Linking Cell Size, V_max and K_m in Phototrophs and Chemotrophs: Insights From Bayesian Inference

Microbial growth is often described in terms of resource uptake rates, making the understanding and parameterisation of these rate-limiting processes critical for microbial modelling. In phototrophic plankton, theoretical studies suggest that nutrient uptake is limited by mechanistic processes involving membrane transporters, and it has been observed that the cell-specific maximum resource uptake rate (V_max) follows a power-law relationship with cell size, as well as a trade-off between V_max and the half-saturation constant (K_m). These constraints may also apply to chemotrophic microorganisms; however, many datasets lack direct cell-size measurements. We therefore leveraged the assumption that prokaryotic cell sizes, V_max, and K_m each follow log-normal distributions, drawing parallels with established phytoplankton scaling laws. Our analysis suggests that chemotrophic organisms generally exhibit higher maximum uptake rate per dry weight (V_maxDW) and K_m values than phototrophs, and that V_maxDW and K_m are not strongly correlated when all chemotroph data are combined. Furthermore, the Bayesian-derived exponents for V_maxDW and K_m exceeded those expected from allometric scaling relationships based on the membrane-transport capacity observed for phototrophs, implying that a range of additional factors likely affect observed kinetic parameters.