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Article

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

1
Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
2
Instituto de Investigación Tecnológica (IIT) and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Pontificia Comillas, E-28015 Madrid, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1014; https://doi.org/10.3390/math8061014
Received: 15 May 2020 / Revised: 11 June 2020 / Accepted: 16 June 2020 / Published: 20 June 2020
(This article belongs to the Special Issue Stochastic Modeling in Biology)
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. View Full-Text
Keywords: receptor-ligand interaction; continuous-time Markov chain; summary statistics; steady-state; first-passage time; approximation receptor-ligand interaction; continuous-time Markov chain; summary statistics; steady-state; first-passage time; approximation
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MDPI and ACS Style

Jeffrey, P.-A.; López-García, M.; Castro, M.; Lythe, G.; Molina-París, C. On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective. Mathematics 2020, 8, 1014. https://doi.org/10.3390/math8061014

AMA Style

Jeffrey P-A, López-García M, Castro M, Lythe G, Molina-París C. On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective. Mathematics. 2020; 8(6):1014. https://doi.org/10.3390/math8061014

Chicago/Turabian Style

Jeffrey, Polly-Anne, Martín López-García, Mario Castro, Grant Lythe, and Carmen Molina-París. 2020. "On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics—An Ecological Perspective" Mathematics 8, no. 6: 1014. https://doi.org/10.3390/math8061014

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