In vitro turnover numbers do not reflect in vivo activities of yeast enzymes

Abstract

Turnover numbers (k_cat values) quantitatively represent the activity of enzymes, which are mostly measured in vitro. While a few studies have reported in vivo catalytic rates (k_app values) in bacteria, a large-scale estimation of k_app in eukaryotes is lacking. Here, we estimated k_app of the yeast Saccharomyces cerevisiae under diverse conditions. By comparing the maximum k_app across conditions with in vitro k_cat we found a weak correlation in log scale of R² = 0.28, which is lower than for Escherichia coli (R² = 0.62). The weak correlation is caused by the fact that many in vitro k_cat values were measured for enzymes obtained through heterologous expression. Removal of these enzymes improved the correlation to R² = 0.41 but still not as good as for E. coli, suggesting considerable deviations between in vitro and in vivo enzyme activities in yeast. By parameterizing an enzyme-constrained metabolic model with our k_app dataset we observed better performance than the default model with in vitro k_cat in predicting proteomics data, demonstrating the strength of using the dataset generated here.

Enzyme turnover numbers, also termed k_cat values, are fundamental parameters that specify the maximum rates of enzymatic reactions and hence determine the rates of biological processes such as metabolism. Determining k_cat is therefore essential for quantitatively understanding, modeling, and engineering cells. Traditionally, k_cat values are measured in vitro, which might differ from the in vivo situation. In addition, the coverage of measured k_cat is poor even for well-studied organisms (1). To address these issues, an approach for estimating in vivo enzyme catalytic rates, also termed k_app values, is to use the equation

$$v=k_{\text{app}}\cdot E,$$ [1]

where $v$ is the metabolic flux through the enzyme and $E$ the enzyme abundance (2). This approach was used to estimate k_app for Escherichia coli using absolute proteomics and flux data from various sources (2, 3), and it was found that the maximum k_app values across conditions, defined as k_max values, correlate well with in vitro k_cat values in log scale (2).

Here, we generate a k_app dataset for Saccharomyces cerevisiae under diverse conditions. We analyze our dataset and correlate in vivo with in vitro enzyme activities in yeast. Finally, we compare the predictive power of an enzyme-constrained metabolic model using in vivo and in vitro kinetic data.

Results and Discussion

To generate the yeast k_app dataset we collected absolute proteomics data of S. cerevisiae under diverse conditions (4–7) (Dataset S1). The absolute protein abundance can be directly adopted as enzyme abundance in Eq. 1. Note that we did not consider enzyme complexes composed of multiple distinct subunits due to the difficulty in calculating the abundance of catalytic sites (2). To determine the metabolic flux in Eq. 1, we performed flux balance analysis (FBA), as done previously (2), using the latest genome-scale metabolic model (GEM) of S. cerevisiae Yeast8 (8) (SI Appendix). Using the absolute proteomics and flux data, we calculated k_app for 358 metabolic reactions under 26 conditions (Dataset S2). By correlating the estimated k_app in log10 scale, we found that yeast k_app varied between conditions with the lowest R² being around 0.4 (Dataset S3). This is different from the findings for E. coli, where log-transformed k_app values correlate strongly across conditions with the lowest R² being above 0.9 (9).

By comparing k_max (Dataset S4), i.e., maximum k_app across all the studied conditions, with the corresponding in vitro k_cat (Dataset S5) we obtained a fairly weak correlation in log scale with R² = 0.28 for S. cerevisiae (Fig. 1A), which is much lower than that of E. coli (R² = 0.62) (2). A weak correlation was also reported for the plant Arabidopsis thaliana (10). By examining in vitro k_cat, we found that some were estimated using purified enzymes obtained through heterologous expression in E. coli, with the others being estimated from yeast extracts. We therefore divided the in vitro k_cat dataset into two groups, i.e., heterologous and homologous expression. We found that there was no correlation for the heterologous expression group (Fig. 1B), suggesting that in vitro k_cat values obtained through heterologous expression poorly represent in vivo catalytic rates of yeast enzymes. This might be due to the lack of natural posttranslational modifications (PTMs) in the expression organism, which could regulate enzyme activity. Indeed, we found that 27 out of the 29 reactions have reported PTMs on the enzymes (Dataset S6), indicating that these PTMs could functionally affect enzyme activity (11). In the homologous expression group we observed an improved correlation of R² = 0.41 in log scale (Fig. 1C) and thus identified the data obtained through heterologous expression as the main source of deviations.

Fig. 1.

