Figure 5

An optimal control model suggests a sudden shift from making bottleneck proteins to full biomass production. (A) The model seeks the optimal allocation function u(t) between making bottleneck protein P and making biomass M, in order to minimize the time to double the biomass.. The function u(t) is the fraction of resources devoted to making M, and 1-u(t) the fraction devoted to making P. The rate of production of P is parameterized by a maximal rate ν. The maximal rate of producing M is the exponential growth rate μ. A logistic term is omitted for simplicity, and including it does not change the qualitative result. The optimal solution for u(t), obtained in the Methods section, is a sharp switch from u = 0 to a value of u = 1, at time τ. Lag1 is the time up to time τ, in which the cells make only P. In lag2 and exponential phases, the period of time after τ, the cells make both bottleneck protein P and biomass M. (B) The level of the bottleneck protein P. See Additional file 1: Figure S3. (C) The level of the biomass M. (D) Lag1 phase duration τ, as a function of initial bottleneck protein concentration P. (E) Lag1 phase duration (τ), as a function of P exponential increase rate ν.