What makes Ribulose-1,5-bisphosphate (RuBP) carboxylase/oxygenase (RuBisCO) kinetic parameters the way they are? This question has now persisted for several decades, without a definitive explanation. Although RuBisCO is the principal carbon-fixing enzyme in the biosphere, its product turnover rate (circa 3s⁻¹ per active site for plants) may be considered, if not particularly slow, rather unexceptional (Bar-Even et al., 2011). The primary substrate (CO₂) must also compete for binding to the RuBP in the RuBisCO active site with the more abundant O₂ in the atmosphere leading to photorespiration, consuming additional energy and compromising the process of photosynthesis. The combined effects of increasing population and anthropogenic climate change have motivated efforts to enhance carbon fixation in plants for increasing both agricultural crop yield and carbon sequestration generally (Niinemets et al., 2017; Andralojc et al., 2018; Erb and Zarzycki, 2018; Fernie et al., 2020; Lawson and Flexus, 2020). Although the possibility of enhancing photosynthesis by improving RuBisCO kinetic traits has been given due consideration (Whitney et al., 2011; Sharwood et al., 2016; Gomez-Fernandez et al., 2018; Wilson et al., 2018; Zhou and Whitney, 2019; Davidi et al., 2020; Lin et al., 2020; Bouvier et al., 2021), a conclusive picture of RuBisCO’s molecular mechanism (Cleland et al., 1998; Tcherkez, 2013, 2015; Cummins et al., 2018b, 2019b; Kannappan et al., 2019; Bathellier et al., 2020; Cummins and Gready, 2020) and a general consensus understanding of the observed tradeoffs between RuBisCO’s kinetic parameters remains elusive, despite having been analyzed in varying ways with the objective of gaining insights into the possible connection between evolutionary and biochemical (or catalytic) constraints (Bouvier et al., 2021). The earliest of these studies, (Tcherkez et al., 2006; Savir et al., 2010) based on general mechanistic assumptions and limited data samples, concluded that variations in the elementary rate constants must be tightly constrained by the limitations inherent in RuBisCOs kinetic mechanism, resulting in an enzyme which provides only limited scope for further optimization (Tcherkez et al., 2006; Tcherkez, 2013, 2015), while later studies of more extensive data sets have challenged this view, revealing greater flexibility (Cummins et al., 2018a, 2019a; Flamholz et al., 2019). Other studies have examined the coevolution of RuBisCO kinetics and carbon concentrating mechanism (CCMs) (Goudet et al., 2020; Iñiguez et al., 2020).

Various forms of CCMs have occurred independently and at different times in a wide range of photosynthetic organisms from diverse environments, directing the evolution of RuBisCO kinetics (Iñiguez et al., 2020). In higher plants, the vast majority follow the C₃ photosynthetic pathway initiated by CO₂ fixing to the bound form of activated RuBP substrate (Cleland et al., 1998) which proceeds through hydrolysis to break down into two molecules of the 3-carbon compound 3-phosphoglyceric acid (3PGA). The C₄ pathway, although present in only about 8,000 species (Sage, 2016), including some important agricultural crops (maize and sorghum), accounts for about 25% of terrestrial photosynthesis. In C₄ photosynthesis, CO₂ is initially converted by carbonic anhydrase (CA) to bicarbonate which is fixed by phosphoenolpyruvate carboxylase into oxaloacetate. Oxaloacetate is converted into malate (4-carbon compound) or aspartate for diffusion into the bundle sheath cells where they are decarboxylated in high concentrations and the released CO₂ is then, as in C₃ photosynthesis, fixed into 3PGA by RuBisCO. By increasing CO₂ supplies and thereby suppressing photorespiration, plant CCMs began evolving from C₃ species, probably in the early Oligocene (circa 30ma) in response to decreasing CO₂ levels, as an efficient way of increasing photosynthesis in the more challenging environmental conditions (Sage, 2004). The evolutionary success of C₄ photosynthesis and the observation of increased carbon assimilation in some C₃ crops under elevated CO₂ (Xu et al., 2016; Thompson et al., 2017) have stimulated research into the possibility of incorporating CCMs into C₃ plant species via genetic modification (McGrath and Long, 2014; Jurić et al., 2019; Kubis and Bar-Even, 2019; Atkinson et al., 2020).

