Heterogeneity and incorporation of chromium isotopes in recent marine molluscs (Mytilus)

Abstract The mollusc genus Mytilus is abundant in various modern marine environments and is an important substrate for palaeo‐proxy work. The redox‐sensitive chromium (Cr) isotope system is emerging as a proxy for changes in the oxidation state of the Earth's atmosphere and oceans. However, potential isotopic offsets between ambient sea water and modern biogenic carbonates have yet to be constrained. We measured Cr concentrations ([Cr]) and isotope variations (δ53Cr) in recent mollusc shells (Mytilus) from open and restricted marine environments and compared these to ambient sea water δ53Cr values. We found a large range in mollusc [Cr] (12–309 ppb) and δ53Cr values (−0.30 to +1.25‰) and in the offset between δ53Cr values of mollusc shells and ambient sea water (Δ53CrseawaterbulkMytilus, −0.17 to −0.91‰). Step digestions of cultivated Mytilus edulis specimens indicate that Cr is mainly concentrated in organic components of the shell (periostracum: 407 ppb, n = 2), whereas the mollusc carbonate minerals contain ≤3 ppb Cr. Analyses of individual Cr‐hosting phases (i.e., carbonate minerals and organic matrix) did not reveal significant differences in δ53Cr values, and thus, we suggest that Cr isotope fractionation may likely take place prior to rather than during biomineralisation of Mytilus shells. Heterogeneity of δ53Cr values in mollusc shells depends on sea water chemistry (e.g., salinity, food availability, faeces). The main control for δ53Cr values incorporated into shells, however, is likely vital effects (in particular shell valve closure time) since Cr can be partially or quantitatively reduced in sea water trapped between closed shell valves. The δ53Cr values recorded in Mytilus shells may thus be de‐coupled from the redox conditions of ambient sea water, introducing additional heterogeneity that needs to be better constrained before using δ53Cr values in mollusc shells for palaeo‐reconstructions.


