Costs of ribosomal RNA stabilization affect ribosome composition at maximum growth rate

  1. Diana Széliová
  2. Stefan Müller
  3. Jürgen Zanghellini

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Abstract

Ribosomes are key to cellular self-fabrication and limit growth rate. While most enzymes are proteins, ribosomes consist of 1/3 protein and 2/3 ribonucleic acid (RNA) (in E. coli ).

Here, we develop a mechanistic model of a self-fabricating cell, validated across diverse growth conditions. Through resource balance analysis (RBA), we explore the variation in maximum growth rate with ribosome composition, assuming constant kinetic parameters.

Our model highlights the importance of RNA instability. If we neglect it, RNA synthesis is always cheaper than protein synthesis, leading to an RNA-only ribosome at maximum growth rate. Upon accounting for RNA turnover, we find that a mixed ribosome composed of RNA and proteins maximizes growth rate. To account for RNA turnover, we explore two scenarios regarding the activity of RNases. In (a) degradation is proportional to RNA content. In (b) ribosomal proteins cooperatively mitigate RNA instability by protecting it from misfolding and subsequent degradation. In both cases, higher protein content elevates protein synthesis costs and simultaneously lowers RNA turnover expenses, resulting in mixed RNA-protein ribosomes. Only scenario (b) aligns qualitatively with experimental data across varied growth conditions.

Our research provides fresh insights into ribosome biogenesis and evolution, paving the way for understanding protein-rich ribosomes in archaea and mitochondria.

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    Referee #3

    Evidence, reproducibility and clarity

    Summary

    In this manuscript, Széliová et al. used a simple self-replicating cell model to study why the ribosome consists of both RNA and protein from an economic point of view. Their base model predicts an RNA-only ribosome, which is not surprising since the smaller RNAP has a higher turnover number compared to the larger ribosome. When rRNA instability is included, the model predicts an "RNA+Protein" ribosome. In particular, the predicted ribosome composition is comparable to the measured ribosome composition when strong cooperative binding of ribosomal proteins to rRNA is considered. The authors conclude that the maximal growth rate is achieved by the real ribosome composition when rRNA instability is taken into account.

    Major comments:

    1. The authors modeled the rRNA degradation rate as a function of the concentration of fully assembled ribosomes (equation 5). However, only partially assembled ribosomes are susceptible to RNase, and they make up only a small fraction of total ribosomes. The majority of ribosomes are fully assembled. In addition, the turnover number obtained from Fazal et al. (2015) and used here is the degradation rate of double-stranded RNA, not the fully assembled ribosomes, which have a stable tertiary structure. In my opinion, the rRNA degradation rate should be modeled as a function of the concentration of partially assembled ribosomes (i.e., pre-R in Figure 7) rather than the concentration of fully assembled ribosomes.
    2. Compared to the work by Kostinski and Reuveni (2020), the authors have made an improvement by avoiding the use of constant ribosome allocation to ribosomal protein (Φ_rP^R) and RNAP (Φ_RNAP^R), allowing these parameters to vary with predicted growth rates (by changing 𝑥_rP). This is indeed important, as bacteria are very likely to adjust these parameters in response to different growth conditions. However, certain other growth rate-dependent parameters are still treated as constants (or treated as nutrient-specific parameters) across predicted growth rates under given conditions. For example, experiments have shown that the fraction of active RNAP (f_RNAP^act) and the ribosome elongation rate (k_R^el) are growth rate-dependent (Bremer and Dennis, 1996). In contrast, when the authors predict the maximum growth rate by changing 𝑥_rP, f_RNAP^act and k_R^el are held constant regardless of the predicted growth rates.
    3. If amino acids or nucleotides are provided in the media, the cell does not have to synthesize all of them de novo. However, the model assumes that the cell always synthesizes all amino acids or nucleotides de novo for growth on growth on amino acid-supplemented media or on LB. This problem could in principle be solved by assuming very fast kinetics of the metabolic reactions in these media, but that should be discussed in the manuscript. Furthermore, why does the turnover number for EAA depend on the growth rate while that of ENT is constant?
    4. All parameters related to transcription (RNAP) and translation (ribosome) used in this manuscript are adopted from Kostinski and Reuveni (2020), which are slightly modified based on Bremer and Dennis' research (1996, 2008). However, the authors changed some of the original parameters or data points, but did not provide explanations for these changes:

    (a) The original data depicted a growth rate-dependent translation elongation rate, but Table 2 presents it as a constant value.

    (b) Figure 2b displays five experimental data points, as opposed to the six data points in the original dataset and other figures in this manuscript.

    (c) The model does not consider the fraction of RNAP transcribing rRNA (Φ_rRNA^RNAP), except in Appendix Figure 4. In the original data (Bremer and Dennis 1996), the fraction of RNAP transcribing rRNA increases dramatically with growth rate; however, in this study, it remains constant at 1. Furthermore, Φ_rRNA^RNAP was first introduced in line 205 but was not explained until line 337. The value(s) of Φ_rRNA^RNAP for Appendix Figure 4 are also missing from this manuscript.

    1. How, exactly, is the unit of flux converted to mmol g-1 h-1?
    2. What is the (dry) mass constraint and how is it defined? In the manuscript, both the second equation in line 101 and the bottom row of Table 1 are dry mass constraint(s). Why are they different? Furthermore, why is the right-hand side of the second equation in line 101 a dimensionless 1, and how does the last row of Table 1 result in the unit of growth rate, time^(-1)?
    3. The concentrations of all components that serve as "substrates" will be zero when growth rate is maximized, as these molecules do not catalyze any reactions, nor do they influence reaction kinetics in the model. These "0" concentration components are C, AA, NT, rP, and rRNA. Why are these concentrations even included in the model?

    Minor comments:

    1. Questions regarding Figure 2:

    (a) The explanation of Figure 2a is unclear. Intuitively, I assumed that it was a comparison between model predictions and experimental data, with the points representing experimental data and the line representing predictions; and the authors wrote in the figure legend "The points represent maximum growth rates in six experimental conditions". However, the growth rates shown in the figure do not match the original experimental data. Are all the data in the figure predictions?

    (b) Figure 2b is difficult to understand. This figure shows the non-optimal solutions of the model. It is unclear how these solutions are achieved and why there are three lines in the figure.

