The Coevolution of RuBisCO, Photorespiration, and Carbon Concentrating Mechanisms in Higher Plants

Ribulose-1,5-bisphosphate (RuBP) carboxylase/oxygenase (RuBisCO) is the carbon-fixing enzyme present in most photosynthetic organisms, converting CO2 into organic matter. Globally, photosynthetic efficiency in terrestrial plants has become increasingly challenged in recent decades due to a rapid increase in atmospheric CO2 and associated changes toward warmer and dryer environments. Well adapted for these new climatic conditions, the C4 photosynthetic pathway utilizes carbon concentrating mechanisms to increase CO2 concentrations surrounding RuBisCO, suppressing photorespiration from the oxygenase catalyzed reaction with O2. The energy efficiency of C3 photosynthesis, from which the C4 pathway evolved, is thought to rely critically on an uninterrupted supply of chloroplast CO2. Part of the homeostatic mechanism that maintains this constancy of supply involves the CO2 produced as a byproduct of photorespiration in a negative feedback loop. Analyzing the database of RuBisCO kinetic parameters, we suggest that in genera (Flaveria and Panicum) for which both C3 and C4 examples are available, the C4 pathway evolved only from C3 ancestors possessing much lower than the average carboxylase specificity relative to that of the oxygenase reaction (SC/O=SC/SO), and hence, the higher CO2 levels required for development of the photorespiratory CO2 pump (C2 photosynthesis) essential in the initial stages of C4 evolution, while in the later stage (final optimization phase in the Flaveria model) increased CO2 turnover may have occurred, which would have been supported by the higher CO2 levels. Otherwise, C4 RuBisCO kinetic traits remain little changed from the ancestral C3 species. At the opposite end of the spectrum, C3 plants (from Limonium) with higher than average SC/O, which may be associated with the ability of increased CO2, relative to O2, affinity to offset reduced photorespiration and chloroplast CO2 levels, can tolerate high stress environments. It is suggested that, instead of inherently constrained by its kinetic mechanism, RuBisCO possesses the extensive kinetic plasticity necessary for adaptation to changes in photorespiration that occur in the homeostatic regulation of CO2 supply under a broad range of abiotic environmental conditions.


INTRODUCTION
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 3 s −1 per active site for plants) may be considered, if not particularly slow, rather unexceptional (Bar-Even et al., 2011). The primary substrate (CO 2 ) must also compete for binding to the RuBP in the RuBisCO active site with the more abundant O 2 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, 2013Tcherkez, , 2015Cummins et al., 2018bCummins et al., , 2019bKannappan 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, 2013Tcherkez, , 2015, while later studies of more extensive data sets have challenged this view, revealing greater flexibility (Cummins et al., 2018a(Cummins et al., , 2019aFlamholz 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 C 3 photosynthetic pathway initiated by CO 2 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 C 4 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 C 4 photosynthesis, CO 2 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 CO 2 is then, as in C 3 photosynthesis, fixed into 3PGA by RuBisCO. By increasing CO 2 supplies and thereby suppressing photorespiration, plant CCMs began evolving from C 3 species, probably in the early Oligocene (circa 30 ma) in response to decreasing CO 2 levels, as an efficient way of increasing photosynthesis in the more challenging environmental conditions (Sage, 2004). The evolutionary success of C 4 photosynthesis and the observation of increased carbon assimilation in some C 3 crops under elevated CO 2 (Xu et al., 2016;Thompson et al., 2017) have stimulated research into the possibility of incorporating CCMs into C 3 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 C 4 photosynthesis over a number of distinct phases (Sage et al., 2018). C 2 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 CO 2 pump that utilizes the two-carbon compound, glycine, to transport and concentrate the photorespiratory CO 2 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 C 3 plants are, therefore, a fundamentally important selection factor initiating the evolution to C 4 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) v where O and C are, respectively, the O 2 and CO 2 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 C 3 plants constitute by far the largest sample, followed by around 40 examples of C 4 plants, while samples of C 3 -C 4 intermediate (extant plants exhibiting C 2 photosynthesis on the pathway to C 4 ) and some C 4 -like plants from Flaveria, a genus adopted as a model for the evolutionary pathway of C 4 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 CO 2 levels and associated increase in O 2 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 C 4 pathway (Sage et al., 2018). However, while photorespiration is not particularly advantageous to C 3 plants due to net loss of carbon, it is also important to recognize that a significant amount of photorespiratory CO 2 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 C 4 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 CO 2 from bicarbonate) and photorespiration have been postulated to form the basis of a homeostatic mechanism that ensures a stable supply of CO 2 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 CO 2 , higher temperatures, and lack of water) in driving evolution of the photorespiratory CO 2 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 C 3 populations could also be a critically important precondition in C 4 evolution. In contrast, C 3 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 CO 2 (Equation 1) through higher CO 2 affinity.