| INTRODUC TI ON
Mollusc shells are extensively used to reconstruct past sea water chemistry as they are known to record environmental parameters in their carbonate shell layers (e.g., Klein, Lohmann, & Thayer, 1996;Vander Putten, Dehairs, Keppens, & Baeyens, 2000). The genus Mytilus is particularly useful as it tolerates a large range of environmental conditions from high to low latitudes (Gosling, 1992). Mytilus are sessile and live in colonies in subtidal or intertidal zones, where they are subjected to extreme environmental conditions regarding, for example, salinity, temperature and exposure to air. Their adaptation mechanism to extreme conditions allows Mytilus to seal their shell valves tightly, and anoxic conditions quickly develop in the sea water trapped between the closed shell valves (Famme & Kofoed, 1980;Widdows & Shick, 1985). Mytilus edulis can tolerate hypoxic and anoxic sea water conditions between 5 and 16 days by closing their shell valves and decreasing oxygen consumption by utilising anaerobic metabolism to conserve energy (Babarro & Zwaan, 2008;Famme & Kofoed, 1980;Widdows & Shick, 1985;de Zwaan, 1977).
Generally, nutrients and trace elements (e.g., HCO − 3 , Ca 2+ , Mg 2+ , Ba 2+ , Sr 2+ ) used for shell formation are derived from ingested particles or directly from sea water. These molecules are transported through two epithelial cell layers and the mantle to the extrapallial space (EPS). Crystallisation pathways of ions from the sea water to the shell via cell membranes include (a) passive ion channels (e.g., Ca 2+ , Mg 2+ , H + , HCO − 3 or SO 4 2− channels), (b) active ion pumps (e.g., the Ca 2+ -pump using the enzyme Ca-ATPase), (c) intercellular diffusion promoted by concentration gradients or (d) vacuolised fluid transport (Bentov, Brownlee, & Erez, 2009;Carré et al., 2006;Cervantes et al., 2001;Erez, 2003;Klein et al., 1996). Chromium (Cr) transport by vacuoles is supported by Chassard-Bouchaud, Boutin, Hallegot, and Galle (1989) who observed Cr in lysosomes and vesicles of Mytilus cells. The authors found insoluble Cr in lysosomes associated with phosphorus and sulphur, possibly in proteins, which may prevent the toxic Cr from diffusion through the cell. In the isolated EPS, an organic matrix containing various macromolecules (e.g., polysaccharide β-chitin, hydrophilic proteins) facilitates the formation of aragonite and calcite crystals (Addadi, Joester, Nudelman, & Weiner, 2006). An organic outer sheath consisting of different organic macromolecules (e.g., proteins, chitin; Meenakshi, Hare, Watabe, & Wilbur, 1969;Nakayama et al., 2013) protects the underlying minerals and the EPS from sea water and creates the site for calcification. The extrapallial fluid (EPF) of M. edulis consists of inorganic ions, insoluble sulphated carbohydrates, free amino acids and proteins, which can bind divalent cations (e.g., Ca 2+ , Cd 2+ , Mn 2+ ) and potentially detoxify heavy metals (Yin, Huang, Paine, Reinhold, & Chasteen, 2015). This composition is different to the composition of the shell proteins (Misogianes & Chasteen, 1979). Mytilus shells secrete byssal threads, which they use to attach themselves onto a substrate. Cr was shown to be capable of adsorbing onto or complexing with the surface of byssal threads of Mytilus (Chassard-Bouchaud et al., 1989).
Skeletal carbonates, such as mollusc shells, occur pervasively throughout the Phanerozoic rock record and are capable of recording the chemical composition of precipitating sea water. The Cr isotope system is increasingly used as a proxy for changes in surface redox conditions in the past as it is assumed that the delivery and distribution of Cr in sea water strongly depend on the oxygenation state of the water column (e.g., Cole et al., 2016;Ellis, Johnson, & Bullen, 2002;Frei, Gaucher, Poulton, & Canfield, 2009;Reinhard et al., 2014). With oxidative weathering of silicate rocks, Cr(III) is oxidised to soluble Cr(VI) and removed by fluids that may reach the oceans through rivers. The reductive removal of Cr(III) from these fluids to chemical sediments is consequently assumed to lead to δ 53 Cr sea water values (δ 53 Cr sea water ranging from 0.13 to 1.55‰; Goring-Harford et al., 2018) that are isotopically heavier compared to bulk silicate earth (−0.12 ± 0.10‰ 2SD; Bonnand, James, Parkinson, Connelly, & Fairchild, 2013;Frei & Polat, 2013;Schoenberg, Zink, Staubwasser, & Blanckenburg, 2008). As the fractionation of Cr isotopes is generally understood to occur during redox-sensitive reactions (Ellis et al., 2002), δ 53 Cr variations recorded in sedimentary rocks have important utility in determining changes in the redox state of ancient sedimentary basins, the oceans and Earth's evolving atmosphere. Laboratory experiments showed that Cr can directly be incorporated into the crystal lattice of carbonate minerals (Tang, Elzinga, Jae Lee, & Reeder, 2007) with insignificant or no isotope fractionation (Rodler, Sánchez-Pastor, Fernández-Díaz, & Frei, 2015). This renders (biogenic) carbonates as potential archives to record δ 53 Cr variations of their precipitating fluid. The offset between biogenic carbonate and ambient sea water δ 53 Cr (Δ 53 Cr carbonate sea water was reported in the range of 0.0-0.9‰ (Bonnand et al., 2013;Frei, Paulukat, Bruggmann, & Klaebe, 2018;Holmden, Jacobson, Sageman, & Hurtgen, 2016;Pereira, Voegelin, Paulukat, Sial, & Ferreira, 2015). Importantly, multiple analysis of a coral (Porites sp.) from the Rocas Atoll (BR) shows δ 53 Cr values of between −0.56 ± 0.09‰ and 0.10 ± 0.14‰ (Pereira et al., 2015) and intra-species variations of core top planktonic foraminifera (Pulleniatina obliquiloculata) from the West Pacific range from 0.21 ± 0.37‰ to 1.85 ± 0.19‰ (2 σ; Wang et al., 2016). This heterogeneity in biogenic carbonates was attributed to changes in surface sea water δ 53 Cr values and water depth. Frei et al. (2018) and Farkaš et al. (2018) recently reported an accumulation of Cr in the carbonate shells of molluscs of the genus Mytilus and proposed these shells as another suitable record of sea water δ 53 Cr values.
However, in contrast to Pereira et al. (2015) and Wang et al. (2016), Frei et al. (2018) report no or only little intra-species variations in mollusc shell samples and attribute the resolvable variations to vital effects. This highlights that despite extensive investigations on biomineralisation processes of marine calcifying organisms (e.g., Bentov et al., 2009;Carré et al., 2006;Weiner & Addadi, 2011;Weiss, Tuross, & Addadi, 2002), only little is known about the transport of ions through membranes and incorporation into shells. This also applies to Cr where the transport through epithelial cells of molluscs and processes that might lead to stable metal isotope fractionation (of Cr) are not well constrained. A first model proposed by Pereira et al. (2015) for Cr uptake pathways and Cr isotope fractionation during incorporation into corals suggests that Cr(VI) is reduced by photo-reduction and subsequently re-oxidised during transport through the endodermal layer. After transportation through a cell membrane via vacuoles, isotopically light Cr(VI) reaches the calcifying space from where chromate can be incorporated into the coral skeleton. The uptake of Cr(VI) as chromate ions (CrO 2− 4 ) into cells can take place in a similar way as phosphate and sulphate uptake through anionic membrane channels. This is facilitated by the structural similarity of chromate and sulphate (Brown et al., 2006). A multiple-step intracellular reaction chain as for sulphate reduction (Canfield, 2001) was also suggested for Cr which is, similar to sulphate, first transported into the cell where the actual reduction takes place (Sikora, Johnson, & Bullen, 2008). The reduction of Cr(VI) may be important considering that Cr(VI) is toxic. Cells therefore use various mechanisms to inhibit or tolerate oxidative damage (Cervantes et al., 2001). A mechanism to inhibit damage by Cr(VI) can be the efflux of CrO 2− 4 with a specific protein (ChrA). Enzymatic or non-enzymatic reduction of Cr(VI) to Cr(III) constitutes another mechanism to detoxify Cr(VI) (Ramírez-Díaz et al., 2008). Thus, a transport by sulphate channels into epithelial cells and a subsequent reduction is a potential transport pathway for Cr from sea water to the EPS of molluscs. Cr(III) is not considered to permeate cell membranes (Cary, 1982) and may thus be irrelevant for Cr uptake. However, Cr(III) complexed with ligands (Cr-L) as well as Cr(VI) contained in the body fluid or sea water can be vacuolised by the cell wall and then transported through cells. Recently, Frei et al. (2018) emphasised the importance of organic substances onto which Cr(III) is adsorbed and incorporated into mollusc shells. Here, it is important to note that complexation with organic matter (OM) may stabilise Cr(III) in solution (Sander & Koschinsky, 2000;Sander and Koschinsky, 2011) and can contribute up to 90% of total dissolved Cr in sea water (Connelly, Statham, & Knap, 2006). Also, in contrast to the typical redox-dependent Cr isotope fractionation, redox-independent Cr isotope fractionation occurs during complexation of Cr with ligands typically present in natural systems, such as organic acids, siderophores or Cl - (Larsen, Wielandt, Schiller, & Bizzarro, 2016;Saad, Wang, Planavsky, Reinhard, & Tang, 2017).
Large amounts of OM favour the reduction of Cr(VI) to Cr(III), for example, as Cr(OH) 2 + , which is the stable Cr(III) species at a slightly lower pH-Eh range of sea water (Connelly et al., 2006;Cranston & Murray, 1980 Figure 1).

