Temperature response of Rubisco kinetics in Arabidopsis thaliana: thermal breakpoints and implications for reaction mechanisms

Abstract Enhancement of Rubisco kinetics could improve photosynthetic efficiency, ultimately resulting in increased crop yield. However, imprecise knowledge of the reaction mechanism and the individual rate constants limits our ability to optimize the enzyme. Membrane inlet mass spectrometry (MIMS) may offer benefits over traditional methods for determining individual rate constants of the Rubisco reaction mechanism, as it can directly monitor concentration changes in CO2, O2, and their isotopologs during assays. However, a direct comparison of MIMS with the traditional radiolabel method of determining Rubisco kinetic parameters has not been made. Here, the temperature responses of Rubisco kinetic parameters from Arabidopsis thaliana were measured using radiolabel and MIMS methods. The two methods provided comparable parameters above 25 °C, but temperature responses deviated at low temperature as MIMS-derived catalytic rates of carboxylation, oxygenation, and CO2/O2 specificity showed thermal breakpoints. Here, we discuss the variability and uncertainty surrounding breakpoints in the Rubisco temperature response and the relevance of individual rate constants of the reaction mechanisms to potential breakpoints.


Introduction
The enzyme Rubisco catalyzes the reaction of CO 2 or O 2 with ribulose-1,5-bisphosphate (RuBP) initiating the photosynthetic carbon reduction cycle or photorespiratory cycle, respectively (Bowes et al., 1971;Andrews et al., 1973). Kinetic studies on Rubisco typically report the Michaelis-Menten constants for carboxylation (K C ) and oxygenation (K O ), the catalytic rate of carboxylation (k catCO2 ) and oxygenation (k catO2 ), and the specificity of the enzyme for CO 2 over O 2 (S C/O ) as these parameters are used for modeling leaf gas exchange (von Caemmerer, 2000). Each of the above Michaelis-Menten parameters is a combination of elementary rate constants that describe the reaction mechanism; however, the rate constants are less well studied as the nature of the chemical mechanism and their intermediates are uncertain (Tcherkez, 2013(Tcherkez, , 2016. Optimization of Rubisco kinetics for enhanced CO 2 reduction has been proposed (Spreitzer and Salvucci, 2002), but this effort is limited by our current understanding of the reaction mechanism (Tcherkez et al., 2006;Tcherkez, 2013).
The carboxylation and oxygenation reaction mechanisms can be separated into elementary rate constant as originally proposed by Farquhar (1979), reviewed by Tcherkez (2013), and reproduced in Fig. 1. Since the initial description of the reaction mechanism (Hurwitz et al., 1956), there has been slow progress in defining rate constants due to experimental difficulties in isolating their individual effects. However, the use of membrane inlet mass spectrometry (MIMS) to study Rubisco kinetics may hold promise. The traditional radiolabel method used in most Rubisco publications relies on 14 C assays to determine k catCO2 , K C , and K O , a separate 3 H assay to determine S C/O , leaving k catO2 to be calculated. Alternatively, the MIMS assay simultaneously measures changing concentrations of CO 2 and O 2 , and can therefore determine all kinetic parameters with a single assay (Cousins et al., 2010;Boyd et al., 2015). An advantage of the MIMS method is that in addition to the abundant isotopologs of CO 2 ( 12 CO 2 ) and O 2 ( 16 O 2 ), the system can monitor less abundant stable isotopologs such as 13 CO 2 and 16 O 18 O. Measurements of primary kinetic isotope effects have been useful in defining enzyme reaction mechanisms (O'Leary et al., 1992); therefore, the MIMS system may provide new information regarding the individual rate constants. At 25 °C the MIMS method has been used for determining both Rubisco carbon fractionation (McNevin et al., 2006(McNevin et al., , 2007Tcherkez et al., 2013), and Michaelis-Menten constants of the carboxylation (v c ) and oxygenation (v o ) reactions (Cousins et al., 2010). Additionally, it was used to determine the temperature dependencies of the Rubisco kinetic parameters in the C 4 species Setaria viridis, where the Arrhenius energy of activation (E a ) is used to describe the temperature dependence of chemical reaction rates (Boyd et al., 2015). However, previous work using the radiolabel method suggests lower E a values for V cmax in C 4 species than that measured by Boyd et al. (2015) (Sage, 2002;Kubien et al., 2003;Perdomo et al., 2015;Sharwood et al., 2016). This suggests that comparisons between the MIMS E a values and the traditional radiolabel method are needed.
Here we measured the temperature response of Rubisco kinetic parameters from Arabidopsis thaliana using two methods. First, we used the traditional method involving the use of radiolabeled substrate and analysis of labeled products following the reaction in known concentrations of CO 2 and O 2 (Jordan and Ogren, 1981). Secondly, we used the MIMS method following the simultaneous consumption of CO 2 and O 2 over time, giving a direct measure of v c , v o , CO 2 , and O 2 , leading to simultaneous determination of k catCO2 , k catO2 , K C , K O , and S C/O (Cousins et al., 2010;Boyd et al., 2015). Additionally, for the radiolabel method, we compared curve fitting CO 2 responses to determine K C and k catCO2 simultaniously in an O 2 -free buffer, and k catCO2 determined at a single bicarbonate concentration in open air. The latter is a common practice for determining k catCO2 temperature responses (Tieszen and Sigurdson, 1973;Sage et al., 1995;Crafts-Brander and Salvucci, 2000;Pittermann and Sage, 2000;Sage, 2002;Kubien et al., 2003;Perdomo et al., 2015).
Recently, the existence of thermal breakpoints in the k catCO2 temperature response was highlighted as a source of variability in the Rubisco temperature response literature (Sharwood et al., 2016). Thermal breakpoints occur when E a values differ between temperature ranges. Initial observations of breakpoints in V cmax temperature responses were determined to be a methodological artifact due to the use of a single bicarbonate concentration at all temperatures and were corrected by varying the bicarbonate concentration with temperature (Björkman and Pearcy, 1970). However, breakpoints were later observed for k catCO2 , k catO2 , and K C at 15 °C using a curve fitting method (Badger and Collatz, 1977). It was suggested that these breakpoints could be due to changes in rate-limiting steps of the reaction mechanism caused by changes in enzyme conformation (Badger and Collatz, 1977). An additional breakpoint was reported in the k catCO2 of Oryza sativa at 22 °C (Sage, 2002), and Kubien et al. (2003) observed different temperature responses when k catCO2 was measured from 0 °C to 12 °C compared with 18 °C to 42 °C in Flaveria bidentis. Most recently, Sharwood et al. (2016) observed breakpoints in k catCO2 at 25 °C for Panicoid grasses when using a curve fitting method. Inconsistencies are evident between studies, and it is unclear if breakpoints are universal to all temperature response studies of plant Rubisco. Here, we discuss the possible causes of breakpoints, focusing on the three previously proposed causes of breakpoints: erroneous bicarbonate concentrations, changes in the rate-limiting step of the reaction mechanism, and deactivation of Rubisco at low temperature, using the radiolabel and MIMS data sets reported here.

