Assessing kinetic fractionation in brachiopod calcite using clumped isotopes

Brachiopod shells are the most widely used geological archive for the reconstruction of the temperature and the oxygen isotope composition of Phanerozoic seawater. However, it is not conclusive whether brachiopods precipitate their shells in thermodynamic equilibrium. In this study, we investigated the potential impact of kinetic controls on the isotope composition of modern brachiopods by measuring the oxygen and clumped isotope compositions of their shells. Our results show that clumped and oxygen isotope compositions depart from thermodynamic equilibrium due to growth rate-induced kinetic effects. These departures are in line with incomplete hydration and hydroxylation of dissolved CO2. These findings imply that the determination of taxon-specific growth rates alongside clumped and bulk oxygen isotope analyses is essential to ensure accurate estimates of past ocean temperatures and seawater oxygen isotope compositions from brachiopods.

Biomineralising marine organisms serve as important geochemical archives of past climate conditions. Brachiopods constitute one group of calcifying invertebrates that have great potential for palaeoenvironmental reconstructions due to their common occurrences in Phanerozoic sediments since the Cambrian 1 . Their high abundance in Palaeozoic sediments makes them particularly valuable for deep-time seawater temperature reconstructions based on shell oxygen isotope compositions 2 . Unlike many other biogenic archives fossil and modern brachiopods can be found from tropical to polar environments and from a great range of water depths 1,3 .
A limitation of the conventional oxygen isotope palaeothermometer method is that it requires an assumption for the oxygen isotope composition of the palaeo-seawater 4 . The common assumption that the seawater δ 18 O VSMOW values remained constantly between −1‰ and 0‰ during the Phanerozoic leads to relatively low apparent oxygen isotope fractionation between ancient seawater and brachiopod calcite, and hence to unrealistically high seawater temperature estimates 2 . Alternatively, it has been claimed that the progressive 18 O depletion of brachiopod shells with age during the Phanerozoic reflects increasing post-depositional alteration or a secular decline in seawater δ 18 O values of about −6‰ compared to the modern ocean 2 . To investigate the underlying cause of presumably erroneous extremely warm Phanerozoic temperature estimates, independent constraints on past seawater temperatures and δ 18 O values are needed.
In contrast to oxygen isotope thermometry, the carbonate clumped isotope thermometer does not require an estimate for the oxygen isotope composition of the seawater, as it considers the fractionation of isotopes exclusively amongst carbonate isotopologues 5 . In thermodynamic equilibrium, the clumped isotope composition (∆ 47 ) of a given carbonate is solely a function of the carbonate precipitation temperature. Fossil brachiopod shells have been analysed both for both their oxygen and clumped isotope composition to independently constrain ocean temperatures and seawater δ 18 O 6-8 . However, previous investigations into the temperature dependence of the clumped isotope composition of modern brachiopod shells have reported inconsistent results. Came et al. 9 reported a significantly steeper ∆ 47 -temperature slope compared to the theoretical calibration 10 and to the 1 Institut für Geowissenschaften, J. W. Goethe-Universität, Altenhöferallee 1, 60438, Frankfurt am Main, Germany. 2 Earth Science Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 84005, Bratislava, Slovakia. 3

Results
Trace element analyses. The magnesium concentration of the studied modern brachiopod shells was between 0.27 mol% (Terebratalia transversa) and 6.8 mol% (Pajaudina atlantica) MgCO 3 . Our results are consistent with the expected range of modern brachiopod calcite and fall along the Global Brachiopod Mg Line 20 ( Supplementary Fig. 1a).
Bulk and clumped isotope analyses. The δ 18 O VPDB values of the modern brachiopod shells analysed in this study range between −2.20(±0.02)‰ and 3.92(±0.02)‰, while the δ 13 C VPDB values range between −0.88(±0.02)‰ and 2.44(±0.01)‰. These values are consistent with the range in isotope compositions of modern brachiopod shells (secondary and tertiary layers) reported elsewhere 20,21,25,27 . The difference between the oxygen and carbon isotope composition of the shells determined using the [Gonfiantini] and the [Brand] sets of isotopic parameters 28 is ~0.01‰. This is similar or less than the 1σ S.E. of replicate measurements and can therefore be ignored (see Methods).
