ABSTRACT
Optimization of Rubisco kinetics could improve photosynthetic efficiency, ultimatly resulting in increased crop yield. However, imprecise knowledge of the reaction mechanism and the individual rate constants limit our ability to optimize the enzyme. Membrane inlet mass spectrometery (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 comparsion of MIMS to 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 the 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 relavance of individual rate constants of the reaction mechanisms to potential breakpoints.
INTRODUCTION
The enzyme Ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) catalyzes the reaction of CO2 or O2 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 (KC) and oxygenation (KO), the catalytic rate of carboxylation (kcatCO2) and oxygenation (kcatO2), and the specificity of the enzyme for CO2 over O2 (SC/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 (Tcherkez, 2013; Tcherkez, 2016). Optimization of Rubisco kinetics for enhanced CO2 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 Figure 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 14C assays to determine kcatCO2, KC, KO, a separate 3H assay to determine SC/O, leaving kcatO2 to be calculated. Alternatively, the MIMS assay simultaneously measures changing concentrations of CO2 and O2 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 isotopologues of CO2 (12CO2) and O2 (16O2) the system can monitor less abundant stable isotopologues such as 13CO2 and 16O18O. 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., 2007; Tcherkez et al., 2013), and Michaelis-Menten constants of the carboxylation (vc) and oxygenation (vo) reactions (Cousins et al., 2010). Additionally, it was used to determine the temperature dependencies of the Rubisco kinetic parameters in the C4 species Setaria viridis (Boyd et al., 2015). However, previous work using the Radiolabel method suggest lower Ea values for Vcmax in C4 species than that measured by Boyd et al. (2015; Sharwood et al., 2016; Sage, 2002; Kubien et al., 2003; Perdomo et al., 2015), suggesting comparisons between the MIMS Ea 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 CO2 and O2 (Jordan and Ogren, 1981), which we referred to as the Radiolabel method. Secondly, we used the MIMS method following the simultaneous consumption of CO2 and O2 over time, giving a direct measure of vc, vo, CO2, and O2 leading to simultaneous determination of kcatCO2, kcatO2, KC, KO, and SC/O (Cousins et al., 2010; Boyd et al., 2015). Additionally, for the Radiolabel method we compared curve fitting CO2 responses to determine KC and kcatCO2 simultaniously in an O2 free buffer, and kcatCO2 determined at a single bicarbonate concentration at all temperatures in open air. The later is a common practice for determining kcatCO2 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 breakpoints in the kcatCO2 temperature response was highlighted as a source of variability in the Rubisco temperature response literature (Sharwood et al., 2016). Initial observations of breakpoints in Vcmax 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 bicarbonate concentration with temperature (Björkman and Pearcy, 1970). However, breakpoints were later observed for kcatCO2, kcatO2, and KC 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 kcatCO2 of Oryza sativa at 22 °C (Sage, 2002) and Kubien et al. (2003) observed different temperature responses when kcatCO2 was measured from 0 to 12 °C compared to 18 to 42 °C in Flaveria bidentis. Most recently, Sharwood et al. (2016) observed breakpoints in kcatCO2 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 rate limiting step of the reaction mechanism, and deactivation of Rubisco at low temperature, using the Radiolabel and MIMS data sets reported here.
MATERIALS AND METHODS
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 days at 4 °C on Promix (Plant Products, Brampton, Canada), transferred to a growth chamber (E-15, Conviron, Winnipeg, Manitoba, Canada) and grown under photoperiod conditions of 10 h light/14 h dark, 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, U.S.A. Seeds of A. thaliana, ecotype Col-0, were placed in 2 L 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, air/night temperature of 23/18 °C, with a 14 hour photoperiod and 10 hours of dark. Plants were fertilized weekly (Peters 20-20-20, Allentown, PA, USA) and watered as needed.