Plant growth
Plants for the radiolabel method were grown and assayed at the University of New Brunswick, Fredericton, Canada. Arabidopsis thaliana (Col-0) seeds were stratified for 3 d at 4 °C on Promix (Plant Products,  (Farquhar,1979). Each reaction, forward and reverse, is numbered in a filled circle following the numbering from Farquhar (1979). Steps 8 and 5 are written as irreversible reactions.
Step 8 includes cleavage, hydration, and reprotonation as a single step.
Step 5 includes cleavage and hydration as a single step. Each step is associated with a rate constant (k) and energy of activation (ΔG ‡ ) following the same numbering as shown in the filled circles. Abbreviations are as follows: E, free activated enzyme; RuBP, d-ribulose-1, Brampton, Canada), transferred to a growth chamber Conviron,Winnipeg,Manitoba,Canada), and grown under a photoperiod of 10 h light and14 h dark, day/night temperatures of 20/18 °C, and a photosynthetic photon flux density (PPFD) of 300 μmol m −2 s −1 . Plants were watered with modified Hoagland's solution as needed.
Plants for MIMS were grown and assayed at Washington State University, Pullman, Washington, USA. Seeds of A. thaliana, ecotype Col-0, were placed in 2 liter pots containing commercial soil (LC1 Sunshine Mix, Sun Gro Horticulture, Vancouver, Canada) and grown in an environmental growth chamber (Biochambers GC-16, Winnipeg, Manitoba, Canada) at a PPFD of 300 µmol m −2 s −1 at plant height, relative humidity was not controlled, and day/night temperature was 23/18 °C, with a 14 h photoperiod and 10 h of dark. Plants were fertilized weekly (Peters 20-20-20, Allentown, PA, USA) and watered as needed.

Sampling for MIMS analysis
The youngest fully expanded leaves of plants 30-40 d after planting were sampled for Rubisco extraction. The mid vein was removed and ~2 g of leaf tissue was ground in 2 ml of ice-cold extraction buffer [100 mM HEPES pH 7.8, 10 mM DTT, 25 mM MgCl 2 , 1 mM EDTA, 10 mM NaHCO 3 , 1% (g ml -1 ) PVPP, 0.5% (v/v) Triton X-100] with a mortar and pestle on ice. Protease inhibitor cocktail (P9599, Sigma-Aldrich), 67 µl per 2 g of fresh leaf tissue, was added to the extraction buffer before grinding. The homogenized extract was centrifuged at 4 °C, for 10 min, at 17 000 g. The supernatant was collected and desalted using an Econo Pac 10DG column (Bio-Rad), filtered through a Millex GP 33 mm syringe-driven filter unit (Millipore), and then centrifuged using Amicon Ultra Ultracel 30K centrifugal filters (Millipore) at 4 °C for 1 h at 3000 g. The layer maintained above the filter unit was collected, brought to 20% glycerol (v/v), flash-frozen in liquid nitrogen, and stored at -80 °C until measured. Rubisco content was determined as described above.

