Fig 1.
Sketch of the growth law relating ribosome mass fraction ϕR to growth rate λ.
The fraction of ribosomal and ribosome-affiliated proteins (R) increases with increasing nutrient quality at the expense of the sector of metabolic proteins (P), while a fraction of the proteome (Q) is kept to be growth rate-independent. Available data for most organisms show a nonzero intercept (see S1 Fig). In E. coli [5], the law deviates from linearity at slow growth (λ ≤ 1 h−1), making the intercept
larger.
Fig 2.
(a) The standard framework divides ribosomes into two categories—active and inactive—and assumes that only the fraction fa of active ribosomes is responsible for protein production. (b) The plot reports the estimated values fa assuming this model and using E. coli data from [5]. The red circle represents the extrapolated point at zero growth.
Table 1.
Summary of the symbols used in the text.
E. coli data are taken from [5, 25, 26]. S. cerevisiae data are taken from [4, 26, 27]. In the text we also use symbols for the number of free, active, inactive and transcript-bound ribosomes, which are Rf, Ra, Ri and Rb, respectively.
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 ϕR(λ) predicted by Eq (6) shows an offset . The offset increases linearly with degradation rate η at a constant ribosome production rate γ. (c) Varying γ also changes
but it also affects the slope of ϕR(λ). Panel (b) reports ϕR(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.
Fig 4.
Protein degradation increases the fraction of active ribosomes.
(a) Sketch of the second model of protein production proposed in this work, which includes both protein degradation and inactive ribosomes. In this model, only some ribosomes contribute to net protein synthesis. As the model in Fig 3, proteins can be lost by protein degradation or diluted by cell growth. (b) Experimental data on mean degradation rates across conditions for E. coli from [38] and for S. cerevisiae from [42]. The green line is a piece-wise linear fit of the data (see Materials and methods) and the cyan line represents the degradation for the standard model (η = 0). (c) Estimated fraction of active ribosomes in the combined model (turquoise symbols) compared to the model neglecting degradation rates (solid line—lower bound). In absence of degradation, the fraction of active ribosomes is estimated from Eq (1), . In presence of degradation, Eq (12) gives
. Turquoise symbols (crosses for E. coli, circles for S. cerevisiae) show the estimates from these formulas for experimental values of the other parameters. The model lower bound (solid line above the shaded area) for the fraction of active ribosomes is the prediction of the active ribosome model, but incorporating the non-null measured degradation rates in these estimates determines considerable deviations from this bound, validating the joint model. Continuous lines are analytical predictions with the constant ratio ansatz, Eq (14). For E. coli, estimates are performed using data for ribosome fractions ϕR and translation rate γ from [5] and degradation rates η from [38]. For S. cerevisiae, estimates are performed using data for ribosome fractions and translation rate from [4] and degradation rates from [42].
Fig 5.
Maintenance ribosomes are responsible for the increase in active ribosomes in the presence of degradation.
(a) Theoretical curves (in the combined model) of the maintenance ribosome fraction as a function of the degradation rate η for different fixed growth rates λ. Crosses and circles are obtained from experimental data in E. coli and S. cerevisiae respectively. Since fbm is a function of the ratio η/λ only, the inset shows that such curves collapse if plotted as a function of the degradation-to-growth rate ratio. (b) Maintenance ribosome fraction as a function of growth rate estimated from data, for S. cerevisiae and E. coli. The fraction of maintenance ribosomes is mathematically identical to the relative difference in total active ribosome fraction between the degradation-only model and the standard framework without degradation. Equivalently, the fraction of active ribosome increases in the presence of degradation due to maintenance ribosomes. Degradation data were derived from [38] (E. coli) and [42] (S. cerevisiae). Total ribosome fraction data used in Eq (19) to estimate fbm come from [5] (E. coli) and [4] (S. cerevisiae).