Sampling for Radiolabel Analysis
Leaf punches were obtained at mid-day, flash frozen in liquid nitrogen and stored at −80 °C until extraction. Leaf tissue was ground (1.1 cm2 disks, ca. 20 mg) in a Tenbroeck glass tissue homogenizer containing 3 mL of ice-cold extraction buffer (100 mM HEPES pH 7.6, 2 mM Na-EDTA, 5 mM MgCl2, 5 mM dithiothreitol [DTT], 10 mg ml−1 polyvinyl polypyrolidone, 2% (vol/vol) Tween-80, 2 mM NaH2PO4, 12 mM amino-n-capronic acid, and 2 mM benzamidine) and 50 μL Protease Inhibitor Cocktail (Sigma). This leaf homogenate was centrifuged at 16000× g at 4 °C for 60 seconds. The resulting supernatant was then desalted and concentrated as described by Cousins et al. (2010), and aliquots were incubated with 20 mM MgCl2 and 10 mM NaHCO3 at 30 °C for 20 min to fully carbamylate Rubisco. Rubisco content was quantified using [14C]carboxy-arabinitol bisphosphate (14CABP)-binding assay (Ruuska et al., 1998, Kubien et al., 2011).
Sampling for MIMS Analysis
The youngest fully expanded leaves of plants 30 to 40 days after planting were sampled for Rubisco extraction. The mid vein was removed and approximately 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 MgCl2, 1 mM EDTA, 10 mM NaHCO3, 1% (g/mL) PVPP, 0.5% (v/v) 100x Triton) with a mortar and pestle on ice. 67 µL of protease inhibitor cocktail (P9599, Sigma-Aldrich, St. Louis, Missouri) to 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 17000× 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 hour at 3000× g. The layer maintained above the filter unit was collected, brought to 20% (v/v) glycerol, 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 (Vcmax) was measured following the methods of Kubien et al. (2011) from 0 to 35 °C, by the incorporation of 14C 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 assay buffer (100 mM Bicine-NaOH (pH 8.2), 1 mM Na-EDTA, 20 mM MgCl2, 5 mM DTT, 400 μM RuBP, and 11 mM NaH14CO3 [~700 Bq nmol−1]), and stopped after 30 to 60 seconds by adding 250 μL of 1 M formic acid. Samples were dried at 90 °C, and 14C acid stable products were counted using a scintillation counter (LS-6500, Beckman-Coulter). Michaelis-Menten parameters for CO2 (KC), and apparent KC at 21% O2 (KC (21% O2)) were determined by assaying Rubisco activity in 7 mL septum-sealed, N2-sparged vials over a range of seven NaH14CO3 concentrations (Paul et al., 1991; Kubien et al. 2008. This analysis, referred to as the ‘curve fitting’ method, gave a separate temperature response of kcatCO2 from the single point method described above. Rubisco SC/O was determined following the method described by Kane et al. (1994). Additional details for these assays are presented in the supplemental files.
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 similar to Boyd et al. (2015); four oxygen concentrations ranging from 40 to 1600 μM, and five CO2 concentrations ranging from 10 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 MgCl2, 0.1 mM α-hydroxypyridinemethanesulfonic acid (α-HPMS), 8 mg mL−1 CA (Sigma), and 0.6 mM RuBP. 10 µL of extract was added per measurement. Rubisco was activated by leaving the extract at room temperature for 10 minutes prior to returning to ice before measurement. Additional details for these measurements are presented in the supplemental files.
