Author response:

Public Reviews:

Reviewer #1 (Public review):

Summary:

The authors use analysis of existing data, mathematical modelling, and new experiments, to explore the relationship between protein expression noise, translation efficiency, and transcriptional bursting.

Strengths:

The analysis of the old data and the new data presented is interesting and mostly convincing.

Thank you for the constructive suggestions and comments. We address the individual comments below.

Weaknesses:

(1) My main concern is the analysis presented in Figure 4. This is the core of mechanistic analysis that suggests ribosomal demand can explain the observed phenomenon. I am both confused by the assumptions used here and the details of the mathematical modelling used in this section. Firstly, the authors' assumption that the fluctuations of a single gene mRNA levels will significantly affect ribosome demand is puzzling. On average the total level of mRNA across all genes would stay very constant and therefore there are no big fluctuations in the ribosome demand due to the burstiness of transcription of individual genes. Secondly, the analysis uses 19 mathematical functions that are in Table S1, but there are not really enough details for me to understand how this is used, are these included in a TASEP simulation? In what way are mRNA-prev and mRNA-curr used? What is the mechanistic meaning of different terms and exponents? As the authors use this analysis to argue ribosomal demand is at play, I would like this section to be very much clarified.

Thank you for raising two important points. Regarding the first point, we agree that the overall ribosome demand in a cell will remain more or less the same even with fluctuations in mRNA levels of a few genes. However, what we refer to in the manuscript is the demand for ribosomes for translating mRNA molecules of a single gene. This demand will vary with the changes in the number of the mRNA molecules of that gene. When the mRNA copy number of the gene is low, the number of ribosomes required for translation is low. At a subsequent timepoint when the mRNA number of the same gene goes up rapidly due to transcriptional bursting, the number of ribosomes required would also increase rapidly. The process of allocation of ribosomes for translation of these mRNA molecules will vary between cells, and this process can lead to increased expression variation of that gene among cells.

Regarding the second point, each of the 19 mathematical functions was individually tested in the TASEP model and stochastic simulation. The parameters ‘mRNA-curr’ and ‘mRNA-prev’ are the mRNA copy numbers at the current time point and the previous time point in the stochastic simulation, respectively. These numbers were calculated from the rate of production of mRNA, which is influenced by the burst frequency and the burst size, as well as the rate of mRNA removal. We would expand this section with explanation for all parameters and terms in the revised manuscript.

(2) Overall, the paper is very long and as there are analytical expressions for protein noise (e.g. see Paulsson Nature 2004), some of these results do not need to rely on Gillespie simulations. Protein CV (noise) can be written as three terms representing protein noise contribution, mRNA expression contribution, and bursty transcription contribution. For example, the results in panel 1 are fully consistent with the parameter regime, protein noise is negligible compared to transcriptional noise.

Thank you for referring to the paper on analytical expressions for protein noise. We introduced translational bursting and ribosome demand in our model, and these are linked to stochastic fluctuations in mRNA and ribosome numbers. In addition, our model couples transcriptional bursting with translational bursting and ribosome demand. Since these processes are all stochastic in nature, we felt that the stochastic simulation would be able to better capture the fluctuations in mRNA and protein expression levels originating from these processes. For consistency, we used stochastic simulations throughout even when the coupling between transcription and translation were not considered.

Reviewer #2 (Public review):

This work by Pal et al. studied the relationship between protein expression noise and translational efficiency. They proposed a model based on ribosome demand to explain the positive correlation between them, which is new as far as I realize. Nevertheless, I found the evidence of the main idea that it is the ribosome demand generating this correlation is weak. Below are my major and minor comments.

Thank you for your helpful suggestions and comments. We note that the direct experimental support required for the ribosome demand model would need experimental setups that are beyond the currently available methodologies. We address the individual comments below.

Major comments:

(1) Besides a hypothetical numerical model, I did not find any direct experimental evidence supporting the ribosome demand model. Therefore, I think the main conclusions of this work are a bit overstated.

Direct experimental evidence of the hypothesis would require generation of ribosome occupancy maps of mRNA molecules at the level of single cells and at time intervals that closely match the burst frequency of the genes. This is beyond the currently available methodologies. However, there are other evidences that support our model. For example, earlier work in cell-free systems have showed that constraining cellular resources required for transcription or translation can increase expression heterogeneity (Caveney et al., 2017). In addition, genome-wide analysis of expression noise in yeast also revealed that the association between protein noise and translational efficiency was highest in the group of genes with the most bursty transcription (Supplementary fig. S20).

(2) I found that the enhancement of protein noise due to high translational efficiency is quite mild, as shown in Figure 6A-B, which makes the biological significance of this effect unclear.

Although we agree with the reviewer’s comment that the effect of translational efficiency on protein noise may not be as substantial as the effect of transcriptional bursting, it has been observed in studies across bacteria, yeast and Arabidopsis (Ozbudak et al., 2003; Blake et al., 2003; Wu et al., 2022). In addition, the relationship between translational efficiency and protein noise is in contrast with the inverse relationship observed between mean expression and noise (Newman et al., 2006; Silander et al., 2012). We also note that the goal of the manuscript was not to evaluate the strength of the association, but to understand the basis of the influence of translational efficiency on protein noise.