    1. Table 1 is also difficult to understand. While the stoichiometric constraints can be easily derived, the capacity constraints and the dry mass constraint cannot be easily derived from related equations from the text.
    2. As the authors ask a question in the title, they should provide an explicit answer in the abstract.
    3. The authors should cite a seminal modeling paper, which was the first to examine resource allocation in simplified self-replicating cell systems (Molenaar et al. 2009, Molecular Systems Biology 5:323).
    4. The meaning of v is not consistently defined throughout the manuscript. It refers to the fluxes of enzymatic reactions in some instances, but in other contexts, it refers to the fluxes of the entire network of enzymatic reactions and protein synthesis reactions (Figure 1, Equation 1, and Line 386).
    5. Line 85, it might be difficult to interpret "RNAP fluxes" as the flux of rRNA synthesis without reading the subsequent text.
    6. Typo in line 102-103. "...protein fluxes 𝒘" → "...protein synthesis fluxes 𝒘".
    7. Line 104, f_RNAP^act and f_R^act are not explained in the text; and their biological significance cannot be understood from their names in Table 2 ("RNAP activity" and "Ribosome activity").
    8. Notion "**" in Table 2. The coupling between transcription and translation means the coupling of "mRNA" transcription and translation, not rRNA. At least in E. coli, the transcription rate of rRNA is faster than that of mRNA.
    9. Is the citation correct in line 136? I didn't find related information in Bremer and Dennis' paper after a quick scan.
    10. Lines 136-138. The statement is not accurate, as the fraction of inactive ribosomes increases with decreasing growth rate in E. coli (Dai et al. 2016, Nat Microbiol 2, 16231). If the studied growth rates are relatively high, it is acceptable to use a constant active ribosome fraction as an approximation, but this approximation should be made explicit.
    11. The citation in line 142 is not accurate. It should be (Bremer and Dennis, 1996).
    12. Lines 192-193: "six" different growth media, not five.
    13. Line 287: The statement "... translation rate does not increase in ribosomes with a higher protein content" could be misinterpreted as discussing translation elongation rate changes with different protein content in ribosomal protein mutant strains in a given species. It should be rephrased to remove ambiguity.
    14. Parameters for the three panels in Figure 8 are missing.

    Significance

    Strengths: Why the ribosome is composed of RNA and protein parts is a fundamental biological question. This manuscript proposes a very interesting hypothesis, arguing that the mixed ribosome composition results from rRNA instability. To test their hypothesis, the authors parameterize a simplified self-replicating cell model with realistic parameters. The model is first developed/parameterized for E. coli, and it could be easily adapted to other organisms with higher ribosomal protein content.

    Limitations: The main limitations of this manuscript lie in the development of the model, especially the modeling of rRNA degradation and the use of constant values for growth rate-dependent parameters.

    Advances: (1) This manuscript proposes a new hypothesis that rRNA instability is a universal factor that influences the ribosome composition across living organisms. (2) Compared to Kostinski and Reuveni's work, the authors have made certain improvements by including adjustable ribosome allocation to RNA and ribosomal protein when maximizing growth rate, which may lead to more realistic conclusions.

    Audience: This work will be of interest to people in the field of theoretical biology, computational biology, and evolution, as well as to researchers studying ribosome structure and function.

    Areas of expertise: Microbial systems biology, computational biology, and prokaryotic genomics.

  5. Version published to 10.1038/s42003-024-05815-4
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    Reply to the reviewers

    We would like to thank all reviewers for their careful evaluation of our manuscript and their thoughtful feedback, which we could use to improve its quality significantly.

    Reviewer #1 (Evidence, reproducibility and clarity):

    Summary: This study addresses the problem of what is the optimal ribosome composition in terms of relative RNA and protein content, to ensure optimal growth rate and minimal energy waste. The RNA-world hypothesis suggests that primitive ribosomes were RNA-only objects, and in fact this would appear to be very advantageous from an energetic point of view, since RNA synthesis requires a much lower energy expenditure than protein synthesis. Yet a large fraction of present-day ribosome mass is protein, ranging from 30% to nearly 70% depending on the organism. The authors hypothesize that one of the main functions of ribosomal proteins is to stabilize the RNA and to protect it against degradation. According to their idea, the fast degradation of a protein-free rRNA would offset the energetic advantage given by its cheaper synthesis. To test the hypothesis, they developed a mathematical model whereby to evaluate the optimal ribosome composition under a number of different conditions.

    Major comments: The paper is well-written and very readable. I am not an expert of mathematical modelling, so I cannot go into the details of the model presented. As a biologist, I can say that the conclusion arrived at are reasonable and well-justified.

    We thank the reviewer for the positive evaluation.

    Perhaps the point of view is rather narrow, since ribosomal proteins are known to be important not only for RNA protection and ribosome stability, but also to ensure the accuracy of decoding and, in certain contexts, to allow the ribosomes to interact with other cellular ligands. The authors make only very slight reference to these questions, so it would be worthwhile to further comment on them.

    Thank you for your suggestion. To address it, we expanded the discussion as follows:
    "Finally, we need to consider that ribosomal proteins may play other roles in the cells, especially in eukaryotic organisms. Ribosomal proteins participate in translation processes, for example, binding of translation factors, release of tRNA, and translocation. They may also affect the fidelity of translation (Nikolay et al., 2015). Furthermore, they play roles in various cellular processes such as cell proliferation, apoptosis, DNA repair, cell migration and others (Kisly and Tamm, 2023). These additional functions might have conferred evolutionary fitness advantages. Nevertheless, the primary role of ribosomal proteins seems to be stabilization and folding of rRNA (Nikolay et al., 2015; Kisly and Tamm, 2023)."

    _Furthermore, their explanation of why ribosome composition should be so different in different organisms (e.g. protein-poor bacterial ribosomes versus protein-rich archaeal ones) is not entirely convincing. For instance, they suggest that archaea may have protein-richer ribosomes than bacteria because they live in extreme environments, thus needing a further aid to stabilize the organelle. While this may be a factor, one must point out that non-extremophilic archaea (e.g. methanogens) have protein-rich ribosomes, making it obvious that other factors must be at play.
    _

    We appreciate the reviewer's feedback. Ribosome composition is indeed complex and influenced by various factors. While extreme environments (may) contribute to protein-rich ribosomes in archaea, it's important to note that not all archaea share this characteristic. Some, like Halobacteriales, Methanomicrobiales, and Methanobacteriales, have ribosomes with protein content similar to bacteria.

    Furthermore, there are species in both archaea and bacteria with low protein content in their ribosomes despite extreme habitats. This suggests that alternative strategies, possibly involving specific sequence variants in the rRNA (Nissley et al., 2023), play a role in stabilizing ribosomes. In our model, these findings would correspond to a decreased kdegmax. However, these sequence variants are not universal.

    Amils et al. (1993) suggest that protein-rich ribosomes in archaea are (more) ancient and proteins may have been lost in some species, possibly to favor higher growth rates (and in agreement with our theoretical analysis). An intriguing avenue for further research would be a phylogenetic analysis of archaeal evolution to investigate the emergence of different ribosome compositions.

    To address your concerns, we added the following paragraph to the discussion:
    "Additionally, some extremophilic organisms, such as the bacteria Chloroflexus aurantiacus or Fervidobacterium islandicum, exhibit ribosomes with lower protein content (approximately 40%) compared to extremophilic archaea (50%). It has been suggested that protein-rich ribosomes can be traced back to the oldest phylogenetic lineages, with some ribosomal proteins being lost over time (Amils et al., 1993; Acca et al., 1993). Organisms with lower protein content in their ribosomes may have evolved alternative strategies to thrive in extreme conditions. Examples of such strategies include the presence of specific rRNA sequence variants or base modifications, as recently discussed by Nissley et al. (2023).