Selective abiotic forces have determined the evolution of C₄ photosynthesis over a number of distinct phases (Sage et al., 2018). C₂ photosynthesis, a crucial step in the early stages of this evolution (Sage et al., 2012; Bräutigam and Gowik, 2016), is characterized by the formation of a photorespiratory CO₂ pump that utilizes the two-carbon compound, glycine, to transport and concentrate the photorespiratory CO₂ into the bundle sheath cells where it can be re-fixed by RuBisCO. The processes involved in elevating levels of photorespiration relative to photosynthesis in C₃ plants are, therefore, a fundamentally important selection factor initiating the evolution to C₄ photosynthesis (Sage et al., 2018). This ratio can be modelled using the rate, or velocity, v, of the oxygenase relative to the carboxylase catalyzed reaction, given by (Laing et al., 1974; Jordan and Ogren, 1984)

where O and C are, respectively, the O₂ and CO₂ concentrations at carboxylation sites, and S_C/O is the specificity of the carboxylase relative to the oxygenase reaction which can be expressed in various algebraic forms as

In an obvious notation, the RuBisCO kinetic parameters V and K denote the maximum catalytic (turnover) rates (V_max or k_cat) and Michaelis constant (K_M), respectively. A recent data compilation contains RuBisCO kinetic parameters (at 25° C) from over 300 species (Flamholz et al., 2019), with more than 50% derived from higher plants. Of these plant species, the ubiquitous C₃ plants constitute by far the largest sample, followed by around 40 examples of C₄ plants, while samples of C₃-C₄ intermediate (extant plants exhibiting C₂ photosynthesis on the pathway to C₄) and some C₄-like plants from Flaveria, a genus adopted as a model for the evolutionary pathway of C₄ photosynthesis (McKown et al., 2005; Kapralov et al., 2011; Sage et al., 2013; Schulze et al., 2013; Mallmann et al., 2014), and other miscellaneous plants, including examples of CCM-containing plants that follow the crassulacean acid metabolism pathway, are fewer in number.

The reduction of atmospheric CO₂ levels and associated increase in O₂ would have undoubtedly enforced adaptation of plants to increased photorespiration over geological time. Increasing temperature also increases v_O/C (Jordan and Ogren, 1984) by decreasing both S_C/O and the ratio of substrate concentrations, C/O, and is an important environmental factor driving the evolution of the C₄ pathway (Sage et al., 2018). However, while photorespiration is not particularly advantageous to C₃ plants due to net loss of carbon, it is also important to recognize that a significant amount of photorespiratory CO₂ can feed into chloroplasts (Sage and Sage, 2009; Tholen and Zhu, 2011; Busch et al., 2013), increasing the potential for the recapture of carbon for photosynthesis and thus facilitating evolution along the C₄ pathway. This creates a negative feedback loop that mitigates the photorespiratory response and thus limiting the increases in v_O/C. Moreover, the combined action of CA (releasing CO₂ from bicarbonate) and photorespiration have been postulated to form the basis of a homeostatic mechanism that ensures a stable supply of CO₂ to RuBisCO, essential for the energy efficient maintenance of photosynthesis (Riazunnisa et al., 2006; Igamberdiev and Roussel, 2012; Igamberdiev, 2015).

While the importance of abiotic environmental conditions leading to carbon restriction (reduced atmospheric CO₂, higher temperatures, and lack of water) in driving evolution of the photorespiratory CO₂ pump is well understood (Sage et al., 2018), the role of RuBisCO kinetic variability, which underpins S_C/O, warrants further critical investigation (Sage, 2013; Sage et al., 2018). In the present study, we have attempted to delineate possible coevolutionary relationships between RuBisCO, photorespiration, and CCMs by analyzing RuBisCO kinetic parameter data for higher plant species derived from the most recent compilation (Flamholz et al., 2019). In two genera, Flaveria and Panicum, the results suggest that in addition to abiotic conditions that increase photorespiration by lowering S_C/O, much lower than average S_C/O in the C₃ populations could also be a critically important precondition in C₄ evolution. In contrast, C₃ plants (e.g., Limonium) that have adapted to extreme abiotic environments are typically characterized by higher than average S_C/O (Galmés et al., 2005), which compensates for the lower levels of photorespiratory CO₂ (Equation 1) through higher CO₂ affinity.