Analysis of k_app and k_max of S. cerevisiae. Correlation in log scale between k_max and in vitro k_cat for all data points (A) and for the data points in which in vitro k_cat were measured using enzymes obtained through heterologous expression (B) and through homologous expression (C). The data points with deviations more than two orders of magnitude are labeled by the enzyme names. Student’s t test was used to calculate P value for Pearson’s correlation. (D) Change in average k_app/k_max of each condition with growth rate. (E) Comparison between k_app/k_max of individual reactions in two groups divided by a growth rate of 0.2/h. A two-sided Wilcoxon rank sum test was used to calculate P value.

To evaluate how uncertainties in the FBA-based flux may impact our dataset we first investigated the effect of flux variability on the estimated k_max (SI Appendix). We found that less than 8% of k_max values could differ, due to flux variability, by more than one order of magnitude (Dataset S4), and after removing these data we found the correlation between in vivo and in vitro values in log scale to be almost unchanged, i.e., R² (all data) = 0.27, R² (heterologous data) = 0.12, and R² (homologous data) = 0.39. Second, we provided another set of k_max values (Dataset S7) estimated using unbiased flux random sampling (SI Appendix), which correlate strongly (R² = 0.97) with the FBA-based k_max values in log scale. To evaluate the effect of a single high outlier value due to protein measurement we also correlated in log scale the second largest k_app across all conditions with in vitro k_cat but found similar R² values, i.e., R² (all data) = 0.25, R² (heterologous data) = 0.1, and R² (homologous data) = 0.39. Moreover, by correlating k_app of each condition with in vitro k_cat we found most correlations to be poor in log scale (Dataset S8). A recent study, using another proteomic dataset and a different GEM, also showed a poor correlation in log scale of R² = 0.27 between yeast k_app and in vitro k_cat at one condition (12).

We analyzed the yeast k_app under various conditions based on the ratio of condition-specific k_app over k_max for each reaction. By plotting the average ratio for each condition versus the corresponding growth rate (μ), we observed an increasing trend (Fig. 1D), which is in line with findings for E. coli (13). Furthermore, we compared the ratio of individual reactions between slow (μ ≤ 0.2/h) and fast (μ > 0.2/h) growth and found that k_app is significantly higher in faster-growing cells (Fig. 1E). We therefore conclude that k_app of yeast enzymes increase with growth rate. This suggests that proteome is more efficiently used at faster growth (13) and also indicates that growth could be controlled by efficiency of specific enzymes independent of conditions.

As turnover numbers are essential parameters in enzyme-constrained GEMs (ecGEMs) (9), we tested the use of k_app and in vitro k_cat in a yeast ecGEM ecYeast8 (8). We parameterized the model with 1) an assumed same k_cat for all enzymes, 2) default in vitro k_cat in the original ecYeast8, 3) general k_max, and 4) μ-dependent k_max. Note that μ-dependent k_max is defined as the maximum k_app across the conditions under which growth rate is not greater than the given μ. To compare model performance, we used the model to predict proteomics data for growth on various carbon sources (14, 15), and we compared with the data not used to estimate our k_app dataset. We found that k_max outperforms the assumed k_cat and default in vitro k_cat (Fig. 2), confirming our estimation of k_max to be reliable. Notably, μ-dependent k_max can further improve the predictions (Fig. 2), meaning that it is more effective to use μ-dependent k_max values than condition-independent maximum values, which are adopted in most published ecGEMs (9). In addition, we found that default in vitro k_cat in the original ecYeast8 outperforms the assumed same k_cat for all enzymes (Fig. 2), meaning that it is still acceptable to use in vitro k_cat when k_app values are unavailable.

Fig. 2.

Predictions of proteomics data on various carbon sources by ecYeast8 parameterized with an assumed same k_cat, default in vitro k_cat, general k_max, and μ-dependent k_max. Model performance is evaluated by root-mean-square error (RMSE) between predicted and measured protein levels on a log10 scale. N is the number of proteins with predicted nonzero concentrations by four parameterization strategies.

Overall, we present a k_app dataset of S. cerevisiae under various conditions, which can be used by ecGEMs for simulating the corresponding conditions. As k_app depends generally on growth rates rather than conditions (Fig. 1D), we believe that our μ-dependent k_max can be used to parameterize ecGEMs for predicting other conditions that are not involved in our dataset.

Materials and Methods

The metabolic fluxes were simulated using Yeast8 constrained by measurements. The absolute proteomics data were processed, i.e., the units of protein abundances were converted to millimoles per gram cell dry weight (gCDW). Details of all the materials and methods are provided in SI Appendix.

Data Availability

The data and codes are available at https://github.com/SysBioChalmers/Yeast_kapp. All other study data are included in the article and/or supporting information.