| Sample preparation
Sea water samples (1.5-2 L) were filtered through 0.45 μm nylon membrane filters (Advantec MFS) and acidified with HCl to a pH of 2 within one day of collection. The shell tissue of all mollusc specimens collected was removed, and encrusted material was abraded using a household sponge or a ceramic knife. All shells were then pre- These shell sample aliquots were then separated into five groups and processed differently depending on the Cr-hosting phase(s) of interest (for the respective procedures, see TA B L E 1 Sample preparation methods. Note that the separated phase(s) describe(s) only those phases, in which the hosted Cr is accessible for chromatographic Cr separation. For example, the shell organic matrix is accessible during the chromatography in L peeled due to incineration, but not in L HCl . Organic matrix = shell organic matrix, for example, organic macromolecules. Samples were incinerated in chemical porcelain crucibles in a muffle furnace the leaching procedures (Table 1) could not be conducted sequentially, but on individual components of different mollusc shells only.

| [Cr] and stable Cr isotope analysis
All sea water samples and all acid-digested bulk, leachate and component samples were evaporated to dryness on a hotplate and subsequently spiked with an adequate amount of a 50 Cr-54 Cr double spike so that a 50 Cr/ 52 Cr ratio in the sample-spike mixture of between 0.15 and 0.70 was reached in order to minimise spike deconvolution error propagation (Ellis et al., 2002;Frei, Gaucher, Døssing, & Sial, 2011;Schoenberg et al., 2008). Next, samples were attacked with approximately 2 ml aqua regia to ensure equilibration between sample and spike. The sample solutions were dried down in Savillex™ Teflon beakers at 125°C overnight.
Shell samples were subjected to a two-step ion chromatographic Cr separation modified from the protocol of D'Arcy, Babechuk, Nørbye, Gaucher, and . Separation of Cr from sea water samples followed the procedure described in Paulukat, Gilleaudeau, Chernyavskiy, and Frei (2016) with minor changes. Anion exchange columns were prepared with pre-cleaned Dowex AG 1 × 8 anion resin.
Samples were re-dissolved in 20 ml (skeletal carbonates) or 200 ml