The data sets for our analysis were accessed from the compilation by Flamholz et al. (2019). Where there are multiple entries per species in this database, these were averaged prior to statistical analysis. The complete list of species and associated kinetic parameters used in the analysis is provided in the Supplementary Material (Supplementary Tables S1 and S2). It is worth noting here that correlations between these kinetic parameters have been recently analyzed using Phylogenetic Generalized Least Squares (PGLS) as opposed to standard least-squares regression (Bouvier et al., 2021). Standard regression analysis assumes independence of the residuals, which may not necessarily be true when looking for correlations between traits in evolutionary biology as those taxa with a more common ancestor (more related) would exhibit similar traits and hence dependent residuals. PGLS methods are often used to account for such dependencies (for a general overview of PGLS methodology, see Mundry, 2014). The PGLS study by Bouvier et al., (2021) suggests that correlations between RuBisCO kinetic parameters are over estimated by standard regression; i.e., a significant phylogenetic signal is present. Nevertheless, the covariance between K_C and V_C appears not affected, which is perhaps not surprising given the interdependence between K and V (Briggs and Haldane, 1925). In view of this underlying covariance present in the enzyme kinetics, which is quite distinct from phylogenetic and catalytic constraints, standard linear least-squares regression analysis was carried out on the total C₃ (excluding Limonium), C₃ Limonium collected from high stress (high temperature and water restricted) habitat (Galmés et al., 2014), Flaveria sample and total C₄ samples. The vast majority of grass species are split fairly evenly between the closely related Panicoideae, Arundinoideae, Chloridoideae, Micrairoideae, Aristidoideae, and Danthonioideae (PACMAD) and Bamboos, Oryzoideae, and Pooideae (BOP) sister clades. Among grasses, C₄ photosynthesis has evolved from C₃ only in PACMAD species (for an overview, see Christin et al., 2013). As both clades are relatively well represented in the kinetic data, correlations are also examined separately for Oryza, Aegilops, Puccinellia (all BOP), and Panicum (PACMAD) species.

The estimation of effect sizes (Cumming, 2012) of primary interest in our analysis is both the differences between mean kinetic parameters and, in particular, the differences between coefficients obtained from linear least-squares regression. As by definition K_M is expressed as an explicit function of V_max (Briggs and Haldane, 1925), they are not independent variables. The Michaelis constant for the carboxylase and oxygenase reactions can be written in the general linear in V_max form (Cummins et al., 2018a),

The coefficient of the K_M intercept and coefficient of V_max obtained by linear regression of the data can be interpreted as the sample mean values of b and m, respectively, which are functions of the rate constants for the elementary steps in the kinetic mechanism (Cummins et al., 2018a). Prior linear regression analysis of the explicit dependence of K_M on V_max indicates that K_M is to some extent dependent on the value of b, which is a function of the dissociation rates (among other rate constants) of the CO₂ and O₂ gas substrates (Cummins et al., 2018a, 2019a).

The margin of error in the difference between two means is estimated using confidence intervals (CIs), calculated from the standard errors of the means (SE). For two independent samples of size n₁ and n₂ with means M₁ and M₂ (e.g., regression coefficients for C₃ and C₄ samples), the combined SE for the difference in the means (∆M) can be obtained by quadrature, giving the CI as follows:

Alternatively, quadrature may be used with fractional errors to express differences as a percentage, as

In Equations (4) and (5), Student’s inverse cumulative distribution function (t⁻¹) is given by

The CIs can be readily interpreted in terms of p values. If │∆M│> CI, the difference may be considered “statistically significant” (null hypothesis may be rejected) at α=p. We consider that only very small p values (at best, p <0.01) should provide a reliable foundation for rejecting a null hypothesis (Cumming, 2012). The statistical analysis was generated using the Real Statistics in Excel software package (Zaiontz, 2020).

Mean values of the RuBisCO kinetic parameters are given in Table 1 for the total samples of C₃ (excluding Limonium), C₃ Limonium and C₄ plants. Since K_C differences increase in proportion to the V_C (probably by around 40% of mean C₃ values), carboxylase specificity (S_C=V_C/K_C) does not make a significant contribution to differences in mean S_C/O. The difference in S_C/O between C₃ and C₄ is therefore determined largely by S_O, primarily through the increase maximum turnover rate for the oxygenase reaction, V_O. The transition from C₃ to C₄ plants is accompanied by an estimated 10–25% decrease in mean S_C/O, due overwhelmingly to changes in the kinetics of the oxygenase reaction alone. Overall, the results in Table 1 are similar to those in the PGLS study (Bouvier et al., 2021); in C₄ species, S_C/O is lower than in C₃, and both V_C and K_C are higher than in C₃ species. The sample of C₃ Limonium species differs from the main C₃ sample in both higher S_C and S_O means, determined largely by decreases in K_C and K_O. The resulting mean S_C/O in Limonium is 15% higher than the mean of the C₃ sample.

