The Na, Si and Al concentrations of the matrix fraction of several replicates of the diatom fraction of TC460 are shown in Fig. 3a–d. Prior to purification, Na and Si concentrations were consistently around 265 and 114 ppm respectively, whereas Al was more variable at 5–25 ppb. The boron content of these matrix samples in all cases was at the blank level. The concentration of these elements in the boron fraction is shown in Fig. 3e–g, highlighting that the column procedure was sufficient to concentrate boron and remove Na and Si, which are both present at the sub-5 ppb level (i.e. at less than 0.002 % of matrix concentration). The Al is likely present in the diatom frustule (e.g. Koning et al., 2007) and is elevated in the boron fraction compared to the matrix fraction (Fig. 3). Diatom-bound Al is likely present as the anion Al(OH)4-, hence its elevation in the boron fraction. Although this is a detectable level of Al, it is unlikely that this level of contamination will influence the mass fractionation of these samples when measured by MC-ICP-MS (Foster et al., 2008; Guerrot et al., 2010).

Throughout the duration of this study, a single dissolution of the diatom fraction of TC460 was measured 18 times in separate analyses at various concentrations, in order to assess external reproducibility of this method. Carbonates generally have a reproducibility of ±0.20 ‰ (2σ) at an analyte concentration of 50 ppb boron using the MC-ICP-MS methods at the University of Southampton (e.g. Chalk et al., 2017). The repeated measurements of TC460 gave a reproducibility of ±0.28 ‰ (2σ) over 18 samples, ranging from 19 to 61 ppb (11 to 34 ng) boron (Fig. 4). The insensitivity of δ11B to the boron concentration analysed confirms that blank contamination during purification is not significant. Figure 4 shows that there is also no correlation between Al content of the boron fraction and measured δ11B, confirming that Al contamination does not influence mass fractionation.

Figure 4 shows the results of the standard addition experiment, and when the uncertainty in the δ11B of the mixture is considered, it is clear that nearly all the mixtures lie within error of the 1 : 1 line, indicating that there is a lack of a significant matrix effect when analysing the δ11B of biogenic silica as described herein. A linear-least-squares regression of the mixtures has a slope of 1.01±0.07 and an intercept of -0.15±0.29 ‰, implying the approach is accurate to ±0.29 ‰, which is remarkably similar to the stated reproducibility of TC460 (±0.28 ‰ at 2σ).

B and Si content were determined separately and combined post-analysis in order to estimate the B/Si ratio for each sample and hence the B concentration. The reproducibility of this method was tested using six repeats of the diatom fraction of TC460. The mean of all six measurements is 2.99±0.64 ppm; (2σ; Fig. 4), implying this multistage method of determining the B content of diatoms is precise to ±20 % at 95 % confidence.

The boron content of T. weissflogii increases as a function of pH from around ∼1 to ∼4 ppm over a range of average culture pH from 7.5 to 8.6 (Fig. 5; Table 2). While this is lower by an order of magnitude than the limited previous studies of boron in sedimentary diatoms (Ishikawa and Nakamura, 1993), it is similar to boron concentration in the bulk diatom fraction of TC460 (Fig. 4d) and to that observed in previous culturing studies of this diatom species (Fig. 5; Mejía et al., 2013). In detail, however, our concentrations are around 2–3 times lower than Mejía et al. (2013), perhaps due to (i) the different analytical methods used (laser ablation ICP-MS vs. solution here), (ii) differences in cleaning methods and/or (iii) differences in culturing methodology. Despite the scatter between our treatments (also seen in Mejía et al., 2013; Fig. 5), a least-squares regression through the treatments is significant at the 95 % confidence level (y=2.15x-15.56, R2=0.46, p=0.015; Fig. 5). The cause of this scatter between treatments is not known but a likely contributor is the relatively high variability in the carbonate system which was observed in each treatment due to the growth of the diatoms in our batch culture setup (Fig. 2).

Boron is an essential nutrient for diatoms (Lewin, 1966), and it is likely that boric acid passively diffuses across the cell wall to ensure the diatom cell has sufficient boron to meet its biological needs. However, if boric acid were the sole source of boron for the diatoms measured here, we might expect a decrease in boron content as pH increases and external dissolved boric acid concentration declines (Fig. 6).

