Fig 3. Protein degradation determines an offset in the first growth law.

(a) Sketch of the first model of protein production proposed in this work, which includes protein degradation but no inactive ribosomes. In this model, ribosomes follow a first-order kinetics to bind the transcripts, and all bound ribosomes contribute to protein synthesis (mass production). Proteins can be lost by protein degradation or diluted by cell growth. (b) The law ϕ_R(λ) predicted by Eq (6) shows an offset ${\varphi }_R^{\text{min}}=\eta /\gamma$. The offset increases linearly with degradation rate η at a constant ribosome production rate γ. (c) Varying γ also changes ${\varphi }_R^{\text{min}}$ but it also affects the slope of ϕ_R(λ). Panel (b) reports ϕ_R(λ) for γ = 7.2 h⁻¹ and η = 0, 0.25, 0.5 h⁻¹. Panel (c) fixes η = 0.25 h⁻¹ and varies γ = 2, 3.6, 7.2 h⁻¹.