Mathematical properties of optimal fluxes in cellular reaction networks at balanced growth

Dourado, Hugo; Liebermeister, Wolfram; Ebenhöh, Oliver; Lercher, Martin J.

doi:10.1371/journal.pcbi.1011156

Cited by 4 publications

(8 citation statements)

References 52 publications

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“…In the future, we aim to use growth balance analysis 53 , 54 . Growth balance analysis allows the integration of nonlinear kinetics, depending not only on catalyst concentrations but also on substrate concentrations.…”

Section: Discussionmentioning

confidence: 99%

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

Széliová,

Müller,

Zanghellini

2024

Commun Biol

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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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Section: Discussionmentioning

confidence: 99%

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

Széliová,

Müller,

Zanghellini

2024

Commun Biol

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“…Importantly, these states maintain a flux mismatch ⇢ i between metabolite in-and outflux at each metabolic step, reflecting the dilution of metabolites by growth (8,22,(30)(31)(32)(33). With the boundary condition j `= , we obtain a decreasing cascade of steady-state mass fluxes,…”

Section: Metabolic Modelmentioning

confidence: 99%

“…Environmental conditions and cell growth thus impose constraints from opposite ends of the metabolic cascade. Partially numerical solutions (30), specific properties of optimal solutions (8,22), as well as an analytical solution of a pathway with two enzymes (33) were studied previously. Here, starting from the two-enzyme system, we iteratively construct optimal balanced growth states of longer pathways by adding a substrate-enzyme pair to the front end (SI, Fig.…”

Section: Metabolic Modelmentioning

confidence: 99%

“…We consider multi-component metabolic pathways that produce and consume intermediate metabolites, and we compute the state of the cell generating maximal growth under the constraint of mass conservation in a population of replicating cells. This is a step towards an analytical solution of optimal states in large metabolic networks, including realistic non-linear kinetics, which has so far remained elusive (21,22). The model predicts broad patterns describing how fluxes, protein expression, and steady-state metabolite concentrations depend on an enzyme's position in the network and on the nutrient environment.…”

Section: Introductionmentioning

confidence: 99%

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Resource allocation in biochemically structured metabolic networks

Seeger,

Pinheiro,

Lässig

2024

Preprint

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Microbes tune their metabolism to environmental challenges by changing protein expression levels, metabolite concentrations, and reaction rates simultaneously. Here, we establish an analytical model for microbial resource allocation that integrates enzyme biochemistry and the global architecture of metabolic networks. We describe the production of protein biomass from external nutrients in pathways of Michaelis-Menten enzymes and compute the resource allocation that maximizes growth under constraints of mass conservation and metabolite dilution by cell growth. This model predicts generic patterns of growth-dependent microbial resource allocation to proteome and metabolome. In a nutrient-rich medium, optimal protein expression depends primarily on the biochemistry of individual synthesis steps, while metabolite concentrations and fluxes decrease along successive reactions in a metabolic pathway. Under nutrient limitation, individual protein expression levels change linearly with growth rate, the direction of change depending again on the enzyme's biochemistry. Metabolite levels and fluxes show a stronger, nonlinear decline with growth rate. We identify a simple, metabolite-based regulatory logic by which cells can be tuned to near-optimal growth. Finally, our model predicts evolutionary stable states of metabolic networks, including local biochemical parameters and the global metabolite mass fraction, in tune with empirical data.

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“…k cat is a central parameter for quantitative studies of enzymatic activities, and is of key importance for understanding cellular metabolism, physiology, and resource allocation. In particular, comprehensive sets of k cat values are essential for metabolic models that consider the cost of producing or maintaining enzymes 1 – 9 , a prerequisite for accurate simulations of cellular physiology and growth 10 . Currently, no high-throughput experimental assays exist for k cat , and experiments are both time consuming and expensive.…”

Section: Introductionmentioning

confidence: 99%

Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning

Kroll

Rousset

et al. 2023

Nat Commun

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The turnover number kcat, a measure of enzyme efficiency, is central to understanding cellular physiology and resource allocation. As experimental kcat estimates are unavailable for the vast majority of enzymatic reactions, the development of accurate computational prediction methods is highly desirable. However, existing machine learning models are limited to a single, well-studied organism, or they provide inaccurate predictions except for enzymes that are highly similar to proteins in the training set. Here, we present TurNuP, a general and organism-independent model that successfully predicts turnover numbers for natural reactions of wild-type enzymes. We constructed model inputs by representing complete chemical reactions through differential reaction fingerprints and by representing enzymes through a modified and re-trained Transformer Network model for protein sequences. TurNuP outperforms previous models and generalizes well even to enzymes that are not similar to proteins in the training set. Parameterizing metabolic models with TurNuP-predicted kcat values leads to improved proteome allocation predictions. To provide a powerful and convenient tool for the study of molecular biochemistry and physiology, we implemented a TurNuP web server.

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Mathematical properties of optimal fluxes in cellular reaction networks at balanced growth

Cited by 4 publications

References 52 publications

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

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

Resource allocation in biochemically structured metabolic networks

Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning

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