The ∆ 47 (CDES 25) values measured for the modern brachiopods shells calculated with the [Gonfiantini] parameters range between 0.671(±0.007)‰ and 0.775 (±0.004)‰, while the 1σ S.E., calculated from 4-10 replicate analyses, ranges between 0.004-0.014‰. The ∆ 47(CDES 25) values for the brachiopods calculated with the [Brand] parameters are between 0.664(±0.007)‰ and 0.767(±0.004)‰, while the 1σ S.E., calculated from 4-10 replicate analyses, ranges between 0.004-0.013‰. The difference between ∆ 47 (CDES 25) values calculated with the [Gonfiantini] and the [Brand] sets of isotopic parameters is between 0.005‰ and 0.008‰. Apparent ∆ 47 -temperature relationship. To obtain a ∆ 47 -temperature relationship for modern brachiopod calcite, a least-squares fit linear regression 29,30 was performed on the measured ∆ 47 (CDES 25) values and the independently-sourced brachiopod growth temperatures 31 (Supplementary Tables 1 and 2). This approach considered uncertainties arising from both the clumped isotope measurements and the growth temperatures. The statistical analyses yielded the following ∆ 47 -temperature relationship ( Fig. 1a  where ∆ 47 is in ‰, T (temperature) is in K and the two-tailed p-values are calculated using a t-test. The slope of our ∆ 47 -temperature calibration line (eqs 1 and 2) is steeper compared to the theoretical calibration 10 and to previous calibrations made at > 70 °C 11,29,32 , and shallower than most 25 °C calibrations 33 . However, the slope of our ∆ 47 -temperature calibration line is indistinguishable from the brachiopod-only calibration of Came et al. 9 20 , respectively. The latter includes a correction for the Mg-effect, which accounts for a 0.17‰ change per mol% MgCO 3 in the δ 18 O values of the calcite, in agreement with laboratory precipitation experiments 20 . Apparent ∆ 47 equilibrium values were calculated using the theoretical calibration of Passey and Henkes 10 , i.e., their eq. 5, with the empirically determined intercept of 0.280 (Fig. 1b,c and Supplementary Fig. 2). This equation considers a 25-90 °C acid fractionation factor of 0.081‰ and has been verified in the 0-40 °C temperature range by empirical and experimental approaches 11,29,36,37 . In addition, offset ∆ 47 values were also calculated assuming that the most recent calibrations of Bonifacie et al. 32 or Kelson et al. 38 represent the clumped isotope equilibrium ( Supplementary Fig. 3). Offset ∆ 47 values were computed using both the [Gonfiantini] and the [Brand] processed data.
Most of the analysed brachiopods in this study exhibit combined offsets from clumped and oxygen isotope equilibrium, irrespective how the offset values were calculated (Fig. 1b,c and Supplementary Figs 2b,c and 3). The largest deviations from the equilibrium ∆ 47 values were observed in the temperate-to cold-water brachiopod species, particularly those of the species Magellania venosa and Magasella sanguinea. In contrast, most of the warm-water (>20 °C) taxa, such as Thecidellina congregata, Argyrotheca sp., Megerlia sp., and P. atlantica, exhibit apparent clumped isotope equilibrium.
