On the effect of heavy water (D₂O) on carbon isotope fractionation in photosynthesis

The authors wish to acknowledge the financial support provided by the franco-australian FAST project, under contract n°12795 WC. GT thanks Prof. Gabriel Cornic for valuable discussions about the manuscript. GD.F. acknowledges the support of the Australian Research Council.

Abdulkadirova KS, Kostrowicka-Wyczalkowska A, Anisimov MA, Sengers JV (2002) Thermodynamic properties of mixtures of H2O and D2O in the critical region. Journal of Chemical Physics 116, 4597–4610.
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In the present study, R_E = R_S is 99.8/0.2, that is, 499, but inlet water is made of natural water (very small R_in). Here, u_e/sER_E is in the range 3.7 10⁻⁴ mol s^–1/(10⁻² m² × 10⁻⁴ mol m^–2 s^–1 × 499) = 0.76, so that the right term in the numerator can be neglected and R_vw_a ~1/1.76 = 0.57. With a value of w_a = 0.01 mol mol^–1, we find R_v~57. Using Eqn A1 we then have R_e = 166, which is equivalent to 99.4% D₂O. In other words, the dilution of heavy water in the leaf by inlet H₂O is very small. This is consistent with the very small effect of heavy v. light inlet water on ¹²C/¹³C isotopic data in the present paper (Figs 1, 2).

As already stated in the main text, heavy water has an effect on two main steps, namely, the Rubisco-catalysed reaction, and the CO₂-HCO₃^– equilibrium, catalysed by carbonic anhydrase (Table 1). Other slowing effects caused by heavy water are negligible in the present study:

1. there is no effect of heavy water on the ¹²C/¹³C isotope effect associated with diffusion in water (Table 2), and

2. the effect of heavy water on the the ¹²C/¹³C isotope effect associated with dissolution in water is unknown, but one may assume it is small, as deuteration of water acts on dissolution through (a), the partition function of CO₂ in the liquid phase and (b), the binding energy between solvent water molecules and CO₂. The effect on binding is thought to be a negligible component (Vogel et al. 1970). Because the degrees of freedom and the motions of CO₂ are similar, the partition function of CO₂ in the liquid phase is likely not to be much influenced by deuteration of water, so that the change in the ratio of ¹³CO₂ and ¹²CO₂ solubility remains unchanged. This would be in agreement with the very small effect of atomic substitution changes on solubility in water: for example, the H₂O/D₂O isotope effect on the solubility of CH₄ is 1.005 but that of (the much larger molecule) CF₄ is 1.017 (Cosgrove and Walkley 1981). If an effect of heavy water on the ¹²C/¹³C isotope effect of dissolution were to occur, the overall impact would be very small, because of its order of magnitude (<1‰).

Thus, heavy water has roughly no effect on the carbon isotope fractionation by diffusion and dissolution (Table 2), and a change in the photosynthetic discrimination, if any, would have to be related to enzymatic effects.

The outlet D₂O vapour mole fraction, denoted as d_a, follows the mass-balance equation for heavy water, that is (as R_in is small compared with 1):

where u_e is the entering air flow through the chamber, Φ is the water flux taken up by the leaf through the petiole, s is the leaf surface area, and R_s the D/H isotope ratio of source water. R_in and w_e are the D/H isotope ratio and the water mole fraction of inlet water, respectively. Because the ratio R_in is very small when natural water in used for inlet air, we have:

Although the leaf transpired heavy water, the natural vapour pressure (H₂O of inlet air) had to be taken into account because it may have entered the leaf in the steady-state (see also above). At ambient temperatures, the combination of both natural and heavy waters behave linearly with respect to their relative quantities (Abdulkadirova et al. 2002) so that the saturation vapour pressure of the mixture at the evaporating sites is (1 − ε)d_i + εw_i, where ε is the proportion of natural water at the evaporative sites, and w_i and d_i are the saturation mole fractions of H₂O and D₂O at leaf temperature [in other words, the actual H₂O vapour mole fraction in the leaf is εw_i and that of D₂O is (1 − ε)d_i]. Then the water exchange between the atmosphere and the leaf is made up of D₂O loss, that is, g_D2O ((1 − ε)d_i − d_a and H₂O uptake, g_H2O(w_a − εw_i), where w_a is the outlet mole fraction of H₂O. As the leaf compensated for the small diffusive influx of H₂O by consuming less D₂O through the petiole we have (assuming a mole-to-mole compensation):

where the diffusion ratio (H₂O/D₂O isotope effect) is denoted as g_H2O/g_D2O = α_k (~1.040) and the saturation mole fraction pressure w_i/d_i denoted as α⁺, The net heavy water uptake by the leaf is denoted as Φ. Rearranging, this gives:

If ε is small enough (see Appendix I), we define the ‘efficient’ heavy water mole fraction as:

The D₂O saturation vapour pressure values (at leaf temperature), denoted as d_sat, were taken from data compiled for the NIST chemistry webbook (http://webbook.nist.gov/chemistry) and from Besley and Bottomley (1973). Stomatal conductance to D₂O is then given by:

The CO₂ conductance was then calculated with the ordinary equations (von Caemmerer and Farquhar 1981), with the ratio of diffusivity between CO₂ and D₂O of 1.5 (instead of 1.6 for H₂O) (Marrero and Mason 1973). It is noted that the diffusion coefficients of CO₂ in (heavy) water vapour and in air are not equal (the H₂O-to-D₂O ratio of CO₂ diffusivity is of around ~1.07), in contrast with the usual case (von Caemmerer and Farquhar 1981). However, the effect on the internal CO₂ concentration (c_i) is very small, typically of around 0.2–0.5 μmol mol^–1, and it was neglected in the present study.