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PreprintCC BY 4.0HAL

A stochastic model of compartmentalized intracellular signalling

  • Léo Darrigade
  • Chloé Weckel
  • Romain Yvinec
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Abstract

Activated membrane receptors can be internalized into endosomes, where they keep signalling, possibly differently from the plasma membrane. We propose a piecewise deterministic Markov process (PDMP) in which receptor internalization and recycling are stochastic, each endosome is tracked individually, and the intracellular reaction networks, at the membrane and inside endosomes, evolve deterministically between jumps. We study the long-time behaviour of this process. We give sufficient conditions for the existence of a stationary measure, for a point to be a Doeblin point, which yields convergence in total variation, and for exponential weak convergence to a stationary measure, by adapting techniques from the theory of randomly switched ODEs. Several examples of biological interest illustrate the results.

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Cite

BibTeXRIS
BibTeX
@misc{darrigade2026stochastic,
  title = {{A stochastic model of compartmentalized intracellular signalling}},
  author = {Léo Darrigade and Chloé Weckel and Romain Yvinec},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  url = {https://inria.hal.science/hal-05794502v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A stochastic model of compartmentalized intracellular signalling
AU  - Léo Darrigade
AU  - Chloé Weckel
AU  - Romain Yvinec
PY  - 2026
DA  - 2026/10/12
PB  - HAL
UR  - https://inria.hal.science/hal-05794502v1
AB  - Activated membrane receptors can be internalized into endosomes, where they keep signalling, possibly differently from the plasma membrane. We propose a piecewise deterministic Markov process (PDMP) in which receptor internalization and recycling are stochastic, each endosome is tracked individually, and the intracellular reaction networks, at the membrane and inside endosomes, evolve deterministically between jumps. We study the long-time behaviour of this process. We give sufficient conditions for the existence of a stationary measure, for a point to be a Doeblin point, which yields convergence in total variation, and for exponential weak convergence to a stationary measure, by adapting techniques from the theory of randomly switched ODEs. Several examples of biological interest illustrate the results.
ER  -