(3) The captions for most of the figures are short and do not provide much explanation, making the figures difficult to read.

We will revise the figure captions to include more details as per the reviewer’s suggestion.

(4) It would be helpful if the authors could define the meanings of noise (e.g., coefficient of variation?) and translational efficiency in the very beginning to avoid any confusion. It is also unclear to me whether the noise from the experimental data is defined according to protein numbers or concentrations, which is presumably important since budding yeasts are growing cells.

For all published datasets where we had measurements from a large number of genes/promoters, we used the measures of adjusted noise (for mRNA noise) and Distance-to-median (DM, for protein noise). For experiments that we performed on a limited number of promoters, we used the measure of coefficient of variation (CV) to quantify noise, as calculation of adjusted noise or DM was not possible. Translational efficiency refers to translation rate which is determined by both the translation initiation rate and the translation elongation rate. The noise at the protein level was quantified from the signal intensity of GFP tagged proteins, which was proportional to protein numbers without considering cell volume. For quantification of noise at the mRNA level, single-cell RNA-seq data was used, which provided mRNA numbers in individual cells.

(5) The conclusions from Figures 1D and 1E are not new. For example, the constant protein noise as a function of mean protein expression is a known result of the two-state model of gene expression, e.g., see Equation (4) in Paulsson, Physics of Life Reviews 2005.

Yes, they are not new, but we included these results for setting the baseline for comparison with simulation results that appear in the later part of the manuscript where we included translational bursting and ribosome demand in our models.

(6) In Figure 4C-D, it is unclear to me how the authors changed the mean protein expression if the translation initiation rate is a function of variation in mRNA number and other random variables.

The translation initiation rate varied from a baseline initiation rate depending on the mRNA numbers and other variables. We changed the baseline initiation rate to alter the mean protein expression levels. We will elaborate this section in the revised manuscript.

(7) If I understand correctly, the authors somehow changed the translation initiation rate to change the mean protein expression in Figures 4C-D. However, the authors changed the protein sequences in the experimental data of Figure 6. I am not sure if the comparison between simulations and experimental data is appropriate.

It is an important observation. Even though we changed the translation initiation rate to change the mean expression (Fig. 4C-D), we noted in the description in the model (Fig. 3D) that the changes in the translation initiation rate was also linked with changes in the translation elongation rate. The translation initiation rate can only increase if the ribosomes already bound to the mRNA traverse quicker through the mRNA. This means that an increase in the translation initiation rate will occur only if the translation elongation rate is also increased, which will lead to lower traversal time of the ribosomes through the mRNA (Fig. 3D). Similarly, an increase in the translation elongation rate will allow more ribosomes to initiate translation. Thus, the parameters translation initiation rate and translation elongation rate are interconnected. This has also been observed in an experimental study by Barrington et al. (2023). Having said that, however, the models can also be expressed in terms of the translation elongation rate, instead of the translation initiation rate, and this modification will not change the results of the simulations due to interconnectedness of the initiation rate and the elongation rate.

References

C. L. Barrington, G. Galindo, A. L. Koch, E. R. Horton, E. J. Morrison, S. Tisa, T. J. Stasevich, O. S. Rissland. Synonymous codon usage regulates translation initiation. Cell Rep. 42, 113413 (2023).

W. J. Blake, M. Kaern, C. R. Cantor, J. J. Collins, Noise in eukaryotic gene expression. Nature 422, 633-637 (2003).

P. M. Caveney, S. E. Norred, C. W. Chin, J. B. Boreyko, B. S. Razooky, S. T. Retterer, C. P. Collier, M. L. Simpson, Resource Sharing Controls Gene Expression Bursting. ACS Synth Biol. 6, 334-343 (2017)

J. R. Newman, S. Ghaemmaghami, J. Ihmels, D. K. Breslow, M. Noble, J. L. DeRisi, J. S. Weissman, Single-cell proteomic analysis of S. cerevisiae reveals the architecture of biological noise. Nature, 441, 840-846 (2006).

E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman, A. van Oudenaarden, Regulation of noise in the expression of a single gene. Nat Genet. 31, 69-73 (2002).

O. K. Silander, N. Nikolic, A. Zaslaver, A. Bren, I. Kikoin, U. Alon, M. Ackermann, A genome-wide analysis of promoter-mediated phenotypic noise in Escherichia coli. PLoS Genet. 8, e1002443 (2012).

H. W. Wu, E. Fajiculay, J. F. Wu, C. S. Yan, C. P. Hsu, S. H. Wu, Noise reduction by upstream open reading frames. Nat Plants. 8, 474-480 (2022).

Figures and data

High mRNA noise combined with high translational efficiency leads to high protein noise

Stochastic fluctuation in mRNA expression, originating from transcriptional bursts, combined with high translational efficiency generates high protein noise.

The model combining transcriptional and translational bursts does not explain the correlation between translational efficiency and protein noise

Inclusion of ribosome demand associated with translation can reveal positive correlation between translational efficiency and protein noise

Impact of changes in translational efficiency on protein noise is dependent on the transcriptional burst characteristics of promoters