Cell design in bacteria as a convex optimization problem

In this paper, we investigate the cell design of bacteria during the exponential growth. To this purpose, we propose to formulate the problem as a non differentiable convex optimization problem equivalent to a Linear Programming feasibility problem. Its resolution predicts for a specific medium not only the distribution of metabolic fluxes and the maximal growth rate, but also the concentrations of the ribosomes and the proteins involved in the metabolic network and thus the composition of the cell for different growth rates. Moreover, our model recovers the known modular structure of the regulation of metabolic pathways for the gram-positive model bacterium Bacillus subtilis.