Modeling Temperature Responses
The temperature responses of the kinetic parameters were calculated for the equation where k25 is the value of the parameter at 25 °C, Ea is the Arrhenius activation energy (kJ mol−1), R is the molar gas constant (0.008314 kJ mol−1 K−1), TK is the temperature in Kelvin, and the term (298.15-TK)/298.15 is the scaling factor so that k25 may be used as the pre-exponential term. The Ea and k25 values for each Rubisco parameter were calculated by a linear regression of the natural log of the data plotted against (TK-298.15)/(TK), such that the y-intercept was equal to natural log of k25 and the slope was equal to Ea/(298.15 R). For comparison the non-transformed temperature response are presented in Supp. Fig. 3. Three replicates of Ea and k25 were determined for each parameter, with the exception of Radiolabel SC/O where the replication was four. For all MIMS and Radiolabel comparisons, other than kcatCO2, only the curve fitting methods are compared. For simplicity we exclude the Radiolabel single point when comparing ratios of kinetic parameters to MIMS. Differences in the k25 and Ea values were determined by ANOVA, followed by pair-wise comparison (Tukey HSD) with a significance cutoff of p < 0.05 in Statistix 9 (Analytical Software, Tallahassee, 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 2008; R Core Team, 2013, http://www.R-project.org/). When breakpoints in the Arrhenius temperature response plots were statistically valid, the Ea values above and below the break points were compared to other Ea values as described above, the k25 value was held constant when fitting for two Ea values above and below the breakpoint.
Equations for Reaction Mechanisms
Figure 1 depicts the currently hypothesized reaction mechanism of Rubisco as originally described by Farquhar (1979). The kinetic parameters kcatCO2, kcatO2, KC, KO, and SC/O can be described by the individual first order rate constants (k) seen in Figure 1 as follows: where the subscript indicates the transition state as numbered in Figure 1 by the black circles. The approximations in Equations 4, 5, and 6 are made by assuming the rates of decarboxylation (k7) and deoxygenation (k4) are negligible.
These first order rate constants can be related to temperature using transition state theory and the Eyring equation where kB is the Boltzmann constant (1.3807·10−23 J K−1), h is the Planck constant (6.6261·10−34 J s), ΔG‡ (J mol−1) is the standard free energy difference between the transition state and the substrate (or intermediate). Note the proportionality constant k, 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 k and ΔG‡
The proposed Rubisco reaction mechanism (Fig. 1) suggests kcatCO2, kcatO2, KC, KO, and SC/O are described by complex terms made up of two or more elementrary reaction rates (Farquhar, 1979; Equations 2 through 6). The rate of an elementary reaction (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 7), where ΔG‡ has enthalpic (ΔH‡) and entropic (ΔS‡) components (Equation 8). From Equation 8, 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‡, ΔS‡ refer to reaction steps initially described by Farquhar (1979) and reproduced in Figure 1. The Eyring equation has been previously used to calculate ΔG‡ values for kcatCO2, kcatO2, and SC/O (Chen and Spreitzer, 1992; Tcherkez et al., 2006; McNevin et al., 2007; Tcherkez, 2013). Because kcatCO2 and kcatO2 are first order rate constants they have been represented as and because SC/O is the ratio of two first order rate constants (Equation 6) it has been represented as
The ΔG‡ terms in Equations 9, 10, and 11 can be calculated directly from measured values, and the ΔH‡ and ΔS‡ terms would describe a linear fit to the temperature response, assuming ΔH‡ and ΔS‡ are constant within the temperature range. However, the use of Equations 9, 10, and 11 do not provide information regarding an elementary rate constant or a corresponding energy barrier. Further modeling to estimate individual rate constants from the measured data is described below.
Modeling of Radiolabel Data
Each of the rate constants (k) in Figure 1 has a corresponding energy of activation (ΔG‡ from Equation 7), which has a corresponding enthalpic and entropic component (ΔH‡ and ΔS‡ from Equation 8). 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 2 through 6 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 k8 (cleavage of carboxylated intermediate) and k9 (enolization of RuBP) were calculated from measured kcatCO2 values following the calculations of Tcherkez et al. (2013) such that k8/k9 is 0.83 at 25 °C. The rate constant k10 (de-enolization) was modeled assuming k9/k10 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 k6 (CO2 addition) as the only remaining unknown when fitting measured values of KC with Equation 4 assuming k7 (de-carboxylation) was negligible. After calculating k6, k3 (O2 addition) was modeled from measured SC/O values and Equation 6, assuming rate constants k7 (decarboxylation) and k4 (deoxygenation) are negligible. Finally, the rate constant k5 (cleavage of the oxygenated intermediate) was calculated from measured KO values and Equation 7, again assuming k4 (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 2 through 6, with the exception of the decarboxyalation and deoxygenation steps that were assumed negligible (Tcherkez et al., 2013; Tcherkez, 2013; Tcherkez, 2016).
