Table 1 Definition of the variables and parameters of nutrient-explicit chemostat equations of the mutualistic cross-feeding system, Eq. (1), for \(i=1,2\) and \(i\ne j\).
From: Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect
Variable | Biological meaning |
|---|---|
\({\rho }_{i}\) | microbial density of species i |
\({S}_{i}\) | substrate of species i (concentration) |
\({P}_{i}\) | cross-fed nutrient, produced by species i (concentration) |
Parameter | Biological meaning |
\(\,d\) | dilution rate |
\({\tilde{S}}_{i}\) | inflow concentration of \({S}_{i}\) |
\({\tilde{P}}_{i}\) | inflow concentration of \({P}_{i}\) |
\({\nu }_{si}\) | consumption/growth ratio (yield) of \({S}_{i}\) by species i |
\({\nu }_{pi}\) | consumption/growth ratio (yield) of \({P}_{i}\) by species i |
\({a}_{ij}\) | production/growth ratio (yield) of \({P}_{i}\) by species j |
\({\mu }_{i}\) | Maximal growth rate of species i |
\({K}_{si}\) | Monod constant for \({S}_{i}\) (consumption by species i) |
\({K}_{pi}\) | Monod constant for \({P}_{i}\) (consumption by species i) |
