The Annals of Applied Probability

Scaling limits of spatial compartment models for chemical reaction networks

Peter Pfaffelhuber and Lea Popovic

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We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has different effects depending on whether the movement of each type of species is faster or slower than the effective reaction dynamics on this molecular type. We obtain results for both when the system is without and with conserved quantities, which are linear combinations of species evolving only on the slower time scale.

Article information

Ann. Appl. Probab., Volume 25, Number 6 (2015), 3162-3208.

Received: February 2013
Revised: July 2014
First available in Project Euclid: 1 October 2015

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Zentralblatt MATH identifier

Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60F17: Functional limit theorems; invariance principles 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30] 80A30: Chemical kinetics [See also 76V05, 92C45, 92E20]

Chemical reaction network multiple time scales stochastic averaging scaling limits quasi-steady state assumption


Pfaffelhuber, Peter; Popovic, Lea. Scaling limits of spatial compartment models for chemical reaction networks. Ann. Appl. Probab. 25 (2015), no. 6, 3162--3208. doi:10.1214/14-AAP1070.

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