Cross-species analysis traces adaptation of Rubisco toward optimality in a low-dimensional landscape

Abstract

Rubisco (D-ribulose 1,5-bisphosphate carboxylase/oxygenase), probably the most abundant protein in the biosphere, performs an essential part in the process of carbon fixation through photosynthesis, thus facilitating life on earth. Despite the significant effect that Rubisco has on the fitness of plants and other photosynthetic organisms, this enzyme is known to have a low catalytic rate and a tendency to confuse its substrate, carbon dioxide, with oxygen. This apparent inefficiency is puzzling and raises questions regarding the roles of evolution versus biochemical constraints in shaping Rubisco. Here we examine these questions by analyzing the measured kinetic parameters of Rubisco from various organisms living in various environments. The analysis presented here suggests that the evolution of Rubisco is confined to an effectively one-dimensional landscape, which is manifested in simple power law correlations between its kinetic parameters. Within this one-dimensional landscape, which may represent biochemical and structural constraints, Rubisco appears to be tuned to the intracellular environment in which it resides such that the net photosynthesis rate is nearly optimal. Our analysis indicates that the specificity of Rubisco is not the main determinant of its efficiency but rather the trade-off between the carboxylation velocity and CO(2) affinity. As a result, the presence of oxygen has only a moderate effect on the optimal performance of Rubisco, which is determined mostly by the local CO(2) concentration. Rubisco appears as an experimentally testable example for the evolution of proteins subject both to strong selection pressure and to biochemical constraints that strongly confine the evolutionary plasticity to a low-dimensional landscape.

Fig. 1.

Carboxylation/oxygenation by Rubisco. (A) Rubisco catalyzes the addition of CO₂ or O₂ to D-ribulose 1,5 bisphosphate (RuBP). Rubisco binds RuBP to form a complex that undergoes enolization. In the case of carboxylation (Upper pathway), this is followed by practically irreversible CO₂ addition that results in a six-carbon intermediate. Through steps of hydration and cleavage, the reaction produces two molecules of 3-phosphoglycerate (3-PGA). Oxygenation follows similar steps (Lower pathway), through a five-carbon intermediate, and results in one 3-PGA and one 2-phosphoglycolate (2-PGY) (12). (B) The Rubisco-catalyzed carboxylation and oxygenation exhibit effective Michaelis–Menten (MM) kinetics. The carboxylation rate per Rubisco molecule, R _C, and oxygenation rate per Rubisco molecule, R _O, when RuBP is in saturation, take the familiar MM form (see equations in the figure). The effective kinetics consist of two irreversible steps. The effective gas binding (k _on,C and k _on,O), which consists of the enolization of the Rubisco–RuBP complex, whose fraction is r = k _e /(k′_e + k _e), and gas addition, determined by the rates k _a,C and k _a,O. This is followed by effective catalysis (v _C and v _O), which includes the steps of hydration and cleavage. The MM constants for gas addition, K _C and K _O, are the effective affinities of the CO₂ and O₂ molecules to the Rubisco–RuBP complex (Methods).

Fig. 2.

Power law correlations among kinetic parameters of Rubisco define the 1D landscape. (A) The four kinetic parameters of 28 Rubiscos from 27 species (Table S1): the effective Michaelis–Menten (MM) constant for CO₂ binding, K _C [μM]; the maximal carboxylation rate, v _C [1/s]; the specificity, S; and the effective MM constant for O₂ binding, K _O [μM]. The parameters K _C and S are known for all 28 Rubiscos. For 25 Rubiscos K _O is known and for 16 Rubiscos all of the kinetic parameters are available. All Rubiscos in the dataset are of the more abundant form I besides the form II Rubiscos from R. rubrum and R. sphaeroides. (B) (Top Left) A 3D projection of the 4D kinetic parameter data. Data from the 16 species for which all four kinetic parameters are available are graphed in logarithmic scale. Each of the 16 species is represented by a point whose coordinates are its v _C, K _C, and S (blue circles). The plot depicts the PCA result that the data are confined to an effectively 1D space and follow, in logarithmic scale, a straight line (blue cylinder). The cylinder axis is the first principal axis and its radius is the standard deviation from this axis. There is one evident outlier (blue triangle), the Rubisco from R. rubrum, the only form II Rubisco in this set. (Top Right and Bottom) Total least-squares fit of the data from all 28 Rubiscos (Methods) to a 1D power law model (black lines). The fits are plotted in logarithmic scale and exhibit clear power law correlations between the kinetic parameters. The correlation coefficient, ρ, and the P value, p, are shown. As before, there are clear outliers (black triangles) that correspond to the form II species, R. rubrum and R. sphaeroides. Note that deviations of form II species from the model are significant mostly in its projections onto the specificity parameter S.

Fig. 3.