Oxygen isotope analyses with ion probe. High resolution (20 μm) in situ oxygen isotope analysis was performed on two M. venosa shells using SIMS (Secondary Ion Mass Spectrometry). In the secondary layer of the two investigated M. venosa shells, the δ 18 O values range from −2.91‰ to 1.35‰ (sample 130) and from −2.02‰ to 0.60‰ (sample 143; Fig. 2). This species does not have a tertiary layer and the primary layer was too thin to be analysed ( Supplementary Fig. 6). The variation in δ 18 O between the outer and inner part of the shell was 4.3‰ for sample 130 and 2.6‰ for sample 143 (Supplementary Data 3, Fig. 2).  32 who, for a given precipitation temperature, did not find any difference in the clumped isotope composition between dolomite and calcite reacted at 90 °C.  A mixture of carbonates of different compositions will mix linearly with respect to δ 13 C and δ 18 O but non-linearly with respect to ∆ 47 . The resulting mixture can, therefore, have a greater or lower ∆ 47 value than the weighted sum of the end-member ∆ 47 values, introducing an artificial bias in ∆ 47 39,40 . The range of variation in δ 18 O and δ 13 C in modern brachiopod shells is usually not larger than 6‰, considering both the variation within secondary layer calcite 19,[21][22][23][24]41 and between the juvenile and the adult parts of the shell 21,22,[24][25][26][27][41][42][43] . Assuming the most-extreme scenario of 50-50% mixing of carbonates precipitated at the same temperature with a 6‰ difference in both their δ 13 C and δ 18 O values, the maximum effect of carbonate mixing on ∆ 47 in modern brachiopods would be +0.009‰ 40 . To further investigate the role of sample heterogeneity on our data, we assessed the range of variation in δ 18 O values in two M. venosa shells that exhibited a high (0.024‰ and 0.038‰, respectively) ∆ 47 offset with respect to Passey and Henkes 10 . Our data show that the difference in δ 18 O values in brachiopod secondary layer calcite can be as high as 4.3‰ between the outer and the inner part of the shell (Fig. 2). A covariance of δ 18 O and δ 13 C along the depth transects of modern brachiopods shells suggests that the range of variation in δ 13 C will be comparable to that of δ 18 O [22][23][24]41,43 . A 50-50% mixing of carbonates precipitated at the same temperature with a 4.3‰ difference in both their δ 13 C and δ 18 O values results in a ∆ 47 mixing effect of +0.005‰ 40 . This bias is much smaller than the observed maximum offset ∆ 47 value of 0.038‰ and unresolvable from the external analytical precision (1σ S.E.) received for most replicates. Thus, it is highly unlikely that a mixing of carbonates of different compositions through the shell significantly contributes to the positive ∆ 47 offsets observed in this study.

Discussion
Differences in laboratory procedures, such as reaction temperatures, have previously been suggested as a possible explanation for the discrepancy in the slopes between the Came et al. 9 calibration, made at 25 °C, and the Henkes et al. 11 calibration, made at 90 °C. Although, Henkes et al. 11 also analysed brachiopods (N = 4), their calibration is predominantly based on molluscs (N = 40). Since our study and that of Came et al. 9 yielded the same calibration slope despite using two different acid digestion temperatures, we consider this slope gradient to be characteristic of brachiopods and exclude acid digestion temperature as a valid explanation for the difference between the lower (25 °C) and the higher (>70 °C) temperature calibration slopes.
Growth rates of the modern brachiopods analysed in this study correlate well with both the offset ∆ 47 (R 2 ≈ 0.55, p-value < 0.01; Fig. 3a) and the offset δ 18 O values (R 2 > 0.52, p-value < 0.01; Fig. 3b,c). The slowest growing brachiopods (T. congregata, Argyrotheca sp., Megerlia sp., P. atlantica) are in apparent clumped isotope equilibrium 10 44 . The slowest growing brachiopods that are closest to clumped isotope equilibrium relative to Passey and Henkes 10 are enriched in 18 O relative to the apparent oxygen isotope equilibrium as predicted by Kim and O'Neil 35 . This strongly implies that growth rate exerts control on the kinetic mechanisms responsible for the observed departures from apparent clumped and oxygen isotope equilibria.
The calcite shells of articulated brachiopods are secreted in the outer epithelium of the mantle. The primary layer is formed by indirect secretion in the extrapallial fluid, while the secondary layer is formed by extracellular mineralization 45,46 . To aid our discussion, we consider a simplified model of calcification, introduced for molluscs and corals, but that has also been applied to brachiopods 47,48 (Supplementary Fig. 4a). In this model, carbonate formation occurs in a semi-isolated volume, separated from the ambient environment by an organic membrane 13,46,49 . The organism requires calcium (Ca 2+ ) and carbonate (CO 3 2− ) ions to enable the precipitation of CaCO 3 . In marine calcifiers, such as corals and molluscs, the organic membrane pumps Ca 2+ into the calcifying fluid using an enzyme (Ca-ATPase), while increasing the pH of the fluid by removing an equivalent number of protons (2H + ) 13 . We note that the presence of this enzyme, to the best of our knowledge, has not been reported from brachiopods to date. As the membrane is only permeable for aqueous carbon dioxide (CO 2(aq) ), the CO 2(aq) in the mineralizing fluid is transformed into bicarbonate (HCO 3 − ) and CO 3 2− ions via hydration (eq. 3) and hydroxylation (eq. 4) reactions: It has recently been demonstrated that kinetic effects related to the CO 2(aq) hydration and hydroxylation reactions, as well as diffusion, can produce a positive ∆ 47 and a negative δ 18 O offset from thermodynamic equilibrium 12,50,51 ( Supplementary Fig. 4b).