STATISTICAL METHODS
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 C 3 (excluding Limonium), C 3 Limonium collected from high stress (high temperature and water restricted) habitat (Galmés et al., 2014), Flaveria sample and total C 4 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, C 4 photosynthesis has evolved from C 3 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 CO 2 and O 2 gas substrates (Cummins et al., 2018a(Cummins et al., , 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 n 1 and n 2 with means M 1 and M 2 (e.g., regression coefficients for C 3 and C 4 samples), the combined SE for the difference in the means (∆M) can be obtained by quadrature, giving the CI as follows: (5) 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). Table 1 for the total samples of C 3 (excluding Limonium), C 3 Limonium and C 4 plants. Since K C differences increase in proportion to the V C (probably by around 40% of mean C 3 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 C 3 and C 4 is therefore determined largely by S O , primarily through the increase maximum turnover rate for the oxygenase reaction, V O . The transition from C 3 to C 4 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 C 4 species, S C/O is lower than in C 3 , and both V C and K C are higher than in C 3 species. The sample of C 3 Limonium species differs from the main C 3 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 C 3 sample.

Mean values of the RuBisCO kinetic parameters are given in
Regression coefficients and their standard errors are given in Table 2 for the C 3 (excluding Limonium), C 3 Limonium, and C 4 samples. Scatter plots of the data and lines of best fit with R 2 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 C 3 , C 3 Limonium, and C 4 plant RuBisCOs. On average, b is negligible (when compared to the product, mV max ) in the C 3 plant sample. For the carboxylase reaction, the gradients (m) and intercept (b) of the lines of best fit decrease and increase, respectively, from C 3 to C 3 Limonium, to C 4 . Also of note are the lower R 2 values (higher variance) for the C 3 and C 4 samples as compared to C 3 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 (7) 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 R 2 ) 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 C 3 plants, while significantly slower for C 3 Limonium, TABLE 1 | Sample sizes (n) and mean values of RuBisCO kinetic parameters: maximum turnover rates, V max (s −1 ), Michaelis constants, K M (μM), and specificities, S = V max /K M (s −1 .mM −1 ) and relative specificities S C/O with standard errors in the means (SE) for C 3 , C 3 Limonium, and C 4 plants. and in C 4 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 C 3 , C 3 Limonium, and C 4 plant groupings. In contrast to the C 3 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 C 3 , C 3 Limonium and C 4 are not significant. Nevertheless, differences between the three groups do become apparent in many of the other correlations. In particular, very strong (R 2 > 0.9) S C vs. S O correlations ( Figure 2D) clearly distinguish the three groups. The different forms in Equation (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. 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(Cummins et al., , 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), C 3 plant data are available for numbers of BOP species from Oryza, Aegilops, and Puccinellia. Both C 3 and C 4 plant data are available for Panicum, while Flaveria is the only genus for which there are parameters for C 3 , C 4 , and transitional (C 3 -C 4 and C 4 -like) species (Supplementary Tables S1 and S2). The results in Figure 4A reveal a high level (R 2 > 0.90) of S C vs. S O correlation between species within the various genera, irrespective of photosynthetic (C 3 or C 4 ) pathway. The distribution of S C/O in these genera is The coefficients of the independent variable (e.g., VC in Figure 1A) and intercept on the dependent variable axis (0)  illustrated more clearly in Figure 4B. For the vast majority of Panicum and Flaveria species (both C 3 and C 4 ), the S C/O is more than one SD below the median of the total C 3 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 C 3 ) species correlates with increased CO 2 affinity (K O/C ), while for Panicum and Flaveria (predominantly C 4 species), increased K O/C has little tendency to increase S C/O , which appears to be true generally for species that have evolved C 4 photosynthesis ( Figure 2G).