    Moreover, certain archaeal species, such as those from Methanobacteriales or Halobacteriales, have transitioned to milder environmental conditions and subsequently shed unnecessary ribosomal proteins (Acca et al., 1993; Amils et al., 1993).

    To gain a comprehensive understanding of ribosome evolution in response to changing conditions, a thorough phylogenetic analysis is warranted. This analysis should be complemented by measurements of growth rate, translation rate, RNA degradation rate, among other parameters, to delineate the order of protein loss or gain, and the emergence of sequence variations and base modifications."

    Minor comments: none in particular. Referencing is adequate, text is clear and the figures are clear and well-organized.

    Thank you.

    Reviewer #1 (Significance):

    As I stated above, the main weakness of this study may be that it concentrates overwhelmingly on a single problem, i.e. the energetic cost of adding proteins to an RNA-only ancestral ribosome. On the other hand, this is a question seldom addressed when talking about ribosome composition, which indeed makes this paper valuable and interesting. The authors expand and advance a previous study of the same kind (to which they make ample reference).

    Although rather specialized, I think this paper, in its general conclusions, may be of interest to most of those working in the field of protein synthesis and ribosome evolution.

    Referee's keywords: archaea, ribosome evolution, translation, translation initiation

    Reviewer #2 (Evidence, reproducibility and clarity):

    The authors explore a mathematical model to rationalize the variable RNA content in ribosomes across species. The mathematical model particularly considers the idea that the protein-to-RNA ratio in ribosomes emerges as a consequence of faster rRNA than r-protein synthesis coupled with a faster degradation of rRNA. This is an interesting analysis. The idea is well explained and the math of the model is overall well explained. Overall, I thus support publication of this analysis.

    We thank the reviewer for the positive evaluation.

    However, while reading the manuscript I was continuously wondering about two major aspects which, I suggest, should be considered more prominently in the text:

    1. How clear is it that rRNA is more unstable than r-protein?
    2. Why should the translation rate (the speed with which ribosomes assemble new proteins) not be highly dependent on the ribosome-to-protein ratio (with some intermediate ratio ensuring efficient synthesis and efficient translation?

    Currently these points are considered briefly in the discussion part. I suggest that these points should at least be discussed more prominently in the introduction. I further appreciate any more detailed thoughts the authors have on these questions.

    Finally, I think the discussion section would benefit strongly from a more detailed consideration of possible future experiments. Which data is needed to probe the idea? What types of experiments could be performed to probe the model.

    We added a paragraph to the discussion with suggestions for experiments:
    "There are still many open questions about ribosome biogenesis and evolution. Our model could guide future experiments. There are a few studies that assessed the effect of individual rP deletions in E. coli, for example mutation in S10 increased RNA degradation (Kuwano et al., 1977), and mutation in L6 lead to disrupted ribosomal assembly (Shigeno et al., 2016). A systematic knock-out screen of all ribosomal proteins could be done (as in Shoji et al. (2011)), complemented with quantification of RNA degradation and misfolding.

    In case of extremophilic organisms with protein-rich ribosomes, temperature sensitivity could also be assessed. We would expect that deletion of the extra proteins would cause growth defects only at high temperatures.

    Furthermore, after removal of proteins from archaeal protein-rich ribosomes, laboratory evolution could be performed to see whether growth rate increases beyond wild-type.

    Comprehensive datasets, akin to the work of Bremer and Dennis in 2008 for E. coli, should be generated for non-standard organisms by measuring various parameters such as transcription and translation rates, ribosome and RNAP activities, and other relevant factors.

    Finally, as mentioned earlier, phylogenetic analysis or ribosome evolution across different species and environments could be done."

    More detailed comments:

    Regarding i: rRNA is pretty stable compared to other RNA types in the cell. The authors argue it is unstable. The specific question then seems to become how stable rRNA is compared to r-protein? Generally, proteins are also stable, but what data is available to support that r-proteins are more stable than rRNA?

    While rRNA that is already integrated into a ribosome is stable, nascent RNA may be susceptible to degradation (Jain, 2018). It has been observed that even during exponential growth, some rRNA is degraded (Gausing, 1997; Jain 2018) and the degradation rate increases if ribosome assembly is delayed (Jain, 2018). This suggests that rRNA that is synthesized in excess cannot be stored and used later. Furthermore, when rRNA is overexpressed in excess of rPs, it is rapidly degraded (half life 15-70 min) (Siehnel and Morgan, 1985).

    On the other hand, the turnover of proteins is negligible (Bremer and Dennis 2008), and most ribosomal proteins can exist in a free form without RNA. For example, under starvation/in stationary phase, rRNA is degraded, but most proteins are stable and can be reused later (Reier et al., 2022; Deutscher, 2003).

    The precise mechanisms of the rRNA instability are not clear. The simplest explanation is that rRNA that is not protected by rPs is attacked by RNases. Another option is that rRNA without proteins is difficult to fold and can get trapped in misfolded states. These are then degraded as a part of quality control. The model developed in this paper allows for both of these mechanisms.

    We added these references to the discussion:
    "In order to explain a mixed (RNA+protein) ribosome, we consider rRNA degradation in our extended model, thereby increasing the costs for RNA synthesis. While rRNA that is already integrated into a ribosome is stable, nascent RNA may be susceptible to degradation (Jain, 2018). Indeed, it has been experimentally observed that even at maximum growth rate, 10% of newly synthesized rRNA is degraded (Gausing, 1977), and the degradation rate increases if ribosome assembly is delayed (Jain, 2018). Furthermore, when rRNA is overexpressed in excess of rPs, it is rapidly degraded (Siehnel and Morgan, 1985). Due to the extremely high rates at which rRNA is synthesized, errors become inevitable, necessitating the action of quality control enzymes such as polynucleotide phosphorylase (PNPase) and RNase R to ensure ribosome integrity (Dos Santos et al., 2018). The absence of the RNases results in the accumulation of rRNA fragments, ultimately leading to cell death (Cheng and Deutscher, 2003; Jain, 2018).

    In contrast, protein turnover is negligible (Bremer & Dennis, 2008), and most ribosomal proteins can exist without rRNA and can be reused (Reier et al., 2022; Deutscher, 2003). Therefore, we do not consider protein degradation in our model."

