Calculation of specificity constants Γ for RUBISCO of different species from microcalorimetric data

Abstract

Based on earlier data concerning the reaction enthalpy of Ribulose 1,5-bisphosphate carboxylase/oxygenase (RUBISCO) from spinach (Frank et al. Phys Chem Chem Phys 2:1301–1304, 2000), it is shown that the specificity constant , indicating the ability of RUBISCO to discriminate between CO₂ and O₂ as substrate, can be determined from an isothermal titration calorimetric (ITC) measurement of as a function of the substrate concentration ratio . The approach does not need any radioactive materials and might be a cost-effective alternative for RUBISCO engineering to screen for variants with a high specificity constant.

Introduction

Ribulose 1,5-bisphosphate carboxylase/oxygenase (RUBISCO) is the key enzyme of the carbon reductive pathway, known as the Calvin-Benson-Bassham (CBB) cycle (Sharkey 2019; Zhao et al. 2024), and for photorespiration. It is a bifunctional enzyme that catalyzes both the carboxylation and oxygenation of the substrate D-ribulose 1,5-bisphospate (RuBP) by carbon dioxide (CO₂) or oxygen (O₂) at the same catalytic site (Cleland et al. 1998; Ogren 2003; Portis and Parry 2007; Prywes et al. 2023). RUBISCO of higher plants has a molecular weight of 550,000 Da and consists of eight large catalytic and eight small regulatory subunits (Andersson and Backlund 2008). The core of the hexadecameric enzyme of higher plants comprises four pairs of L-2 dimers which are similar in structure to the dimeric RUBISCO from Rhodospirillum rubrum (Knight et al. 1990). RUBISCO from higher plants shows more complex regulation properties (Lorimer 1981; Portis 1992), a higher carboxylase/oxygenase ratio (Jordan and Ogren 1981), and an apparent negative co-operativity behavior compared with the bacterial enzyme (Johal et al. 1985; Jensen and Zhu 1992). RUBISCO is activated in the presence of magnesium ions (Mg²⁺) and CO₂ (Lorimer et al. 1976). In the presence of Mg²⁺ and CO₂, all RUBISCO enzymes catalyze both the carboxylation and oxygenation of RuBP (Christeller 1981). Partitioning between both reactions is strongly influenced by divalent ions like Mg²⁺, Fe²⁺, Ni²⁺, Mn²⁺ and Co²⁺ (Christeller 1981). Transition metal ions strongly support the oxygenase reaction, while Mg²⁺ favours the carboxylation reaction (Christeller 1981). An important quantity in this respect is the specificity constant (or specificity factor) (defined below), which is a measure of the inherent ability of RUBISCO to discriminate between CO₂ and O₂ (Laing et al. 1974; Jordan and Ogren 1981). In the literature, this constant is also denoted as (Tabita 1999), (Parry et al. 2003), (Uemura et al. 1997), or (Prywes et al. 2023; Aguiló-Nicolau et al. 2024). As is evident from the recent literature (Davidi et al. 2020; Bouvier et al. 2021; Aguiló-Nicolau et al. 2023), the determination of still relies largely on radioisotope labeling involving ¹⁴C and/or ³H (Zhu et al. 1992; Harpel et al. 1993; Kane et al. 1994). It has been noticed that these methods are inefficient and costly and pose limitations for high-throughput evaluation of RUBISCO variants in a biotechnological or agricultural context (Zhao et al. 2024). There are other methods for the determination of that do not require radioisotope labeling. These methods involve the measurement of O₂ decline during the full consumption of RuBP using a Clarke-type electrode (Parry et al. 1989), quantification of the reaction products by anion-exchange chromatography (Uemura et al. 1996), nuclear magnetic resonance (NMR) spectroscopy (Wang et al. 1998), gas chromatography mass spectrometry (Whitney and Andrews 1998), and membane inlet mass spectrometry (Cousins et al. 2010). However, these methods appear to have not been widely implemented, which might be due to their complexity or systematic errors (Iñiguez et al. 2021).

In a former publication, we reported microcalorimetric measurements of the molar reaction enthalpy of the total RUBICSO reactions (Frank et al. 2000). Based on previously determined values of (Jordan and Ogren 1981, 1983), it was possible to derive separate values for the reaction enthalpies of the carboxylase and of the oxygenase reaction (Frank et al. 2000). Here, it is shown that the specificity constant Γ can be calculated from , , and independently. For this purpose, the reaction enthalpy of the total reaction has to be measured as a function of the concentration ratio of the gaseous substrates CO₂ and O₂. Therefore, we propose isothermal titration calorimetric (ITC) measurements as a possibly efficient screening method for RUBISCO variants with high specificity constants.