Photorespiration in the Evolution of RuBisCO and C 4 Photosynthesis
The evolutionary pathway to C 4 photosynthesis necessitates extensive structural, biochemical, and genetic modifications in the ancestral C 3 plants (Gowik et al., 2011). Considering the current understanding of C 4 evolution has been achieved through a broad multidisciplinary approach (Sage et al., 2018), it is noteworthy that the numbers of published RuBisCO kinetic studies over the last decade have shown a steep decline (Hanson, 2016). C 4 photosynthesis is a prime example of convergent evolution (Blount et al., 2018), having arisen on at least 66 occasions over the past 30 ma (Sage et al., 2011), producing many thousands of species spread globally over many diverse plant families (Sage, 2016). Despite being the most extensively studied enzyme, at least in terms of kinetics (Jeske et al., 2019), compilations of the C 4 RuBisCO kinetic parameters (Flamholz et al., 2019) barely scratch the surface of the total global C 4 , and for that matter, C 3 populations.
Despite the large gaps in the available data, what exactly can be understood in relation to the coevolution of RuBisCO kinetics and C 4 photosynthesis? Table 1 shows clear differences between sample means of most C 3 and C 4 kinetic parameters. However, it seems that the fundamental question is whether, or to what extent, these differences arise from adaptation over time along the evolutionary C 4 pathway, or they are mostly traits inherited, with minimal change, from the ancestral C 3 species? Comparing sample means can only provide the answer if the evolving C 4 plants were randomly selected from the broader C 3 population. The evidence suggests this may not be the case, as both Flaveria and Panicun C 3 species exhibit S C/O values much lower than the C 3 average (Figure 4B), which could well be an advantage in the early-stage evolution of C 4 plants, as the first stages of C 4 evolution involve establishment of the photorespiratory CO 2 pump (C 2 photosynthesis). Given this initial requirement for photorespiratory CO 2 , it would not be unexpected to find positive selection of C 3 species with low S C/O . While C 4 evolution may have followed a number of different pathways (Schüssler et al., 2017), in the Flaveria model, C 2 photosynthesis is associated with intermediate C 3 -C 4 species, transitioning to C 4 -like in the final "optimization" stages (Sage et al., 2018); phylogenetic analysis of C 3 , transitional and C 4 species in Flaveria (Kubien et al., 2008;Kapralov et al., 2011) reveals correlations with variation in kinetic parameters. While not so apparent in the combined C 3 and C 4 samples (Figure 2C), the expected negative S C/O vs. V C trend (Tcherkez et al., 2006) found in Flaveria (Kubien et al., 2008) is reproduced in Figure 5A. One interpretation of this result is that increased CO 2 and decreased O 2 levels favor selection of RuBisCO with lower S C and higher V C , with little change in oxygenase kinetics. This appears to be supported in Figure 5B which reveals that the trend is determined exclusively by decreasing S C (increasing K C ), as S O vs. V C in Flavaria shows no correlation, so that by inference the observed reduction of S C/O with increasing V C in Flaveria must arise from S C alone. However, as we explain below, these trends in the adaptation of RuBisCO would most likely have arisen much later in the evolution of C 4 , well after the establishment of a functional CCM.
