Optimal allocation between nutrient uptake and growth in a microbial trichome

Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature

“…Section 7 will develop a numerical method to approximate the corresponding switching curve in the state space. One more significant argument in favor of our problem statement with the terminal constraint (14) is that this method in principle will not depend on a particular time horizon, i. e., we will obtain the same results when applying it to the related infinite-horizon problem in the overtaking optimality sense (under the a priori assumption of entering p * opt ,r * opt by the overtaking optimal state trajectories).…”

“…In compliance with [8,[13][14][15]17], we adopt the hypothesis that regulation mechanisms in the cells are aimed at maximizing the accumulation of structural biomass under current environmental conditions. For our model, this leads to the criterion…”

“…The following inequalities hold: (14). LetḠ denote the closure of the strongly invariant domain G. In the set G\{0, 1}, the system (11) with α ≡ α * opt has only one steady state p * opt ,r * opt , and the latter is a stable node or a stable focus due to Theorem 4.1.…”

“…Several studies developed large-scale network modeling frameworks [10][11][12], which are essentially numerical. Alternatively, it is possible to propose less computationally expensive models that focus on smaller amounts of substantial characteristics and allow wider analytical investigation, but still lead to reasonable and useful conclusions [8,[13][14][15][16]. This approach is employed in the current work.…”

“…This approach is employed in the current work. Also note that, in comparison with purely steady-state considerations, dynamic modeling perspectives can give more realistic descriptions of bacterial growth and resource allocation [8,12,14,15].…”