Chen Y et al. (2023), Protein homeostasis from diffusion-dependent co...

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bioRxiv 2023 Apr 28; doi: 10.1101/2023.04.24.538146.

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Protein homeostasis from diffusion-dependent control of protein synthesis and degradation.

Chen Y , Huang JH , Phong C , Ferrell JE .

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It has been proposed that the concentration of proteins in the cytoplasm maximizes the speed of important biochemical reactions. Here we have used the Xenopus extract system, which can be diluted or concentrated to yield a range of cytoplasmic protein concentrations, to test the effect of cytoplasmic concentration on mRNA translation and protein degradation. We found that protein synthesis rates are maximal in ∼1x cytoplasm, whereas protein degradation continues to rise to an optimal concentration of ∼1.8x. This can be attributed to the greater sensitivity of translation to cytoplasmic viscosity, perhaps because it involves unusually large macromolecular complexes like polyribosomes. The different concentration optima sets up a negative feedback homeostatic system, where increasing the cytoplasmic protein concentration above the 1x physiological level increases the viscosity of the cytoplasm, which selectively inhibits translation and drives the system back toward the 1x set point.

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	Figure 2. The rate of mRNA translation is maximal at a cytoplasmic concentration of ~1x.(A) Titration of mRNA concentration for eGFP expression. The indicated concentration (2.5 μg/mL) was chosen for the experiments in (B-E).(B) eGFP expression as a function of time for various dilutions of a 1x extract.(C) Translation rate as a function of cytoplasmic concentration. These are the directly-measured data from experiments where the eGFP mRNA concentration was kept constant and the translation machinery was proportional to the cytoplasmic concentration. Data are from 6 experiments for dilution from 1x extracts and 7 experiments for dilution from 2x retentates. Data are normalized relative to the translation rates at a cytoplasmic concentration of 1x. Means and standard errors are overlaid on the individual data points. In this and the subsequent panels, the darker green represents data from diluting 2x retentates and the lighter green from diluting 1x extract.(D) Inferred translation rates for the situation where the mRNA concentration as well as the ribosome concentration is proportional to the cytoplasmic concentration. The rates from (C) were multiplied by the relative cytoplasmic concentrations.(E) Inferred translation rates for the situation where both the mRNA concentration and the ribosome concentration are kept constant at all dilutions. The rates from (C) were divided by the relative cytoplasmic concentrations.(F) TCA-precipitable 35S incorporation as a function of time for translation from endogenous mRNAs. Various dilutions of a 1x extract are shown. CHX denotes a 1x extract treated with 100 μg/mL cycloheximide.(G) Inferred translation rates for the situation where mRNA concentration is kept constant and ribosome concentration is proportional to the cytoplasmic concentration. The rates from (H) were divided by the relative cytoplasmic concentration. The grey data points are from CHX (100 μg/mL)-treated 1x extracts.(H) Translation rate as a function of cytoplasmic concentration. These are the directly-measured data from experiments where the 35S concentration was kept constant but both the (endogenous) mRNA concentration and translational machinery were proportional to the cytoplasmic concentration. Data are from 3 experiments for dilution from 1x extracts and 3 experiments for dilution from 2x retentates. Data are normalized relative to the translation rates at a cytoplasmic concentration of 1x. Means and standard errors are overlaid on the individual data points.(I) Inferred translation rates for the situation where both the mRNA concentration and the ribosome concentration are kept constant at all dilutions. The rates from (H) were divided twice by the relative cytoplasmic concentrations (i.e. by the relative concentration squared).
	Figure 3. The rate of protein degradation is maximal at cytoplasmic concentrations of ~1.8x.(A) Titration of substrate protein concentration for DQ-BSA degradation experiments. The indicated concentration (5 μg/mL) was chosen for the experiments in (B-E).(B) DQ-BSA fluorescence as a function of time for various dilutions of a 1x extract.(C) Degradation rate as a function of cytoplasmic concentration. These are the directly-measured data from experiments where the DQ-BSA concentration was kept constant and the proteolysis machinery was proportional to the cytoplasmic concentration. The grey data points denoted MG132 are from 1x extracts treated with 200 μM MG132, a proteosome inhibitor. Data are from 4 experiments for dilution from 1x extracts and 4 experiments for dilution from 2x retentates. Data are normalized relative to the degradation rates at a cytoplasmic concentration of 1x. Means and standard errors are overlaid on the individual data points. In this and the subsequent panels, the darker purple represents data from diluting 2x retentates and the lighter purple from diluting 1x extract.(D) Inferred degradation rates for the situation where the substrate concentration as well as the proteosome concentration is proportional to the cytoplasmic concentration. The rates from (C) were multiplied by the relative cytoplasmic concentrations.