Optimal allocation of building blocks between nutrient uptake systems in a microbe

A bacterial cell must distribute its molecular building blocks among various types of nutrient uptake systems. If the microbe is to maximize its average growth rate, this allocation of building blocks must be adjusted to the environmental availabilities of the various nutrients. The adjustments can be found from growth balancing considerations. We give a full proof of optimality and uniqueness of the optimal allocation regime for a simple model of microbial growth and internal stores kinetics. This proof suggests likely candidates for optimal control regimes in the case of a more realistic model. These candidate regimes differ with respect to the information that the cell's control system must have access to. We pay particular attention to one of the three candidates, a feedback regime based on a cellular control system that monitors only internal reserve densities. We show that allocation converges rapidly to balanced growth under this control regime.