Revisiting Trade-offs between Rubisco Kinetic Parameters

Abstract

Rubisco is the primary carboxylase of the Calvin cycle, the most abundant enzyme in the biosphere, and one of the best-characterized enzymes. On the basis of correlations between Rubisco kinetic parameters, it is widely posited that constraints embedded in the catalytic mechanism enforce trade-offs between CO₂ specificity, S_C/O, and maximum carboxylation rate, k_cat,C. However, the reasoning that established this view was based on data from ≈20 organisms. Here, we re-examine models of trade-offs in Rubisco catalysis using a data set from ≈300 organisms. Correlations between kinetic parameters are substantially attenuated in this larger data set, with the inverse relationship between k_cat,C and S_C/O being a key example. Nonetheless, measured kinetic parameters display extremely limited variation, consistent with a view of Rubisco as a highly constrained enzyme. More than 95% of k_cat,C values are between 1 and 10 s^-1, and no measured k_cat,C exceeds 15 s^-1. Similarly, S_C/O varies by only 30% among Form I Rubiscos and <10% among C₃ plant enzymes. Limited variation in S_C/O forces a strong positive correlation between the catalytic efficiencies (k_cat/K_M) for carboxylation and oxygenation, consistent with a model of Rubisco catalysis in which increasing the rate of addition of CO₂ to the enzyme-substrate complex requires an equal increase in the O₂ addition rate. Altogether, these data suggest that Rubisco evolution is tightly constrained by the physicochemical limits of CO₂/O₂ discrimination.

Figure 1

Description of the catalytic mechanism of Rubisco. The “middle-out” diagram in panel A shows the ordered mechanisms of carboxylation and oxygenation. Circles represent carbon atoms. RuBP is isomerized to an enediolate before carboxylation or oxygenation. Addition of CO₂ or O₂ to the enediolate of RuBP is considered irreversible as are the subsequent hydration and cleavage steps of the carboxylation and oxygenation arms. (B) Carboxylation displays effective Michaelis–Menten kinetics (maximum catalytic rate k_cat,C, half-maximum CO₂ concentration K_M = K_C) with competitive inhibition by O₂ (assuming half-maximum inhibitory O₂ concentration K_i = K_O). Carboxylation results in net addition of one carbon to the five-carbon RuBP, producing two 3PG molecules. 3PG is part of the CBB cycle and can therefore be used to continue the cycle and produce biomass. Oxygenation also displays effective Michaelis–Menten kinetics (k_cat,O, K_M = K_O, half-maximum inhibitory CO₂ concentration K_I = K_C). Oxygenation of RuBP produces one 3PG and one 2PG. Rates of carboxylation (R_C) and oxygenation (R_O) are calculated from kinetic parameters and the CO₂ and O₂ concentrations. The reaction coordinate diagram in panel C describes carboxylation and oxygenation as a function of two “effective” barriers. The first effective barrier includes enolization and gas addition, while the second includes hydration and cleavage. (D) Given standard assumptions (Supporting Information), catalytic efficiencies (k_cat/K_M) are related to the height of the first effective barrier while k_cats are related to the second. The first barrier to oxygenation is drawn higher than for carboxylation because oxygenation is typically slower than carboxylation. Net reactions of RuBP carboxylation and oxygenation are both quite thermodynamically favorable.

Figure 2

Scenarios that produce strong correlations between enzyme kinetic parameters. As the logs of the kinetic parameters are linearly related to energy barriers, linear energetic trade-offs should manifest as log–log correlations between kinetic parameters (power laws). Panel A describes a situation in which two kinetic parameters are inextricably linked by the enzyme mechanism, diagrammed here as negative coupling between k_cat,C and S_C/O as an example. These couplings take the form of “equality constraints” in which one parameter determines the other within measurement error. Correlation is expected as long as diverse enzymes are measured. In panel A, selection moves enzymes along the blue curve but cannot produce enzymes off the curve (gray) because they are not feasible. Panel B diagrams an alternative scenario in which the enzyme mechanism imposes an upper limit on two parameters (an inequality constraint). In the “selection within limits” scenario, effective selection is required for correlation to emerge because suboptimal enzymes (e.g., ancestral sequences) are feasible. In the examples plotted, different environmental CO₂ and O₂ concentrations should select for different combinations of rate (k_cat,C) and affinity (S_C/O), resulting in present-day enzymes occupying distinct regions of the plots in panels A and B.

Figure 3

Summary of the full extended data set. We collected measurements of Rubisco kinetic parameters from a variety of organisms (A) representing four classes of Rubisco isoforms (B). Form I enzymes from plants, cyanobacteria, and algae make up the bulk of the data (A and B). (C) Rubisco kinetic parameters display a narrow dynamic range. The box plot and gray points describe the distribution of Form I Rubiscos, while data for Form II Rubiscos are colored yellow. Colored boxes give the range of the central 50% of FI values, and the notch indicates the median. N is the number values, and σ* gives the geometric standard deviation of Form I data. σ* < 3 for all parameters, meaning a single standard deviation varies by <3-fold. All data are from wild-type Rubiscos measured at 25 °C and near pH 8. More detailed histograms are given in Figure S4.

