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

Polly-Anne Jeffrey, Martín López-García, Mario Castro, Grant Lythe and Carmen Molina-París
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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

Mathematics, 2020, vol. 8, issue 6, 1-31

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.

Keywords: receptor-ligand interaction; continuous-time Markov chain; summary statistics; steady-state; first-passage time; approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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