Materials and methods

For completeness, we summarize here key aspects of the experiments performed earlier, whose details are described elsewere (Frank et al. 2000). The CO₂ concentration was adjusted via the NaHCO₃ concentration and pH of the solution. At pH 8.0, 40 mM NaHCO₃ are in equilibrium with 0.6 mM CO₂ (Hall et al. 1983). Stepwise dilution of NaHCO₃ resulted in high and low CO₂ concentrations. At low CO₂ concentration below 10 µM, endogenous CO₂ has to be taken into account. Boiling of solutions removes CO₂. Resulting NaHCO₃ (CO₂) concentrations should be measured by a phosphoenolpyruvate carboxylase (PEPC) based assy (Hall et al. 1983). Another possibility is the use of gas syringes for mixing CO₂ and O₂ gas in appropriate ratios, followed by equilibrating the solutions. The main part of CO₂ is dissolved as HCO₃⁻, only traces exists as CO₂ in solution (Hall et al. 1983). To circumvent low grades of activation, high concentrations of enzyme can be used (Frank et al. 2000). The overall reaction enthalpy comprises both the carboxylase and oxygenase reaction catalyzed by RUBISCO. The molar enthalpy change is the sum of the evolved heat per mole of RuBP produced in the carboxylase and oxygenase reaction which contribute in a different manner (Frank et al. 2000). In the presence of Mg²⁺ as cofactor, the carboxylase reaction is favored in comparison to the oxygenase reaction at pH 8.0, 10 mM MgCl₂ and 40 mM NaHCO₃ (Christeller 1981). The ratio of the rates of carboxylase and oxygenase reaction is given by (Laing et al. 1974; Jordan and Ogren 1981)

1

with the specificity constant

2

Here, and are the maximal reaction rates for the carboxylase and oxygenase reaction, respectively, while and are the Michaelis-Menten constants for and , respectively. Let us denote the change of the RuBP (substrate) concentration due to turnover of the carboxylase activity by and correspondingly the change due the oxygenase activity by . Then, it holds at a constant ratio

3

that (Frank et al. 2000)

4

If we define the part of RuBP converted in the carboxylase reaction as

5

we obtain

6

or, after rearrangement

7

The total reaction enthalpy of RUBISCO can be written as the weighted sum of the reaction enthalpies and of the carboxylase and oxygenase reaction, respectively, according to

8

Results

Taking together Eqs. (7) and (8), the molar reaction enthalpy of the total reaction can be calculated according to

9

To calculate , the values for , , and should be known. To demonstrate our procedure without additional measurements, we produced a dataset by calculating based on Eq. (9) for several values of (Table 1). = – 401 ± 8 kJ/mol and = – 62.3 ± 0.6 kJ/mol as determined earlier (Frank et al. 2000) are applied for RUBISCO from spinach along with known values of representing the status of RUBISCO with either Mg²⁺ or Mn²⁺ as cofactors. For RUBISCO from R. rubrum, the same molar reaction enthalpies and are chosen for illustrative purposes along with the appropriate values of for this species (Jordan and Ogren 1981, 1983).

Table 1.

is calculated for several values ofwith= – 401 ± 8 kJ/mole and= – 62.3 ± 0.6 kJ/mole (Frank et al. 2000) and different values ofobtained from the literature for RUBISCO from spinach and R. rubrum (Jordan and ogren 1981, 1983)

(kJ/mol) Spinach, Mg2+	(kJ/mol) R. rubrum, Mg2+	(kJ/mol) Spinach, Mn2+	(kJ/mol) R. rubrum, Mn2+	[CO2] (µM)
379	396.8	400.15	400.72	0.25	0.0008333
361	392.8	399.3	400.33	0.5	0.0016666
330	384.9	397.6	399.3	1	0.0033333
265.4	363.3	392.7	398.2	2.5	0.0083333
208	333.26	384.9	392.7	5	0.0166666
175	308.6	377.3	388.75	7.5	0.025
153	286.1	370.1	384	10	0.033333
106.2	212.8	333.2	363.3	25	0.083333
85	159.1	288	333.2	50	0.16666
78.1	133.6	255.7	308.4	75	0.25
74.5	118.7	231.5	288.1	100	0.33333
67.3	81.6	158.9	212.8	250	0.8333
64.8	75.3	118.6	158.8	500	1.6666
63.56	68.9	92.5	118.6	1000	3.3333

Of course, can be measured by ITC for different fixed ratios . A graph of as a function of allows to determine both molar reaction enthalpies , and . If one extrapolates [CO₂] to infinity (), approaches . For [CO₂] → 0 (), → . Both reaction enthalpies can be derived from a graph of as a function of (Fig. 1). Least square nonlinear regression fits yield also und at and , respectively.

Fig. 1.

from Table 1 is displayed for several values of . A: for spinach RUBISCO with Mg²⁺ as cofactor. B: for R. rubrum RUBISCO with Mg²⁺ as cofactor. C: for spinach RUBISCO with Mn²⁺ as cofactor. D: for R. rubrum RUBISCO with Mn²⁺ as cofactor. Values of obtained from the literature (Jordan and Ogren 1981; Jordan and Ogren 1983). Figure made with SigmaPlot 13 (© 2014 Systat Software Inc.)

