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A stochastic analysis of particle systems with pairing

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  • Fromion, Vincent
  • Robert, Philippe
  • Zaherddine, Jana

Abstract

Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each particle follows a random path in the medium, when a particle and an agent meet, they may bind and form a pair which has some specific functional properties. Such a pair is also subject to random events and it splits after some random amount of time. In a stochastic context, using a Markovian model for the vector of the number of paired particles, and by taking the total number of particles as a scaling parameter, we study the asymptotic behavior of the time evolution of the number of paired particles. Two scenarios are investigated: one with a large but fixed number of agents, and the other one, the dynamic case, when agents are created at a bounded rate and may die after some time when they are not paired. A first order limit theorem is established for the time evolution of the system in both cases. The proof of an averaging principle of the dynamic case is one of the main contributions of the paper. The impact of dynamical arrivals of agents on the level of pairing of the system is discussed.

Suggested Citation

  • Fromion, Vincent & Robert, Philippe & Zaherddine, Jana, 2024. "A stochastic analysis of particle systems with pairing," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    • Handle: RePEc:eee:spapps:v:178:y:2024:i:c:s0304414924001868
    DOI: 10.1016/j.spa.2024.104480
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    References listed on IDEAS

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    1. Jin Yang & Brent W. Anderson & Asan Turdiev & Husan Turdiev & David M. Stevenson & Daniel Amador-Noguez & Vincent T. Lee & Jue D. Wang, 2020. "The nucleotide pGpp acts as a third alarmone in Bacillus, with functions distinct from those of (p)ppGpp," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    2. Andreas Petrides & Glenn Vinnicombe, 2018. "Enzyme sequestration by the substrate: An analysis in the deterministic and stochastic domains," PLOS Computational Biology, Public Library of Science, vol. 14(5), pages 1-23, May.
    3. Jae Kyoung Kim & Eduardo D Sontag, 2017. "Reduction of multiscale stochastic biochemical reaction networks using exact moment derivation," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-24, June.
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