Trait-based models of nutrient uptake in microbes extend the Michaelis- Menten framework

In microbial competition theory, the Michaelis-Menten (MM) half-saturation coefficient is often considered to be a trait of an organism defining competitive strength in a trade-off conflict with maximum uptake rate. Theoretical studies have shown that a quadratic model characterizes the uptake rate, and that this model can be approximated by a MM model. Here, we review recent developments in nutrient uptake modeling with particular emphasis on cell size, uptake sites, and molecular diffusion. We quantify the bias of the MM approximation to be up to 50% in some configurations. More importantly, we find no mechanistic foundation for a trade-off conflict between the half-saturation coefficient and the maximum specific uptake rate. Measured MM coefficients need to be interpreted in an extended framework where nutrient uptake is explicitly parameterized in terms of cell size, uptake sites, and molecular diffusion. This provides a richer and more mechanistic picture of the way in which uptake rate varies with traits of the organism and environmental variables. Estimates of these key traits can be obtained from measured properties like affinity, the MM half saturation coefficient, and the maximum uptake rate. Using recent estimates of allometric scaling of MM coefficients, we find that handling time, uptake site density, and specific affinity decrease with cell size. Unlike the half-saturation coefficient, specific affinity is a consistent and meaningful measure of competitive strength of microbes, but it is not in a trade-off conflict with maximum uptake rate if the cell is surrounded by a diffusive boundary layer. Early work with chemostats extended the MichaelisMenten (MM) enzyme kinetics to growth of whole organisms such as bacteria (Monod 1949). Later, Dugdale (1967) introduced MM to represent the effect of nutrient concentration on phytoplankton uptake rate (V):