Regression coefficients and their standard errors are given in Table 2 for the C₃ (excluding Limonium), C₃ Limonium, and C₄ samples. Scatter plots of the data and lines of best fit with R² are shown in Figure 1 for correlations between parameters from the same reaction (carboxylase or oxygenase), and in Figure 2 for correlations between carboxylase and oxygenase parameters. Results obtained for carboxylase (Figure 1A) indicate differences between carboxylation parameters in C₃, C₃ Limonium, and C₄ plant RuBisCOs. On average, b is negligible (when compared to the product, mV_max) in the C₃ plant sample. For the carboxylase reaction, the gradients (m) and intercept (b) of the lines of best fit decrease and increase, respectively, from C₃ to C₃ Limonium, to C₄. Also of note are the lower R² values (higher variance) for the C₃ and C₄ samples as compared to C₃ Limonium sample.

The actual trend lines for S vs. V_max (Figures 1B,D) can be calculated by expressing the specificity (V_max/K_M) in the general hyperbolic in V_max form

and substituting m and b with the corresponding K_M vs. V_max regression coefficients given in Table 2. S increases from zero with increasing V_max, reaching the asymptotic limit value m⁻¹ when mV_max>>b. It is also clearly apparent that the linear equation obtained from regression of the Limonium data (with higher R²) is tangential to the predicted curves in the vicinity of the data points. That the coefficient corresponding to m⁻¹ should approximate the mean value of S is easily verified by comparing the results in Tables 1 and 2, justifying the underlying assumptions of the regression analysis. The rate at which this limit is reached depends on m.b⁻¹ (verifiable from the corresponding coefficients in Table 2). For carboxylase, we find that the rate of increase in S with respect to increasing V_max is relatively fast in the sample of C₃ plants, while significantly slower for C₃ Limonium, and in C₄ plants, the limiting value is reached very slowly. Unlike carboxylase, the regression coefficients obtained for the oxygenase reaction (Figure 1C) indicate little difference between the C₃, C₃ Limonium, and C₄ plant groupings. In contrast to the C₃ sample which shows practically no correlation between S_C and V_C (Figure 1B), all groups exhibit positive correlations for S_O vs. V_O (Figure 1D).

Varying degrees of correlation are evident between carboxylase and oxygenase kinetic parameters (Figure 2). Positive correlations are observed in both V_O vs. V_C (Figure 2A) and K_O vs. K_C (Figure 2B), although the differences between C₃, C₃ Limonium and C₄ are not significant. Nevertheless, differences between the three groups do become apparent in many of the other correlations. In particular, very strong (R²>0.9) S_C vs. S_O correlations (Figure 2D) clearly distinguish the three groups. The different forms in Equation (2) suggest similarly strong linear correlations should also be obtained for V_C/V_O vs. K_C/K_O (Figure 2F). Inverting the linear equations obtained from the V_C/V_O vs. K_C/K_O regression provide hyperbolic-like functions which accurately predict the reciprocal V_C/V_O vs. K_O/K_C plots (Figure 2H) for each of the three group samples. Other correlations, S_C/O vs. V_C, S_C/O vs. V_C/O, and S_C/O vs. K_O/C, relevant for the discussion and interpretation of Equation (2) are also shown in Figure 2.

As shown in Figure 1, the correlation coefficients obtained from the linear regression of K_M vs. V_max in Table 2 can be used to predict the correlations in S vs. V_max. The relatively high level of correlation in the Limonium data suggests that an accurate estimation of the curve for S_C vs. S_O should be obtainable using parametric equations derived from S_C vs. V_C and S_O vs. V_C. Equations for S_C vs. V_C and S_O vs. V_O are already defined (Figures 1B,D), and an equation (Figure 3C) for V_O in terms of V_C derived from nonlinear regression of V_O vs. V_C (Figure 2A) can be substituted for V_O in the equation for S_O vs. V_O, yielding the desired equation for S_O vs. V_C (Figure 3B). In each case, the linear equations obtained from regression of data in Figure 3 are quite clearly tangential to the predicted curves in the vicinity of the data points. Moreover, the predicted curve for S_C vs. S_O (Figure 3A) is in fact very nearly linear.

For each genus, the near-linear trend predicted in Figure 3A suggests performing the linear regression for S_C vs. S_O with the intercept fixed at zero (Figure 4A). Further, the gradient (regression coefficient) of the regression line in this way quite accurately predicts the sample S_C/O means for each of the genera (Figure 4B), which again validates our basic assertion that the coefficients of the linear regression should correspond to sample means (Cummins et al., 2018a, 2019a). Examples of genera with data for more than a few species are rather limited. In addition to Limonium, for which there is a reasonably sized sample (Table 1), C₃ plant data are available for numbers of BOP species from Oryza, Aegilops, and Puccinellia. Both C₃ and C₄ plant data are available for Panicum, while Flaveria is the only genus for which there are parameters for C₃, C₄, and transitional (C₃-C₄ and C₄-like) species (Supplementary Tables S1 and S2). The results in Figure 4A reveal a high level (R²>0.90) of S_C vs. S_O correlation between species within the various genera, irrespective of photosynthetic (C₃ or C₄) pathway. The distribution of S_C/O in these genera is illustrated more clearly in Figure 4B. For the vast majority of Panicum and Flaveria species (both C₃ and C₄), the S_C/O is more than one SD below the median of the total C₃ sample.

