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On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective

Author

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  • Polly-Anne Jeffrey

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Martín López-García

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Mario Castro

    (Instituto de Investigación Tecnológica (IIT) and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Pontificia Comillas, E-28015 Madrid, Spain)

  • Grant Lythe

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

  • Carmen Molina-París

    (Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK)

Abstract

Cellular receptors on the cell membrane can bind ligand molecules in the extra-cellular medium to form ligand-bound monomers. These interactions ultimately determine the fate of a cell through the resulting intra-cellular signalling cascades. Often, several receptor types can bind a shared ligand leading to the formation of different monomeric complexes, and in turn to competition for the common ligand. Here, we describe competition between two receptors which bind a common ligand in terms of a bi-variate stochastic process. The stochastic description is important to account for fluctuations in the number of molecules. Our interest is in computing two summary statistics—the steady-state distribution of the number of bound monomers and the time to reach a threshold number of monomers of a given kind. The matrix-analytic approach developed in this manuscript is exact, but becomes impractical as the number of molecules in the system increases. Thus, we present novel approximations which can work under low-to-moderate competition scenarios. Our results apply to systems with a larger number of population species (i.e., receptors) competing for a common resource (i.e., ligands), and to competition systems outside the area of molecular dynamics, such as Mathematical Ecology.

Suggested Citation

  • Polly-Anne Jeffrey & Martín López-García & Mario Castro & Grant Lythe & Carmen Molina-París, 2020. "On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective," Mathematics, MDPI, vol. 8(6), pages 1-31, June.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1014-:d:374290
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    References listed on IDEAS

    as
    1. Vidyadhar G. Kulkarni, 1999. "Introduction to matrix analytic methods in stochastic modeling, by G. Latouche and V. Ramaswamy," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-2, January.
    2. Economou, A. & Gómez-Corral, A. & López-García, M., 2015. "A stochastic SIS epidemic model with heterogeneous contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 78-97.
    3. Jared C Weddell & P I Imoukhuede, 2014. "Quantitative Characterization of Cellular Membrane-Receptor Heterogeneity through Statistical and Computational Modeling," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-19, May.
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