Modeling of MIMS Data
For the MIMS data, where measurements of kcatO2 were available and non-linearity of Arrhenious plots were observed, the rate constants and corresponding ΔG‡, ΔH‡, and ΔS‡ values were determined differently. The ΔH‡ and ΔS‡ values corresponding to the rate constants for k8 (cleavage of carboxylated intermediate), k5 (cleavage of oxygenated intermediate), and k9 (RuBP enolization) were determined by fitting to measured kcatCO2 and kcatO2 values, assuming k8/k9 was 0.83 at 25 °C, and using Equations 2 and 3. Because kcatCO2 showed a breakpoint, it is possible that k8 and k9 have different temperature responses, with a crossover at approximatly 25 °C. However, kcatO2 also showed a breakpoint at 25 °C and the carbxylated intermediate cleavage rate (k8) is much greater than the oxygenated cleavage rate (k5) because measured kcatCO2 values are greater than measured kcatO2. Therefore, a crossover of k5, k8, and k9 at a single temperature is not possible and a breakpoint in kcatCO2 and kcatO2 co-occuring at a single temperature cannot be modeled as a changing rate limiting step. Therefore, we modeled the breakpoint in kcatO2 by allowing k5 to have separate ΔH‡ and ΔS‡ values above and below the breakpoint, and assuming k9 had the same values of ΔH‡ and ΔS‡ above and below the breakpoint. Because k9 (rate constant of RuBP enolization) temperature response was assumed constant for models of kcatO2, it was also assumed constant when modeling kcatCO2.Therefor, k8 was allowed to have separate values of ΔH‡ and ΔS‡ above and below the breakpoint. The k10 (rate constant of de-eneolization) was subsequently calculated assuming the ratio k9/k10 was 0.43 and constant with temperature. The value k6 (rate constant of CO2 addition) was then calculated from measured KC and the approximation of Equation 4 assuming decarboxylation is negligible. This was also done for k3 (rate constant for O2 addition) using KO and the approximation of Equation 5 assuming de-oxygenation (k4) was negligable. It was required that k6 and k3 have seperate ΔH‡ and ΔS‡ values above and below the breakpoint to model linear Arrhenious plots of KC and KO. 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 2 through 6), with the exception of the decarboxyalation and deoxygenation steps, which were assumed negligable.
RESULTS
Breakpoints
The Davies test indicated significant breakpoints for the kcatCO2, kcatO2, and SC/O temperature response for the MIMS data as well as for the Radiolabel single point measurement of kcatCO2 (Table 1, Figures 2 and 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, Figures 2, 3 and 4).
Arrhenius Activation Energies and Modeled Value at 25 °C
The Ea, and k25 for kcatCO2, kcatO2 (Table 2), KC, KO, SC/O (Table 3) and ratios of interest (Table 4) were calculated from the linear regressions shown in Figures 2 through 4. For the MIMS derived parameters with breakpoints (kcatCO2, kcatO2, SC/O), and the Radiolabel single point estimate of kcatCO2 the lower temperatures Ea values were larger than Ea values estimated at higher temperatures (Table 2 and 3). Above 25 °C, the Ea values were similar for all parameters between the Radiolabel and MIMS curve fitting methods. The Radiolabel Ea for kcatCO2 determined by curve fitting across all temperatures was intermediate to the two Ea values estimated above and below the breakpoint from the single point Radiolabel data. The k25 values for kcatCO2 estimated from Radiolabel and MIMS methods were not different from each other, but were larger than the k25 for kcatO2 determined by MIMS (Table 2). The Ea and k25 values for KC and KO were not significantly different between methods (Table 3). However, the MIMS SC/O measured from 10 to 25 °C had a lower (more negative) Ea value than the MIMS SC/O Ea value measured from 25 to 40 °C and the Radiolabel SC/O Ea value (Table 3).
