Theoretical isotopic fractionation of magnesium between chlorophylls

Magnesium is the metal at the center of all types of chlorophyll and is thus crucial to photosynthesis. When an element is involved in a biosynthetic pathway its isotopes are fractionated based on the difference of vibrational frequency between the different molecules. With the technical advance of multi-collectors plasma-mass-spectrometry and improvement in analytical precision, it has recently been found that two types of chlorophylls (a and b) are isotopically distinct. These results have very significant implications with regards to the use of Mg isotopes to understand the biosynthesis of chlorophyll. Here we present theoretical constraints on the origin of these isotopic fractionations through ab initio calculations. We present the fractionation factor for chlorphyll a, b, d, and f. We show that the natural isotopic variations among chlorophyll a and b are well explained by isotopic fractionation under equilibrium, which implies exchanges of Mg during the chlorophyll cycle. We predict that chlorophyll d and f should be isotopically fractionated compared to chlorophyll a and that this could be used in the future to understand the biosynthesis of these molecules.

whether such effect should affect chl d and chl f. Finally, we propose that by combining our calculations with natural Mg isotopic data would permit to better understand the biosynthetic formation of chlorphyll.

Methods
Magnesium has only three stable isotopes, 24 Mg, 25 Mg and 26 Mg. The isotopic composition of Mg is usually presented using the δ per mill (‰) notation defined as: And we define the difference of δ x Mg between two species X and Y a Δ x Mg X-Y , with x = 25 or 26 as: x x x Computational method. Orbital geometries, vibrational frequencies, Gibbs free energies of aqueous Mg species are computed using density functional theory (DFT) as implemented by the Gaussian03 code 13 . The DFT method employed is a hybrid density functional consisting of Becke's three-parameter non-local hybrid exchange potential (B3) 14 with Lee-Yang-and Parr (LYP) non-local functionals. The 6-311 + G(d,p) basis set, which is an all-electron basis set, will be chosen for H, C, O, and Mg. For the solvation effect, CPCM continuum solvation method (CPCM: conductor-like polarizable continuum model) is used. For the structure of chlorophyll a, b, d and f we used an optimized geometry shown in the Fig. 1 (data are available as supplementary materials).