| Data quality
Multiple analyses of double-spiked NIST SRM 979 standard aliquots were conducted to monitor external reproducibility. The external reproducibility of the δ 53 Cr value keeping the 52 Cr signal at 1V results in ± 0.08‰ 2SD. We measure the NIST SRM 979 standard at δ 53 Cr = −0.08‰, an offset from the certified 0‰ values that is explained by original calibration of our double spike against NIST 3112a and accounted for in all results.
Carbonate rock standards JDo-1 and JLs-1 were repeatedly analysed to determine the external reproducibility achieved on rock standards (  Pereira et al., 2015;Rodler et al., 2015). Multiple procedural blanks (n = 8) remained < 3.7 ng Cr for the sea water separation procedure and ≈1 ng for bulk shell sample separation (Table 1, procedure 1). These blank concentrations are significantly below the Cr concentrations of our samples and are therefore not expected to affect the isotope composition of our samples.
Corrections for contamination by detrital Cr (δ 53 Cr = −0.12 ± 0.10‰) are usually conducted using concentrations of immobile elements such as Ti or Al (Algeo & Maynard, 2004;Gilleaudeau et al., 2016;Reinhard et al., 2013;Rodler et al., 2015;Schoenberg et al., 2008). The strong acids used to dissolve our samples may leach Cr associated with detrital Cr and contaminate δ 53 Cr values. We analysed aliquots of selected mollusc shell samples (bulk and L NaOCl ; Table 1) for their Al concentrations using ICP-MS (conducted at the Geological Survey of Denmark and Greenland, Denmark) along with a standard reference material (BHVO-1, basalt, USGS). However, these analyses resulted in Al concentrations below detection limit (≈50 ppb), and thus, detrital Cr in our sample is not significant. This is in agreement with previous studies where Al concentrations were below detection limit (Pereira et al., 2015) and δ 53 Cr values of carbonate standards (JDo-1 and JLs-1) leached with 0.5 M HCl and 2 M HCl were within error (Rodler et al., 2015).

| Cr in different shell components and detrital contamination
We analysed coupled bulk M. edulis shell samples and targeted acidleached samples to compare Cr in bulk shells and Cr that is associated with different components such as the shell carbonate or with OM. To rule out contamination by detrital Cr, we analysed Al of selected samples (bulk and L NaOCl ), which resulted in Al concentrations below the detection limit (≈50 ppb). The Al concentrations measured in our samples indicate that an insignificant fraction (<1‰) of total Cr is derived from leached detrital grains and the Cr analysed is thus not thought to be associated with a detrital component.
However, NaOCl leachates (L NaOCl ) likely overestimate the offset since NaOCl leaches not only the periostracum, but to some extent also Cr associated with the shell organic matrix. To deter-

| Cr in bulk Mytilus samples
In addition, bulk Mytilus shells and ambient sea water from different locations were measured to better constrain spatial (global) Cr variability as well as the range of variability at individual locations. (

| Isotopic offset between bulk Mytilus and sea water
All Mytilus samples (averages) are generally characterised by less positive Cr isotopic compositions relative to local sea water (Tables 3 and   4; Figures 4 and 5). The Δ 53 Cr bulk Mytilus sea water offsets of (average) Mytilus vary between 0.17‰ and 0.91‰ across all locations (Table 4). At Kiel Fjord, two sea water samples were taken during the shell sampling and return a range of δ 53 Cr values between 0.62 ± 0.19‰ and 0.50 ± 0.14‰ (Table 3)

| D ISCUSS I ON
Our results of step digestions of cultivated M. edulis (Kiel Fjord, DE) provide crucial information on Cr-hosting phases in carbonate shells contributing to our understanding of Cr uptake mechanisms into biogenic carbonates. This approach helps to characterise potential impact of vital effects (e.g., feeding strategies, calcification mechanism)   The fractionation factor α characterises the 53 Cr/ 52 Cr ratios of the product and the reactant (Equation 6), and its association with the fractionation factor ε* is described in Equation 7.
We note that ε* uses f ≥ 1 and thus differs from ε.

