Prediction of microbial growth rate versus biomass yield by a metabolic network with kinetic parameters

Abstract

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 E. coli, including intracellular flux rates and changes in gene expression levels under different growth rates. Most importantly, MOMENT is shown to predict growth rates of E. coli under a diverse set of media that are correlated with experimental measurements, markedly improving upon existing state-of-the art stoichiometric modeling approaches. These results support the view that a physiological bound on cellular enzyme concentrations is a key factor that determines microbial growth rate.

Figure 1. Enzyme turnover numbers and enzyme molecular weights are significantly correlated with metabolic flux rates.

(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 E.coli under glucose minimal media in low and high growth rates were taken from Ishii et al. , and Schuetz et al. data , respectively. Each bar represents a correlation between flux rates and a single or multiple data sources (marked by ‘+’ signs). (B) Enzyme turnover numbers correlate with measured metabolic flux rates in E. coli (both in log₁₀ scale). Linear regression line in red.

Figure 2. Enzyme turnover rates show higher correlation with average flux across media and with flux under aerobic conditions.

(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.

Figure 3. Growth rate prediction accuracy by MOMENT versus other approaches.

The prediction of E.coli growth rate under 24 different minimal media based on MOMENT, FBAwMC, and MOMENT with random enzyme turnover rates (with the error bar representing standard deviation over 1000 randomly shuffled turnover numbers). As shown, only MOMENT (with the true turnover rates) achieves a statistically significant Pearson correlation between predicted and measured growth rates (p-values are shown on top of each bar).

Figure 4. The prediction of growth rates by MOMENT.

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

Figure 5. Metabolic flux and gene expression level predictions via MOMENT versus other approaches.

(A) The prediction of flux rates in E.coli under glucose minimal media based on MOMENT in comparison to FBAwMC, FBA, and MOMENT with random enzyme turnover rates (error bar representing standard deviation over randomly shuffled turnover numbers). (B) The prediction of differential gene expression levels in E.coli under glucose minimal media, between low and high growth rate conditions (with the high growth rate condition involving overflow metabolism). p values are shown above each bar.