The Ea value for the carboxylation efficiency (kcatCO2/KC) below 25 °C was significantly different from zero for the MIMS method, where the carboxylation efficiency increased with temperature; however, above 25 °C the Ea was not significantly different from zero (Table 4). The MIMS Ea for oxygenation efficiency (kcatO2/KO) was significantly different from zero above and below 25 °C (Table 4). The Ea for the ratio of catalytic rates (kcatCO2/kcatO2) measured by MIMS was only significantly different than zero above 25 °C (Table 4). The Ea for KO/KC was significantly different from zero for both Radiolabel and MIMS methods (Table 4).
Modeling k and ΔG‡
Above 25 °C the ΔG3‡-ΔG6‡ for SC/O from Radiolabel and MIMS (Fig. 5) are similar to previous calculations for C3 species reported by Tcherkez et al. (2006). However, the MIMS entropy difference between O2 and CO2 addition (ΔS3‡-ΔS6‡, slope of line in Fig. 5, see Eq. 11, Supp. Table 1), from data colleted below 25 °C appear more similar to the ΔS3‡-ΔS6‡ of red algae rather than higher plants, when compared to data presented in Tcherkez et al. (2006).
The free energy of activation associated with kcatCO2 (ΔGkcatCO2 ‡) plotted against temperature, increased linearly for the Radiolabel curve fit method, while the ΔGkcatCO2 ‡ calculated from MIMS measurements decreased from 10 to 25 °C and then increased from 25 to 40 °C (Fig. 6). A similar temperature response was also observed for MIMS ΔGkcatO2 ‡, although the absolute values of ΔGkcatO2 ‡ are larger than ΔGkcatCO2 ‡ as evident by a lower kcatO2 compared to kcatCO2 at all temperatures (i.e. larger energy barriers result in slower reactions). The slope of ΔGkcatCO2 ‡ values presented in Figure 6 (equivalent to the entropy term ΔSkcatCO2 ‡, Supp. Table 2) calculated for Radiolabel and MIMS above 25 °C are slightly larger than those reported for Nicotiana tabacum (McNevin et al., 2007). The MIMS ΔSkcatCO2 ‡ and ΔSkcatO2 ‡ showed a sign change above and below the breakpoint (negative slope to positive slope, Fig. 6, Supp. Table 2).
Temperature responses of the rate constants (k) and corresponding energy barriers of the transition states (ΔG‡) are shown in Figure 7, while the modeled ΔH‡ and ΔS‡ values are presented in Suppemental Table 3. Calculations of elementary rate constants and corresponding ΔG‡ are similar to previous calculations at 25 °C from Tcherkez (2013) and Tcherkez (2016). In order to model breakpoints in the MIMS kcatCO2, kcatO2, and SC/O parameters, breakpoints are neeeded in the rate constants for the cleavage (k8 and k5) and for gas addition (k6 and k3). This is required because it was not possible to model a simultaneous change in the rate limiting step for both the kcatCO2 and kcatO2 parameter (Supp. Fig. 2). This further required that breakpoints were needed in the rate constants for CO2 and O2 addition (k6 and k3, respectively) to maintain the observed linearity for KC and KO Arrhenius plots (Fig. 2).
DISCUSSION
Temperature Responses of Rubisco Michaelis-Menten Kinetic Parameters
The Rubisco kinetic parameters for Arabidopsis thaliana measured with the Radiolabel and MIMS curve fitting methods were similar at and above 25 °C. Additionally, the modeled 25 °C values (k25) and Arrhenius activation energy (Ea) above 25 °C agree with many of the literature values for other C3-type Rubiscos, 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 CO2 over O2 (SC/O) at 25 °C vary widely for C3 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).
Galmés et al. (2016) highlighted contradictory trends in the temperature response of KO when measured by in vitro assay; either increasing or decreasing with temperature (when expressed in units of molarity; converting between molarity and partial pressure changes the temperature response because the solubility of O2 decreases with temperature). Here, both the Radiolabel and MIMS method show increases in KO with temperature, with lower Ea values compared to KC. The two data sets presented here confirm trends from the growing literature on C3 Rubisco temperature responses, at least for values measured above 25 °C.