Knudsen-diffusion predicts that a gas diffusing through a membrane will be depleted in 18 O but enriched in ∆ 47 , relative to the residual gas 51 . When correlating the ∆ 47 and δ 18 O offsets from equilibrium, the diffused and residual gas fractions would plot along a slope of −0.023. An identical slope would be obtained if kinetic fractionations were evoked by diffusion of CO 2(aq) through water 51 .
The reaction rate of hydration and hydroxylation of the dissolved CO 2 is orders of magnitude slower than the reaction rate of bicarbonate dissociation 52 . Both CO 2(aq) hydration and hydroxylation preferentially select light isotopes ( 16 O, 12 C) and discriminate against heavy isotopes ( 18 O, 13 C). If the carbonate precipitation rate is high, HCO 3 − can dissociate into CO 3 2− and H + before reaching equilibrium with CO 2(aq) in the calcifying fluid, therefore, the solid carbonate will inherit lighter δ 18 O values 49,53 . Simultaneously, incomplete CO 2(aq) hydration or hydroxylation results in an increased ∆ 47 value of the aqueous HCO 3 − , which can be inherited by the solid carbonate if the precipitation rate is high 14 . Theoretical calculations predict a regression slope between the offset ∆ 47 offset and offset δ 18 O values in the order of −0.05 and −0.01 for kinetic controls associated with hydration and hydroxylation reactions, respectively 12,54 (Supplementary Fig. 4b). Carbonic anhydrase, an enzyme often present in calcifying organisms, such as corals, promotes rapid oxygen isotope exchange between dissolved inorganic carbon species 55,56 . If this enzyme was present in brachiopods, it could reduce or eliminate the kinetic isotope effects caused by the slow hydration and hydroxylation reactions. However, carbonic anhydrase has not been identified in the calcifying fluid of modern brachiopods 57 .
Our data exhibits an offset ∆ 47 -δ 18 (Fig. 1c). Both slopes are significant and stay consistent, irrespective of data processing, i.e., [Gonfiantini] vs. [Brand] parameters, and the clumped isotope calibration we used to calculate the offset values (Supplementary Figs 2b,c and 3).
The observed correlation slopes (−0.017 to −0.039, depending on the seawater δ 18 O dataset) between offset ∆ 47 and offset δ 18 O point to the importance of kinetic effects associated with diffusion and incomplete hydration and hydroxylation of CO 2(aq) . The hydration and hydroxylation reactions occur superimposed onto the diffusion of CO 2(aq) . Consequently, diffusion alone cannot be the sole kinetic mechanism responsible for the observed trend in our data. If heterogeneous oxygen isotope exchange between water and CO 2(aq) proceeds to equilibrium, it would erase the offsets from equilibrium ∆ 47 and δ 18 O generated during diffusion. Tang et al. 37 precipitated calcites at a pH < 9 and >10 and observed that ∆ 47 values increased by approximately 0.016‰ for every 1‰ decrease in δ 18 O at high (>10) pH. They suggested that a combined effect of diffusion and hydroxylation could be responsible for the observed slope. Interestingly, their slope is indistinguishable from the one we observe when we exclusively use the Global Seawater Oxygen-18 Database 34 to infer seawater δ 18 O. However, pH > 10 would be inconsistent with the internal pH range of modern brachiopods, which is likely to be between 7.7 and 8.2, calculated from δ 11 B values 41 . Hydration is more prominent at low (<8.4) pH while hydroxylation is more prominent at high (>8.4) pH, assuming temperature and salinity values characteristic of modern seawater 49,52 (Fig. 4). In the pH range characteristic for modern brachiopods, only 10-40‰ of the oxygen isotope exchange between water and CO 2(aq) should occur via the hydroxylation reaction, whereas 60-90% should proceed via the hydration reaction 52 (Fig. 4). Such a dominance of hydration over hydroxylation would result in an offset ∆ 47 -δ 18 O slope of −0.034 to −0.046, assuming estimated slopes of −0.05 and −0.01 to be characteristic of the hydration and hydroxylation reactions, respectively 12,54 . This range of slopes is in agreement with our result based on the dataset that combines gridded seawater δ 18 O data with directly measured values ( Fig. 1c and Supplementary Figs 2c and  3b,d).