Radiolabel measurement of Rubisco kinetic parameters
The maximum carboxylation rate of fully activated Rubisco (V cmax ) was measured following the methods of Kubien et al. (2011) from 0 °C to 35 °C, by the incorporation of 14 C into acid-stable products. This method is later referred to as the 'single point' method. Assays were initiated by the addition of 50 μl of activated extract (as described above) to 250 μl of assay buffer [100 mM Bicine-NaOH (pH 8.2), 1 mM Na-EDTA, 20 mM MgCl 2 , 5 mM DTT, 400 μM RuBP, and 11 mM NaH 14 CO 3 (~700 Bq nmol −1 )] and stopped after 30-60 s by adding 250 μl of 1 M formic acid. Samples were dried at 90 °C, and 14 C acid-stable products were counted using a scintillation counter (LS-6500, Beckman-Coulter). The catalytic rate of carboxylation (k catCO2 ) was calculated using the equation where active sites are measured by the 14 CABP method described above. It was assumed that there is a one to one relationship between the moles of 14 CABP and active sites, resulting in units for k catCO2 of mol CO 2 mol −1 active site s −1 that simplifies to s −1 .
Michaelis-Menten parameters for CO 2 (K C ), and apparent K C at 21% O 2 [K C (21% O2) ] were determined by assaying the initial rate of Rubisco carboxylation (v c ) in 7 ml septum-sealed, N 2 -sparged vials over a range of seven NaH 14 CO 3 concentrations (Paul et al., 1991;Kubien et al., 2008). Concentrations of NaHCO 3 varied depending on temperature (e.g. 0.01-3.0 mM at 10 °C, versus 0.3-13.0 mM at 35 °C). The temperature effect on pH using pK a values (Edsall and Wyman, 1958) to calculate the CO 2 concentration was incorporated and the Henry coefficients (Sander, 2015) were used to account for the temperature effect on CO 2 solubility (see Supplementary Table S1 at JXB online). Assays were initiated by injecting 50 μl of the activated extract into vials containing CO 2 -free assay buffer [100 mM Bicine-NaOH (pH 8.2 at 25 °C), 20 mM MgCl 2 , 1 mM Na 2 -EDTA, 400 μM RuBP, and 10 μg ml −1 carbonic anhydrase], stopped after 30-60 s by adding 250 μl of 1 M formic acid, and counted as described above. The response of v c to partial pressures of CO 2 were fit to the Michaelis-Menten equation in SigmaPlot (Systat Software, San Jose, CA, USA) solving for V cmax and K C . This analysis, referred to as the 'curve fitting' method, gave a separate temperature response of k catCO2 from the single point method described above. From the same extract, the apparent K C at 21% O 2 [K C(21% O2) ] was determined, and the Michaelis constant for oxygenation (K O ) was calculated from the relationship Rubisco specificity for CO 2 over O 2 (S C/O ) was determined following the method described by Kane et al. (1994). Septa-sealed vials containing Rubisco, buffer [30 mM triethanolamine-acetate (pH 8.3), 20 mM Mg-acetate], and 0.2 mg ml −1 carbonic anhydrase were incubated in humidified gas (0.1% CO 2 in O 2 , with a total flow rate of 2000 ml min −1 ; G400 gas mixing system, Qubit Systems, Kingston Canada) at each measurement temperature, with oscillatory shaking. Reactions were initiated by injecting 2 nmol of [ 3 H]RuBP (3 kBq nmol −1 ) into the vial and terminated after 60 min by the addition of alkaline phosphatase. To prepare the sample for separation, the reaction products were applied to a 0.5 ml column of BioRad AG1-X8 anion exchange resin (200-400 mesh, formate form), washed with 10 column volumes of ddH 2 O, and radioactively labeled glycerate and glycolate eluted with 10% H 2 SO 4 . The [ 3 H] glycerate and [ 3 H]glycolate were separated via HPLC (system described in Shay and Kubien, 2013) on an Aminex HPX-87H column (BioRad, Canada) maintained at 60 °C. The mobile phase was 7.5 mM H 2 SO 4 , and the flow rate was 0.4 ml min −1 . Glycerate and glycolate fractions were collected in drop-synchronization mode (Fraction Collector III, Waters), and the amount of 3 H in each fraction was determined via scintillation counting. The S C/O was calculated from the ratio of [ 3 H[glycerate to [ 3 H] glycolate and the mole fractions of CO 2 and O 2 in the humidified gas, giving S C/O expressed as a ratio of partial pressures (Kane et al., 1994). Finally, the average value of each parameter was used to calculate the catalytic rate of oxygenation (k catO2 ) from the relationship

MIMS measurement of Rubisco kinetic parameters
Rubisco assays were conducted in a 600 µl temperature-controlled cuvette linked to an isotope ratio mass spectrometer (Thermo-Fischer Delta V) and calibrated as previously described (Cousins et al., 2010;Boyd et al., 2015). Samples were measured similarly to Boyd et al. (2015); four oxygen concentrations ranging from 40 μM to 1600 μM, and five CO 2 concentrations ranging from 0 μM to 200 μM at each oxygen level were made. Measurements were made in 5 °C intervals from 10 °C to 40 °C, and the same three replicates were measured at each temperature. The assay buffer contained 200 mM HEPES (pH 7.7 at each measurement temperature), 20 mM MgCl 2 , 0.1 mM α-hydroxypyridinemethanesulfon ic acid (α-HPMS), 8 mg ml −1 carbonic anhydrase (Sigma), and 0.6 mM RuBP. A 10 µl aliquot of extract was added per measurement. Rubisco was activated by leaving the extract at room temperature for 10 min prior to returning to ice before measurement.
The measured v c , v o , and the corresponding CO 2 and O 2 concentrations were fit simultaneously to the following equations It should be noted that plant growth temperature, photoperiod, extraction protocol, and assay conditions were similar but not identical between the MIMS and radiolabel experiments, and, as discussed below, should be taken into account when comparing these two data sets.

