Fig. 5: Numerical and analytical predictions for heterologous gene expression and its effects on the host cell.

a, b Hill activation and repression functions respectively relate translational burden to the steady-state heterologous protein mass fraction \({\overline{\phi }}_{X}\) and cell growth rate \(\overline{\lambda }\). c In the steady state, \({\overline{\phi }}_{X}\), the mass fraction of heterologous proteins in the cell, is linearly related to \(\overline{\lambda }:{\overline{\lambda }}^{NB}\), the ratio of the corresponding growth rate to that without burden. The dotted vertical line denotes the \({\overline{\phi }}_{X}=0.25\) threshold, right of which model predictions become unreliable. d The rate of total protein production per cell as a function of the translational burden. ξ_max (vertical lines) is the burden value maximizing heterologous protein synthesis. All simulations assume σ = 0.5; the parameters and ODEs used in simulations are given in Supplementary Note S3.1. Source data are provided as a Source Data file.