| Cr incorporation model into cultivated M. edulis
The δ   Sea water contains dissolved Cr as chromate (CrO 2− 4 ) or complexed with ligands (Cr-L) as well as particle-bound Cr, that is, Cr adsorbed to and/or structurally incorporated into detrital (e.g., silt or clay) and organic (e.g., phytoplankton) particles. Mytilus filter sea water for feeding and are able to open and close their shell (4) δ 53 Cr t = (δ 53 Cr 0 + 1,000) * f ( −1) − 1,000 valves depending on food availability (step 1). While particlebound Cr is ingested into the digestive system, dissolved Cr species can directly be accumulated from sea water. To reach the EPS from the body cavity or the digestive system, Cr has to pass two layers of epithelial cells (step 2). As a possible transport pathway of Cr through an epithelial cell, dissolved chromate may be transported via sulphate channels (Figure 7, reaction 5). This was observed for microbial cells where chromate can enter cells via sulphate channels and is effluxed by the ChrA protein (Cervantes et al., 2001). In another possible pathway, Cr contained in sea water or the body fluid is vacuolised by an epithelial cell via endocytosis (Bentov & Erez, 2006). Cr is then transported through the cell, possibly as Cr(III) in association with sulphur and phosphorus (Chassard-Bouchaud et al., 1989), before it is exocytosed into the EPS (Figure 7, reaction 6). From the EPS, chromate may be bound to the organic matrix where it may substitute organic sulphates (e.g., acidic sulphated sugars; Dauphin et al., 2003Dauphin et al., , 2005 that are major constituents of the organic matrix (step 3). In the EPF, Cr(III) could form new chelates with available ligands, similar to Mn 2+ (Misogianes & Chasteen, 1979). Cr(III) adsorbed onto organic macromolecules was proposed to bind to chitin-containing organic interlamellar sheets of the organic matrix Nudelman et al., 2008;. The low proportions of Cr associated with the carbonate minerals (approximately 13% in L HCl ) suggest that the quantities of Cr incorporated into the crystal lattice during calcification of molluscs may be very small. This contrasts the findings of Pereira et al. (2015) who suggested Cr(VI) incorporation into the lattice of carbonate crystals in corals. However, the growth mechanisms of corals are considerably different from the mechanisms used by molluscs since coral growth involves symbiotic algae (zooxanthellae).

| Cr fractionation during sea water ingestion and Cr uptake
The physiology of Mytilus provides ideal conditions to cause a redox-dependent Cr fractionation because anoxic conditions can quickly evolve between closed shell valves due to the immediate drop of oxygen uptake from 0.2 ml O 2 g −1 hr −1 to 0 ml O 2 g −1 hr −1 (Famme & Kofoed, 1980;Widdows & Shick, 1985). We hypothesise that Cr fractionation with variable fractionation factors likely takes place in sea water trapped between the shell valves due to changing redox conditions (step 1; Figure 8 Depending on the period of shell valve closure time (average closure time 59 ± 22 min; Riisgaard et al., 2006), Cr(VI) will be partially or quantitatively reduced. Under open system conditions with normal food availability and thus normal valve gaping rate, Cr may be partially reduced (Figure 8a) due to the onset of anoxic conditions (step 1). Regardless whether the sea water is Cr(VI)-or Cr(III) dominated, Cr(VI) that is trapped between the valves can be partially reduced with an * 1 of −0.04‰. Subsequently, Cr is transported through epithelial cells, a process that also might induce Cr isotope fractionation. Although we cannot rule out Cr isotope fractionation occurring during transport through sulphate channels, we do not suspect any fractionation as no redox changes take place (Figure 8a).
The transported Cr(VI) may then directly be fixed in the carbonate shell without inducing Cr isotope fractionation (step 3). Hence, this pathway (Ia, Figure 8a) could lead to relatively high sea water-like  Step 1 S tep 2 Step 3 F I G U R E 8 Conceptual model and box model illustrating Cr uptake from sea water under open (a) or closed system conditions (b). Two cases are considered, where nearly 100% of total Cr is present I) as Cr(VI) with a δ 53 Cr sea water, maximum of 0.62 ± 0.19‰ and II) as Cr(III) with a δ 53 Cr sea water of approximately the bulk silicate earth value (−0.12 ± 0.10‰; Schoenberg et al., 2008). We propose two possible sites for Cr fractionation, step 1 with * 1 and step 2 with * 2 . (a) Under open system conditions with normal valve gaping rates, Cr(VI) is reduced to Cr(III) in step 1 with a fractionation factor of * 1 = −0.04, regardless of the dominant Cr species. In step 2, Cr(VI) can be transported through epithelial cells via sulphate channels without fractionation, resulting in a δ 53 Cr M. dulis value close to sea water (Ia: +0.58‰). Further, C(VI) transport via vesicles could induce Cr reduction with * 2 = −0.04‰, leading to a δ 53 Cr M. edulis value of +0.54‰ (Ib). If Cr(III) is the dominant Cr species, the small proportion of Cr(VI) present could be reduced during vesicular transport ( * 2 = −0.04‰), leading to a low δ 53 Cr M. edulis value of −0.20‰ (II: δ 53 Cr M. edulis < δ 53 Cr sea water ). (b) In a closed system with long-term closed shell valves, sea water trapped between the valves becomes anoxic, leading to quantitative Cr reduction (step 1, * 1 = 0‰). Reduced Cr(III) is then transported via vesicles to the EPS, assuming a fractionation factor ( * Step 1 Step 2 Step 3 reduction reactions as, for example, reactions with Fe(II)-bearing minerals can reduce 50% of total Cr(VI) within 35 min while biotic reduction requires 4 hr to 2 days (Basu and Johnson, 2012;Sikora et al., 2008). Vesicular Cr transport through epithelial cells may also induce Cr isotope fractionation ( * 2 = −0.04‰). The resulting δ 53 Cr M. edulis values may range between 0.58‰ (Ib) and −0.  such as salinity, OM or water depth that significantly impact δ 53 Cr sea water values (e.g., Goring-Harford et al., 2018;Paulukat et al., 2016;Scheiderich, Amini, Holmden, & Francois, 2015) also control the Cr isotope signature incorporated into Mytilus shells.