Modeling temperature responses
The temperature responses of the kinetic parameters were calculated for the equation where k 25 is the value of the parameter at 25 °C, E a is the Arrhenius activation energy (kJ mol −1 ), R is the molar gas constant (0.008314 kJ mol −1 K −1 ), T K is the temperature in Kelvin, and the term (298.15-T K )/298.15 is the scaling factor so that k 25 may be used as the pre-exponential term. The E a and k 25 values for each Rubisco parameter were calculated by a linear regression of the natural log of the data plotted against (T K -298.15)/(T K ), such that the y-intercept was equal to the natural log of k 25 and the slope was equal to E a /(298.15 R). For comparison, the non-transformed temperature responses are presented in Supplementary Fig. S1 and Supplementary Table S2. Three replicates of E a and k 25 were determined for each parameter, with the exception of radiolabel S C/O where the number of replicates was four. For all MIMS and radiolabel comparisons, other than k catCO2 , only the curve fitting methods are compared. For simplicity, we exclude the radiolabel single point when comparing ratios of kinetic parameters with MIMS. Differences in the k 25 and E a values were determined by ANOVA, followed by pair-wise comparison (Tukey HSD) with a significance cut-off of P<0.05 in Statistix 9 (Analytical Software, Tallahassee, FL, USA). Arrhenius plots for all kinetic parameters were examined for thermal breaks using the package 'segmented' in R, which first tests for differences between slopes using the Davies test (Davies, 1987), and then estimates the breakpoints in linear models using maximum likelihood (Muggeo, 2003(Muggeo, , 2008R Core Team, 2013). When breakpoints in the Arrhenius temperature response plots were statistically valid, the E a values above and below the break points were compared with other E a values as described above; the k 25 value was held constant when fitting for two E a values above and below the breakpoint. Figure 1 depicts the currently hypothesized reaction mechanism of Rubisco as originally described by Farquhar (1979). The kinetic parameters k catCO2 , k catO2 , K C , K O , and S C/O can be described by the individual first-order rate constants (k) seen in Fig. 1 as follows:

Equations for reaction mechanisms
where the subscript indicates the transition state as numbered in Fig. 1 by the black circles. The approximations in Equations 11-13 are made by assuming that the rates of decarboxylation (k 7 ) and deoxygenation (k 4 ) are negligible. These first-order rate constants can be related to temperature using transition state theory and the Eyring equation where k B is the Boltzmann constant (1.3807 × 10 -23 J K −1 ), h is the Planck constant (6.6261 × 10 -34 J s), and ΔG ‡ (J mol −1 ) is the standard free energy difference between the transition state and the substrate (or intermediate).
Note that the proportionality constant κ, describing the proportion of vibrations that lead to product formation, has been assumed equal to one and left out of the equation. The ΔG ‡ has components of entropy (ΔS ‡ ) and enthalpy (ΔH ‡ ) as defined by where the double dagger symbol ( ‡ ) denotes the transition state.

Modeling rate constants (k) and ΔG ‡
The proposed Rubisco reaction mechanism ( Fig. 1) suggests that k catCO2 , k catO2 , K C , K O , and S C/O are described by complex terms made up of two or more elementrary reaction rates (Farquhar, 1979; Equations 9-13). The rate constant (k) is related to the energy barrier for the transition state of the reaction, often referred to as the activation energy (ΔG ‡ ). The relationship between k, ΔG ‡ , and temperature is described by the Eyring equation (Equation 14), where ΔG ‡ has enthalpic (ΔH ‡ ) and entropic (ΔS ‡ ) components (Equation 15). From Equation 15, a plot of ΔG ‡ with temperature has a slope of ΔS ‡ and a y-intercept of ΔH ‡ . For the discussion of Rubisco kinetics, all numbering of k, ΔG ‡ , ΔH ‡ , and ΔS ‡ refers to reaction steps initially described by Farquhar (1979) and reproduced in Fig. 1. The Eyring equation has been previously used to calculate ΔG ‡ values for k catCO2 , k catO2 , and S C/O (Chen and Spreitzer, 1992;Tcherkez et al., 2006;McNevin et al., 2007;Tcherkez, 2013). Because k catCO2 and k catO2 are first-order rate constants, they have been represented as and and because S C/O is the ratio of two first-order rate constants (Equation 13), it has been represented as The ΔG ‡ terms in Equations 16-18 can be calculated directly from measured values, and the ΔH ‡ and ΔS ‡ terms would describe a linear fit of ΔG ‡ to the temperature response, assuming ΔH ‡ and ΔS ‡ are constant within the temperature range. However, the use of Equations 16-18 does not provide information regarding an elementary rate constant or a corresponding energy barrier. Modeling to estimate individual rate constants from the measured data is described below.