There is no difference between the C 3 and C 4 mean S C to suggest there is adaptation toward decreased carboxylation (K C ) in favor of speed (V C ); increased V C alone causes the increase in K C , maintaining the stability in S C (Table 1). Rather, the difference between C 3 and C 4 mean S C/O stems from S O alone, predominately through higher oxygenase turnover (V O ). If sampling is restricted to the C 3 species with S C/O less than one SD below the median (Figure 4B), the resulting mean values of V O (1.43 s −1 ) and K O (489 μM) are comparable to the corresponding values obtained for the C 4 sample. The C 3 species with lower S C/O and C 4 species exhibit very similar oxygenase traits. These similarities suggest that the C 4 plants sampled (Panicum and Flaveria) may have evolved from C 3 with S C/O well below the mean of the total C 3 population. Notwithstanding the other preconditions (Gowik et al., 2011), if this restriction extends more generally to the Poaceae and Asteraceae families, it alone would have significantly limited the numbers of C 4 species that could have evolved. The increased mean V C observed in the C 4 sample is consistent with adaptation in response to increased supply of CO 2 to the enzyme following development of the CCM, decreasing the selection pressure to optimize the oxygenase reaction (V O , K O ) and carboxylation (K C ) traits.

Photorespiration and the Homeostatic Maintenance of Chloroplast CO 2 Levels in C 3 Photosynthesis
Although the mitigation of photorespiration is seen as a pathway for improving crop yields, it is well recognized that under some conditions it is likely essential for healthy plant growth (Betti et al., 2016). Photorespiration can protect photosynthesis from light damage and help maintain cellular redox balance as well as plant immune responses (Voss et al., 2013). While the current evidence is largely circumstantial (Ratcliffe, 2018), another study suggests that photorespiration may not waste as much energy a first thought and enhances nitrate assimilation (Bloom and Lancaster, 2018). The scavenging of photorespiratory CO 2 in plant cells helps maintain chloroplast C levels in C 3 photosynthesis (Sage and Sage, 2009;Tholen and Zhu, 2011;Busch et al., 2013). The flow of chloroplast CO 2 should be sufficient to occupy all available RuBisCO sites (Igamberdiev, 2015). When ambient CO 2 decreases to lower than normal levels (as under extreme climatic conditions), CA may be unable to produce enough CO 2 from the reservoir of bicarbonate to fuel RuBisCO, resulting in the underutilization of the energy produced by  Figure 1D). the light reactions, but this can be mitigated by the supply of photorespiratory CO 2 (Igamberdiev, 2015). Moreover, the efficient operation of C 3 photosynthesis may require that fluctuations in O and C be contained within certain limits (Roussel and Igamberdiev, 2011), which we expect would then tend to limit v O/C (Equation 1). Based on these considerations, we might posit that v O/C should also be maintained within certain limits. The availability of photorespiratory CO 2 to chloroplasts supports a homeostatic mechanism that helps renormalizes v O/C and CO 2 levels by negative feedback of photorespiratory CO 2 into chloroplasts in response to decreasing C levels.
Apart from substrate concentrations (C and O), the other factor that determines v O/C is S C/O , which must then also be somehow constrained to keep v O/C within certain limits. Loosely correlated changes in S C and S O , which may result in an increase in one and a decrease in the other, have the potential to produce much larger variations in S C/O than are observed ( Figure 2D). The strong (R 2 > 0.90) positive correlations between S C and S O produce tightly constrained S C/O variability (Figure 2D), particularly within C 3 genera ( Figure 4A). An increase in S C is accompanied by a proportionate increase in S O , facilitating the containment of v O/C within the limits required for efficient photosynthesis. Such correlations between kinetic traits have usually been attributed to constraints inherent in RuBisCO's catalytic mechanism (Tcherkez et al., 2006;Tcherkez, 2013Tcherkez, , 2015Flamholz et al., 2019), which we consider in detail below. However, another recent study suggests phylogenetic, rather than catalytic (or mechanistic), constraints have largely determine RuBisCO adaptation (Bouvier et al., 2021).