| Micro-environmental sea water conditions
Mytilus are sessile and attach to a substrate (e.g., rock or older Mytilus shell) as larvae or juveniles, and younger individuals may overgrow older ones. Thus, small-scale changes (e.g., mucus) in sea water chemistry may significantly influence the δ 53 Cr values of some Mytilus while others are unaffected. We hypothesise that in a dense population of Mytilus, a chemical gradient may establish between well-mixed open sea water containing mainly dissolved Cr(VI) and restricted organic-rich sea water (Cr(III)) caught in the limited space between shells. Mytilus growing on the periphery of the colony have access to "un used" sea water with low Cr(III) concentrations. Around the innermost individuals, OM from biodeposits (faeces and pseudofaeces, including mucus [protein-polysaccharide complexes]) and microalgae may accumulate due to limited exchange with "un used" sea water under low energy conditions. The presence of mucus further stimulates the growth of microalgae (Cognie & Barikle, 1999). In the presence of large amounts of dissolved OM in the restricted central area of a colony, the solubility of Cr(III) may increase as it is known to be stabilised in solution by organic complexation (Sander & Koschinsky, 2000). We propose that increased OM concentrations stabilising Cr(III) in solution in restricted dense parts of the Mytilus colonies may induce Cr fractionation within sea water, potentially leading to heterogeneous [Cr] and isotopic compositions within a Mytilus colony (e.g., M. edulis from Kiel Fjord). However, since the position of individual shells relative to other shells was not recorded during our sampling campaign, we are unable to substantiate the above hypothesis.

