Bridging ribosomal synthesis to cell growth through the lens of kinetics

doi:10.1016/j.bpj.2022.12.028

. 2023 Feb 7;122(3):544-553.

doi: 10.1016/j.bpj.2022.12.028. Epub 2022 Dec 22.

Bridging ribosomal synthesis to cell growth through the lens of kinetics

Luan Quang Le¹, Kaicheng Zhu², Haibin Su³

Affiliations

¹ School of Materials Science and Engineering, Nanyang Technological University, Singapore, Singapore; Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
² Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
³ Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China; Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. Electronic address: haibinsu@ust.hk.

PMID: 36564946
PMCID: PMC9941725
DOI: 10.1016/j.bpj.2022.12.028

Bridging ribosomal synthesis to cell growth through the lens of kinetics

Luan Quang Le et al. Biophys J. 2023.

. 2023 Feb 7;122(3):544-553.

doi: 10.1016/j.bpj.2022.12.028. Epub 2022 Dec 22.

Authors

Luan Quang Le¹, Kaicheng Zhu², Haibin Su³

Affiliations

¹ School of Materials Science and Engineering, Nanyang Technological University, Singapore, Singapore; Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
² Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China.
³ Department of Chemistry, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China; Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. Electronic address: haibinsu@ust.hk.

PMID: 36564946
PMCID: PMC9941725
DOI: 10.1016/j.bpj.2022.12.028

Abstract

Understanding prokaryotic cell growth requires a multiscale modeling framework from the kinetics perspective. The detailed kinetics pathway of ribosomes exhibits features beyond the scope of the classical Hopfield kinetics model. The complexity of the molecular responses to various nutrient conditions poses additional challenge to elucidate the cell growth. Herein, a kinetics framework is developed to bridge ribosomal synthesis to cell growth. For the ribosomal synthesis kinetics, the competitive binding between cognate and near-cognate tRNAs for ribosomes can be modulated by Mg²⁺. This results in distinct patterns of the speed - accuracy relation comprising "trade-off" and "competition" regimes. Furthermore, the cell growth rate is optimized by varying the characteristics of ribosomal synthesis through cellular responses to different nutrient conditions. In this scenario, cellular responses to nutrient conditions manifest by two quadratic scaling relations: one for nutrient flux versus cell mass, the other for ribosomal number versus growth rate. Both are in quantitative agreement with experimental measurements.

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Conflict of interest statement

Declaration of interests The authors declare no competing financial interests.

Figures

**Figure 1**
The generalized Hopfield model (GHM) of ribosomal protein synthesis. (a) Three states are: free ribosomes ( $R_{f r e e}$ ), GTPase activation at initial selection $(R_{A c t})$ , and proofreading $(R_{PR})$ comprising peptide formation and rejection. Arrow thickness reflects the magnitude of rate constants depending on cognates or near-cognates. (b) The partition of ribosomes in three states at various $[{Mg}^{2 +}]$ is dominated by $R_{f r e e}$ (*white*), $R_{P R^{c}}$ for cognates (*green*), and $R_{P R^{n c}}$ for near-cognates (*brown*). (c) The relation among $k_{s y n}^{e f f}$ , accuracy, and $[{Mg}^{2 +}]$ . The magenta and blue dots indicate the maximum value of $k_{s y n}^{e f f}$ . To see this figure in color, go online.

**Figure 2**
Cellular characteristics by the bacterial growth model (BGM). (a) The schematic illustration of BGM (b) The characteristics of ribosomal synthesis in terms of protein synthesis speed $k_{s y n e f f}^{c e l l}$ -accuracy relation (at $[T_{3}] = 100 μ M$ ). Experimental data are from refs. and . (c) $[{Mg}^{2 +}]$ regulated optimal cell growth rate under different nutrient conditions. The optimal growth rates $λ^{*}$ as *large, solid dots*. (d) The quadratic scaling between number of ribosomes per cell $R^{*}$ and optimal growth rate $λ^{*}$ with the experimental data of *E. coli* (1,42). The inset shows a linear relation between $λ^{*}$ and ribosomal mass fraction $φ_{R}^{*}$ with the experimental data of *E. coli* (3,29,31). (e) The quadratic scaling between intake flux $J_{M}^{*}$ and cell mass $M^{*}$ with the experimental data of *E. coli* (1,30,42). The *right inset* shows metabolic fluxes of different bacteria species (43). The linear $M^{*} - λ^{*}$ relation is shown in the *left inset*. To see this figure in color, go online.

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References

1. Bremer H., Dennis P. Modulation of chemical composition and other parameters of the cell at different exponential growth rates. EcoSal Plus. 2008;3 doi: 10.1128/ecosal.5.2.3. - DOI - PubMed
1. Dalbow D.G., Young R. Synthesis time of β-galactosidase in Escherichia coli B/r as a function of growth rate. Biochem. J. 1975;150:13–20. - PMC - PubMed
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[1] Bremer H., Dennis P. Modulation of chemical composition and other parameters of the cell at different exponential growth rates. EcoSal Plus. 2008;3 doi: 10.1128/ecosal.5.2.3. - DOI - PubMed

[2] Bremer H., Dennis P. Modulation of chemical composition and other parameters of the cell at different exponential growth rates. EcoSal Plus. 2008;3 doi: 10.1128/ecosal.5.2.3. - DOI - PubMed

[3] Dalbow D.G., Young R. Synthesis time of β-galactosidase in Escherichia coli B/r as a function of growth rate. Biochem. J. 1975;150:13–20. - PMC - PubMed

[4] Dalbow D.G., Young R. Synthesis time of β-galactosidase in Escherichia coli B/r as a function of growth rate. Biochem. J. 1975;150:13–20. - PMC - PubMed

[5] Forchhammer J., Lindahl L. Growth rate of polypeptide chains as a function of the cell growth rate in a mutant of Escherichia coli 15. J. Mol. Biol. 1971;55:563–568. - PubMed

[6] Forchhammer J., Lindahl L. Growth rate of polypeptide chains as a function of the cell growth rate in a mutant of Escherichia coli 15. J. Mol. Biol. 1971;55:563–568. - PubMed

[7] Reynolds N.M., Lazazzera B.A., Ibba M. Cellular mechanisms that control mistranslation. Nat. Rev. Microbiol. 2010;8:849–856. - PubMed

[8] Reynolds N.M., Lazazzera B.A., Ibba M. Cellular mechanisms that control mistranslation. Nat. Rev. Microbiol. 2010;8:849–856. - PubMed

[9] Parker J. Errors and alternatives in reading the universal genetic code. Microbiol. Rev. 1989;53:273–298. - PMC - PubMed

[10] Parker J. Errors and alternatives in reading the universal genetic code. Microbiol. Rev. 1989;53:273–298. - PMC - PubMed

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Bridging ribosomal synthesis to cell growth through the lens of kinetics

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Bridging ribosomal synthesis to cell growth through the lens of kinetics

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