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Stochastically Modeled Reaction Networks with Absolute Concentration Robustness

Banff International Research Station for Mathematical Innovation and Discovery

Deterministic reaction networks equipped with a kinetics are termed absolute concentration robust (ACR) if one or more species have the same value at any positive steady state of the system. This property is particular interesting from a biological point of view, since it implies that the expression of certain molecules at a stationary regime does not change under modification of the total mass of the system. Structural conditions implying absolute concentration robustness have been found for mass action models. Surprisingly, under the same structural conditions it has been shown that the associated stochastically modeled systems undergo an extinction event with probability 1. This leads to a discrepancy between the deterministic model, where some species have always the same value at equilibrium, and the stochastic model, where the same species eventually absorb the total mass of the system. I will present a result which solves the discrepancy between the two models at typical time frames. The result implies that, under certain conditions, the averages of the ACR species counts tend to their ACR equilibria. Specifically, this holds up to any fixed time point, when the total number of molecules tends to infinity in an appropriate multiscale fashion. Finally, I will show by examples that absolute concentration robustness does not necessarily imply an extinction event for the stochastically modeled system, contrary to what could be believed.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Mathematical biology

video/mp4

Author affiliation: University of Copenhagen

2017-12-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63787

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/