Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro kcat measurements

Abstract

Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kmax(vivo), the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation ofr(2)= 0.62 in log scale (p < 10(-10)), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between kmax(vivo) and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.

Keywords: flux balance analysis; kcat; kinetic constants; proteomics; turnover number.

Fig. 1.

Using omics data to estimate the catalytic rate of enzymes in vivo. (A) Flux $\left(v\right)$ and enzymatic active site abundance $\left(E\right)$ are integrated to calculate the rate of a single enzyme. Because v and E will change between conditions, the catalytic rate, $k_{\text{app}}$, is defined per condition $\left(C\right)$. From Eq. 1, $k_{\text{app}}$ equals the maximal rate $\left(k_{\text{cat}}\right)$ times a condition-dependent function η. (B) For each metabolic reaction in the cell, there exists a condition in which the catalytic rate of enzyme i is maximal. $k_{{\text{max}}_i}^{\text{vivo}}$ is the maximal value of $k_{{\text{app}}_i}$ over many growth conditions ($N=31$ in this study), and represents a lower bound estimate of the maximal catalytic capacity of enzyme i in vivo. The relation between in vivo $k_{\text{max}}^{\text{vivo}}$ and in vitro $k_{\text{cat}}$, i.e., the maximal value of η, is investigated in this study.

Fig. 2.

In vivo and in vitro maximal catalytic rates. Log–log plot of $k_{\text{max}}^{\text{vivo}}$ values verses in vitro $k_{\text{cat}}$ values for all measured enzymes in E. coli $\left(N=132\right)$. Each data point represents an enzyme-reaction-direction combination and is labeled by the name of the enzyme (if not overlapping with other labels; data labels appear just above the data points for points that are above the y = x line, and just below the data points for points that are below the line). The y = x line is shown in black. Values show a correlation of $r^2=0.62\hspace{0.17em}(p<{10}^{-10})$ and span a similar range of 6 orders of magnitude. Dashed brown line represents the best fit by total least squares in ${\text{log}}_{10}$ scale with slope = $1.23\hspace{0.17em}\pm \hspace{0.17em}0.07$, intercept = $-0.6\hspace{0.17em}\pm \hspace{0.17em}0.1$, and an RMSD of 0.54.

Fig. 3.

The rate of an enzyme can be described as $k_{\text{cat}}$ times a factor $\left(\eta \right)$ decomposed into saturation effects, backward flux (from thermodynamic effects), and vivo–vitro effects (e.g., regulation, pH, crowding, cofactors). In log scale, the residual between $k_{\text{max}}^{\text{vivo}}$ and $k_{\text{cat}}$ on the y axis is the sum of saturation, thermodynamic, and ambient effects, as shown in the Inset. The first two effects can only reduce the catalytic rate of the enzyme relative to its maximum, $k_{\text{cat}}$. Ambient-specific effects can result in slower or faster catalytic rates. Correction of $k_{\text{max}}^{\text{vivo}}$ by saturation and thermodynamic effects shows improved correlation, for the relatively small dataset for which such information is available. Brown dots represent $k_{\text{max}}^{\text{vivo}}$ values achieved via taking the maximum across all conditions, as shown previously in Fig. 2; black points represent $k_{\text{max}}^{\text{vivo}}$ values divided by the saturation and thermodynamic terms. The correlation between $k_{\text{max}}^{\text{vivo}}$ and $k_{\text{cat}}$ is $r^2=0.55$ and $r^2=0.92$ before and after the correction, respectively $\left(N=13\right)$. Stacked bars represent the relative contribution of undersaturation (blue) and backward-flux (yellow) effects to the residual between $k_{\text{max}}^{\text{vivo}}$ and $k_{\text{cat}}$.

Fig. S1.

Comparison of $k_{\text{max}}^{\text{vivo}}$ values obtained via pFBA versus MFA [expression levels from proteomics (20, 24, 25)]. Data points (N = 13) represent the maximum of $k_{\text{app}}$ values across all available conditions, i.e., glucose limited chemostat at specific growth rates of 0.1, 0.2, 0.4, and 0.5 h⁻¹, and show a correlation of $r^2=0.85,p<{10}^{-5}$; blue line represents y = x.

Fig. S2.

The range of $k_{\text{max}}^{\text{vivo}}$ relative to $k_{\text{cat}}$ measurements. Flux variability analysis was performed for the pFBA solution for all reactions (N = 132). Data points correspond to Fig. 2 in main text. The y = x line is shown in black; dashed brown line represents the best fit by orthogonal regression in ${\log }_{10}$; error bars (typically so small to be within the size of the points themselves) represent the range between the upper and lower $k_{\text{max}}^{\text{vivo}}$ estimates.

Fig. S3.

Nongrowth related ATP requirement has negligible effect on $k_{\text{max}}^{\text{vivo}}$ values. (A) $k_{\text{max}}^{\text{vivo}}$ values given flux of 6.30 mmol gCDW⁻¹ h⁻¹ (200% of reported maintenance value, x axis) compared with 3.15 mmol gCDW⁻¹ h⁻¹ (y axis) through the ATP maintenance reaction. (B) $k_{\text{max}}^{\text{vivo}}$ values given flux of zero (x axis) compared with 3.15 mmol gCDW⁻¹ h⁻¹ (y axis) through the ATP maintenance reaction. Blue line indicates the y = x line.