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Wrote the paper: RA TS. Conceived and designed the computational analysis: RA RM TS. Performed the computational analysis: RA. Performed the in-vivo experiments: BV MH.

The authors have declared that no competing interests exist.

Identifying the factors that determine microbial growth rate under various environmental and genetic conditions is a major challenge of systems biology. While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, including maximal biomass yield, the prediction of actual growth rate is a long standing goal. This gap stems from strictly relying on data regarding reaction stoichiometry and directionality, without accounting for enzyme kinetic considerations. Here we present a novel metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts metabolic flux rate and growth rate by utilizing prior data on enzyme turnover rates and enzyme molecular weights, without requiring measurements of nutrient uptake rates. The method is based on an identified design principle of metabolism in which enzymes catalyzing high flux reactions across different media tend to be more efficient in terms of having higher turnover numbers. Extending upon previous attempts to utilize kinetic data in genome-scale metabolic modeling, our approach takes into account the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, considering isozymes, protein complexes, and multi-functional enzymes. MOMENT is shown to significantly improve the prediction accuracy of various metabolic phenotypes in

While current genome-scale metabolic modeling approaches enable us to successfully predict a variety of metabolic phenotypes, identifying the factors that determine microbial growth rate and the prediction of growth rates under various conditions is still an open challenge. Here we present a metabolic network-based approach, MetabOlic Modeling with ENzyme kineTics (MOMENT), which predicts growth rates by integrating standard stoichiometric modeling with prior data on enzyme turnover rates and enzyme molecular weights, considering a physiological bound on total enzymes' concentration. The method is based on a finding that enzymes catalyzing high flux reactions tend to be more efficient in terms of having higher turnover numbers. MOMENT predicts growth rates of

Traditional metabolic modeling techniques involve the reconstruction of kinetic models based on detailed knowledge on enzyme kinetic parameters for all enzymes in a certain system

Flux Balance Analysis (FBA) is a commonly used CBM approach that enables to predict biomass production yield (in units of gram biomass/gram nutrient) based solely on reactions' stoichiometry and directionality (i.e. without measurements of nutrient uptake rates). Given information only on reactions' stoichiometry and directionality, the prediction of biomass yield works by searching for a feasible flux distribution with maximal flux through the biomass production reaction, considering an arbitrary upper bound on the uptake rate of the carbon nutrient. The maximal biomass production rate predicted by FBA reflects optimal yield metabolism and is equal to the assumed uptake rate multiplied by maximal biomass yield. The prediction of actual growth rate by FBA is theoretically possible when experimental measurement of nutrient uptake rates is available and is used to constrain the uptake flux in the model (or alternatively, by multiplying FBA-predicted biomass yield with the measured uptake rates). However, experimental studies have shown that microorganisms exhibit non optimal-yield metabolism under various conditions, for example, in the case of over-flow metabolism where excess nutrient uptake is metabolized inefficiently

FBA with Molecular Crowding (FBAwMC) is a recently developed extension of FBA which was shown to enable the prediction of growth rates of

In this paper, we present a method, MetabOlic Modeling with ENzyme kineTics (MOMENT), for predicting metabolic fluxes and growth rates by accounting for the maximal cellular capacity for metabolic enzymes without the requirement of experimentally determined uptake rates. Extending upon FBAwMC, MOMENT accurately quantifies the enzyme concentrations required for catalyzing each metabolic reaction based on known kinetic constants, accounting for isozymes, protein complexes and multi-functional enzymes. MOMENT is shown to predict growth rates for

An enzyme turnover number is defined as the maximal number of molecules of substrate that the enzyme can convert to product per catalytic site per unit of time. We extracted enzyme turnover numbers for 251 reactions from BRENDA

When comparing the enzyme kinetic parameters in

(A) Correlations of enzyme turnover numbers, enzyme molecular weights, gene expression levels, and combinations of the latter via a linear regression model with measured metabolic flux rates. Measured flux rates in _{10} scale). Linear regression line in red.