From Eq. (8) we learn that the part of RuBP converted in the carboxylase reaction can be expressed in terms of the reaction enthalpies according to

10

Then, we can compute

11

Thus, if and have been determined by extrapolation, it is possible to compute and plot it against . According to Eq. (6), the slope of this plot is the specificity constant . An example calculated from the values for of spinach in Table 1 and with = – 401 kJ/mol and = – 62.3 kJ/mol is shown in Fig. 2.

Fig. 2.

Linear graph of for RUBISCO of spinach as a function of with Mg²⁺ as cofactor. The specificity constant Γ can be calculated as the slope of the graph and is determined from linear regression (with zero intercept) to be 80.4 ± 0.1. Figure and fit made with SigmaPlot 13 (© 2014 Systat Software Inc.)

Discussion

In a previous ITC study, the total molar enthalpy change associated with the carboxylase and oxygenase reaction catalyzed by RUBISCO of spinach was reported (Frank et al. 2000). Based on known ratios of the carboxylase and oxygenase reaction, the enthalpy changes and could be determined separately from . For of the carboxylase reaction predominatly catalyzed with Mg²⁺ as cofactor, a value of – 62.3 kJ/mol was obtained (Frank et al. 2000). For the oxygenase reaction, which is more efficiently catalyzed by Mn²⁺-activated RUBISCO from spinach than by the Mg²⁺-activated enzyme, a much higher negative reaction enthalpy of = – 401 kJ/mol was determined (Frank et al. 2000). Obviously, the oxygenase reaction is an energy rich reaction, which probably proceeds via a peroxide intermediate (Bathellier et al. 2020). This is consistent with the finding that in the presence of Mn²⁺-ions, RUBISCO from spinach shows chemiluminescence during catalysis (Mogel and McFadden 1990), which is a good indicator for an energy rich process.

Here, we propose a two-step approach to determine the specificity constant Γ of RUBISCO by microcalorimetric measurements. The first step is to measure the molar reaction enthalpy for the carboxylase and oxygenase reaction and their different contribution to the total reaction as a function of the ratio . This can be done by variation of the CO₂ concentration at a fixed atmospheric O₂ concentration of 0.3 mM at 25 °C. A graph of versus yields the value of in the limit and that of in the limit . We demonstrated that the part of RuBP converted in the carboxylase reaction can be computed from the reaction enthalpy values. A plot of as a function of allows for a determination of the specificity constant Γ from the slope of the graph.

In a recent paper, Bloom and Kameritsch used ITC to investigate the thermodynamics of RUISCO metal binding (Bloom and Kameritsch 2017). However, to our knowledge, ITC has never been used to determine the specificity constant. In our earlier work (Frank et al. 2000), we also did not recognize this possibility. Nonetheless, it is apparent from Fig. 1 that due to the significant difference in reaction enthalpy between the carboxylase and the oxygenase reaction, which should be a conserved property of RUBISCO, the net reaction enthalpy becomes a function of the substrate ratio . This dependence should enable a determination of Γ with errors that are determined by the accuracy of the calorimetric approach. In fact, microcalorimetric data are very precise. The experimental error is 2% for and 1% for . Therefore, the calculation of from , , and for different ratios is very robust. In our earlier work (Frank et al. 2000), we used high protein concentrations to circumvent the effects of low activation grade. The ratio of RuBP/RUBISCO was between 1 and 2.5. Such high ratios are not necessary due the the catalytic properties of RUBISCO. We did not work out the minimum RUBISCO concentration, but high RUBISCO concentations lead to a quick response and a total conversion of RuBP.

In our view, the ITC approach has advantages over other approaches, since there is no need to use radioactive materials or to quantify the products of the carboxylation and oxygenation reaction. In particular, the latter procedure is often a source of errors in the determination of Γ (Iñiguez et al. 2021). We are presently not able to fully validate the ITC method against other approaches. Here, we merely show a proof of principle based on test data and hope that other researchers will take up the idea and perform further experiments for a benchmarking.

As a prospect, ITC could become an important tool for a screening of RUBISCO enzymes af various origin for high carboxylase/oxygenase reactions which may be useful to select and exploit plants with a highly efficient CO₂-reduction pathway (Zhao et al. 2024). Analysis of their protein structure, in particular of their reaction centers, will be of high value to engineer plants with enhanced crop yields.

Author contributions

J.F. derived equations and analysed data. F.M. derived equations and prepared figures. All authors interpreted data and wrote and reviewed the manuscript.

Funding

Open access funding provided by Johannes Kepler University Linz.

Data availability

All data are contained within the article.

Declarations

Ethical approval

Not applicable.

Competing interests

The authors declare no competing interests.