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
Índice de impacto JCR y cuartil WoS: 1.747 - Q1 (2019)
Referencia DOI: 10.3390/math8061014
Publicado en papel: Junio 2020. Publicado on-line: Junio 2020.
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, Junio 2020. [Online: Junio 2020]