Enzymes and Substrates Are Balanced at Minimal Combined Mass Concentration<i>in vivo</i>

Dourado, Hugo; Maurino, Veronica G; Lercher, Martin J.

doi:10.1101/128009

Cited by 14 publications

(19 citation statements)

References 54 publications

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“…To ensure optimal metabolic 38 efficiency, gene regulation has to balance available resources appropriately. Modern methods of 39 modeling metabolism rely strongly on the assumption of metabolic optimality under physico-chemical 40 constraints (Oberhardt et al, 2009; de Oliveira Dal'Molin et al., 2010;Dourado et al, 2017). Accordingly, 41 resource allocation and its constraints are under intense investigation, although these studies are mostly 42 restricted to unicellular organisms.…”

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confidence: 99%

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution

Sundermann

Lercher

Heckmann

2018

Preprint

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Summary-The regulation of resource allocation in biological systems observed today is the cumulative result of natural selection in ancestral and recent environments. To what extent are observed resource allocation patterns in different photosynthetic types optimally adapted to current conditions, and to what extend do they reflect ancestral environments? Here, we explore these questions for C3, C4, and C3-C4 intermediate plants of the model genus Flaveria.-We developed a detailed mathematical model of carbon fixation, which accounts for various environmental parameters and for energy and nitrogen partitioning across photosynthetic components. This allows us to assess environment-dependent plant physiology and performance as a function of resource allocation patterns.-To achieve maximal CO2 fixation rates under growth conditions differing from those experienced during their evolution, C4 species need to re-allocate significantly more nitrogen between photosynthetic components than their C3 relatives. As this is linked to a limited phenotypic plasticity, observed resource distributions in C4 plants still reflect optimality in ancestral environments, allowing their quantitative inference.-Our work allows us to quantify environmental effects on resource allocation and performance of photosynthetic organisms. This understanding paves the way for interpreting present photosynthetic physiology in the light of evolutionary history.

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confidence: 99%

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution

Sundermann

Lercher

Heckmann

2018

Preprint

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“…A similar minimization of the density with respect to the reactants, keeping the reaction flux fixed, was used to analyze metabolic reactions in isolation. 19 Differently from ref. 18, in this case the objective function received contributions from the densities of both the enzyme and its substrates.…”

Section: Introductionmentioning

confidence: 87%

“…Substituting α from (19) in the metabolic part of the balanced-growth equalities (15), the latter can be written as…”

Section: Balanced-growth Equalities Of the Metabolitesmentioning

confidence: 99%

“…While we and others 21,[26][27][28][29][31][32][33]72,73 have selected to maximize the growth rate of the model at a fixed density (either ρ dry or ρ macro ), some studies minimize the total enzyme density at a fixed output flux (e.g., the flux through the "ribosome" in the case of growth). 19,20,75 In Fig 8, the optimization studied in the current paper is depicted as being at the top of a hierarchy of possible optimization problems that are reached after one or two simplifying assumptions. The scheme we examined is in the rectangle at Level 0.…”

Section: B Relation To Other Formulationsmentioning

confidence: 99%

“…This relationship was demonstrated to hold, without any fitting parameter, for the enzyme-substrate pairs of reactions that are the dominant sink of their substrates, and which thus could legitimately be treated as being approximately isolated. 19 The minimization of the total enzyme mass density at a fixed reaction flux (i.e., fixed growth rate) had also been studied for general metabolic networks in refs. 20 and 21, where the optimal solutions were shown to be elementary flux modes.…”

Section: Introductionmentioning

confidence: 99%

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Structure of autosynthetic models of balanced cell growth and numerical optimization of their growth rate

Sezer

Schubert

Lercher

2020

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Genome-scale reaction network models are available for many prokaryotic organisms. Yet, to predict the proteome and metabolome of the cell from them, additional information about (i) the nonlinear enzyme kinetics and (ii) the regulation of protein expression by metabolic signals is necessary. Knowledge about the latter could be sidestepped by assuming that expression regulation has evolved to achieve the protein composition that maximizes cellular growth rate. A general mathematical framework for optimizing the growth rate of models comprising an arbitrarily complex metabolic network and a relatively simple protein-synthesis network was recently formulated independently by two research groups [de Groot et al., PLoS Comput. Biol. 16, e1007559 (2020); Dourado & Lercher, Nature Commun. 11, 1226 (2020)]. Here, this formalism is further developed with particular focus on carrying out the optimization numerically. To this end, we identify the concentrations of the enzymes as the independent variables of the optimization problem and propose novel multiplicative updates for the iterative calculation of the dependent metabolite concentrations. The reduced gradient method, with analytical derivatives, is employed for the numerical optimization. Additionally, the roles of the dilution of the metabolite concentrations by growth and the commonly invoked constraint on the cell dry mass density are clarified. These developments should lay the basis for the practical optimization of large-scale kinetic models, thus formally connecting the physiological “macrostate” of the cell, characterized by its growth rate, to its “microstate”, described by the cell proteome and metabolome.Author summaryAn evolving population of non-interacting, unicellular organisms in a constant environment will maximize its growth rate. By expressing the growth rate as a mathematical function of the cellular composition, it becomes possible to formulate an optimization problem whose solution yields the cell proteome and metabolome at the maximal growth rate. The formulation and solution of such an optimization problem has the potential to elucidate fundamental optimality principles in living cells and to enable the engineering of complex biological systems. Building on previous work, here we address the task of solving this optimization problem numerically. In the process, we elucidate the mathematical role of some common simplifying approximations. This allows us to organize many of the existing formulations of the optimization problem into a hierarchy, whose lower levels are reached by invoking these approximations.

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An analytical theory of balanced cellular growth

2020

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The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.

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Enzymes and Substrates Are Balanced at Minimal Combined Mass Concentrationin vivo

Abstract: The corresponding organizing principle -the minimization of the summed mass concentrations of solutes -may facilitate reducing the complexity of kinetic models and will contribute to the design of more efficient synthetic cellular systems.peer-reviewed)

Cited by 14 publications

References 54 publications

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution

Structure of autosynthetic models of balanced cell growth and numerical optimization of their growth rate

An analytical theory of balanced cellular growth

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Enzymes and Substrates Are Balanced at Minimal Combined Mass Concentrationin vivo

Abstract: The corresponding organizing principle -the minimization of the summed mass concentrations of solutes -may facilitate reducing the complexity of kinetic models and will contribute to the design of more efficient synthetic cellular systems.peer-reviewed)

Cited by 14 publications

References 54 publications

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C4 Plants and Infers Environments of C4 Photosynthesis Evolution

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C4 Plants and Infers Environments of C4 Photosynthesis Evolution

Structure of autosynthetic models of balanced cell growth and numerical optimization of their growth rate

An analytical theory of balanced cellular growth

Contact Info

Product

Resources

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Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution

Modeling Cellular Resource Allocation Reveals Low Phenotypic Plasticity of C₄ Plants and Infers Environments of C₄ Photosynthesis Evolution