RuBisCO Mechanistic Constraints
A fundamental understanding of correlations between RuBisCO parameters requires consideration of its kinetic mechanism (Figure 6), together with a knowledge of the functional dependence of V max , m and b in Equation (3)  and oxygenase reactions. As indicated in Figure 6, V max , m and b share a number of k i associated with product turnover, while only m and b depend on the k i that determine substrate affinity. Correlations between kinetic traits arising out of RuBisCOs mechanism must derive from correlations between the k i . However, the k i are unknown quantities, difficult if not impossible to determine empirically with any certainty, and without simplifying assumptions (Tcherkez et al., 2006), complexity of the functional relationships hinders efforts to uncover such correlations (for details of the actual kinetic equations, see Cummins et al., 2018a). Nevertheless, several important observations can be made based on the results of the present analysis.
The absence of correlation between S C and V C in the C 3 sample ( Figure 1B) demonstrates that the k i on which V C depends are not correlated to that associated with CO 2 affinity for enolized RuBP (k 5 ). When mV C >> b, S C converges asymptotically to the mean value for the sample. Compared to C 3 Limonium and C 4 plants, S C converges very quickly to this mean value for the C 3 sample (Table 1), and so the dependence of K C on b, which depends on the decarboxylation rate (k 6 ), may be neglected. This would suggest a lesser significance of k 6 in C 3 species, resolving to some extent the apparent differences of opinion on the issue of decarboxylation (Tcherkez et al., 2018;Cummins et al., 2019a). Nevertheless, the results suggest significant (mV max ≈ b) decarboxylation in both C 3 Limonium and C 4 samples ( Figure 1A) and deoxygenation (k 12 , i.e., breakdown of the Michaelis complex by dissociation of O 2 ) in all three (Figure 1C).  Figure 4.
FIGURE 6 | The kinetic mechanism of RuBisCO. RuBisCO processes the three substrates, ribulose-1,5-bisphosphate (RuBP), and CO 2 or O 2 , the complete reactions taking place over several stages. RuBP (R) binds first, forming a complex (ER) with the activated form of the enzyme (E), followed by enolization of RuBP (ER*) which facilitates binding with the CO 2 (C) or O 2 (O) molecule to R* forming the ERC or ERO enzyme-substrate complexes. The 6-carbon compound formed by the addition of carbon dioxide to RuBP breaks apart forming a product complex (EP) which dissociates into two molecules of the 3-carbon compound (P), 3-phosphoglyceric acid (3PGA). Oxygenation proceeds through analogous steps except that the dissociation products (X) are one 3PGA molecule and one of 2-phosphoglycolate (2PG) to be recycled into 3PGA by photorespiration, producing CO 2 which can be made available for photosynthesis. The rate constants can be associated with turnover of product or affinity of CO 2 or O 2 substrate molecules for RuBP. The functional dependence of V max , m and b in K M (Equation 3) on the elementary rate constants is indicated for each of the reactions. A derivation of the actual kinetic equations is given in the Supplementary Material.
Correlations between carboxylase and oxygenase reactions are not precluded. The carboxylase and oxygenase reactions are preceded by enolization of the bound RuBP required for activation of CO 2 or O 2 binding, which has been shown to co-limit V max . As a consequence of this co-limitation, the forward rate constant (k 3 ) for the enolization of RuBP is a common factor of V C and V O , which effectively couples the two reaction rates. However, the actual correlation observed between V C and V O is overall weak (Figure 2A) and variable between genera (Figure 5D), with only Limonium and Aegilops (both C 3 ) exhibiting a moderate level of correlation. Consequently, these correlations are more likely due to adaptation, rather than by a tradeoff enforce by RuBisCO's mechanism. In Limonium, the linear correlation between V C and V O maintains a more or less constant ratio V C/O (in the range 2-3; Figure 2E), limiting variation in S C/O , and hence photorespiration, to mainly the ratio of K M s, i.e., K O/C (Figure 2G).