Several studies note that a number of higher plants have mechanisms for also actively taking up boron, leading to large variations in internal boron concentrations (Pfeffer et al., 2001; Dordas and Brown, 2000; Brown et al., 2002). Indeed, on the basis of a similar dataset to that collected here, Mejía et al. (2013) suggested that borate is likely transported across the cell wall of T. weissflogii as some function of external borate concentration, which shows a positive relationship with external pH (Fig. 6). This hypothesis is developed and discussed further in the next section.

The δ11B of T. weissflogii is isotopically light compared to seawater (39.6 ‰; Foster et al., 2010), with an average value across all treatments of -3.95 ‰ (Table 2). Despite the scatter between treatments, similar to the [B] data, Fig. 5 shows that there is a clear relationship between the δ11B of the diatom frustule and pH (R2=0.46, p<0.01), albeit with a negative and relatively shallow slope (y=-2.61x+17.12).

These results confirm that biogenic silica, free from clay contamination, has a very light boron isotopic composition (Ishikawa and Nakamura, 1993). However, the observed relationship between δ11B in T. weissflogii and pH is radically different to that which is observed in carbonates (Fig. 5), implying a distinctive incorporation mechanism for boron into diatom opal. Much work has been carried out in recent years to show that boron is incorporated in carbonates predominantly as the borate ion with minor, if any, isotopic fractionation (e.g. see Branson, 2018 for a review). It is similarly thought that the borate ion is incorporated into opal in an analogous fashion to its incorporation into clays (Ishikawa and Nakamura, 1993; Kolodny and Chaussidon, 2004). However, such a mechanism in isolation would only be able to generate δ11B in opal of ∼13 ‰ (at the lowest pH). Given the preponderance of isotopically light diatoms, radiolaria and chert δ11B in the literature (including this study; Kolodny and Chaussidon, 2004; Ishikawa and Nakamura, 1993), it is therefore likely that there is an additional light isotopic fractionation of boron on its incorporation into opal, although its absolute magnitude is currently unknown (Kolodny and Chaussidon, 2004).

To make their frustules out of biogenic silica, aqueous Si(OH)4 is taken up by the diatom cell via active transport by silicon transporter proteins (Amo and Brzezinski, 1999). Once Si(OH)4 has entered the cell, it accumulates in vacuoles that tend to have a high pH in order to prevent polycondensation of Si(OH)4 at its higher concentration in the vacuole (Vrieling et al., 1999). The accumulated Si(OH)4 is then transported to the silicon deposition vesicle (SDV), which is an acidic compartment where the formation of biogenic silica and the construction of the frustule occurs. Without knowledge of the isotopic fractionation of boron on incorporation into biogenic silica, the interpretation of our new δ11B data is challenging. This difficulty is further increased given that the fluid in the SDV is unlikely to have the same δ11B as external seawater, and its relatively acidic pH (∼5.5; Mejía et al., 2013; Vrieling et al., 1999) is likely to promote polymerisation of Si(OH)4. Nonetheless, the broad similarity between the δ11B of our cultured T. weissflogii with the bulk diatom fraction measured here from sample TC460 and the bulk diatom fraction and radiolarian skeleton measured by Ishikawa and Nakamura (1993; ∼3 ‰) suggests that a large part of the light isotopic composition of biogenic silica is driven by the isotopic fractionation on incorporation rather than “vital effects” relating to the δ11B and pH of the SDV in the different species and organisms. That being said, the >3 ‰ range between different pH treatments in T. weissflogii and the >10 ‰ difference between our Chaetoceros-dominated bulk diatom fraction from TC460 and the cultured T. weissflogii, as well as the negative relationship between pH and diatom δ11B (Fig. 5), argue against a simple two-step model involving borate ion incorporation from seawater with a fixed isotopic fractionation.

The δ11B of the fluid from which our T. weissflogii precipitated their frustules can be calculated if we assume the pH in the SDV of our T. weissflogii is 5.5 across all our treatments (Mejía et al., 2013). Given that at this pH the δ11B of borate is ∼13 ‰, the isotopic composition of this fluid is lighter than seawater, even if we assume an arbitrary -10 ‰ isotopic fractionation on incorporation (blue circles in Fig. 7a). Furthermore, the δ11B of the SDV fluid is inversely correlated with the δ11B of either dissolved borate or dissolved boric acid (Fig. 7a).