| Local environmental sea water conditions
The different average δ 53 Cr values measured in Mytilus from Kiel Fjord, Disko Bay and Thorsminde could suggest that each sampled a local Cr pool of a water body that is isotopically distinct. Mytilus shell samples influenced by the low-saline Baltic Sea have approximately 0.1‰ higher δ 53 Cr values than samples from the more saline North Atlantic coasts (Figure 4). The elevated δ 53 Cr value measured in Mytilus from Limfjord (DK) might be caused by restriction of the water body and its overall lower salinity (brackish water, 6 PSU; Lewis et al., 2013). Similarly, elevated δ 53 Cr values in two M. edulis from Kiel Fjord may be influenced by the strong annual variation in salinity 2016:(13-24 PSU; bsh.de). The δ 53 Cr sea water values are influenced by the salinity of the water body (e.g., heavy rainfalls diluting the water bodies with freshwaters, elevated temperatures leading to increased salinities due to evaporation). Riedel (1984) found that high salt and therefore also high sulphate contents can reduce the uptake of Cr(VI) as it is in competition with chromate. Low salinity and high Cr(VI) conditions on the other hand facilitate the uptake of Cr(VI) by algae (Wang, Griscom, & Fisher, 1997) and therefore increase the δ 53 Cr values in the remaining sea water as discussed above. Changes in freshwater input can thus enhance the δ 53 Cr variability in mollusc shells. This fits well with our δ 53 Cr results around Denmark.
The isotopically light Mytilus from Syracuse (IT; −0.04 ± 0.26‰) may be explained by comparably higher primary productivity in the warmer Mediterranean Sea relative to northern ocean basins and therefore by an increased food availability associated with light Cr.
The frequency of algal blooms in different water bodies may influence δ 53 Cr variability in biogenic carbonates as algae blooms can significantly affect δ 53 Cr values of sea water. For example, seasonal algae blooms in the Sound (DK) occur from late summer to autumn.
These algae blooms may cause the variability in δ 53 Cr values between approximately 0.63 ± 0.13‰ in October and 0.35 ± 0.11‰ in June (Køge Bay) (Paulukat et al., 2016), as Cr was shown to be reduced to Cr(III) under high OM conditions (Semeniuk, Maldonado, & Jaccard, 2016;Sikora et al., 2008). The isotopically heavy sea water samples in October and April may be caused by algal reduction of Cr, where 52 Cr(III) is preferentially removed from solution by algae.
Mytilus from areas with high algae production may thus differ from samples from low-productivity sites.

| Scenarios leading to heterogeneous δ 53 Cr Mytilus values
Connecting the observed Cr fractionation factors and δ 53 Cr variability to the Cr uptake model as well as to environmentally controlled sea water biogeochemistry, we can describe different scenarios for open and closed shell valves (open and closed systems) that are able to cause the observed δ 53 Cr variability. The periostraca are excluded from these scenarios as Cr associated with the organic outer sheath is likely taken up directly from sea water, similarly to Cr uptake into byssal threads (Chassard-Bouchaud et al., 1989).

| Open system
The δ 53 Cr values similar to or higher than sea water with high Cr fractionation factors (ε* ≈ 0.01-0.10‰) are observed in few bulk shell samples from Kiel Fjord (DE-KI_3: δ 53 Cr = 0.74 ± 0.25‰ and DE-KI_19: δ 53 Cr = 1.25 ± 0.10‰). Mytilus specimens growing at the periphery of the colony may filter sea water with elevated δ 53 Cr sea water values as they have access to dissolved Cr(VI) and are less exposed to increased Cr(III) concentrations compared with specimens growing in the OM-and Cr(III)-rich central areas (Section 4.2.1). As no information on growth position of Mytilus samples relative to other specimens is available, we can only infer that they may have been growing on the periphery of a colony or in loosely populated subtidal areas with access to Cr(VI)-rich sea water. Further, the Cr isotopic composition of sea water is heterogeneous (Scheiderich et al., 2015) and it is likely that the sea water samples from Kiel Fjord we analysed in this study do not represent the full range of δ 53 Cr values that may occur in Kiel Fjord.
For example, increased reductive Cr removal in the presence of an algae bloom may lead to δ 53 Cr sea water values exceeding the sea water values we measured (maximum δ 53 Cr sea water value for Kiel Fjord analysed in this study: 0.62 ± 0.19‰). Provided an uptake mechanism that is capable of transporting this isotopically heavy Cr(VI) with little or no fractionation (e.g., via sulphate channels) from the body cavity to the EPS, biogenic carbonates can potentially record δ 53 Cr values that are elevated compared to average sea water values (Ia, Figure 8a).    (2008)), Cr reduction in sea water trapped between the shell valves may be quantitative, leading to a Cr fractionation factor of * 1 = 0‰ (Ib, Figure 8b).

| Closed system
Step 2 may then induce presumably constant and small Cr isotope fractionation (e.g., * 2 = −0.04‰), leading to δ 53 Cr M. edulis values similar to or only slightly lower than the ambient sea water value (Ib and II, Figure 8b). A closed system with closed shell valves can occur during periods of starvation or due to exposure to air. M. edulis samples from Kiel Fjord are not subjected to significant tidal influence, but starvation periods are possible and may cause nearly quantitative Cr reduction.  Table 3). Using targeted leaches, we determined that up to 40% of the total Cr in a Mytilus shell is associated with the periostracum, suggesting that it is the primary Cr-bearing phase in these samples. Further, based on mass balance arguments, we estimate an average δ 53 Cr composition for periostraca from our Kiel Fjord samples to be 0.37‰. These values are close to δ 53 Cr sea water values measured at the same location, indicating that little fractionation occurred during Cr uptake into the periostracum. This suggests that Cr(VI) may adsorb directly from sea water and that uptake of Cr(VI) into the periostracum may be quantitative, leaving no time for fractionation processes to take place. This is in agreement with previous findings that Cr may be adsorbed onto byssal threads of Mytilus directly from sea water (Chassard-Bouchaud et al., 1989).