The free energy trade-offs. (A) Representation of the effective Michaelis–Menten (MM) kinetics in terms of free energy profiles. The effective kinetics consist of two irreversible steps, effective gas binding (i.e., enolization and gas addition) and effective catalysis (i.e., hydrolysis and cleavage) (Fig. 1B), which correspond to two effective energy barriers. The first energy barriers are related to the rates of effective gaseous addition, k _on,C ∼ exp(–ΔG _1,C), k _on,O ∼ exp(–ΔG _1,O). The second barriers are linked to the effective catalysis rates, v _C ∼ exp(–ΔG _2,C), v _O ∼ exp(–ΔG _2,O). The specificity depends on the difference between the first energy barriers, S = exp(ΔG _1,O – ΔG _1,C). (B) The power law correlation k _on,C = v _C/K _C ∼ 1/v _C (solid line, triangle is the R. rubrum outlier), indicates that a shift in carboxylation barrier, ΔG _2,C, is accompanied by a shift by the same magnitude in the CO₂ addition barrier, such that their sum is conserved, ΔG _1,C + ΔG _2,C = const. The change in ΔG _2,C involves only a shift in the intermediate energy level but may also involve a shift in the catalysis transition-state level. (C) Another trade-off arises from the correlation between the effective addition rates of CO₂ and O₂, k _on,O = v _O/K _O ∼ (v _C/K _C)^0.5 = k _on,C ^0.5 (solid line, triangle is the R. rubrum outlier). This indicates that a decrease in the CO₂ addition barrier, ΔG _1,C, is associated with a smaller (by a factor of ) decrease in the O₂ addition barrier, ΔG _1,O, such that 0.5 · ΔG _1,C – ΔG _2,O = const. The negative correlation between v _C and S is the outcome of the two trade-offs: As v _C decreases, k _on,C increases and, as a result, k _on,O also increases, but by a smaller factor, and the difference between the gas addition barriers increases resulting in a decrease of the specificity, S = exp(ΔG _1,O – ΔG _1,C).

Fig. 4.

The optimality of Rubisco. (A) Carboxylation rate, R _C, oxygenation rate, R _O, and net photosynthesis rate (NPR), f = R _C – 0.5 · R _O, as a function of carboxylation velocity, v _C, for [CO₂] = 80 μM. In an anaerobic environment the NPR equals the carboxylation rate, f = R _C ([O₂] = 0) (blue dashed line) and exhibits a clear optimum. The presence of oxygen, [O₂] = 260 μM, reduces the NPR (green line) in two ways: R _C (blue line) is reduced because oxygenation sequesters a fraction of the available Rubisco, an effect that is responsible for most of the NPR decrease. A smaller reduction of the NPR is due to the photorespiration factor, 0.5 · R _O (red line). The presence of oxygen shifts the optimal carboxylation velocity v _C* toward lower values (4). Most of the shift in v _C* is due to the decrease in R _C rather than the increase in R _O. For example, C₃ plants that operate at [CO₂] ≈ 7–8 μM are far from the optimal values for [CO₂] = 80 μM. However, C₄ plants possess CCM and operate at CO₂ concentrations that are at least 10 times larger than those of C₃ plants and their carboxylation rates are nearly optimal at [CO₂] = 80 μM. (B) The NPR as a function of v _C for three environments, [CO₂] = 10, 80, and 250 μM, which correspond to groups with no CCM (C₃ plants and some algae), medium-range CCM (C₄ plants, some algae, and photosynthetic bacteria), and strong CCM (cyanobacteria). The average v _C of each class is plotted and appears to be close to the values that yield maximal NPR. The solid and dashed curves correspond to aerobic and anaerobic conditions, [O₂] = 260 and 0 μM, respectively. The optimal parameters of Rubisco are determined mostly by the CO₂ concentration. (C) The CO₂ environments that are predicted to be optimal to the observed v _C from Eq. 4 (dashed line, anaerobic; solid line, [O₂] = 260 μM). Cyanobacteria are optimal in the CO₂-rich environment, [CO₂]* ≈ 240 μM. C₄ plants, algae, and photosynthetic bacteria are optimal at intermediate CO₂ levels, [CO₂]* ≈ 30–80 μM. C₃ plants and nongreen algae, which are suspected to lack CCM, are optimal at low CO₂ levels, [CO₂]* ≈ 5–15 μM.

Fig. 5.

(A) Normalized NPR as a function of v _C (fully optimal Rubisco has a normalized NPR of 100%). For example, the cyanobacteria in a strong CCM environment (red line), [CO₂] = 250 μM, have normalized NPR of ∼99%. However, if one put this Rubisco in an environment typical of C₃ plants (blue line), [CO₂]=10 μM, it would achieve only 34% of the maximal possible NPR while C₃ plants achieve normalized NPR of 95%. In accord, photosynthesis was impaired when Rubisco of R. rubrum replaced the native Rubisco of cyanobacteria or tobacco (30, 31). (B) The axes represent any two kinetic parameters with negative correlation (dashed line), such as S and v _C. Rubisco (blue dots) resides in an effectively one-dimensional fitness landscape (the region near the correlation line), which may be the outcome of two possible scenarios: In the first, Rubisco is confined to a limited region of phenotypes (Left). In the second, the observed relation may be only an upper limit (Right) and it is selection that pushes Rubisco to the edge.