As discussed above and illustrated schematically in Fig. 8, Mejía et al. (2013) suggested that there are two sources of boron in a diatom cell: (i) passively diffused and isotopically heavy boric acid and (ii) actively transported isotopically light borate ion (see Fig. 8). Assuming that (a) no additional fractionation occurs during uptake and diffusion and (b) only the borate ion is incorporated into the frustule, we can calculate the relative contribution of these two sources of boron as a function of external pH (Fig. 7b). This treatment shows that the relative concentration of borate-derived boron in the SDV fluid increases as external pH increases, though the absolute values here are a function of the magnitude of the isotopic fractionation on incorporation, so we only have confidence in the trends shown in Fig. 7b. Nonetheless, given that the dissolved boric acid concentration decreases and dissolved borate increases as pH is increased (Fig. 6), this is perhaps not surprising.

While this finding is entirely compatible with the trend of increasing boron content of T. weissflogii observed as pH increases (Fig. 5), an added complication is that at pH ∼ 5.5 the concentration of borate ion in the SDV is likely to be relatively low (Fig. 6). However, the timescales required to reach equilibrium in the boron system are short (e.g. around 95 µs; Zeebe et al., 2001), meaning that any aqueous borate incorporated into the frustule would be immediately replenished to its equilibrium value by conversion from the more abundant boric acid. Although relevant partition coefficients are likely to be different, a similar process ensures the quantitative removal of boron from pH < 7 solutions by the Amberlite 743 anion exchange resin used for boron purification prior to analysis by MC-ICP-MS (see above; Lemarchand et al., 2002).

Active bicarbonate ion uptake accounts for a substantial amount of the carbon fixed by phytoplankton (e.g. Tortell et al., 2006). As a result, Mejía et al. (2013) proposed that the enrichment of borate ion into the SDV of T. weissflogii and T. pseudonana was the result of the active co-transport of borate ion with bicarbonate ion by bicarbonate transporter proteins. Borate is transported because of its similar charge and size to HCO3- and the phylogenetic similarity between bicarbonate and borate transporters (Mejía et al., 2013). In our model, as external borate ion concentration increases, the borate leak into the diatom cell is also increased. An additional factor is HCO3- transport, which may be proportionally upregulated as external CO2 content decreases (and external pH increases) in order to provide the diatom cell with sufficient carbon (Mejía et al., 2013). This may therefore offer a way of driving an elevation of the borate content of the SDV as pH increases (Mejía et al., 2013). Regardless of the exact mechanism, an SDV fluid with an inverse relationship between δ11B and pH is required to explain the δ11B of the T. weissflogii frustule measured here. A simple model whereby external borate ion is an increasingly important contributor to the boron in the SDV as pH increases is able to explain the observed dependency of boron content and δ11B on pH. However, a more complete model of the boron systematics in diatom opal requires a better understanding of isotopic fractionation on incorporation of boron into biogenic silica, the environmental controls on this fractionation, and the nature of the partitioning of boron within the diatom cell and into biogenic silica.

The δ11B–pH and B–pH relationships derived here for T. weissflogii potentially offer two independent means to reconstruct the past pH of seawater, particularly in those regions key for CO2 and heat exchange where foraminifera are largely absent (e.g. at high latitudes). However, the current calibrations (Fig. 5) are relatively uncertain, which may preclude their application to some situations. For instance, recasting the δ11B–pH relationship in terms of δ11B as the dependent variable and using a regression method that accounts for uncertainty in X and Y variables (SIMEX; Carroll et al., 1996) gives the calculated residual pH of the regression as ±0.28 pH units. For the [B] vs. pH relationship, this uncertainty is ±0.36 pH units. At typical surface ocean conditions, such a variability in pH would translate to seawater pCO2 variability of up to ca. ±250 ppm. Although encouraging, this treatment suggests that additional work is needed before the relationship between δ11B and boron content of diatom opal and seawater pH is a sufficiently precise proxy for a fully quantitative past ocean pH. In particular, future culturing efforts should aim to more carefully control the pH of the culture media. This could be achieved by either using larger volume dilute batch cultures, by harvesting the diatoms earlier in the experiment prior to any significant drift in the carbonate system and/or by using a more robust steady-state chemostat method (e.g. Leonardos and Geider, 2005).