Summary:
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
JCR Impact Factor and WoS quartile: 2,258 - Q1 (2020); 2,400 - Q1 (2022)
DOI reference:
https://doi.org/10.3390/math8061014
Published on paper: June 2020.
Published on-line: June 2020.
Citation:
P.A. Jeffrey, M. López-García, M. Castro, G. Lythe, C. Molina-Paris, On exact and approximate approaches for stochastic receptor-ligand competition dynamics - An ecological perspective. Mathematics. Vol. 8, nº. 6, pp. 1014-1 - 1014-31, June 2020. [Online: June 2020]
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