Enzyme molecular weights were computed based on genomic sequences, extracted from KEGG

While enzyme kinetic parameters are scarcely used in genome-scale metabolic modeling approaches, gene expression data is commonly utilized as the basis for metabolic flux prediction

Having shown that enzyme turnover numbers are significantly correlated with measured flux rates under glucose minimal media, we set to examine the correlation between enzyme turnover numbers and flux rates under a diverse set of growth media. Towards this end, we applied FBA to predict likely flux distributions under a set of media (listed in the

(A) Histogram of Pearson correlations between enzyme turnover numbers and predicted flux rates under different single carbon and energy source media (in blue). The Pearson correlation between enzyme turnover numbers and the averaged flux distribution across conditions (in green) is shown to be markedly higher than those obtained under the different media. (B) Pearson correlations between enzyme turnover numbers and predicted fluxes under a set of single carbon and energy source media under either aerobic versus anaerobic conditions. As shown, under most growth conditions, the correlation between enzyme turnover numbers and fluxes is higher when fluxes are predicted under aerobic conditions.

The fact that enzyme turnover numbers and the molecular weights of enzymes are significantly correlated with metabolic flux rates suggests that the utilization of the latter data sources within metabolic modeling approaches may provide improved prediction accuracy of metabolic phenotypes (as also shown in

To evaluate MOMENT's ability to predict microbial growth rates, we experimentally measured

The prediction of

MOMENT predicted growth rates achieving a Pearson correlation of 0.47 (p-value = 0.02) with the measured growth rates.

Protein mass was previously shown to account for 56%(g enzymes/g_{DW}) of cellular mass (based on experimental measurements _{DW}) (suggesting that only 48% of protein mass is taken by metabolic enzymes). Hence, practically, in order to scale the predicted growth rates to the correct range, prior knowledge on the total mass of metabolic enzymes should be used. In this case, the identified fraction of proteins mass devoted to metabolic enzymes in

While the growth rate predictions obtained by MOMENT are significantly correlated with the measured ones, the standard deviation of the predicted rates (across the different media) is markedly lower than that of the measured growth rates (0.054 for predicted rates versus 0.14 for measured rates). A potential explanation for the differences between the standard deviations in the observed and predicted growth rates could be that the fraction of protein mass devoted to metabolic enzymes increases under high growth rates. Notably, checking this hypothesis would require high-throughput protein concentration data measured under various growth rates, though this kind of data is currently unavailable. Overall, utilizing additional experimental data on the total enzyme concentration in a specific growth condition of interest is expected to further improve MOMENT's predictive performance.

To evaluate the importance of the utilized enzyme turnover numbers, we repeated MOMENT's growth rate predictions with randomly shuffled turnover numbers, which were found to provide significantly lower prediction accuracy (

To benchmark our new method, we tested the prediction performance of the previously developed FBAwMC. Here, FBAwMC was provided with the very same enzyme turnover rates given to MOMENT, while performing a sampling procedure for missing parameters as described in Beg et al did not improve the predicted performance (data not shown). We found that the growth rate prediction achieved by FBAwMC are not significantly correlated with the measured ones (

To evaluate the performance of MOMENT in predicting intracellular fluxes, we compared experimental flux measurements for 28 reactions in

(A) The prediction of flux rates in

To further evaluate the predictive performance of MOMENT, we extracted data from

Notably, naïve FBA was not evaluated here as it cannot be applied to predict differential metabolism across different growth rates. As a further benchmark, we applied a recently developed method called Parsimonious enzyme usage FBA (pFBA), to classify genes in

Computational prediction of microbial growth rates represents a major challenge. Here, we present a novel computational approach, MOMENT, that addresses this challenge by integrating genome-scale metabolic modeling with enzyme kinetic parameters. MOMENT is shown to predict growth rates for

While MOMENT enables genome-scale prediction of metabolic phenotypes it is bound to make simplifying assumptions that in some cases may lead to false predictions: (i) MOMENT requires as input information on the fraction of total protein concentrations that is devoted to metabolic enzymes. Since this information is difficult to obtain for each modeled condition, here we assumed that this fraction remains constant across a variety of growth media, which is expected to bias the predictions. (ii) MOMENT does not take into account several important factors that affect growth rate such as the cost of protein synthesis by ribosomes and local substrate turnover numbers, etc ^{nd} law of thermodynamics as done in

From an applicative standpoint, the improved metabolic modeling performance achieved by MOMENT is expected to significantly contribute to metabolic engineering applications and specifically to optimal strain design. Specifically, the additional constraints employed by MOMENT on the requirement for specific enzyme concentrations for catalyzing predicted metabolic flux rates, can be integrated and potentially improve the accuracy of computational metabolic engineering methods such as OptKnock, RobustKnock, OptStrain, etc