Modeling of radiolabel data
Each of the rate constants (k) in Fig. 1 has a corresponding energy of activation (ΔG ‡ from Equation 14), which has a corresponding enthalpic and entropic component (ΔH ‡ and ΔS ‡ from Equation 15). We assumed that the values of ΔH ‡ and ΔS ‡ are constant within the temperature range. Therefore, we fit Michaelis-Menten parameters calculated from elementary rate constants using Equations 9-13 to the measured Michaelis-Menten parameters by varying the corresponding ΔH ‡ and ΔS ‡ values. All modeling used the solver function in Excel (2016, Microsoft, Redmon, WA, USA) to minimize the sum of the differences squared between modeled and measured parameters. The rate constants k 8 (cleavage of carboxylated intermediate) and k 9 (enolization of RuBP) were calculated from measured k catCO2 values following the calculations of Tcherkez et al. (2013) such that k 8 /k 9 is 0.83 at 25 °C. The rate constant k 10 (de-enolization) was modeled assuming k 9 /k 10 is 0.43 at 25 °C following the calculations of Tcherkez et al. (2013); we further assumed that this ratio remained constant with temperature. This allowed for calculation of the rate of k 6 (CO 2 addition) as the only remaining unknown when fitting measured values of K C with Equation 11 assuming k 7 (de-carboxylation) was negligible. After calculating k 6 , then k 3 (O 2 addition) was modeled from measured S C/O values and Equation 13, assuming rate constants k 7 (decarboxylation) and k 4 (deoxygenation) are negligible. Finally, the rate constant k 5 (cleavage of the oxygenated intermediate) was calculated from measured K O values and Equation 14, again assuming k 4 (deoxygenation) was negligible. This process allowed for estimation of the temperature response for k and ΔG ‡ values for each step of the reaction mechanism listed in Equations 9-13, with the exception of the decarboxylation and deoxygenation steps that were assumed to be negligible Tcherkez, 2013Tcherkez, , 2016.

Modeling of MIMS data
For the MIMS data, where measurements of k catO2 were available and non-linearity of Arrhenious plots was observed, the rate constants and corresponding ΔG ‡ , ΔH ‡ , and ΔS ‡ values were determined differently from what was described above for the radiolabel data. The ΔH ‡ and ΔS ‡ values corresponding to the rate constants for k 8 (cleavage of carboxylated intermediate), k 5 (cleavage of oxygenated intermediate), and k 9 (RuBP enolization) were determined by fitting to measured k catCO2 and k catO2 values, assuming k 8 /k 9 was 0.83 at 25 °C, and using Equations 9 and 10. Because k catCO2 showed a breakpoint, it is possible that k 8 and k 9 have different temperature responses, with a crossover at ~25 °C. However, k catO2 also showed a breakpoint at 25 °C and the carboxylated intermediate cleavage rate (k 8 ) is much greater than the oxygenated cleavage rate (k 5 ) because measured k catCO2 values are greater than measured k catO2 . Therefore, a crossover of k 5 , k 8 , and k 9 at a single temperature is not possible and a breakpoint in k catCO2 and k catO2 co-occuring at a single temperature cannot be modeled as a changing rate-limiting step. Therefore, we modeled the breakpoint in k catO2 by allowing k 5 to have separate ΔH ‡ and ΔS ‡ values above and below the breakpoint, and assuming k 9 had the same values of ΔH ‡ and ΔS ‡ above and below the breakpoint. Because k 9 (rate constant of RuBP enolization) temperature response was assumed constant for models of k catO2 , it was also assumed constant when modeling k catCO2 . Therefore, k 8 was allowed to have separate values of ΔH ‡ and ΔS ‡ above and below the breakpoint. The k 10 (rate constant of deeneolization) was subsequently calculated assuming the ratio k 9 /k 10 was 0.43 and constant with temperature. The value k 6 (rate constant of CO 2 addition) was then calculated from measured K C and the approximation of Equation 11 assuming decarboxylation is negligible. This was also done for k 3 (rate constant for O 2 addition) using K O and the approximation of Equation 12 assuming de-oxygenation (k 4 ) was negligable. It was required that k 6 and k 3 have seperate ΔH ‡ and ΔS ‡ values above and below the breakpoint to model linear Arrhenious plots of K C and K O . This process provided estimates of the temperature response for k and ΔG ‡ values for each step of the reaction mechanisms making up the measured Michaelis-Menten parameters (Equations 9-13), with the exception of the decarboxylation and deoxygenation steps, which were assumed to be negligable.

Breakpoints
The Davies test indicated significant breakpoints for the k catCO2 , k catO2 , and S C/O temperature response for the MIMS data as well as for the radiolabel single point measurement of k catCO2 (Table 1; Figs 2, 4). Both the Davies test and the maximum likelihood segmented analysis indicated that the breakpoints in these parameters were near 25 °C (Table 1). All other parameters showed no breakpoints in their temperature responses for either the MIMS or radiolabel data sets (Table 1; Figs 2-4).

Arrhenius activation energies and modeled value at 25 °C
The modeled 25 °C values (k 25 ) and Arrhenius activation energy (E a ) above 25 °C agree with many of the literature values for other C 3 -type Rubisco, including in vitro and in vivo measurements of A. thaliana (Flexas et al., 2007;Whitney et al., 2011;Walker et al., 2013;Weise et al., 2015;Galmés et al., 2016). Although, previous reports of Rubisco specificities for CO 2 over O 2 (S C/O ) at 25 °C vary widely for C 3 species, including for A. thaliana which range from below 2125 to above 2655 (Pa Pa −1 ; Flexas et al., 2007;Whitney et al., 2011;Walker et al., 2013;Weise et al., 2015). For the MIMS-derived parameters with breakpoints (k catCO2 , k catO2 , and S C/O ), and the radiolabel single point estimate of k catCO2 , the lower temperature E a values were larger than E a values estimated at higher temperatures (Tables 2, 3). Above 25 °C, the E a values were similar for all parameters between the radiolabel and MIMS curve fitting methods. The radiolabel E a for k catCO2 determined by curve fitting across all temperatures was intermediate to the two E a values estimated above and below the breakpoint from the single point radiolabel data. The k 25 values for k catCO2 estimated from radiolabel and MIMS methods were not different from each other, but were larger than the k 25 for k catO2 determined by MIMS ( Table 2). The E a and k 25 values for K C and K O were not significantly different between methods (Table 3). However, the MIMS S C/O measured from 10 °C to 25 °C had a lower (more negative) E a value than the MIMS S C/O E a value measured from 25 °C to 40 °C and the radiolabel S C/O E a value (Table 3).
The E a value for the carboxylation efficiency (k catCO2 /K C ) below 25 °C was significantly different from zero for the MIMS method, where the carboxylation efficiency increased with temperature; however, above 25 °C, the E a value was not significantly different from zero (Table 4). The MIMS E a for oxygenation efficiency (k catO2 /K O ) was significantly different from zero above and below 25 °C (Table 4). The E a for the ratio of catalytic rates (k catCO2 /k catO2 ) measured by MIMS was only significantly different from zero above 25 °C (Table 4).
The E a for K O /K C was significantly different from zero for both radiolabel and MIMS methods (Table 4).