Results and Discussion
The vibrational modes v 1 , v 2 , and v 3 of hexaaqua complexes are the fundamental intramolecular vibration modes. The validity of vibrational frequencies and atomic distances of Mg-O of hydrated Mg 2+ ion computed is discussed in detail in Schott et al. 15 6 2+ increases vibrational frequencies, but the effect is smaller than setting water molecules in the second coordination sphere.
Calculating how physicochemical properties vary with hydration of the species is a common strategy for examining the accuracy of theoretical calculations of aqueous species 16,17 . In the theoretical study on the hydration enthalpy of Fe 2+ and Fe 3+ , Li et al. 18 tested a small cluster model of 6 H 2 O molecules as the first coordination sphere and a large cluster model of 12 additional H 2 O molecules as the second coordination sphere. For Fe 3+ , the large cluster model brought the calculated data closer to the experimental results. For Fe 2+ , both the small and the large cluster modes reproduced the experimental results. Similarly, the hydration enthalpies of Ni 2+ and Zn 2+ were appropriately reproduced by using both the small and the large cluster models. Magnesium ion is a divalent one. The small cluster model may be applicable.
The hydration enthalpy of Mg(H 2 O) n 2+ (n = 6 or 18) was also examined. In order to relate the calculated quantities to the experimental hydration enthalpy (ΔH°h yd ) at 298 K, the following correction terms were considered 18 , . This term, which contains the entropic contribution to the solvation free energy for the continuum dielectric part, was neglected. ΔH vap is the heat of vaporization of water, which is 10.50 kcal/mol 19 . The ΔE(Cp) term arises from the difference in heat capacity of the components of the system, which corresponds to a small correction of ~1 kcal/mol at 298 K 18 . ΔE zp is the difference in vibrational zero-point energy in forming clusters, ΔE rel is a correction due to relativistic effects for metal centers, and ΔE geom is a correction due to geometry relaxation for H 2 O during the formation of the clusters. The magnitude of "−ΔE zp + ΔE rel + ΔE geom " was reported to be negligibly small (a few kcal/mol) 18 , and hence these corrections were not included in our calculation. The calculated value of ΔH°h yd is shown in  11 vs Gaussian09 in the present study and Schott et al. 15 .
While the relative difference between the lnβ 26/24 Mg of chl b and chl a ( Table 3) that we obtain (0.34) is slightly lower than in Black et al. 11 (0.67); it is closer than the experimental data (0.43). The accuracy of our calculation using Gaussian09 for Mg isotopologues was tested by comparing our calculations with experimental data for a large set of aqueous species (sulphides, citrates, EDTA, oxalates, hydroxides; see ref. 23).
The calculated theoretical isotopic fractionation between the four chlorophylls species considered here (chl a, chl d and chl f compared to chl b, see Table 3 Our results suggest that each type of chlorophyll should exhibit a distinct Mg isotopic composition. It is therefore possible to test whether Mg were exchanged at equilibrium via the Mg isotopic composition of the different chlorophyll. Following this approach, Black et al. 11 proposed that Mg were exchanged at equilibrium between chl a and chl b based on the similarity between the measured and calculated isotopic composition, suggesting that the timescale of Mg exchanges were similar to the lifetime of the chlorophylls. Our new results show even better agreements with the measurements further suggesting that Mg were exchanged during the lifetime of the chlorophyll.
It is known that the relative abundance of chl a and chl b in plants or green algae changes as a function of the light conditions 25 suggesting that the biosynthesis of chl a and chl b are closely linked. Tanaka et al. 26 isolated the gene encoding for the formation of chl b by oxygenation of chl a and proposed a chlorophyll cycle with an intermediary molecule, 7-hydroxymethyl. From their model, Mg is not involved in the cycle and, therefore, chl a and chl b should have similar isotopic composition. The fact that the Mg isotopes are fractionated between isolated chl a and chl b and follow our theoretical prediction confirms that the biosynthesis of chl a and chl b are closely linked and implies the Mg is also exchanged during the chlorophyll cycle. Our results imply that the biochemical pathway of the synthesis of chl a and chl b is more complex that presently modeled.
In this study we have expended our calculations to the two most recently discovered chlorophylls, chl d and chl f. Both chl d and chl f are always found in association with chl a 27 . Chlorphyll d and f are red-shifted chlorophyll .
that can adsorb light with wavelength up to 760 nm while chl a and b do not absorb light <700 nm. These pigments have only been discovered in a limited set of organisms so far (e.g. Acaryochloris Marina, Halomicronema Hongdechloris) and are supposed to represent the consequence of adaptation of the micro-organisms to specific   Table 3. Theoretical isotopic fractionation between different forms of chlorophylls and chlorophyll a for 298 K. ecological niches. The understanding of the biosynthesis of these novel pigments is still limited and while there is no consensus on the existence of chl d-chl a and/or chl f-chl a cycles there are hints that the biosynthesis of chl d and f are linked to chl a. Using spiked oxygen marking Schliep et al. 28 suggested that chl d was formed directly from chl a via oxygenase-type reactions but the enzymes responsible for the synthesis have yet to be discovered. Our new results on the two long wave-length absorbing chlorophylls exhibit distinct isotopic composition suggesting that it would also be possible to test the kinetic of Mg exchanged compared to the lifetime of chl d and chl f. Isotopic fractionation of Mg at equilibrium between 4 types of chlorophylls (a, b, d, and f) was demonstrated theoretically. We show that our data are consistent with previous calculations and confirms that chl a and chl b are isotopically fractionated in plants following a thermodynamic equilibrium. This implies that during the synthesis of chl b and chl a, Mg is also exchanged. We expand these calculations to the two latest discovered pigments, chl d and chl f and show that their Mg isotopes should also be isotopically fractionated during equilibrium exchanges reactions.