There are some other correlations of note that distinguish the various genera (Figure 5). Significant S_C/O vs. V_C correlations are obtained for both Limonium and Flaveria (5A), but only for Limonium in S_O vs. V_C (5B). In Figure 5C, increased S_C/O in Limonium, Oryza, Aegilops, and Puccinellia (exclusively C₃) species correlates with increased CO₂ affinity (K_O/C), while for Panicum and Flaveria (predominantly C₄ species), increased K_O/C has little tendency to increase S_C/O, which appears to be true generally for species that have evolved C₄ photosynthesis (Figure 2G).

Analysis of the RuBisCO kinetic data presented here suggests that the evolution of kinetic parameters in higher plants, rather than being highly constrained or subjected to tradeoffs imposed by the enzyme’s kinetic mechanism, has adapted to variations in photorespiration as part the homeostatic maintenance of a constant CO₂ supply to the enzyme under disparate environmental conditions. The positive correlations observed between S_C and S_O, particularly between phylogenetically related species, reflect similarities in the physical binding properties of the two substrates CO₂ and O₂ to RuBP, which serve to contain S_C/O within the limits required for maintaining balance between photosynthesis and photorespiration in the regulation of carbon flux when mutations occur. Significantly, the limitation on product turnover (V_C) is the extent to which RuBisCO kinetics can adapt to the availability of carbon. Apparent tradeoffs between turnover and specificity are not symptomatic of an inefficient enzyme, but reflects the necessary adaptation of a flexible one to the changing levels of accessible CO₂ as a consequence of changes in abiotic environmental conditions.

Over the past 30ma, the evolution of C₄ photosynthesis has dramatically reduced photorespiration in a relatively small number (a few percent) of plant species by maintaining high levels of chloroplast CO₂, although somewhat paradoxically high levels of photorespiration were instrumental at the beginning the evolutionary process. The C₄ RuBisCOs in the Panicum and Flaveria samples do not exhibit the “average” C₃ kinetics, but inherit traits largely unchanged from a small proportion of the ancestral C₃ population (i.e., those with much lower than the mean S_C/O and, therefore, increased photorespiration). Nevertheless, differences in leaf anatomy and biochemistry indicate that a C₄ plant is not simply a C₃ with an attached CCM, and prodigious efforts to artificially introduce CCMs into commercial C₃ crops are ongoing but have yet to bear fruit. Recent modeling suggests that achieving C₂ photosynthesis in rice may be a more realistic goal (Bellasio and Farquhar, 2019).

While this research continues, however, are there any prospects for reengineering C₃ RuBisCOs with the objective of improving its kinetic traits? Despite decades of research, while some progress has been made through directed evolution, a demonstrably better RuBisCO for agriculture also remains elusive (Zhou and Whitney, 2019). What is meant by a “better” RuBisCO needs to be carefully defined, and the traits to be improved should at least, if not necessarily improve yield under the prevailing settings, increase the fitness of a species to survive the expected increases in the frequency and severity of hot and dry weather events over the coming decades. In this regard, C₄ plants demonstrate the importance of a secure supply of carbon under such climatic conditions, and the evolution of increases in product turnover (V_C), although perhaps modest compared to V_C found in other taxa (Davidi et al., 2020), may well only have been maintained by the increased availability of carbon provided by the CCM. C₃ plants with higher S_C/O suffer from the concomitant reduction in the contributions to chloroplast CO₂ levels that would otherwise had been made by photorespiration. In these cases, increasing the affinity of CO₂ relative to O₂ for RuBP makes more efficient uptake of the meager supply of carbon under high stress environmental conditions. In the absence of a functional CCM, the reengineering of RuBisCOs with increased S_C/O, if possible, may help to futureproof C₃ crops in a rapidly changing climate.

Publicly available data sets were analyzed in this study. This data can be found at: https://pubs.acs.org/doi/abs/10.1021/acs.biochem.9b00237/supplfile/bi9b00237si005.xlsx.

The author confirms being the sole contributor of this work and has approved it for publication.

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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