Figure 4

Correlations between measured kinetic parameters are attenuated by the addition of new data. This figure gives Pearson correlations (R) between pairs of log-transformed kinetic parameters of Form I Rubiscos. When multiple measurements of the same enzyme were available, the median value was used (Materials and Methods). S_C/O–K_C, S_C/O–k_cat,C, and K_C–k_cat,C correlations are of particular interest because they were highlighted in previous works, which found R values of 0.8–0.95. None of these pairs have R values exceeding 0.7 in the extended data set.

Figure 5

Focal correlations of previous analyses are not robust to new data. Points with black outlines are from ref (6), and dashed gray lines represent the best fit to FI Rubisco data. Histograms for k_cat,C, S_C/O, and K_C are plotted on parallel axes. Panel A plots k_cat,C against S_C/O. k_cat,C and S_C/O correlate with an R of approximately −0.6 among FI Rubiscos as compared to ≈0.9 previously.^, The 95% confidence intervals are (−4.0, −2.0) for the fit exponent and (3 × 10⁴, 2 × 10⁸) for the prefactor (slope and intercept on a log–log scale, respectively), indicating that the form of k_cat,C–S_C/O correlation is very uncertain. Notably, S_C/O displays very limited variation overall and especially within physiological groupings with sufficient data. Median S_C/O values are 177 for red algae (σ* = 1.2; N = 6), 98 for C₃ plants (σ* = 1.1; N = 162), 80 for C₄ plants (σ* = 1.1; N = 35), and 48 for cyanobacteria (σ* = 1.1; N = 16). Panel B plots k_cat,C against K_C. Here, the R is ≈0.5 as compared to ≈0.9 previously. This fit is more robust, with 95% confidence intervals of (0.3, 0.5) and (0.8, 1.5) for the fit exponent and prefactor, respectively.

Figure 6

Negative power-law correlation between k_cat,C and k_cat,C/K_C is not supported by the extended data set. In the model diagrammed in panel A, CO₂-specific Rubiscos have low barriers to enolization and CO₂ addition (first effective carboxylation barrier ΔG_1,C), but lowering the first effective barrier necessarily increases the second effective barrier (ΔG_2,C), reducing k_cat,C. In this view, stabilizing the first carboxylation TS also enhances selectivity but also slows carboxylation (Figure S2). ΔG_1,C and ΔG_2,C should be negatively correlated, which would manifest as negative power-law correlation between k_cat,C and k_cat,C/K_C under certain assumptions (Supporting Information). (B) The extended data set does not evidence the expected correlation (for Form I enzymes, R = 0.02 and p = 0.8). While previous analyses gave an R of approximately −0.9, the 95% confidence interval for R now includes 0.0. Restricting our focus to particular physiologies like C₃ plants does not result in the expected correlation.

Figure 7

Second mechanistic proposal that is remarkably well-supported by the extended data set. (A) In this proposal, mutations increasing the rate of addition of CO₂ to the Rubisco–RuBP complex also increase the rate of O₂ addition. In energetic terms, lowering the effective barrier to enolization and CO₂ addition (ΔG_1,C) lowers the first effective barrier to O₂ addition (ΔG_1,O), as well. Given this model, barrier heights should be positively correlated, which would manifest as a positive linear correlation on a log–log plot of k_cat,C/K_C against k_cat,O/K_O. (B) S_C/O displays limited variation within physiological groups such as C₃ and C₄ plants for which we have substantial data. Dashed lines give the geometric mean of S_C/O values. The multiplicative standard deviation, σ*, sets the width of the shaded region. (C) S_C/O = (k_cat,C/K_C)/(k_cat,O/K_O), so restricted S_C/O variation implies a power-law relationship (k_cat,C/K_C) = S_C/O(k_cat,O/K_O). k_cat,C/K_C is strongly correlated with k_cat,O/K_O on a log–log scale (R = 0.94; p < 10^–10). Fitting FI measurements gives k_cat,C/K_C = 119(k_cat,O/K_O)^1.04. A 95% confidence interval for the exponent is (0.94, 1.13), which includes 1.0. The geometric mean of measured S_C/O values predicts k_cat,O/K_O = (k_cat,C/K_C)/S_C/O and vice versa. This simple approach accurately predicts the k_cat,O/K_O for FI Rubiscos (prediction R² = 0.80), C₃ plants (R² = 0.84), C₄ plants (R² = 0.96), and cyanobacteria (R² = 0.79). Other groups, e.g., red algae, are omitted because of insufficient data.

Figure 8

A power-law relationship between k_cat,C/K_C and k_cat,O/K_O can be explained by an active site that fluctuates between “reactive” and “unreactive” states. (A) In this model, CO₂ and O₂ react with bound RuBP only when the enzyme is in the reactive state, which has an occupancy φ. (B) φ can vary between related enzymes. In the reactive state, CO₂ and O₂ react with the bound RuBP with intrinsic reactivities ΔG*_1,C and ΔG*_1,O that do not vary between related Rubiscos. If the difference in intrinsic reactivities (ΔG*_1,O – ΔG*_1,C) is constant, we derive a power-law relationship between k_cat,C/K_C and k_cat,O/K_O with an exponent of 1.0. This relationship requires a constant S_C/O (Supporting Information).