(E) Inferred degradation rates for the situation where both the substrate concentration and the proteosome concentration are kept constant at all dilutions. The rates from (C) were divided by the relative cytoplasmic concentrations.(F) Degradation of securin-CFP as a function of time for various dilutions of a 1x extractt.(G) Degradation rate as a function of cytoplasmic concentration. These are the directly-measured data from experiments where the securin-CFP concentration was kept constant but the proteosome concentration was proportional to the cytoplasmic concentration. Data are from 4 experiments for dilution from 1x extracts and 4 experiments for dilution from 2x retentates. Data are normalized relative to the degradation rates at a cytoplasmic concentration of 1x. Means and standard errors are overlaid on the individual data points.(H) Inferred degradation rate for the situation where both the substrate and proteosome concentrations are proportional to the cytoplasmic concentration. The rates from (G) were multiplied by the relative cytoplasmic concentrations.(I) Inferred degradation rates for the situation where both the substrate and the proteosome concentration are kept constant at all dilutions. The rates from (G) were divided by the relative cytoplasmic concentrations.
	Figure 4. The effect of cytoplasmic concentration on diffusion, and the effect of Ficoll 70 on translation and protein degradation.(A) The sizes of various macromolecules and complexes involved in translation and degradation.(B) Single particle traces for diffusion of 100 nm fluorescent beads in 1x cytoplasmic extracts. Two examples of location-to-location variability are highlighted.(C) Mean-squared displacement for 110 individual trajectories (black) and average mean-squared displacement (red) as a function of the time difference τ. Effective diffusion coefficients were calculated from the first 1 s of data.(D) Effective diffusion coefficients for 100 nm fluorescent beads as function of relative cytoplasmic concentration. Data are from 3 experiments for the 2x extract dilution and from 2 experiments for the 1x extract dilution. Error bars for the 2x extract dilution represent means ± standards errors.(E) Effective diffusion coefficients for beads of different diameter (nominally 40 nm, 100 nm, and 200 nm) as a function of relative cytoplasmic concentration. Data are from 3 experiments. Means and standard errors are overlaid on the individual data points.(F) The scaling factor μ (from Eq. 1) as a function of bead diameter. The apparent bead diameters (nominally 40, 100, and 200 nm) were calculated from their diffusion coefficients in extract buffer with no sucrose using the Stokes-Einstein relationship. Scaling factors are from 3 experiments and are shown as means ± S.E. Bead diameters are from 3 experiments for the 40 nm beads and 4 experiments for the 100 and 200 nm beads, and again are plotted as means ± S.E. The diameters of proteosomes and polyribosomes are shown for comparison.(G) Diffusion coefficients of 40 nm beads as a function of Ficoll 70 concentration. Extracts were prepared at 0.7x, 0.8x, and 0.9x as indicated and supplemented with Ficoll to yield the final concentrations (w/vol) shown on the x-axis. Data are from 3 experiments. Means and standard errors are overlaid on the individual data points. Diffusion coefficients for the undiluted 1x extracts were also measured and the average is shown for reference.(H) Translation rates, using the eGFP assay, as a function of Ficoll 70 concentration. Extracts were prepared at 0.7x, 0.8x, and 0.9x as indicated and supplemented with Ficoll to yield the final concentrations (w/vol) shown on the x-axis. Data are from the same 3 experiments shown in (G). Means and standard errors are overlaid on the individual data points. Translation rates for the undiluted 1x extracts were also measured and the average is shown for reference.(I) Degradation rates, using the DQ-BSA assay, as a function of Ficoll 70 concentration. Extracts were prepared at 0.7x, 0.8x, and 0.9x as indicated and supplemented with Ficoll to yield the final concentrations (w/vol) shown on the x-axis. Data are from the same 3 experiments shown in (G). Means and standard errors are overlaid on the individual data points. Degradation rates for the undiluted 1x extracts were also measured and the average is shown for reference.
	Figure 5. Homeostasis in a model of the effect of cytoplasmic concentration of translation and protein degradation.(A) Plot of Eq. 11, which relates a bimolecular reaction rate to the relative cytoplasmic concentration, for various sizes of proteins. We assumed a=0.018nm−1 (from Figure 4F).(B) Calculated optimal relative cytoplasmic concentration for proteins of different assumed sizes, again assuming a=0.018nm−1(C) Fits of Eq. 11 to the experimental data for translation (green) and degradation (purple) as a function of cytoplasmic concentration, calculated assuming that both the substrate and enzyme varied with the cytoplasmic concentration. All of the data from Figures 2D, H and 3D, H were included in the fits. The R2 values are 0.92 for the translation data and 0.95 for the degradation data. The fitted values for the size of the proteins involved are 104 ± 2 nm (mean ± S.E.) for translation and 14 ± 1 nm (mean ± S.E) for degradation. The fitted optimal cytoplasmic concentrations are 1.07 ± 0.02 for translation and 8.1 ± 0.8 for degradation (mean ± S.E.).

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