Alternatively, below 25 °C the Radiolabel and MIMS derived parameters had different temperature responses where the Arrhenius plots of MIMS determined kcatCO2, kcatO2, and SC/O were non-linear (Fig. 2, Fig. 4). Different temperature responses at high and low temperatures were interpreted as breakpoints for these kinetic parameters at 25 °C (Fig. 2). However, for the Radiolabel curve fit data all kinetic parameters appeared sufficiently linear. This could suggest methodology artifacts; however, it is difficult to identify methodological errors that may give rise to breakpoints given that they have also been observed by different laboratories using varying methods and species (Badger and Collatz, 1977; Sage 2002, Kubien et al., 2003; Sharwood et al., 2016).
Evidence for Breakpoints in the Literature
Björkman and Pearcy (1970) first identified a thermal breakpoint occurring in the temperature response of Vcmax from two Atriplex species. However, in the same publication they determined that the apparent breakpoints were caused by non-saturating or inhibitory bicarbonate concentrations at varying temperatures and, when corrected, they obtained sufficiently linear Arrhenius plots. Subsequently, Badger and Collatz (1977) identified breakpoints in kcatCO2, kcatO2, and KC occuring at 15 °C, with sufficiently linear Arrhenius plots of KO. While Badger and Collatz (1977) did not discuss SC/O, using Equation S6 with their data suggests a breakpoint in SC/O. Badger and Colloatz (1977) hypothesized that breakpoints were the result of possible changes in enzyme conformation which change the rate limiting step of the reaction mechanism. Sage (2002) idenified breakpoints in kcatCO2 at 22 °C for Oryza sativa, but observed linear Arrhenius plots for other species. Furthermore, Kubien et al. (2003) also observed a breakpoint in kcatCO2 between 12 and 18 °C for Flaveria bidentis, and suggested it was caused by deactivation of the enzyme at low temperature, possibly by dissociation of the haloenzyme. These analyses generally identified Ea values above the breakpoint similar to what is often reported in the literature for the temperature response of Rubisco (Ea for kcatCO2 ~60 kJ mol−1), with larger Ea values at low temperatures.
Recently, Sharwood et al. (2016) suggested breakpoints occuring at 25 °C for kcatCO2 in eleven Panicoid grasses and tobacco. While Ea values at lower temperatures remain larger than the Ea values at higher temperatures, Sharwood et al.’s (2016) findings differs from the previous breakpoint publications, because the Ea below the breakpoint is around the expected value (~60 kJ mol−1) and the Ea above the breakpoint is lower than expected (~30 kJ mol−1). Sharwood et al. (2016) did not observe breakpoints in SC/O, but it is worth noting that they calculated SC/O from a separate assay from kcatCO2 using the ratio of 3H-glycerate to 3H-glycolate as described here for the Radiolabel method. They also did not measure the temperature responses of KC, KO or kcatO2 limiting direct comparisons to the data presented here.
Radiolabel Single Point kcatCO2 Breakpoint
The Radiolabel single point method reported here utilized a single bicarbonate concentration with temperature (11 mM). This method resulted in a breakpoint, having an Ea value of 79.5 kJ mol−1 at low temperatures, and 42.1 kJ mol−1 at higher temperatures (Fig. 2, Table 2). Similar to Björkman and Pearcy (1970), the linear Arrhenius plot (Radiolabel curve fit) has an Ea value intermediate to the two Ea values determined when using a single bicarbonate concentration (~59.6 kJ mol−1, Fig. 2, Table 2). Because Björkman and Pearcy (1970) suggested that there could be inhibition at low temperature and sub-saturating concentrations at high temperature, we plotted the predicted CO2 concentration achieved by 11 mM NaHCO3 at each temperature against the measured and modeled CO2 response of the enzyme determined by both Radiolabel and MIMS curve fitting methods (Supp. Fig. 1). The CO2 concentration provided by the 11 mM NaHCO3 is less saturating at higher temperatures because the KC of Rubisco increases with temperature and the pKa temperature response favors HCO3− at higher temperatures (Supp. Fig. 1).