    Regarding ii: Building on their model results, the authors rationalize the highly varying RNA-to-protein ratio in ribosomes across species. The model considers a non-varying rate with which ribosomes synthesize new proteins. This is briefly discussed in the discussion section. However, this appears to be a major assumption that, I think, should be stated clearly stated earlier in the text, including the abstract and introduction. Second, I wonder how the authors then rationalize variations in translation rate across species. Translation rates and the speeds with which ribosomes are varying strongly across species (indicated for example well by the change in the slope between ribosome content/rRNA and growth rate - slope in Fig. 2A). Why could the rRNA-to-protein ratio not be important in playing a role here?

    We decided not to consider the effect of rRNA/protein ratio in ribosomes on translation rate mainly because it is not clear in what way it affects it. Proteins are better catalysts than rRNA. Yet, eukaryotic ribosomes which have higher protein content, have lower translation rates. For archaea and mitochondria, we were not able to find data but it is unlikely that the translation rates are faster because the growth rates are not faster.

    We added a paragraph to the introduction that explains our assumption:
    "We focus on the primary role of ribosomal proteins, which is stabilizing rRNA (by preventing its degradation or misfolding).

    Ribosome protein content might also affect other parameters, such as translation rate. Proteins are generally better catalysts than RNA (Jeffares et al., 1998), but the ribosome's catalytic core is formed by rRNA (Tirumalai et al., 2021) and operates at a relatively slow catalytic rate compared to typical enzymes. This suggests that there is little evolutionary pressure to increase the catalytic rate. Furthermore, ribosomes with the lowest protein content, like the E. coli ribosome, exhibit the highest translation rates (Bonven and Gulløv, 1979; Hartl and Hayer-Hartl, 2009; Bremer and Dennis, 2008). Therefore, we do not consider the impact on translation rate in this study."

    And a sentence to the abstract:
    "In this study, we develop a (coarse-grained) mechanistic model of a self-fabricating cell and validate it under various growth conditions. Using resource balance analysis (RBA), we examine how the maximum growth rate varies with ribosome composition, assuming that all kinetic parameters remain independent of ribosome composition."

    More minor point, but I was also not sure about the justification that ribosome mass is constant (line 111). The mass of an amino acid and a nucleotide is quite different. Why should overall mass matter, and not for example the number of amino acids and proteins. I think it also would be good here to motivate the assumption better early on instead of commenting on it in the discussion section.

    Thank you for your suggestion. We agree with the reviewer that we should make our assumption of keeping the ribosome mass constant, which we used for simplicity, clearer from the beginning. Therefore, we have added the following statement to the introduction:
    "For simplicity, we assume a constant ribosome mass."

    Reviewer #2 (Significance):

    Protein synthesis by ribosomes is a major determinant of the rate with which microbes and other fast growing cells accumulate biomass. To better understand cell growth it is thus essential to better understand the makeup of ribosomes. Széliová et al present a mathematical model to entertain the idea that the varying RNA content in ribosomes across species is a consequence of RNA degradation. The model makes clear predictions which can guide future experiments.

    Reviewer #4 (Evidence, reproducibility and clarity):

    Summary

    In this manuscript, Széliová et al. used a simple self-replicating cell model to study why the ribosome consists of both RNA and protein from an economic point of view. Their base model predicts an RNA-only ribosome, which is not surprising since the smaller RNAP has a higher turnover number compared to the larger ribosome. When rRNA instability is included, the model predicts an "RNA+Protein" ribosome. In particular, the predicted ribosome composition is comparable to the measured ribosome composition when strong cooperative binding of ribosomal proteins to rRNA is considered. The authors conclude that the maximal growth rate is achieved by the real ribosome composition when rRNA instability is taken into account.

    Major comments:

    1. The authors modeled the rRNA degradation rate as a function of the concentration of fully assembled ribosomes (equation 5). However, only partially assembled ribosomes are susceptible to RNase, and they make up only a small fraction of total ribosomes. The majority of ribosomes are fully assembled. In addition, the turnover number obtained from Fazal et al. (2015) and used here is the degradation rate of double-stranded RNA, not the fully assembled ribosomes, which have a stable tertiary structure. In my opinion, the rRNA degradation rate should be modeled as a function of the concentration of partially assembled ribosomes (i.e., pre-R in Figure 7) rather than the concentration of fully assembled ribosomes.

    We agree with the reviewer that the way we model the process is not entirely biologically accurate. The problem is that even if we add the assembly intermediates, their concentration would be zero as they do not catalyze any reaction (similarly to the metabolites). Therefore, the degradation rate would also always be zero. Given the current modeling setup, the obvious proxy for the intracellular rRNA concentration is the rRNA concentration in the (assembled) ribosome, c_R*(1-x_rP).

    1. _Compared to the work by Kostinski and Reuveni (2020), the authors have made an improvement by avoiding the use of constant ribosome allocation to ribosomal protein (Φ_rP^R) and RNAP (Φ_RNAP^R), allowing these parameters to vary with predicted growth rates (by changing 𝑥_rP). This is indeed important, as bacteria are very likely to adjust these parameters in response to different growth conditions. However, certain other growth rate-dependent parameters are still treated as constants (or treated as nutrient-specific parameters) across predicted growth rates under given conditions. For example, experiments have shown that the fraction of active RNAP (f_RNAP^act) and the ribosome elongation rate (k_R^el) are growth rate-dependent (Bremer and Dennis, 1996). In contrast, when the authors predict the maximum growth rate by changing 𝑥rP, f_RNAP^act and k_R^el are held constant regardless of the predicted growth rates.

    The fraction of active RNAP (f_RNAP^act) was growth-rate dependent in all our simulations (see Table 2), only the fraction of active ribosomes (f_R^act) was kept constant according to Bremer and Dennis, 1996 & 2008.

    We decided to keep the elongation rate (k_R^el) constant similar to Scott et al. 2010 (their explanation is in the supplementary material “Correlation [1] and the control of ribosome synthesis”).

    We reran the simulations with variable k_R^el. It has no impact on the predictions of optimal ribosome composition. However, the linear dependence of RNA/protein ratio is less steep and predicts an offset at zero growth rate.

    We added the results to the supplementary material and the following text to the results section (for the base model):
    "…the base model correctly recovers the well-known linear dependence of the RNA to protein ratio and growth rate (Scott et al. 2010), see Figure 2a, but not the offset at zero growth rate, since our model does not contain any non-growth associated processes and we assume constant translation elongation rate kelR as in Scott et al. (2010). At low growth rate, kelR decreases, most likely because of the lower availability of the required substrates (Bremer and Dennis, 2008; Dai et al., 2016). Interestingly, when we use variable kelR, we observe a nonzero offset (Appendix 1, Figure 2)."

    and in a later section:
    "Using variable or constant kelR has no impact on the predicted optimal ribosome composition. As in the base model, variable kelR leads to predicted non-zero offset of RNA/protein ratio at zero growth rate (Appendix 1, Figure 6)."