| Cr isotope offset between bulk Mytilus shells and ambient sea water
The majority of the bulk Mytilus samples from different sampling sites measured in this study shows a negative offset from ambient sea water Δ 53 Cr bulk Mytilus sea water of between 0.17 and 0.91‰ (Table 3), despite the large variability in δ 53 Cr values (from −0.30 ± 0.11 to +1.25 ± 0.10‰ 2SD). This supports the preferential incorporation of lighter Cr into primary (biogenic) carbonates during precipitation (e.g., Pereira et al., 2015). The range of Δ 53 Cr carbonate sea water values found in this study is in agreement with previous results, revealing a consistently negative offset between δ 53 Cr values of (mostly biogenic) carbonates and their ambient sea water (Δ 53 Cr carbonate sea water ; Figure 5; Bonnand et al., 2013;Pereira et al., 2015;Wang et al., 2016;Farkaš et al., 2018;Frei et al., 2018). These offsets range from 0.00 to 0.35‰ in ooids (Bonnand et al., 2013), ≈0.3 to 0.4‰ in modern bivalves , ≈0.45‰ in modern marine biogenic carbonates from the Great Barrier Reef (Farkaš et al., 2018), 0.46 ± 0.14‰ (2SD) in modern marine carbonate sediments from the Caribbean Sea (Holmden et al., 2016) to approximately 0.9‰ in corals (Pereira et al., 2015).

| CON CLUS IONS
The heterogeneity of δ 53 Cr values of analysed shell fractions of M. edulis from Kiel Fjord and bulk Mytilus shells from a range of other sample sites (−0.30 ± 0.11‰ to +1.25 ± 0.10‰ 2SD) indicates that besides uptake of Cr(III) as suggested by previous studies (e.g., Frei et al., 2018;Pereira et al., 2015;Wang et al., 2016), significant amounts of Cr(VI) can be incorporated into Mytilus shells. We hypothesise that the heterogeneous δ 53 Cr values are mainly controlled by i) vital effects (shell valve closure time), ii) micro-environmental parameters such as the presence of mucus that influence shell valve closure time and thus the extent of Cr reduction and iii) sea water biogeochemistry of the local environment (e.g., salinity) influencing the local δ 53 Cr sea water value. Our model for Cr incorporation into Mytilus is compatible with the heterogeneity of δ 53 Cr values in the analysed Mytilus shells and is capable of explaining the mostly negative Cr isotopic offset between Mytilus shells and sea water that may be induced by Cr reduction during shell valve closure time and during cellular Cr transport. The feeding mechanism of Mytilus involves frequent closure of the shell valves, which is likely an important control on δ 53 Cr values. During shell valve closure, anoxic conditions immediately evolve in the sea water trapped between the valves and Cr may be partially or quantitatively reduced. Thus, Cr reduction likely takes place in the sea water trapped between the closed shell valves. Cr(III) and Cr(VI) contained in sea water that is either filtered with open shell valves (open system) or trapped between closed shell valves (closed system) can be vacuolised by epithelial cells and reach the EPS via exocytosis, perhaps including Cr reduction to insoluble Cr(III). As an alternative pathway, Cr(VI) can be transported using sulphate channels.
We found evidence that only small proportions of Cr (≤3.4 ppb) are incorporated in the crystal lattice of carbonate minerals. Instead, the shell organic matrix may be the main Cr-hosting fraction and incorporate both Cr(VI) and Cr(III) adsorbed onto organic macromolecules such as ligands or sulphated polysaccharides. Additionally, the periostracum may host significant proportions of Cr (up to 534 ppb) and Cr may directly diffuse from sea water into or adsorb onto the periostracum.
Sea water biogeochemistry may further influence the pronounced heterogeneity of δ 53 Cr values in Mytilus shells from both within a colony and from different locations. Micro-(e.g., gradient of mucus and thus OM from central to peripheral colony) and regional environmental conditions (e.g., algae blooms, salinity) impact δ 53 Cr sea water values and thus the Cr signature incorporated 643084. SB is grateful to Alexandra Rodler for her support during the writing process of the manuscript. We thank Noah Planavsky and two anonymous reviewers for constructive comments that contributed to improve the original manuscript.