From the data presented here, the CO2 concentration appears saturating at 10 and 15 °C, but becomes increasingly less saturating at higher temperatures, as indicated where the shaded area intersects the modeled CO2 response. This suggest the lower Ea value of the single point method at high temperatures could be caused by sub-saturating CO2 concentrations. The sub-saturating CO2 concentrations is likely due to both an increase in KC with temperature and the predicted concentration of CO2 decreases with temperature given the temperature response of the pKa (Harned and Bonner, 1945). Alternatively, an inhibitory concentrations of CO2 was not observed under any of the measurement conditions.
MIMS kcatCO2, kcatO2, and SC/O Breakpoints
The non-linearity of Arrhenius plots of kcatCO2, kcatO2, and SC/O for the MIMS data were interpreted as 25 °C breakpoints. Badger and Collatz (1977) also observed breakpoints in kcatCO2, kcatO2, and SC/O; however, they observed an additional thermal breakpoint in KC, which was not observed with the MIMS data presented here. As SC/O is a ratio of kcatCO2, KC, KO, and kcatO2 (Eq. S6), the differences in SC/O breakpoints between Badger and Collatz (1977) and our MIMS data could suggest different mechanisms driving the thermal response of SC/O. Furthermore, no breakpoint in SC/O has been observed in any study using the 3H-RuBP method.
The breakpoints observed in MIMS kcatCO2 and kcatO2 are unlikely to be caused by insufficient or inhibitory CO2 concentrations, as is possible for the breakpoint observed in the Radiolabel single point kcatCO2 measurement, as sub-saturation or inhibition should be evident in the CO2 response curves (Supp. Fig. 1). A breakpoint in both kcatCO2 and kcatO2 could be caused by deactivation of the enzyme as was suggested by Kubien et al. (2003). However, deactivation is unlikely to change the kcatCO2/kcatO2 temperature response as was observed in Figure 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 kcatCO2 and SC/O were sufficiently linear.
Nevertheless, breakpoints have persisted in the Rubisco literature for over forty years without sufficient explanation and warrant further investigations into their underlying causes. Badger and Collatz (1977) suggested changes in the rate-limiting step of the reaction mechanism 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 crossover causing a change in 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
Radiolabel modelling
For the Radiolabel data, where all Arrhenius plots were sufficiently linear, a model of how the energy barriers for the Rubisco reaction mechanism change with temperature is presented in Figure 7, Panel C and E, and depicted as a kinetic energy barrier diagram in Panel A and B. As previously suggested by Tcherkez (2013) the kcatCO2 and kcatO2 values can be modeled assuming identical temperature responses for the rate of enolization (k9), and cleavage for the carboxylated intermediate (k8) and oxygenated-intermediate (k5). Interestingly, the modeled addition of CO2 (ΔG6‡) had high entropic cost leading to a decreasing temperature response for the rate of CO2 addition (k6), suggesting the reaction becomes slower with increasing temperature. Additionally, the increase in the energy barrier for CO2 addition (ΔG6‡) is greater than that for O2 addition (ΔG3‡) such that the ratio k6/k3 decreased with temperature. This fits with the observation that ΔG3‡-ΔG6‡ decreases with temperature (Fig. 5). While our model for both CO2 and O2 addition has positive entropy of the transition states, the greater entropic cost for CO2 addition could be the cause of SC/O decreases with temperature, more than would be assumed if ΔG3‡-ΔG6‡ remained constant with temperature.