    1. _If amino acids or nucleotides are provided in the media, the cell does not have to synthesize all of them de novo. However, the model assumes that the cell always synthesizes all amino acids or nucleotides de novo for growth on growth on amino acid-supplemented media or on LB. This problem could in principle be solved by assuming very fast kinetics of the metabolic reactions in these media, but that should be discussed in the manuscript. Furthermore, why does the turnover number for EAA depend on the growth rate while that of ENT is constant?
      _

    We focused on the “enzyme” EAA because it forms a significant fraction of the proteome. However, for consistency, we now also made ENT turnover number depend on growth rate. It made no significant impact on the simulation results.

    We agree with the reviewer that the model is currently very simplified and the enzymes ENT and EAA are used even in the media supplemented with AAs/NTs. However, these enzymes represent lumped pathways that aim to take into account not only AA/NT synthesis but also the different ‘nutrient efficiencies’ of the carbon sources (as in Scott et al. 2010). Therefore, to approximate these effects we increase the kcat of EAA (and now also ENT) with growth rate.

    We added a paragraph to the results section to explain these simplifications:
    "We used parameters from E. coli grown in six different media. Three of them are rich media (Gly+AA, Glc+AA, LB) where amino acids (and nucleotides) are provided so cells only have to express the corresponding transporters instead of the synthesis pathways. In our model, the enzymes ENT and EAA represent lumped pathways for glycolysis and nucleotide / amino acid synthesis, and we only consider one type of transporter. Therefore, to model the changing `nutrient quality' of the different media (inspired by Scott et al. 2010), we assume that turnover numbers of EAA and ENT increase with growth rate."

    1. All parameters related to transcription (RNAP) and translation (ribosome) used in this manuscript are adopted from Kostinski and Reuveni (2020), which are slightly modified based on Bremer and Dennis' research (1996, 2008). However, the authors changed some of the original parameters or data points, but did not provide explanations for these changes:

    (a) The original data depicted a growth rate-dependent translation elongation rate, but Table 2 presents it as a constant value.

    Please see the reply to point 2 above.

    (b) Figure 2b displays five experimental data points, as opposed to the six data points in the original dataset and other figures in this manuscript.

    The values for the transcription rate were taken from Bremer and Dennis’s paper from 1996 which only contains five growth rates. We updated the Figure 2b – it now displays data from Bremer and Dennis 2008 for six growth rates.

    _(c) The model does not consider the fraction of RNAP transcribing rRNA (ΦrRNA^RNAP), except in Appendix Figure 4. In the original data (Bremer and Dennis 1996), the fraction of RNAP transcribing rRNA increases dramatically with growth rate; however, in this study, it remains constant at 1.

    Our goal was to keep the model as simple as possible and keep the number of required parameters to a minimum. We only included the figure in the supplementary material because it does not change the conclusions, even though it makes the predictions quantitatively better. In the future we would like to achieve this improvement by expanding the model (with mRNA, tRNA, non-specific RNAP binding to DNA etc.). We added a sentence to the discussion to point out again how the results are affected if Φ_rRNA^RNAP is included, and how this parameter could be mechanistically included in the model in the future.

    "Furthermore, incorporating other types of RNA (mRNA, tRNA) and energy metabolism, or even constructing a genome-scale RBA model (Hu et al., 2020), will likely lead to more quantitative predictions of fluxes and growth rate. A strong indication of this is that including a variable RNAP allocation into the model leads to quantitatively better predictions (see Appendix 1, Figure 5). Therefore, in the future, we aim to model RNAP allocation mechanistically. This will involve for example adding other RNA species (mRNA, tRNA), and considering non-specifically bound RNAP which is a significant fraction of RNAP (Klumpp and Hwa, 2008)."

    _Furthermore, ΦrRNA^RNAP was first introduced in line 205 but was not explained until line 337.

    We added an explanation to the sentence in line 205:
    "If we consider RNAP allocation to rRNA (k_RNAP^el^bar = k_RNAP^el f_act^RNAP Φ_rRNA^RNAP, where Φ_rRNA^RNAP is the fraction of RNAP allocated to the synthesis of rRNA), the results get closer to the experimental data (Appendix 1, Figure 5)."

    _The value(s) of ΦrRNA^RNAP for Appendix Figure 4 are also missing from this manuscript.

    We added the missing values to the figure caption.

    1. How, exactly, is the unit of flux converted to mmol g-1 h-1?

    We are not exactly sure what the reviewer means by this question. As an example of unit conversion, we provide an explanation for the conversion of literature RNAP fluxes. The RNAP fluxes predicted by the model are in mmol g^-1 h^-1. The RNAP fluxes in Bremer and Dennis (2008) were in nt min^-1 cell^-1. To convert them to mmol g^-1 h^-1, we used the values of dry mass/cell from Bremer and Dennis (2008) and the number of nucleotides in rRNA (the stoichiometric coefficient n_rRNA). The code for the conversion is available on GitHub (https://github.com/diana-sz/RiboComp) in the script fluxes_vs_growth_rate.py.

    1. What is the (dry) mass constraint and how is it defined? In the manuscript, both the second equation in line 101 and the bottom row of Table 1 are dry mass constraint(s). Why are they different? Furthermore, why is the right-hand side of the second equation in line 101 a dimensionless 1, and how does the last row of Table 1 result in the unit of growth rate, time^(-1)?

    These are two forms of the same constraint. We added a paragraph to the methods section that explains how to convert the equations (capacity constraints, dry mass constraint) into the form in Table 1.

    In the first form of the equation, ⍵Tc = 1, the units of ⍵ are g/mmol, and the units of c are mmol/g, so they cancel out.

    The rows in Table 1 are multiplied by the vector of fluxes, so we get ⍵C [g/mmol] * vIC [mmol/gh] = μ [1/h].

    1. The concentrations of all components that serve as "substrates" will be zero when growth rate is maximized, as these molecules do not catalyze any reactions, nor do they influence reaction kinetics in the model. These "0" concentration components are C, AA, NT, rP, and rRNA. Why are these concentrations even included in the model?

    The reviewer is correct in pointing out that these species have zero concentrations at maximum growth, and it would be possible to simplify the model accordingly. However, we have chosen not to merge these reactions to maintain clarity in distinguishing between metabolic and macromolecular synthesis processes. Additionally, while we currently use the model to predict optimal behavior, it is not inherently limited to this purpose, as it can equally describe sub-optimal states (as in Figure 2b). Finally, if needed, we can easily introduce minimum concentration constraints (e.g. obtained from measurements) for any of these species without affecting our overall arguments.

    Minor comments:

    1. Questions regarding Figure 2:

    (a) The explanation of Figure 2a is unclear. Intuitively, I assumed that it was a comparison between model predictions and experimental data, with the points representing experimental data and the line representing predictions; and the authors wrote in the figure legend "The points represent maximum growth rates in six experimental conditions". However, the growth rates shown in the figure do not match the original experimental data. Are all the data in the figure predictions?