Modeling k and ΔG ‡
Above 25 °C, the ΔG 3 ‡ -ΔG 6 ‡ for S C/O from radiolabel and MIMS (Fig. 5) are similar to previous calculations for C 3 species reported by Tcherkez et al. (2006). However, the MIMS entropy difference between O 2 and CO 2 addition (ΔS 3 ‡ -ΔS 6 ‡ , Fig. 2. The natural log of Rubisco parameters from Arabidopsis thaliana measured using radiolabel (single point, open circle; curve fit, black circle) and MIMS (gray circle) methods are plotted against the inverse of the temperature in Kelvin offset to a y-intercept of 25 °C. The temperature response of catalytic turnover for CO 2 (k catCO2 , s −1 , A) and O 2 (k catO2 , s −1 , B), and the Michaelis-Menten constant for CO 2 (K C , Pa, C) and O 2 (K O , kPa, D) are shown. The lines represent the model fit to the measured data. The radiolabel k catO2 model in (B) was determined from the relationship with S C/O described by  Arrhenius plots were examined using the package 'segmented' in R (R Core Team, 2013), which determines the significance of breakpoints in linear models and estimates breakpoint locations as described by Davies (1987). Additionally, breakpoint locations and confidence intervals (CIs, lower and upper) were independently estimated using a maximum likelihood test (Muggeo, 2003(Muggeo, , 2008. * indicates a P-value <0.05 for the Davies test and ns is not significant. slope of the line in Fig. 5; see Equation 18; see Supplemenary Table S3) from data colleted below 25 °C appear more similar to the ΔS 3 ‡ -ΔS 6 ‡ of red algae rather than of higher plants, when compared with data presented in Tcherkez et al. (2006).
The free energy of activation associated with k catCO2 (ΔG kcatCO2 ‡ ) plotted against temperature increased linearly for the radiolabel curve fit method, while the ΔG kcatCO2 ‡ calculated from MIMS measurements decreased from 10 °C to 25 °C and then increased from 25 °C to 40 °C (Fig. 6). A similar temperature response was also observed for MIMS ΔG kcatO2 ‡ , although the absolute values of ΔG kcatO2 ‡ are larger than ΔG kcatCO2 ‡ as evident by a lower k catO2 compared with k catCO2 at all temperatures (i.e. larger energy barriers result in slower reactions). The slope of ΔG kcatCO2 ‡ values presented in Fig. 6 (equivalent to the entropy term ΔS kcatCO2 ‡ ; see Supplementary Table S4) calculated for radiolabel and MIMS above 25 °C are slightly larger than those reported for Nicotiana tabacum (McNevin et al., 2007). The MIMS ΔS kcatCO2 ‡ and ΔS kcatO2 ‡ showed a sign change above and below the breakpoint (negative slope to positive slope, Fig. 6; Supplementary Table S4).
Temperature responses of the rate constants (k) and corresponding energy barriers of the transition states (ΔG ‡ ) are shown in Fig. 7, while the modeled ΔH ‡ and ΔS ‡ values are presented in Suppementary Table S5. Calculations of elementary rate constants and corresponding ΔG ‡ are similar to previous calculations at 25 °C from Tcherkez (2013Tcherkez ( , 2016. In order to model breakpoints in the MIMS k catCO2 , k catO2 , and S C/O parameters, breakpoints are neeeded in the rate constants for the cleavage (k 8 and k 5 ) and for gas addition (k 6 and k 3 ). This is required because it was not possible to model a simultaneous change in the rate-limiting step for both the k catCO2 and k catO2 parameter ( Supplementary Fig. S2). This further required that breakpoints were needed in the rate constants for CO 2 and O 2 addition (k 6 and k 3 , respectively) to maintain the observed linearity for the K C and K O Arrhenius plots (Fig. 2). Fig. 3. The natural log of the Rubisco parameter ratios from Arabidopsis thaliana measured using radiolabel (black circle) and MIMS (gray circle) are plotted against the inverse of the temperature in Kelvin offset to a y-intercept of 25 °C. The temperature response of the catalytic efficiency of the carboxylation (k catCO2 /K C , A) and oxygenation (k catO2 /K O , B) reactions, catalytic turnover ratio for CO 2 over O 2 (k catCO2 /k catO2 , C), and the Michaelis-Menten constant ratio for O 2 over CO 2 (K O /K C , D) are shown. Lines represent the combination of models represented in Fig. 2 and are not the result of linear regressions to the ratios.

