Data integration across conditions improves turnover number estimates and metabolic predictions

Abstract

Turnover numbers characterize a key property of enzymes, and their usage in constraint-based metabolic modeling is expected to increase the prediction accuracy of diverse cellular phenotypes. In vivo turnover numbers can be obtained by integrating reaction rate and enzyme abundance measurements from individual experiments. Yet, their contribution to improving predictions of condition-specific cellular phenotypes remains elusive. Here, we show that available in vitro and in vivo turnover numbers lead to poor prediction of condition-specific growth rates with protein-constrained models of Escherichia coli and Saccharomyces cerevisiae, particularly when protein abundances are considered. We demonstrate that correction of turnover numbers by simultaneous consideration of proteomics and physiological data leads to improved predictions of condition-specific growth rates. Moreover, the obtained estimates are more precise than corresponding in vitro turnover numbers. Therefore, our approach provides the means to correct turnover numbers and paves the way towards cataloguing kcatomes of other organisms.

Fig. 1. Schematic overview of the PRESTO approach for k_cat correction.

The approach uses a GECKO-formatted pcGEM containing turnover numbers from BRENDA. Using available data from n experimental conditions, $n$ condition-specific models are generated using nutrient uptake rates and protein contents. PRESTO then uses data on abundances for the enzymes measured across the $n$ investigated conditions and solves a linear program that minimizes a weighted sum of two objectives, the relative error to measured specific growth rates and the sum of positive $k_{\mathrm{cat}}$ corrections, δ. The optimal weighting factor, λ, which modulates the trade-off between the two objectives, is then determined by cross-validation (Tr: training set; Ts: test set), choosing the parameter, which is associated with the lowest average relative error. Using the optimal value for λ, PRESTO combines all models for the experimental conditions to find a $k_{\mathrm{cat}}$ correction for each enzyme with measured abundance. Last, the precision of δ values is assessed by variability analysis as well as by sampling and corrected $k_{\mathrm{cat}}$ values are validated by comparing them to values obtained from other approaches.

Fig. 2. Comparison of predicted growth of S. cerevisiae from pcGEMs with k_cat corrections from GECKO and PRESTO.

Condition-specific pcGEMs with corrected $k_{\mathrm{cat}}$ values generated by the GECKO heuristic were used to predict the specific growth rate for each condition (n = 27, a, b). The boxplots indicate the distribution of the relative error resulting from each set of condition-specific corrected $k_{\mathrm{cat}}$ values obtained from the GECKO heuristic. Relative prediction error from each set is indicated by a circle. The red diamonds show the relative error of the predicted specific growth rate from the PRESTO model $\left(\lambda ={10}^{-7}\right)$ by using the single set of corrected $k_{\mathrm{cat}}$ values in the respective pcGEM. a Only the measured total protein pool was used to constrain the solution and condition-specific uptake rates were bounded by 1000 $\frac{\mathrm{mmol}}{\mathrm{h}\mathrm{gDW}}$; b measured uptake rates were also considered; c abundances of enzymes measured in all conditions were used as additional constraints. The compared pcGEMs in each condition (n = 19) used the same respective biomass reaction, GAM, $\sigma$, and $P_{\mathrm{tot}}$ values (see the “Methods” section). L: Lahtvee et al., D: Di Bartolomeo et al., Y20: Yu et al., Y21: Yu et al.. Middle line and boxes in the box charts in panels a–c indicate the median and 25th and 75th percentiles, respectively. Outlier values (circles outside the whisker range) are more than 1.5× the interquartile range away from the top or bottom of the box, and whiskers connect the lower or upper quartiles with the non-outlier minimum or maximum. Source data are provided as a Source Data file.

Fig. 3. Comparison of enzymes with corrected k_cat values by both GECKO and PRESTO.

a KEGG Pathway terms significantly enriched in the set of enzymes corrected by PRESTO $\left(\lambda ={10}^{-7}\right)$ in the S. cerevisiae pcGEM. The x-axis gives the number of corrected enzymes linked to the given term. The one-sided p-values were calculated using the hypergeometric density distribution and corrected for multiple hypothesis testing using the Benjamini–Hochberg procedure. b Venn diagram showing the overlap of enzymes whose $k_{\mathrm{cat}}$ values were manually corrected (“Manual”), automatically corrected by the GECKO heuristic in any of the conditions (“GECKO”), or corrected by PRESTO (“PRESTO”). c Log-transformed $k_{\mathrm{cat}}$ values corrected using both the GECKO heuristic and PRESTO are not associated (Spearman correlation coefficient of 0.166, p-value = 0.45). Source data are provided as a Source Data file.

Fig. 4. Comparison of predicted growth of E. coli from pcGEMs with k_cat corrections from GECKO and PRESTO.

Condition-specific pcGEMs with corrected $k_{\mathrm{cat}}$ values generated by the GECKO heuristic were used to predict the specific growth rate for each condition (a: n = 31, b: n = 27). The boxplots indicate the distribution of the relative error resulting from each set of condition-specific corrected $k_{\mathrm{cat}}$ values obtained from the GECKO heuristic. Relative prediction error from each set is indicated by a circle. The red diamonds show the relative errors of predicted specific growth rates from the PRESTO model $\left(\lambda ={10}^{-5}\right)$ by using the single set of corrected $k_{\mathrm{cat}}$ values in the respective pcGEM. a Only the measured total protein pool was used to constrain the solution and condition-specific uptake rates were bounded by 1000 $\frac{\mathrm{mmol}}{\mathrm{h}\mathrm{gDW}}$; b abundances of enzymes measured in all conditions were used as additional constraints. Missing data points originate from the infeasibility of the respective models. The compared pcGEMs in each condition used the same respective biomass coefficients, GAM $\sigma$, and $P_{\mathrm{tot}}$ values (see the “Methods” section). P: Peebo et al., V: Valgepea et al., S: Schmidt et al.. Middle line and boxes in the box charts in panels a and b indicate the median and 25th and 75th percentiles, respectively. Outlier values (circles outside the whisker range) are more than 1.5× the interquartile range away from the top or bottom of the box, and whiskers connect the lower or upper quartiles with the non-outlier minimum or maximum. Source data are provided as a Source Data file.