A steady-state model of microbial acclimation to substrate limitation
Fig 3
Schematic of steady-state nutrient acclimation.
A)—Optimal transporter abundances n* (solid green line) lie at the porter limitation (blue shaded region) boundary. All points above and below this boundary fail to maximize growth rate; for all points below, the uptake rate is sub-maximal; for all points above, some transporters are unoccupied. Over an interval of bulk substrate concentrations S∞ ≤ S*, this boundary is met with diffusion limitation (orange shaded region), where the catalytic rate exceeds the encounter rate; as concentrations exceed S*, the porter limitation boundary transitions to an internal growth rate limit (yellow shaded region), where the catalytic rate exceeds the rate of some downstream reaction. B)—For smaller cells, or for transporters with slower kcat, membrane surface area limitation (a special case of porter limitation) may be encountered. In the interval bounded by and
, n* is constrained to nmax (black dashed line). C)—Growth rates of optimally acclimated cells (solid green line) follow the intersection of two limits: the diffusive limit (purple dashed line) and the internal growth limit
(black dashed line). These rate limits are, again, bisected by S* with a sharp transition. D)—If surface area limitation is encountered, growth rates in the interval
follow a more gradual, hyperbolic transition from diffusion limitation to growth limitation.