The δ 18 O values of the temperate modern brachiopod shells analysed in this study correlate well with corresponding δ 13 C values (R 2 = 0.89, p-value < 0.001; Fig. 5a). Brand et al. 58 showed that parallel correlations are present between shell δ 18 O and δ 13 C among tropical (latitudes < 30°), temperate (latitudes 30°-60°) and polar (latitudes > 60°) brachiopods, respectively. These parallel trends are related to the distinct habitat seawater temperatures and oxygen isotopic compositions of these groups 58   The balance between the rates of hydration and hydroxylation reactions is defined as R = (k CO2 /(k CO2 + k OH /aH) * 100, where k CO2 and k OH are the rate constants for CO 2(aq) hydration and hydroxylation, respectively and aH is the H + activity 52 . R is calculated for three salinity (S) -temperature (T) scenarios, characteristic to modern seawater. The shaded area represents the internal pH range of modern brachiopods 41 .
values of the modern brachiopod shells analysed in this study correlate with corresponding δ 13 C values (R 2 > 0.29, p-value < 0.05; Fig. 5b,c). A covariation of δ 18 O and δ 13 C has been also observed in single brachiopod shells by other authors [22][23][24]41,43 . A synchronous depletion of the heavy isotopes ( 18 O and 13 C) in biogenic carbonates, as observed for the modern brachiopods analysed in this study (Fig. 5a,b,c), agrees with the preferential selection of light isotopes during CO 2(aq) hydration and hydroxylation reactions 49,53,59 .
There is still an ongoing debate if the experiments of Kim and O'Neil 35 are characteristic for the attainment of overall equilibrium between calcite and water. A natural example for equilibrium precipitation might be the Devil's Hole carbonate that grew extremely slowly in a constant geochemical environment. Its isotope composition has therefore been postulated not to be affected by kinetics 60 . The δ 18 O value of the Devil's Hole carbonate is approximately +1.5‰ higher than could be calculated using the equation of Kim and O'Neil 35 . Laboratory experiments, comparing oxygen isotope fractionation factors of slowly and rapidly precipitated synthetic calcites 61 , and theoretical computations 62 provide further evidence that the Kim and O'Neil 35 equation is not representative of thermodynamic equilibrium between calcite and water. The δ 18 O values of the modern brachiopods analysed in this study, which show apparent clumped isotope equilibrium, are enriched by up to 1‰, relative to the Kim and O'Neil 35 equilibrium (Fig. 1b,c and Supplementary Figs 2b,c and 3). This finding is in line with the hypothesis [60][61][62] that oxygen isotope equilibrium between calcite and water is expressed by fractionations exceeding those of Kim and O'Neil 35 .
In summary, the oxygen and clumped isotope composition of modern brachiopod shells are affected by growth rate-induced kinetic effects (i.e., incomplete hydration and/or hydroxylation of CO 2(aq) at higher growth rates) as indicated by (1)

Methods
Sampling of shells. Organic tissue and encrusting organisms were removed from the brachiopod shells using a metal pin and a brush. Specimen S006L, DS420L, and DS430L were submerged in diluted NaOCl for 5-10 minutes to soften the organic material. The shells were cleaned in an ultrasonic bath using deionized water. Afterwards, the shells were dried using pressured air and stored at room temperature. For the larger species, the primary layer of the shells was mechanically removed using a hand-held electric drill (Proxxon Micromot IBS/E) on the lowest speed setting and only the secondary and/or tertiary layers were sampled. An approximately 0.5 cm 2 area from the anterior part of the ventral valve was crushed and homogenised using an agate mortar and pestle. We avoided sampling the umbo area, the hinge area, the muscle scar area and the youngest parts of the shell. Exceptions to this were the micromorphic shells of P. atlantica, T. congregata, Argyrotheca sp., and Megerlia sp., where 4 to 20 whole shells had to be crushed to acquire enough material for multiple replicate analyses.