Radiolabel single point k catCO2 breakpoint
The radiolabel single point method reported here utilized a single bicarbonate concentration with temperature (11 mM) and resulted in a thermal breakpoint similar to Björkman and Pearcy (1970). Because Björkman and Pearcy (1970) suggested that there could be inhibition at low temperature and subsaturating concentrations at high temperature, we plotted the predicted CO 2 concentration achieved by 11 mM NaHCO 3 at each temperature against the measured and modeled CO 2 response of the enzyme determined by both radiolabel and MIMS curve fitting methods ( Supplementary Fig. S3). The CO 2 concentration provided by the 11 mM NaHCO 3 appears saturating at 10 °C and 15 °C, but becomes increasingly less saturating at higher temperatures, as indicated where the shaded area intersects the modeled CO 2 response ( Supplementary Fig. S3). This suggests that the lower E a value of the single point method at high temperatures could be caused by subsaturating CO 2 concentrations.

MIMS k catCO2 , k catO2 , and S C/O breakpoints
The non-linearity of Arrhenius plots of k catCO2 , k catO2 , and S C/O for the MIMS data were interpreted as 25 °C breakpoints. Badger and Collatz (1977) also observed breakpoints in k catCO2 , k catO2 , and S C/O ; however, they observed an additional thermal breakpoint in K C , which was not observed with the MIMS data presented here. As S C/O is a ratio of k catCO2 , K C , K O , and k catO2 (Equation 4), the differences in S C/O breakpoints between Badger and Collatz (1977) and our MIMS data could suggest different mechanisms driving the thermal response of S C/O . Furthermore, no breakpoint in S C/O has been observed in any study using the [ 3 H]RuBP method.
The breakpoints observed in MIMS k catCO2 and k catO2 are unlikely to be caused by insufficient or inhibitory CO 2 concentrations, as subsaturation or inhibition should be evident in the CO 2 response curves ( Supplementary Fig. S3). A breakpoint in both k catCO2 and k catO2 could be caused by deactivation of the enzyme, as was suggested by Kubien et al. (2003). However, deactivation is unlikely to change the k catCO2 /k catO2 temperature response as was observed in Fig. 3C, because both catalytic rates are expected to be affected in the same way by deactivation. Alternatively, the observed breakpoints in MIMS could be related to methodology as the radiolabel Arrhenius plots presented here for k catCO2 and S C/O were sufficiently linear.  The k 25 and E a values are the mean of 3-4 replicates, calculated from linear regressions of Arrhenius plots. The temperature ranges for each regression were determined by segment analysis. Letters indicate significant differences between groups (Tukey HSD, P<0.05).

Limitations of methodological comparisons
The Rubisco kinetic parameters for A. thaliana measured with the radiolabel and MIMS curve fitting methods were similar at and above 25 °C, suggesting similar kinetic parameters under these conditions, despite slight differences in plant growth environments, as well as sample extraction and assay conditions. However, at lower temperatures, the observed breakpoints in MIMS and the corresponding linearity of the Radiolabel temperature responses could imply that plant-specific growth differences were important. For example, spinach Rubisco appears to acclimate to growth temperature, with warmgrown Rubisco showing a thermal breakpoint in the carboxylation rate at 15 °C, below which rates are lower than those of a cold-grown enzyme (Yamori et al., 2006). This is similar to the breakpoint evident in the MIMS data set presented here; however, the daytime temperature differential between plants grown for the MIMS (23 °C) and radiolabel (20 °C) plants was much smaller than the 15 °C differential used by Yamori et al. (2006). Further, the MIMS technique had a lower S C/O than radiolabel parameters at temperatures above 25 °C, and a higher value at temperatures below 25 °C, opposite to what Yamori et al. (2006) observed, suggesting that the kinetic differences between the MIIMS and radiolabel measurements were not due to temperature acclimation of Rubisco. The possibility remains that the differences, particularly at cold temperatures, are due to methodology artifacts arising from differences in buffer composition. However, preparations of Rubisco for MIMS or radiolabel assays both include components known to affect Rubisco stability (i.e. DTT, MgCl 2 , and NaHCO 3 ), albeit at different concentrations. It is also possible that either the MIMS or the radiolabel assays causes erroneous kinetic estimates at low temperatures; however, this uncertainty is difficult to explain given that breakpoints have been observed by different laboratories using varying methods and species (Badger and Collatz, 1977;Sage, 2002, Kubien et al., 2003Sharwood et al., 2016). Therefore, additional analysis of diverse species with the MIMS system is needed to better understand if this is a technique-or species-specific phenomenon.
Nevertheless, breakpoints have persisted in the Rubisco literature for >40 years without sufficient explanation and warrant further investigations into their underlying causes. Badger and Collatz (1977) suggested that changes in the rate-limiting step of the reaction mechanism were brought about by conformational changes. If the elementary rate constants defining a specific parameter have different temperature responses then this could cause breakpoints if they cross over, causing a change in the rate-limiting step. The discussion below utilizes the currently accepted reaction mechanism of Rubisco ( Fig. 1) and transition state theory to explore breakpoints as a function of changes in energy barriers to elementary reactions.