In contrast, the positive correlations between S C and S O seem to establish a manifest constraint between carboxylase and oxygenase (Figures 2D, 4A) kinetic parameters. The correlation becomes stronger (as measured by R 2 ) the more closely related the species; R 2 values tend to be somewhat higher within genera (Figure 4A), than within the general C 3 , C 4 , or total plant sample ( Figure 2D). The positive correlation seems to be preserved in mutants when the changes in kinetic parameters are relatively small (Genkov et al., 2010), while breaks for mutations that cause large perturbations to the kinetics, sometimes resulting in decreased S C and increased S O , i.e., increasing photorespiration (Whitney et al., 1999). This tends to suggest some level of correlation between carboxylase and oxygenase k i , most likely with those associated with substrate affinity (Figure 6). Both substrates present similar electrostatic potentials to the RuBisCO active site (Kannappan and Gready, 2008), so that the binding of CO 2 to enolized RuBP induces a redistribution of charge similar to that induced by O 2 binding (Cummins et al., 2018b;Kannappan et al., 2019;Bathellier et al., 2020;Cummins and Gready, 2020) which will then interact similarly with the external (to the active site) electrostatic field, which is thought to be the primary driver in enzyme catalysis (Warshel et al., 2006;Fried and Boxer, 2017). Moreover, evolutionary changes in this electrostatic field have been linked to RuBisCO substrate specificity (Poudel et al., 2020) This electrostatic field would change slightly with sequence variation outside the highly conserved active site to produce the small free energy changes required to maintain the correlation between S C and S O when mutations occur. However, other types of biophysical constraints may limit the fitness of some mutations (Studer et al., 2014;Duraõ et al., 2015), and while superior traits are still being discovered (Davidi et al., 2020), the practical limits of RuBisCO's kinetic variability remain unclear.
The effect of abiotic environmental stress on RuBisCO in C 3 plants may be succinctly rationalized in terms of the ratios of Figure 2H).
Both the carboxylase and oxygenase reactions produce 3PGA (Figure 6), although RuBisCO processes the primary substrate (CO 2 ) more efficiently than O 2 due to superior kinetic traits (V max , K M ) and the fact that one of the oxygenase products (2PG) has to be reprocessed into 3PGA by photorespiration, albeit costing a certain amount of additional energy and carbon. On the other hand, the additional CO 2 produced as a byproduct in photorespiration may be reutilized in photosynthesis if captured by chloroplasts. Thus V C/O seems to strike a practical balance between photosynthesis and photorespiration as a measure of 3PGA production efficiency; the higher V C/O the more energy efficiently 3PGA is produced. According to the familiar form of the classical Michaelis-Menten (MM) equation (Michaelis and Menten, 1913;Briggs and Haldane, 1925;Michaelis et al., 2011),  (Laisk, 1985;Laisk and Oja, 1998;Ruuska et al., 1998) due to some other limiting factors (Igamberdiev, 2015). To reach saturation, lower values of K C require less CO 2 , and higher values of K O more O 2 . In terms of the RuBisCO kinetic mechanism (Figure 6), lower K C can be best achieved by increasing CO 2 affinity (k 5 /k 6 ), and higher K O by decreasing O 2 affinity (k 11 /k 12 ) for the enolizied form of RuBP. The curvature of the predicted trend lines in Figure 7 is largely determined by the explicit linear dependence of K M on V max (Equation 3); increasing V C/O produces the monotonic decrease in K O/C . There is no obvious explanation for the divergence of K O/C , and hence S C/O , curves between C 3 Limonium and the mainstream C 3 species at lower V C/O as arising from mechanistic constrains imposed by the enzyme. Alternatively, it is posited that the observed trends arise from adaptation of RuBisCO in response to changes in chloroplast carbon (C) levels according to the prevailing environmental conditions. Under more temperate conditions (applicable to most of the C 3 sample), in species with less than the mean V C/O of about three (Table 1), C can be supplemented by increased photorespiration (decreasing S C/O ). Increasing S C/O reduces photorespiration and hence the maintenance of C, requiring increased K O/C (higher CO 2 relative to O 2 affinity) to maintain sustainable levels of photosynthesis under high stress at the lower end of V C/O . In fact, a unique study provides some empirical evidence that those (Limonium) species with higher S C/O are associated with reduced C (Galmés et al., 2014).