Growth rate. The growth of brachiopods can be described by the von Bertalanffy asymptotic function 63 .
Juvenile individuals grow the fastest and the growth rate decreases with age, before reaching the species-specific maximum size. To acquire comparable, species-specific growth rates, we estimated a minimum and a maximum growth rate for each analysed species. The maximum growth rate, in our case, depicted the average growth rate of the brachiopod until it reached 50% of its maximum size. Similarly, the minimum estimate was the average growth rate after the brachiopod had already reached 50% of its maximum size. For M. venosa 63 , M. fragilis 64 , M. sanguinea 65 , C. inconspicua 66 , T. transversa 67 and L. neozelanica 68 , detailed studies were available, thus both a maximum and a minimum growth rate estimate could be calculated. Such a study has not, to date, been made for N. nigricans, therefore we used the available average juvenile growth rate 69 as a maximum estimate. For the micromorphic brachiopods P. atlantica, Argyrotheca sp., Megerlia sp., and T. congregata, we assumed a 0.5 mm/ yr and a 1.2 mm/yr as a minimum and as a maximum growth rate estimate, respectively. These growth rates are characteristic for micromorphic brachiopods 70 .
Trace element analyses. The magnesium content of the studied brachiopod shells was analysed using a Thermo Scientific iCap 6000 dual view ICP-OES (Inductively Coupled Plasma -Optical Emission Spectrometry) at the Goethe University, Frankfurt, Germany. For the analyses, we took 120-150 μg of carbonate powder from the homogenised batches that were also used for the isotope measurements and dissolved them in 0.500 cm 3 2% HNO 3 . An aliquot of 0.300 cm 3 of the sample solution was diluted with 1.500 cm 3 yttrium water (until 1.000 mg/dm 3 ) prior to measurement to correct for matrix biases during analyses. The Mg/Ca measurements were drift-corrected and standardized to an internal consistency standard (ECRM 752-1) measured alongside with the samples. The external reproducibility (2σ S.E.) for this standard was ±0.1 mmol/mol Mg/Ca. Finally, the MgCO 3 concentration values (mol%) were adjusted to a 100% carbonate basis and were normalised to a combined Ca and Mg value of 395,000 ppm 20 .
Stable isotope analyses. Clumped isotope analyses were made using a fully automated gas extraction and purification line connected to a ThermoFisher MAT 253 gas-source isotope-ratio mass spectrometer at the Goethe University, Frankfurt, Germany. Homogenised carbonate powder was reacted at 90 °C with >105% phosphoric acid. In general, six replicate analyses were made every day including one carbonate standard, one equilibrated gas (1000 °C or 25 °C) and four sample replicates. Background correction was performed for the sample and the reference gas separately, as described in Fiebig et al. 71 (Supplementary Fig. 5). Background-corrected equilibrated gas data displays slopes that are within errors indistinguishable from zero (Supplementary Data 1). Additional information concerning the methodology of the clumped isotope measurements can be found in the Supplementary Information.
Secondary Ion Mass Spectrometry. The ion probe analyses were carried out using a Caméca IMS 1280-HR2 at CRPG-CNRS (Nancy, France). A short summary of the technique is reported in the Supplementary Information. The exact location of the ion probe transects and the analysed points are shown on Supplementary Figure 6. The two analysed shells were also investigated for clumped isotopes. The ventral valve of each brachiopod was cut in half from anterior to posterior part to produce a longitudinal section. One half was mounted in epoxy and polished with diamond paste down to 1µm. Transects from the outermost (primary layer) to the innermost part (closest to mantle cavity) of the shell were performed with 20 µm spots and with a constant step of 50 µm. The number of analysis was determined by the shell thickness. The location of the transect was approximately 3 mm above the anterior margin, at the exact location where the shell was sampled for the clumped and trace element analyses. Data availability. All data pertinent to this manuscript and its reported findings can be found in the manuscript itself or the associated Supplementary Information file.