    Yes, the points are predictions and the line is a linear fit. We changed the figure caption as follows:
    "The model predicts a linear relationship between RNA to protein ratio and growth rate. The points represent the predicted maximum growth rates in six experimental conditions (Table 2). The line is a linear fit."

    (b) Figure 2b is difficult to understand. This figure shows the non-optimal solutions of the model. It is unclear how these solutions are achieved and why there are three lines in the figure.

    We expanded the figure caption to make it clearer:
    "Alternative RNAP fluxes at different non-optimal growth rates in glucose minimal medium. These are obtained by varying the growth rate step by step from zero to maximum and enumerating all solutions (elementary growth vectors as defined in Müller et al. (2022)) for each growth rate. The grey and blue lines are the alternative solutions. The blue line corresponds to solutions, where rRNA and ribosomes do not accumulate (constraints rRNA' andcap R' in Table 1 are limiting)."

    1. Table 1 is also difficult to understand. While the stoichiometric constraints can be easily derived, the capacity constraints and the dry mass constraint cannot be easily derived from related equations from the text.

    We added a paragraph into the methods section that explains how to convert the equations (capacity constraints, dry mass constraint) into matrix form.

    1. As the authors ask a question in the title, they should provide an explicit answer in the abstract.

    We added a sentence to the abstract:
    "Our model highlights the importance of RNA instability. If we neglect it, RNA synthesis is always ``cheaper' than protein synthesis, leading to an RNA-only ribosome at maximum growth rate. However, when we account for RNA turnover, we find that a mixed ribosome composed of RNA and proteins maximizes growth rate."

    1. The authors should cite a seminal modeling paper, which was the first to examine resource allocation in simplified self-replicating cell systems (Molenaar et al. 2009, Molecular Systems Biology 5:323).

    The citation was added.

    1. The meaning of v is not consistently defined throughout the manuscript. It refers to the fluxes of enzymatic reactions in some instances, but in other contexts, it refers to the fluxes of the entire network of enzymatic reactions and protein synthesis reactions (Figure 1, Equation 1, and Line 386).

    We have made the notation more consistent. When we refer to the fluxes of the entire network we now use v_tot instead of v.

    1. Line 85, it might be difficult to interpret "RNAP fluxes" as the flux of rRNA synthesis without reading the subsequent text.

    _We added the explanation in brackets.
    "_We validate the model by predicting RNAP fluxes (rRNA synthesis fluxes)."

    1. Typo in line 102-103. "...protein fluxes 𝒘" → "...protein synthesis fluxes 𝒘".

    Thank you for spotting that, we added the missing word.

    1. Line 104, f_RNAP^act and f_R^act are not explained in the text; and their biological significance cannot be understood from their names in Table 2 ("RNAP activity" and "Ribosome activity").

    We added a sentence that explains these parameters:
    "f_RNAP^act is the fraction of actively transcribing RNAPs, and f_R^act is the fraction of actively translating ribosomes."

    1. Notion "**" in Table 2. The coupling between transcription and translation means the coupling of "mRNA" transcription and translation, not rRNA. At least in E. coli, the transcription rate of rRNA is faster than that of mRNA.

    The transcription rate of the archaeal RNAP was determined in vitro. To our knowledge, data for transcription rates of rRNA vs. mRNA in vivo are not available. Therefore, the translation rate is only a very rough estimate.

    1. Is the citation correct in line 136? I didn't find related information in Bremer and Dennis' paper after a quick scan.

    We corrected the citation. Additionally, we added references that indicate that if rRNA is transcribed in excess of available r-proteins, it gets rapidly degraded:
    "In fact, the accumulation of free rRNA in a cell is biologically not realistic as it is bound by rPs already during transcription (Rodgers and Woodson, 2021). Furthermore, if rRNA is expressed in excess of rPs, it is rapidly degraded (Siehnel and Morgan, 1985)."

    1. Lines 136-138. The statement is not accurate, as the fraction of inactive ribosomes increases with decreasing growth rate in E. coli (Dai et al. 2016, Nat Microbiol 2, 16231). If the studied growth rates are relatively high, it is acceptable to use a constant active ribosome fraction as an approximation, but this approximation should be made explicit.

    We used the fractions of active ribosomes as reported in Bremer and Dennis, 2008 which are constant between growth rates of 0.4-2.1 1/h. In Dai et al. 2016, it was similarly observed that above the growth rate of ~0.5 1/h, the active fraction is quite constant. We rephrase the text to make it more accurate:
    "For the growth rates studied here (0.4-2.1 1/h), the fraction of inactive ribosomes stays roughly constant at 15-20% (Bremer and Dennis, 1996, 2008; Dai et al., 2016). In our model, we have already incorporated this fraction using the effective translation elongation rate (k_R^el^bar = k_R^el*f_R^act). However, below the growth rate of ~0.5 1/h, the fraction of active ribosomes rapidly decreases (Dai et al. 2016)."

    1. The citation in line 142 is not accurate. It should be (Bremer and Dennis, 1996).

    We corrected the citation.

    1. Lines 192-193: "six" different growth media, not five.

    Thank you for pointing that out, we corrected it.

    1. Line 287: The statement "... translation rate does not increase in ribosomes with a higher protein content" could be misinterpreted as discussing translation elongation rate changes with different protein content in ribosomal protein mutant strains in a given species. It should be rephrased to remove ambiguity.

    We rephrased the sentence as follows:
    "…translation rate does not increase in ribosomes from different species which have higher protein content."

    1. Parameters for the three panels in Figure 8 are missing.

    The parameters used for mitochondria are the same as for E. coli in glucose minimal media. The only difference is that a fraction of rPs can be imported. We added a sentence to the figure caption to clarify this:
    "The model can be adjusted to predict mitochondrial protein-rich ribosome composition. All parameters used for the simulation of mitochondria are the same as for E. coli in glucose minimal media, except a fraction of rPs can be imported for free from the cytoplasm and does not have to be synthesized. For simplicity, we assumed that 1/3 of rPs are imported. (In reality, almost all rPs are imported, but mitochondria make additional proteins to provide energy for the whole cell.)"

    Reviewer #4 (Significance):

    Strengths: Why the ribosome is composed of RNA and protein parts is a fundamental biological question. This manuscript proposes a very interesting hypothesis, arguing that the mixed ribosome composition results from rRNA instability. To test their hypothesis, the authors parameterize a simplified self-replicating cell model with realistic parameters. The model is first developed/parameterized for E. coli, and it could be easily adapted to other organisms with higher ribosomal protein content.

    Limitations: The main limitations of this manuscript lie in the development of the model, especially the modeling of rRNA degradation and the use of constant values for growth rate-dependent parameters.

    Advances: (1) This manuscript proposes a new hypothesis that rRNA instability is a universal factor that influences the ribosome composition across living organisms. (2) Compared to Kostinski and Reuveni's work, the authors have made certain improvements by including adjustable ribosome allocation to RNA and ribosomal protein when maximizing growth rate, which may lead to more realistic conclusions.

