ArticleJournal of the Royal Society, Interface2014
Stochastic analysis of biochemical reaction networks with absolute concentration robustness.
Article in Journal of the Royal Society, Interface, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Topological criterion for robust perfect adaptation of reaction fluxes in biological networks.iScience · 2025Article
- Derivation of stationary distributions of biochemical reaction networks via structure transformation.Communications biology · 2021Article
- A hidden integral structure endows absolute concentration robust systems with resilience to dynamical concentration disturbances.Journal of the Royal Society, Interface · 2020Article
- Absolutely robust controllers for chemical reaction networks.Journal of the Royal Society, Interface · 2020Article
- Discrepancies between extinction events and boundary equilibria in reaction networks.Journal of mathematical biology · 2019Article
- Conditions for extinction events in chemical reaction networks with discrete state spaces.Journal of mathematical biology · 2018Article
- Solving moment hierarchies for chemical reaction networks.Journal of physics. A, Mathematical and theoretical · 2017Article
- Transient absolute robustness in stochastic biochemical networks.Journal of the Royal Society, Interface · 2016Article
- Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks.Bulletin of mathematical biology · 2015Article
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Authors and funding
3 authors.
Funding
Abstract
It has recently been shown that structural conditions on the reaction network, rather than a 'fine-tuning' of system parameters, often suffice to impart 'absolute concentration robustness' (ACR) on a wide class of biologically relevant, deterministically modelled mass-action systems. We show here that fundamentally different conclusions about the long-term behaviour of such systems are reached if the systems are instead modelled with stochastic dynamics and a discrete state space. Specifically, we characterize a large class of models that exhibit convergence to a positive robust equilibrium in the deterministic setting, whereas trajectories of the corresponding stochastic models are necessarily absorbed by a set of states that reside on the boundary of the state space, i.e. the system undergoes an extinction event. If the time to extinction is large relative to the relevant timescales of the system, the process will appear to settle down to a stationary distribution long before the inevitable extinction will occur. This quasi-stationary distribution is considered for two systems taken from the literature, and results consistent with ACR are recovered by showing that the quasi-stationary distribution of the robust species approaches a Poisson distribution.
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