Rubisco reaction mechanisms and breakpoints
For the MIMS data, the breakpoints observed in k catCO2 and k catO2 could be due to changes in the rate-limiting step, as suggested by Badger and Collatz (1977). For example, k catCO2 is a function of the rate of cleavage of the carboxylated intermediate (k 8 ) and the rate of RuBP enolization (k 9 ). This would mean that k 8 and k 9 have different a temperature response such that they cross over at around the breakpoint observed at 25 °C. However, modeling this change in rate-limiting steps due to different temperature responses cannot simultaneously explain the observed breakpoint in k catCO2 and k catO2 , because the value of k 5 defining the cleavage of the oxygenated intermediate is lower than k 8 . This means that k 9 cannot cross over both k 8 and k 5 at 25 °C ( Supplementary Fig. S2).
In order to model the reaction mechanism suggested by MIMS measurements, breakpoints in four elementary rate constants (k 3 , k 5 , k 6 , and k 8 ) are needed to describe the breakpoints in k catCO2 , k catO2 , and S C/O (Fig. 7D, E). While it seems unlikely that such an entropy change could be driven by a conformation change in the enzyme brought about by such minimal changes in temperature, a similar change in entropy ‡ calculated from the data presented in Fig. 4. Both measurement methods show a decrease with temperature. Solid black circles are the mean of four replicates measured using radiolabel, filled gray circles are the means from three replicates using MIMS; the SE is shown. The solid lines indicate the linear regression fit to calculated values. Fig. 6. The temperature response of ΔG kcatCO2 ‡ for MIMS and radiolabel methods, and ΔG kcatO2 ‡ for MIMS calculated from the data presented in Fig. 2. Two regressions were fit to the MIMS data on either side of the 25 °C breakpoint; a single regression is fit to the radiolabel data. Solid black circles are the mean of three replicates measured using radiolabel, filled gray circles are the means from three replicates using MIMS; the SE is shown.
for k catCO2 was observed between wild-type N. tabacum and a mutant (L335V) Rubisco (McNevin et al., 2007). This could suggest that the entropy changes proposed here may be possible given enzyme conformational changes with temperature.
The modeling presented here is largely based on isotope exchange studies, which suggest similar energy barriers between enolization (ΔG 9 ‡ ) and cleavage (ΔG 8 ‡ ). However, these measurements have been limited to 25 °C (Van Dyk and Schloss, 1986;Tcherkez et al., 2013), and extension of isotope exchange studies to temperature responses would help constrain how the elementary rate constants vary with temperature. Contrary to the above proposal that the cleavage transition state (k 8 ) undergoes changes above and below 25 °C, is that Rubisco discrimination against 13 CO 2 is believed to remain constant with temperature (Christeller and Laing, 1976). If the rate of cleavage (k 8 ) decreases, then the decarboxylation reaction (k 7 ) may increase, or the k 7 /k 8 ratio could increase, which would change Rubisco discrimination against 13 CO 2 . Furthermore, the above modeling relies on the assumption that decarboxylation (k 7 ) was negligible at all temperatures; therefore, changes in fractionation with temperature for an enzyme exhibiting breakpoints should help test the validity of these assumptions.

Conclusion
The measured temperature responses of Rubisco kinetic parameters were consistent between methods at and above 25 °C; however, there were thermal breakpoints at 25 °C in the MIMS data set for k catCO2 , k catO2 , and S C/O . Additionally, the radiolabel method Fig. 7. A kinetic energy barrier diagram showing the modeled temperature responses of the energy barrier to the transition state (ΔG ‡ ) and the corresponding first-order rate constant k. The ΔG ‡ and k are indicated by the numbered step of the reaction following Fig. 1. The assumptions made for this model are stated in the Materials and methods. For steps 3 and 6 (O 2 and CO 2 addition, respectively), the rate constants were multiplied by ambient concentrations O 2 (21 kPa) and CO 2 (41 Pa) as a pseudo-first-order approximation for comparison with the other rate constants and to calculate their respective ΔG ‡ . For the bottom figure, the left-hand column is modeled on the radiolabel data and the right-hand column on the MIMS data so that comparisons between continuous and breakpoint temperature responses can be made. The values for intermediates were taken from Tcherkez (2013) for (A) and Tcherkez (2016) for (B) and assumed to remain constant with temperature. using a single bicarbonate concentration showed a breakpoint for k catCO2 probably caused by non-saturating CO 2 concentrations at higher temperatures. Previous studies suggest that breakpoints are caused by either a change in the rate-limiting step of the reaction mechanism or deactivation of the enzyme at low temperatures. By modeling elementary steps of the reaction mechanism, we showed that neither cause is sufficient to explain simultaneous breakpoints in k catCO2 , k catO2 , and S C/O . Instead, breakpoints in the elementary rate constants would be needed. Because the modeling presented here is largely based on isotope exchange studies, moving forward, the temperature response of isotopic substitution experiments would advance our understanding of how elementary rate constants change in relation to one another with temperature.

Supplementary data
Supplementary data are available at JXB online. Fig. S1. Temperature response of Rubisco parameters from Arabidopsis thaliana measured using radiolabel and MIMS methods. Fig. S2. Two possible crossover models that result in breakpoints for k catCO2 for MIMS data. Fig. S3. CO 2 response curves from 10 °C to 40 °C showing measured values from the radiolabel and MIMS curve fitting methods. Table S1. pKa values used in calculations. Table S2. Average Rubisco kinetic parameters measured at each temperature with ±SE. Table S3. The ΔH ‡ and ΔS ‡ calculated for the ΔG ‡ values presented in Fig. 5 using Equation 18. Table S4. The ΔH ‡ and ΔS ‡ calculated for the ΔG ‡ values presented in Fig. 6 using Equations 16 and 17. Table S5. The ΔH ‡ and ΔS ‡ calculated for the ΔG ‡ values presented in Fig. 7 using Equations 9-15.