    Audience: This work will be of interest to people in the field of theoretical biology, computational biology, and evolution, as well as to researchers studying ribosome structure and function.

    Areas of expertise: Microbial systems biology, computational biology, and prokaryotic genomics.

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    Referee #4

    Evidence, reproducibility and clarity

    Summary

    In this manuscript, Széliová et al. used a simple self-replicating cell model to study why the ribosome consists of both RNA and protein from an economic point of view. Their base model predicts an RNA-only ribosome, which is not surprising since the smaller RNAP has a higher turnover number compared to the larger ribosome. When rRNA instability is included, the model predicts an "RNA+Protein" ribosome. In particular, the predicted ribosome composition is comparable to the measured ribosome composition when strong cooperative binding of ribosomal proteins to rRNA is considered. The authors conclude that the maximal growth rate is achieved by the real ribosome composition when rRNA instability is taken into account.

    Major comments:

    1. The authors modeled the rRNA degradation rate as a function of the concentration of fully assembled ribosomes (equation 5). However, only partially assembled ribosomes are susceptible to RNase, and they make up only a small fraction of total ribosomes. The majority of ribosomes are fully assembled. In addition, the turnover number obtained from Fazal et al. (2015) and used here is the degradation rate of double-stranded RNA, not the fully assembled ribosomes, which have a stable tertiary structure. In my opinion, the rRNA degradation rate should be modeled as a function of the concentration of partially assembled ribosomes (i.e., pre-R in Figure 7) rather than the concentration of fully assembled ribosomes.
    2. Compared to the work by Kostinski and Reuveni (2020), the authors have made an improvement by avoiding the use of constant ribosome allocation to ribosomal protein (Φ_rP^R) and RNAP (Φ_RNAP^R), allowing these parameters to vary with predicted growth rates (by changing 𝑥_rP). This is indeed important, as bacteria are very likely to adjust these parameters in response to different growth conditions. However, certain other growth rate-dependent parameters are still treated as constants (or treated as nutrient-specific parameters) across predicted growth rates under given conditions. For example, experiments have shown that the fraction of active RNAP (f_RNAP^act) and the ribosome elongation rate (k_R^el) are growth rate-dependent (Bremer and Dennis, 1996). In contrast, when the authors predict the maximum growth rate by changing 𝑥_rP, f_RNAP^act and k_R^el are held constant regardless of the predicted growth rates.
    3. If amino acids or nucleotides are provided in the media, the cell does not have to synthesize all of them de novo. However, the model assumes that the cell always synthesizes all amino acids or nucleotides de novo for growth on growth on amino acid-supplemented media or on LB. This problem could in principle be solved by assuming very fast kinetics of the metabolic reactions in these media, but that should be discussed in the manuscript. Furthermore, why does the turnover number for EAA depend on the growth rate while that of ENT is constant?
    4. All parameters related to transcription (RNAP) and translation (ribosome) used in this manuscript are adopted from Kostinski and Reuveni (2020), which are slightly modified based on Bremer and Dennis' research (1996, 2008). However, the authors changed some of the original parameters or data points, but did not provide explanations for these changes:

    (a) The original data depicted a growth rate-dependent translation elongation rate, but Table 2 presents it as a constant value.

    (b) Figure 2b displays five experimental data points, as opposed to the six data points in the original dataset and other figures in this manuscript.

    (c) The model does not consider the fraction of RNAP transcribing rRNA (Φ_rRNA^RNAP), except in Appendix Figure 4. In the original data (Bremer and Dennis 1996), the fraction of RNAP transcribing rRNA increases dramatically with growth rate; however, in this study, it remains constant at 1. Furthermore, Φ_rRNA^RNAP was first introduced in line 205 but was not explained until line 337. The value(s) of Φ_rRNA^RNAP for Appendix Figure 4 are also missing from this manuscript.

    1. How, exactly, is the unit of flux converted to mmol g-1 h-1?
    2. What is the (dry) mass constraint and how is it defined? In the manuscript, both the second equation in line 101 and the bottom row of Table 1 are dry mass constraint(s). Why are they different? Furthermore, why is the right-hand side of the second equation in line 101 a dimensionless 1, and how does the last row of Table 1 result in the unit of growth rate, time^(-1)?
    3. The concentrations of all components that serve as "substrates" will be zero when growth rate is maximized, as these molecules do not catalyze any reactions, nor do they influence reaction kinetics in the model. These "0" concentration components are C, AA, NT, rP, and rRNA. Why are these concentrations even included in the model?

    Minor comments:

    1. Questions regarding Figure 2:

    (a) The explanation of Figure 2a is unclear. Intuitively, I assumed that it was a comparison between model predictions and experimental data, with the points representing experimental data and the line representing predictions; and the authors wrote in the figure legend "The points represent maximum growth rates in six experimental conditions". However, the growth rates shown in the figure do not match the original experimental data. Are all the data in the figure predictions?

    (b) Figure 2b is difficult to understand. This figure shows the non-optimal solutions of the model. It is unclear how these solutions are achieved and why there are three lines in the figure.

    1. Table 1 is also difficult to understand. While the stoichiometric constraints can be easily derived, the capacity constraints and the dry mass constraint cannot be easily derived from related equations from the text.
    2. As the authors ask a question in the title, they should provide an explicit answer in the abstract.
    3. The authors should cite a seminal modeling paper, which was the first to examine resource allocation in simplified self-replicating cell systems (Molenaar et al. 2009, Molecular Systems Biology 5:323).
    4. The meaning of v is not consistently defined throughout the manuscript. It refers to the fluxes of enzymatic reactions in some instances, but in other contexts, it refers to the fluxes of the entire network of enzymatic reactions and protein synthesis reactions (Figure 1, Equation 1, and Line 386).
    5. Line 85, it might be difficult to interpret "RNAP fluxes" as the flux of rRNA synthesis without reading the subsequent text.
    6. Typo in line 102-103. "...protein fluxes 𝒘" → "...protein synthesis fluxes 𝒘".
    7. Line 104, f_RNAP^act and f_R^act are not explained in the text; and their biological significance cannot be understood from their names in Table 2 ("RNAP activity" and "Ribosome activity").
    8. Notion "**" in Table 2. The coupling between transcription and translation means the coupling of "mRNA" transcription and translation, not rRNA. At least in E. coli, the transcription rate of rRNA is faster than that of mRNA.
    9. Is the citation correct in line 136? I didn't find related information in Bremer and Dennis' paper after a quick scan.
    10. Lines 136-138. The statement is not accurate, as the fraction of inactive ribosomes increases with decreasing growth rate in E. coli (Dai et al. 2016, Nat Microbiol 2, 16231). If the studied growth rates are relatively high, it is acceptable to use a constant active ribosome fraction as an approximation, but this approximation should be made explicit.
    11. The citation in line 142 is not accurate. It should be (Bremer and Dennis, 1996).
    12. Lines 192-193: "six" different growth media, not five.
    13. Line 287: The statement "... translation rate does not increase in ribosomes with a higher protein content" could be misinterpreted as discussing translation elongation rate changes with different protein content in ribosomal protein mutant strains in a given species. It should be rephrased to remove ambiguity.
    14. Parameters for the three panels in Figure 8 are missing.

