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Translation of proteins is a fundamental part of gene expression that ismediated by ribosomes. As ribosomes significantly contribute to both cellularmass and energy consumption, achieving efficient management of the ribosomepopulation is also crucial to metabolism and growth. Inspired by biologicalevidence for nutrient-dependent mechanisms that control both ribosome activedegradation and genesis, we introduce a dynamical model of protein production,that includes the dynamics of resources and control over the ribosomepopulation. Under the hypothesis that active degradation and biogenesis areoptimal for maximizing and maintaining protein production, we aim toqualitatively reproduce empirical observations of the ribosome populationdynamics. Upon formulating the associated optimization problem, we firstanalytically study the stability and global behaviour of solutions underconstant resource input, and characterize the extent of oscillations andconvergence rate to a global equilibrium. We further use these results tosimplify and solve the problem under a quasi-static approximation. Usingbiophysical parameter values, we find that optimal control solutions lead toboth control mechanisms and the ribosome population switching between periodsof feeding and fasting, suggesting that the intense regulation of ribosomepopulation observed in experiments allows to maximize and maintain proteinproduction. Finally, we find some range for the control values over which sucha regime can be observed, depending on the intensity of fasting.

Optimal control of ribosome population for gene expression under periodic nutrient intake