As V C/O increases from its mean toward the maximum value, the requirement for additional carbon appears to diminish; photorespiratory CO 2 declines with a drift toward increased S C/O . Thus, there is a positive correlation between V C/O and photorespiratory C, which is also clearly apparent in C 4 evolution where the establishment of increased C levels (by the CCM) is followed by optimization of V C . Increased throughput of product can only be maintained by increased supply of CO 2 substrate, necessitating the adaptation of RuBisCO kinetic traits. Most of the C 3 sample is tightly clustered about the mean V C or V C/O (Figures 2C,E). If V C/O falls much below the mean, C requires supplementation depending on environmental conditions, either by increased photorespiration (low stress) or by increased CO 2 relative to O 2 affinity (high stress), necessitating RuBisCO accommodate an expansive range of S C/O . As discussed, C 4 plants have likely evolved only from C 3 with below average S C/O , and this appears to be supported by the parallel trends in C 3 and C 4 illustrated in Figure 7. C 3 species with the minimal values of S C/O (lower values for K O/C ) produce additional photorespiratory CO 2 under high stress conditions, as required for the evolution of C 2 and C 4 photosynthesis. The CCM maintains consistently higher C levels, regardless of stress factors, reducing the pressure on RuBisCO to adapt, so that its kinetics have remained, except perhaps for a tendency toward higher V C , relatively unchanged by evolution.

CONCLUSION
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 CO 2 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 CO 2 and O 2 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 CO 2 as a consequence of changes in abiotic environmental conditions.
Over the past 30 ma, the evolution of C 4 photosynthesis has dramatically reduced photorespiration in a relatively small number (a few percent) of plant species by maintaining high levels of chloroplast CO 2 , although somewhat paradoxically high levels of photorespiration were instrumental at the beginning the evolutionary process. The C 4 RuBisCOs in the Panicum and Flaveria samples do not exhibit the "average" C 3 kinetics, but inherit traits largely unchanged from a small proportion of the ancestral C 3 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 C 4 plant is not simply a C 3 with an attached CCM, and prodigious efforts to artificially introduce CCMs into commercial C 3 crops are ongoing but have yet to bear fruit. Recent modeling suggests that achieving C 2 photosynthesis in rice may be a more realistic goal (Bellasio and Farquhar, 2019).
While this research continues, however, are there any prospects for reengineering C 3 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, C 4 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 FIGURE 7 | The effect of abiotic environmental stress on RuBisCO kinetics in C 3 plants. The trend lines ( Figure 2H) in relative specificity, S C/O , are obtained by the product of V C/O = V C /V O , a measure of 3PGA product turnover efficiency, and K O/C = K O /K C , a measure of CO 2 relative to O 2 affinity for enolizied RuBP. The efficiency of C 3 photosynthesis also relies on the constant supply of CO 2 to RuBisCO, which photorespiration can help maintain. Abiotic stress factors increase the photorespiration relative to photosynthesis (Equation 1). Most C 3 species, with more or less average S C/O , are situated in usually low stress (or temperate) habitats; however, some level of photorespiratory CO 2 may be necessary to maintain photosynthesis during short periods of increased stress (Igamberdiev, 2015). Some C 3 plants can leverage off the additional photorespiratory CO 2 produced by their much lower than average S C/O in high stress environments (C 2 photosynthesis). Some of these C 2 plants may go on to evolve fully developed carbon concentrating mechanisms (C 4 photosynthesis). Alternatively, the much higher than average S C/O in other C 3 plants, while mitigating photorespiration, may compensate for the carbon restriction (reduced levels of chloroplast CO 2 ) associated with high stress environments by gains in CO 2 relative to O 2 affinity.
Frontiers in Plant Science | www.frontiersin.org 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. C 3 plants with higher S C/O suffer from the concomitant reduction in the contributions to chloroplast CO 2 levels that would otherwise had been made by photorespiration. In these cases, increasing the affinity of CO 2 relative to O 2 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 C 3 crops in a rapidly changing climate.

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

FUNDING
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.