Fig. 6: Active degradation rates are generally uncoupled from cell division rates.

A Two simple models describing the relationship between cell division and protein-specific turnover rates. The total protein turnover rate (k_total) is the sum of the active degradation rate (k_active) and the dilution rate due to cell division (k_dilution). In the “scaled model,” active degradation rates increase proportionally to division rates with a protein-specific constant (α_p), i.e., active degradation remains a constant fraction of the total protein turnover rate. In the “constant model,” protein-specific active degradation rates are constant (β_p), regardless of changing division rates. In this case, for slower-dividing cells, the contribution of active degradation increases relative to dilution. B t_{1/2, total} is the time taken to replace half the protein. A theoretical plot of t_{1/2, total} from two conditions (i, j) where cell division rates change by a factor of r_i,j < 1. In the scaled model, t_{1/2, total} values for all the proteins lie on a straight line with slope r_i,j (orange). In the constant model, the t_{1/2, total} values follow a nonlinear relationship between the two doubling times (purple). For proteins with very high active degradation rates, the constant model predicts that t_{1/2, total} will approach the same value for both doubling times, indicated by the slope 1 line (black). For diluting proteins with no active degradation, both models converge to the doubling times of conditions i and j. C Scatter plots of protein t_{1/2, total} for E. coli grown at doubling times of 6 h (C-lim), 3 h (C-lim), and 0.7 h (defined minimal media batch) compared to 12 h (C-lim). The dotted lines represent the dilution limit. We observe a strong statistical preference for the “constant model,” in which active degradation rates are uncoupled from cell cycle duration. Shown are the likelihood ratios (L) of the constant models compared to the scaled models assuming normally distributed errors.