    Significance

    Strengths: Why the ribosome is composed of RNA and protein parts is a fundamental biological question. This manuscript proposes a very interesting hypothesis, arguing that the mixed ribosome composition results from rRNA instability. To test their hypothesis, the authors parameterize a simplified self-replicating cell model with realistic parameters. The model is first developed/parameterized for E. coli, and it could be easily adapted to other organisms with higher ribosomal protein content.

    Limitations: The main limitations of this manuscript lie in the development of the model, especially the modeling of rRNA degradation and the use of constant values for growth rate-dependent parameters.

    Advances: (1) This manuscript proposes a new hypothesis that rRNA instability is a universal factor that influences the ribosome composition across living organisms. (2) Compared to Kostinski and Reuveni's work, the authors have made certain improvements by including adjustable ribosome allocation to RNA and ribosomal protein when maximizing growth rate, which may lead to more realistic conclusions.

    Audience: This work will be of interest to people in the field of theoretical biology, computational biology, and evolution, as well as to researchers studying ribosome structure and function.

    Areas of expertise: Microbial systems biology, computational biology, and prokaryotic genomics.

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    Referee #2

    Evidence, reproducibility and clarity

    The authors explore a mathematical model to rationalize the variable RNA content in ribosomes across species. The mathematical model particularly considers the idea that the protein-to-RNA ratio in ribosomes emerges as a consequence of faster rRNA than r-protein synthesis coupled with a faster degradation of rRNA. This is an interesting analysis. The idea is well explained and the math of the model is overall well explained. Overall, I thus support publication of this analysis. However, while reading the manuscript I was continuously wondering about two major aspects which, I suggest, should be considered more prominently in the text:

    i. How clear is it that rRNA is more unstable than r-protein?

    ii. Why should the translation rate (the speed with which ribosomes assemble new proteins) not be highly dependent on the ribosome-to-protein ratio (with some intermediate ratio ensuring efficient synthesis and efficient translation?

    Currently these points are considered briefly in the discussion part. I suggest that these points should at least be discussed more prominently in the introduction. I further appreciate any more detailed thoughts the authors have on these questions. Finally, I think the discussion section would benefit strongly from a more detailed consideration of possible future experiments. Which data is needed to probe the idea? What types of experiments could be performed to probe the model.

    More detailed comments:

    Regarding i: rRNA is pretty stable compared to other RNA types in the cell. The authors argue it is unstable. The specific question then seems to become how stable rRNA is compared to r-protein? Generally, proteins are also stable, but what data is available to support that r-proteins are more stable than rRNA?

    Regarding ii: Building on their model results, the authors rationalize the highly varying RNA-to-protein ratio in ribosomes across species. The model considers a non-varying rate with which ribosomes synthesize new proteins. This is briefly discussed in the discussion section. However, this appears to be a major assumption that, I think, should be stated clearly stated earlier in the text, including the abstract and introduction. Second, I wonder how the authors then rationalize variations in translation rate across species. Translation rates and the speeds with which ribosomes are varying strongly across species (indicated for example well by the change in the slope between ribosome content/rRNA and growth rate - slope in Fig. 2A). Why could the rRNA-to-protein ratio not be important in playing a role here?

    More minor point, but I was also not sure about the justification that ribosome mass is constant (line 111). The mass of an amino acid and a nucleotide is quite different. Why should overall mass matter, and not for example the number of amino acids and proteins. I think it also would be good here to motivate the assumption better early on instead of commenting on it in the discussion section.

    Significance

    Protein synthesis by ribosomes is a major determinant of the rate with which microbes and other fast growing cells accumulate biomass. To better understand cell growth it is thus essential to better understand the makeup of ribosomes. Széliová et al present a mathematical model to entertain the idea that the varying RNA content in ribosomes across species is a consequence of RNA degradation. The model makes clear predictions which can guide future experiments.

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    Referee #1

    Evidence, reproducibility and clarity

    Summary: This study addresses the problem of what is the optimal ribosome composition in terms of relative RNA and protein content, to ensure optimal growth rate and minimal energy waste. The RNA-world hypothesis suggests that primitive ribosomes were RNA-only objects, and in fact this would appear to be very advantageous from an energetic point of view, since RNA synthesis requires a much lower energy expenditure than protein synthesis. Yet a large fraction of present-day ribosome mass is protein, ranging from 30% to nearly 70% depending on the organism. The authors hypothesize that one of the main functions of ribosomal proteins is to stabilize the RNA and to protect it against degradation. According to their idea, the fast degradation of a protein-free rRNA would offset the energetic advantage given by its cheaper synthesis. To test the hypothesis, they developed a mathematical model whereby to evaluate the optimal ribosome composition under a number of different conditions.

    Major comments: The paper is well-written and very readable. I am not an expert of mathematical modelling, so I cannot go into the details of the model presented. As a biologist, I can say that the conclusion arrived at are reasonable and well-justified. Perhaps the point of view is rather narrow, since ribosomal proteins are known to be important not only for RNA protection and ribosome stability, but also to ensure the accuracy of decoding and, in certain contexts, to allow the ribosomes to interact with other cellular ligands. The authors make only very slight reference to these questions, so it would be worthwhile to further comment on them.
    Furthermore, their explanation of why ribosome composition should be so different in different organisms (e.g. protein-poor bacterial ribosomes versus protein-rich archaeal ones) is not entirely convincing. For instance, they suggest that archaea may have protein-richer ribosomes than bacteria because they live in extreme environments, thus needing a further aid to stabilize the organelle. While this may be a factor, one must point out that non-extremophilic archaea (e.g. methanogens) have protein-rich ribosomes, making it obvious that other factors must be at play.

    Minor comments: none in particular. Referencing is adequate, text is clear and the figures are clear and well-organized.

    Significance

    As I stated above, the main weakness of this study may be that it concentrates overwhelmingly on a single problem, i.e. the energetic cost of adding proteins to an RNA-only ancestral ribosome. On the other hand, this is a question seldom addressed when talking about ribosome composition, which indeed makes this paper valuable and interesting. The authors expand and advance a previous study of the same kind (to which they make ample reference).

    Although rather specialized, I think this paper, in its general conclusions, may be of interest to most of those working in the field of protein synthesis and ribosome evolution.

    Referee's keywords: archaea, ribosome evolution, translation, translation initiation

  10. Version published to 10.1101/2023.07.07.548114v2 on bioRxiv
  11. Version published to 10.1101/2023.07.07.548114v1 on bioRxiv