The wild-type Escherichia coli K-12 strain BW25113 was used for all experiments. Cells were cultivated in M9-minimal medium with different carbon source added. The carbon sources were added so that the amount of reducible carbon equaled the amount present in a concentration of 2 g/L glucose. M9 minimal medium was prepared in the following way: To 700 mL of autoclaved, purified water, 200 mL of 5× base salt solution (211 mM Na_{2}HPO_{4}, 110 mM KH_{2}PO_{4}, 42.8 mM NaCl, 56.7 mM (NH_{4})_{2}SO_{4}, autoclaved), 10 mL of trace elements (0.63 mM ZnSO_{4}, 0.7 mM CuCl_{2}, 0.71 mM MnSO_{4}, 0.76 mM CoCl_{2}, autoclaved), 1 mL 0.1 M CaCl_{2} solution (autoclaved), 1 mL 1 M MgSO_{4} solution (autoclaved), 2 mL of 500× thiamine solution (1.4 mM, filter sterilized) and 0.6 mL 0.1 M FeCl_{3} solution (filter sterilized) were added. The resulting solution was filled up to 1 liter with water. Carbon source were added to the medium from stock solutions adjusted to pH 7. All media were filtrated prior to use (Steritop-GP 500 mL, Millipore). All chemicals used were obtained from Sigma-Aldrich if not indicated otherwise.

The growth rates were determined using an automated cultivation device (Tecan Infinite 200 Pro plate reader). Cells were grown to a steady state in the respective growth medium in shake flasks, then washed twice in minimal medium. 4 µL of the washed cells were inoculated into a well on a 96-well plate (black, Greiner) with 196 µL of medium. The plate was covered with a transparent plastic cover and sealed with parafilm. Cultivation was done at the maximal linear shaking speed (160 min-1, 1 mm displacement) and the following settings for optical density (OD) measurement (Interval time 5 min, shaking 4∶42, reading (no shaking) 18 s; number of flashes 1; wavelength 600 nm, bandwidth 9 nm). The cells were grown to stationary phase or for at least 50 hours to ensure observation of steady state growth. The measured OD-values were corrected for the non-linearity of the device using an empirical function derived from samples with known OD-values (measured by spectrometry) from 10 to 0.001.

Enzyme turnover rates were extracted from BRENDA

Similar to FBA, MOMENT searches for a feasible flux distribution vector _{DW}/h) with maximal growth rate (i.e. flux through the biomass production reaction), satisfying mass-balance and reaction directionality constraints based on the following linear constraints:

Where _{ij}_{lb}_{ub}_{lb}_{ub}_{DW}), such that each flux rate in

For a reaction

For a reaction

For a reaction

This can be formulated in a linear equation by defining an auxiliary variable _{a&b}_{a}_{b}

To account for more complex gene-to-reaction mappings, where multiple alternative enzyme complexes can catalyze a certain reaction, we applied the above rules recursively by adding auxiliary variables for AND and OR operators. For enzymes whose turnover number is unknown, we use the me median turnover number across all reactions in

The enzymes solvent capacity constraint is formulated as;_{i}

To maximize ATP yield per sum of flux square,

(A) Histogram of Pearson correlations between enzyme turnover numbers and predicted flux rates, uniquely determined by Flux Variability Analysis (FVA), under different single carbon and energy source media in blue (average Pearson correlation is 0.49;

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The prediction of growth rates by FBAwMC. FBAwMC predicted growth rates achieving a Pearson correlation of 0.29(p-value = 0.17) with the measured growth rates.

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Metabolic flux and gene expression level predictions via MOMENT. (A) The prediction of flux rates in

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Correlations of enzyme turnover numbers, enzyme molecular weights, gene expression levels, and combinations of the latter via a linear regression model with metabolic flux rates.

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The contribution of kinetics parameters to the prediction of metabolic flux in

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Measured and predicted growth rates.

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The prediction accuracy of growth rate predictions made by MOMENT versus FBAwMC.

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Metabolic flux predictions in

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Prediction of differential gene expression levels in

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Turnover numbers.

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FVA formulation for MOMENT and the relation between growth rate and the total enzyame mass.

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We are grateful to Naama Brenner for highly valuable discussions and comments on the manuscript.