Fig. 1.

Design criterion of DOL. (A) Model framework for an intracellular pathway within a single population (SC). Substrate (S) is converted to intracellular intermediate (M), which diffuses into the extracellular environment (M_e) and is directly converted to final product (P). Enzyme expression (E₁ and E₂) suppress the growth of the population. (B) Model framework for an intracellular pathway within two populations (DOL). S is converted to intracellular intermediate (M₁), which diffuses into extracellular environment (M_e) and then into population 2 (M₂), where it is converted to P. Enzyme expression (E₁ and E₂) suppresses the growth of the population they are contained in. (C) The design criterion defines when DOL is favored over SC. The left-hand side of the inequality represents the gain in biomass by DOL; the right-hand side represents the inefficiency of DOL. (D) The criterion determines the parametric spaces where each design strategy is favored. The color of the heat map indicates the magnitude of $\text{ln}({\overline{\upsilon }}_{DOL}^2/{\theta }_I({\upsilon }^2+\epsilon \upsilon ))$. Expressions for each term in the inequality are detailed in the main text and SI Appendix. To the left of the border $(\text{ln}({\overline{\upsilon }}_{DOL}^2/{\theta }_I({\upsilon }^2+\epsilon \upsilon ))=1)$, SC produces more P than DOL (Top). To the right of the border, DOL produces more P than SC (Middle). Above a certain level of burden, DOL always outperforms SC because the SC population goes extinct (white region, Bottom). Past a maximum level of burden, both DOL populations go extinct (black region).