MIMS modeling
For the MIMS data, the breakpoints observed in kcatCO2 and kcatO2 could be due to changes in rate limiting step as suggested by Badger and Collatz (1977). For example, kcatCO2 is a function of the rate of cleavage of the carboxylated-intermediate (k8) and the rate of RuBP enolization (k9). This would mean that k8 and k9 have different temperature response such that they crossover 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 kcatCO2 and kcatO2, because the value of k5 defining the cleavage of the oxygenated intermediate is lower than k8. This means that k9 cannot crossover both k8 and k5 at 25 °C (Supp. Fig. 2). Therefore, we proposed that rather than a crossover between elementary rate constants, a conformation change in the enzyme could change the temperature response for the cleavage reactions for both carboxylated (k8) and oxygenated (k5) intermediates (Fig. 7). The needed change in cleavage reactions (k8 and k5) to model a breakpoint suggests a positive entropy for the transition state below the breakpoint (decreasing ΔG5‡ with temperature) and a negative entropy of the transitions state above the breakpoint (increasing ΔG5‡ with temperature). 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 for kcatCO2 was observed between wild type Nicotiana tabacum and a mutant (L335V) Rubisco (McNevin et al., 2007). The amino acid substitution in the mutant was suggested to affect the loop that closes over RuBP as it is bound. This could suggest that the entropy changes to the cleavage reactions (k5 and k8) proposed here maybe possible given enzyme conformational changes with temperature.
The MIMS data also indicates a breakpoint in SC/O suggesting larger Ea values at low temperatures compared to higher temperatures, therefor the term ΔG3‡-ΔG6‡ was modeled with a non-linear temperature response (Fig. 5). As SC/O can be approximated as k6/k3, this could suggest a breakpoint in the temperature response of CO2 addition (k6), O2 addition (k3), or both. The individual values for k6 and k3 cannot be derived from SC/O measurements; however, in order for the observed constant temperature response of KC and KO to remain constant with temperature the cleavage reactions discussed above need to be offset by breakpoints in both k6 and k3 (Fig. 7F). Therefore, to model the reaction mechanism suggested by MIMS measurements, breakpoints in four elementary rate constants are needed to describe the breakpoints in kcatCO2, kcatO2, and SC/O but not in KC or KO.
The modeling presented here is largely based on isotope exchange studies, which suggest similar energy barriers between enolization (ΔG9‡) and cleavage (ΔG8‡). 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 (k8) undergoes changes above and below 25 °C, is that Rubisco discrimination against 13CO2 is believed to remain constant with temperature (Christeller et al., 1976). If the rate of cleavage (k8) decreases, then the decarboxylation reaction (k7) may increase, or the ratio k7/k8 could increase, which would change Rubisco discrimination against 13CO2. Furthermore, the above modeling relies on the assumption that decarboxylation (k7) 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 dataset for kcatCO2, kcatO2, and SC/O. Additionally, the Radiolabel method using a single bicarbonate concentration showed a breakpoint for kcatCO2 at 25 °C but the curve fitting did not, suggesting this breakpoint was caused in part by non-saturating CO2 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 a simple change in rate limiting step is not sufficient to explain simultaneous breakpoints in both kcatCO2 and kcatO2, and that breakpoints in the elementary rate constants are likely needed. Additionally, it is unclear how deactivation would cause the observed breakpoint in SC/O. Moving forward, the temperature response of isotopic substitutions experiments would advance our understanding of how elementary rate constants change in relation to one another with temperature.
ACKNOWLEDGEMENT
This work was supported by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, Department of Energy (grant no. DE–FG02– 09ER16062), the National Science Foundation (Major Research Instrumentation grant no. 0923562), the National Science and Engineering Research Council of Canada (Discovery grant no. 327103; and PGS-D scholarship to APC), and the Seattle chapter of the Achievement Rewards for College Scientists Foundation (R.A.B.). A.B.C. and D.S.K. proposed the original concept and design for the project; R.A.B. and A.P.C. performed the experiments and data analysis; R.A.B. wrote the article with the contributions of all the authors; A.B.C. supervised and complemented the writing. We would like to thank Chuck Cody for maintaining plant growth facilities and current members of Cousins Lab for helpful and insightful discussions.