoS Computational Biology  
We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria.  ...  Mathematical modelling has become an established tool for studying the dynamics of biological systems.  ...  Typical choices are mass-action kinetics, Michaelis-Menten and Hill kinetics.  ... 
doi:10.1371/journal.pcbi.1005751 pmid:28972969 pmcid:PMC5626113 fatcat:5ekszqldsvbuxnrxlt3mukfxka

Homo-Oligomers in Signal Transduction: Modelling Approaches, Homeostasis, Ultrasensitivity, Bistability [article]

Daniel Koch
2019 bioRxiv   pre-print
It furthermore can lead to bistability without feedback by enabling pseudo-multisite modification and kinetic pseudo-cooperativity via multi-enzyme regulation, thereby significantly reducing the requirements  ...  previously thought necessary for the occurrence of bistability.  ...  Foundation for nancial support (PhD studentship).  ... 
doi:10.1101/758789 fatcat:nqab7hjqrjggdb6wcbuycob4lm

Diffusive coupling of two well-mixed compartments elucidates elementary principles of protein-based pattern formation [article]

Fridtjof Brauns, Jacob Halatek, Erwin Frey
2020 arXiv   pre-print
We demonstrate this approach for several paradigmatic model systems.  ...  For intracellular systems, the total numbers of proteins are conserved on the relevant timescale of pattern formation.  ...  In short, the minimal model employs mass-action law kinetics to account for the attachment and detachment of MinD and MinE to and from the membrane and for their interactions there: Membrane-bound MinD  ... 
arXiv:2010.15095v1 fatcat:vs5vusjo75gsncy5ydksphb32u

Towards a Stochastic Relaxation for the Quasi‐Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria and Chaotic Dynamics

Boualem Khouider, Etienne Leclerc
2019 Journal of Advances in Modeling Earth Systems  
Subsequently, the QE assumption was relaxed, and instead, prognostic equations for the cloud work function (CWF) and the cumulus kinetic energy (CKE) were derived and used.  ...  Qualitative analysis and numerical simulations show that the CKE-CWF-cloud area fraction equations exhibit interesting dynamics including multiple equilibria, limit cycles, and chaotic behavior both when  ...  We are grateful to Mitch Moncrieff and the two other anonymous referees for their thoughtful comments and suggestions that greatly helped improve this paper from its original submission.  ... 
doi:10.1029/2019ms001627 fatcat:cnzuz4zshjgnfknuubj2krrnxi

Noise in Gene Regulatory Networks

I. Lestas, J. Paulsson, N. E. Ross, G. Vinnicombe
2009 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
It is discussed that bistability in the deterministic mass action kinetics and bimodality in the steady-state solution of the master equation neither always imply one another nor do they necessarily lead  ...  The examples are taken from systems with macroscopic models leading to bistability.  ...  approximation are the two stable equilibria in the mass action kinetics.  ... 
doi:10.1109/tcsi.2007.911347 fatcat:z6nw2zxxwnb4vdrl5uxv5quruu

Noise in Gene Regulatory Networks

Ioannis Lestas, Johan Paulsson, Nicholas E. Ross, Glenn Vinnicombe
2008 IEEE Transactions on Automatic Control  
It is discussed that bistability in the deterministic mass action kinetics and bimodality in the steady-state solution of the master equation neither always imply one another nor do they necessarily lead  ...  The examples are taken from systems with macroscopic models leading to bistability.  ...  approximation are the two stable equilibria in the mass action kinetics.  ... 
doi:10.1109/tac.2007.911347 fatcat:ofqwnvivlvc5bd72i2qepvbhqe

Bifurcation phenomena in non-smooth dynamical systems

R.I. Leine, D.H. van Campen
2006 European Journal of Mechanics. A, Solids  
The aim of the paper is to give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems.  ...  It is often desirable to know how the equilibria and periodic solutions of a system alter when a parameter of the system is varied.  ...  For μ < 0, the system (8) has two distinct equilibria equilibrium 1: x 1 = − 2 3 μ, x 2 = 2μ, equilibrium 2: x 1 = 2μ, x 2 = 2μ, (9) while it has no equilibria for μ > 0.  ... 
doi:10.1016/j.euromechsol.2006.04.004 fatcat:ddqxl47ijvaotj3d7cvtn6q6fi

Self-organisation of Protein Patterns [article]

Erwin Frey, Fridtjof Brauns
2020 arXiv   pre-print
We would like to thank all of our collaborators that over the years have shaped our understanding of pattern formation in biological systems, especially Silke Bergeler, Jonas Denk, Raphaela Geßele, Andriy  ...  They are a continuous source of stimulation and inspiration for our theoretical work.  ...  While type II instability is generic for two-component MCRD systems, this is not true for systems with more components and/or multiple conserved species, where the band of unstable modes can be bound away  ... 
arXiv:2012.01797v1 fatcat:2uufuztk5jftlmbp2sd65boowa

Blow-up for realizing homotopy classes in the three-body problem [article]

Richard Montgomery
2015 arXiv   pre-print
The main novelty is my use of energy-balance to motivate the transformation of McGehee.  ...  This expository note describes McGehee blow-up McGehee in its role as one of the main tools in my recent proof with Rick Moeckel RM2 that every free homotopy class for the planar three-body problem can  ...  The first thing one learns in a class in dynamical systems is to look for equilibria. But Newton's equations have no equilibria! N stars cannot just sit there, still, in space.  ... 
arXiv:1507.07982v1 fatcat:ldmrbfmconbezbnpajiqmwxhse
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