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# Ribosomes are optimized for autocatalytic production

## Abstract

Many fine-scale features of ribosomes have been explained in terms of function, revealing a molecular machine that is optimized for error-correction, speed and control. Here we demonstrate mathematically that many less well understood, larger-scale features of ribosomes—such as why a few ribosomal RNA molecules dominate the mass and why the ribosomal protein content is divided into 55–80 small, similarly sized segments—speed up their autocatalytic production.

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## Acknowledgements

S.R. was supported by a James S. McDonnell Foundation fellowship. S.R. and J.P. were supported by NSF-DMS grant PD127334 and NIH grant R01GM095784. J.P. and M.E. were supported by HFSP grant RGP0042 and M.E. was further supported by the Swedish Research Council and the Wallenberg Foundation (RiboCORE). We are grateful to R. Ward, A. Hilfinger, R. Milo, R. Jajoo and M. Landon for discussions.

## Author information

Authors

### Contributions

S.R. and J.P. conceived the work, derived results and wrote the paper. M.E. contributed extensive advice and ideas.

### Corresponding author

Correspondence to Johan Paulsson.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

Reviewer Information Nature thanks I. Golding, M. Oeffinger, S. Klumpp and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Figure 1 Stochastic production of individual r-proteins may not substantially limit efficiency in ribosome biogenesis.

a, Schematic of the way in which stochastic gene expression creates temporary shortages of some r-proteins and surpluses of others. The number of complete ribosomes assembled is then limited by the r-protein that is present in lowest abundance, and the average value of the difference between the minimum and the mean 〈Δ〉 is the mean number of unmatched r-proteins. b, The relative mean free r-protein pool (from a) increases very slowly with the number of ribosomal proteins n. For illustrative purposes we used negative binomial distributions with mean μ and different variances σ2 (Supplementary Information), because this distribution has been observed and predicted in many studies of stochastic gene expression. The inset shows a curve collapse for . We obtained similar results for more complete kinetic models. c, The fraction of the r-protein mass in the form of nascent peptides or free pools arising from noisy expression (assuming Poisson noise for simplicity, but with similar results for many other noise models). There is technically an optimal number of r-proteins nopt, but the curves around and above this value are very shallow, meaning that there is practically no upper limit.

### Extended Data Figure 2 The r-proteins are statistical outliers in terms of size compared to the rest of the genome.

a, Distribution of the average protein length in 106 random samples of 56 proteins taken from the genome of E. coli; the mean length of a protein in the bacterial ribosome is also marked (inset ribosome with arrow). The probability of generating an average protein length as small as that seen in the bacterial ribosome is vanishingly small (at most 10−17). b, The Chernoff upper bound (Supplementary Information) on the probability that the average length of r-proteins could arise at random, that is, with no size selection, is computed for: 104 archaea (orange), 1,248 bacteria (blue) and 74 eukarya (green). The value for E. coli is 10−17 (see a); vanishingly small probabilities are attributed to all organisms that we examined.

### Extended Data Figure 3 The r-proteins are unusually similar to each other in size even when conditioning on the average size.

Cumulative frequency of for randomly generated protein complexes of varying numbers of proteins is shown. See Supplementary Information for details. a, b, Only complexes in which the average protein length is identical (±5 amino acids) to that seen in the ribosomes of E. coli (a) and S. cerevisiae (b) entered the statistics. As the number of proteins in a complex gradually increases from 2 to the number of proteins in the ribosome—55 in E. coli (protein S1 was excluded; see main text) and 79 in S. cerevisiae—the occurrence of coefficients of variation (CVL) as low as those seen for the set of r-proteins becomes extremely rare.

### Extended Data Figure 4 Differences between different types of ribosomes are qualitatively as expected from considering efficiency in their biogenesis.

Bacterial ribosomes contain about 55 r-proteins (blue) that average about 130 amino acids and make up 30%–35% of the ribosome mass. Eukaryotic ribosomes contain about 80 r-proteins (blue) that average about 165 amino acids and make up about 45% of the ribosome mass. In both these cases, ribosomes catalyse their own production. By contrast, in mitochondrial ribosomes, which do not produce themselves, rRNA (grey) is more scarce and r-proteins are much larger, making up as much as 80% of the ribosome mass.

## Supplementary information

### Supplementary Information

This file contains Supplementary Text and Data – see contents page for details. (PDF 420 kb)

### Supplementary Data

This file contains a list of proteomes. (XLSX 26 kb)

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Reuveni, S., Ehrenberg, M. & Paulsson, J. Ribosomes are optimized for autocatalytic production. Nature 547, 293–297 (2017). https://doi.org/10.1038/nature22998

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• DOI: https://doi.org/10.1038/nature22998

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