In culture and field experiments, replicate samples and controls were incubated at room temperature (∼25◦C) in a transparent (SRP method) or black (fluorescence method) 96-well plate. To ensure linearity of the hydrolysis rates, samples and controls were measured at multiple time points during the incubation period on a multimode plate reader (Molecular Devices). Overall incubation times were optimized depending on the sample type, P substrate, and the detection method employed. The SRP and fluorescence techniques were characterized by substantial differences in sensitivity. For example, the lower limit of detection, defined as three times the standard deviation of replicate blank measurements, was 800 nmol P L−1 for the SRP method and 2 nmol P L−1 for the fluorescence method. The upper limits of detection for the fluorescence method, defined as the P concentration above which the calibration curves begin to lose linearity, was 500 nmol L−1 P. Thus, samples exhibiting MUF-P hydrolysis rates within the limits of detection of the fluorescence method had to be incubated at least 1.6 times and up to 400 times longer before reaching detectable levels of SRP. The actual incubation times for the various sample types and analytical methods were as follows: whole seawater samples (fluorescence method: 12–15 h, SRP method: 24–65 h), cell-free culture filtrates (fluorescence method: 1–2 h, SRP method: 30 min to 24 h), whole culture samples (fluorescence method: 5 min to 1 h).

The SRP method was not used with whole culture samples due to interferences associated with the uptake/adsorption of enzymatically released phosphate by the cultures, which was problematic at high cell densities. To verify the lack of such interference in whole seawater samples, SRP calibration curves (2–20 µM P) were prepared in each sample and analyzed at multiple time points throughout the incubation period.

#### Genome Searches

fmars-05-00380 October 23, 2018 Time: 14:30 # 5

Putative APs were identified in the translated genomes of T. pseudonana CCMP1335 (taxid: 296543) and T. oceanica CCMP1005 (taxid: 159749) with NCBI's BLASTP search tool. The following protein sequences were used as queries: PhoA from Escherichia coli (GenBank: AAA83893), PhoD from Bacillus subtilis (UniProt: P42251), and PhoX from Pseudomonas fluorescens (Protein Data Bank: 4A9V). Only hits with an E-value < 1 × 10−4 are reported.

#### Proteomics

Concentrated exoproteome samples were digested using an insolution tryptic digestion kit (ThermoScientific), according to the manufacturer's instructions. Peptide samples were analyzed at the Proteomics and Mass Spectrometry (PAMS) facility at the University of Georgia on a Thermo-Fisher LTQ Orbitrap Elite mass spectrometer coupled with a Proxeon Easy NanoLC system (Waltham, MA, United States).

The enzymatic peptides were loaded into a reversed-phase column (self-packed column/emitter with 200 Å 5 µM Bruker MagicAQ C18 resin), then directly eluted into the mass spectrometer. Briefly, the two-buffer gradient elution (0.1% formic acid as buffer A and 99.9% acetonitrile with 0.1% formic acid as buffer B) starts with 5% B, holds at 5% B for 2 min, then increases to 25% B in 60 min, to 40% B in 10 min, and to 95% B in 10 min.

The data-dependent acquisition method was used to acquire MS data. A survey MS scan was acquired first, and then the top 5 ions in the MS scan were selected following collision-induced dissociation (CID) and higher-energy collisional dissociation (HCD) MS/MS analysis. Both MS and MS/MS scans were acquired by the Orbitrap mass spectrometer at resolutions of 120,000 and 30,000, respectively. Data were acquired using Xcalibur software (version 2.2, Thermo Fisher Scientific).

Protein identification was performed using Thermo Proteome Discoverer (version 1.4) with Mascot (Matrix Science). The reference database for T. oceanica CCMP1005 consisted of the translated whole genome (NCBI Bioproject PRJNA36595) (Lommer et al., 2012) amended with a list of common contaminants, such as human keratin. The T. pseudonana CCMP1335 database was compiled from the translated nuclear (Bioproject PRJNA191), chloroplast (Bioproject PRJNA20561), and mitochondrial (Bioproject PRJNA15818) genomes (Armbrust et al., 2004; Oudot-Le Secq et al., 2007), and was also amended with common contaminant sequences. Databases included a reversed 'decoy' version for false discovery rate (FDR) analysis. The FDR of identified peptides was ∼2%. Protein matches were also filtered to exclude hits with fewer than two unique peptide identifications. Gene ontology (GO) annotations were integrated into results using the ProteinCenter Annotation node.

# Statistical Analysis

P hydrolysis rates in diatom cell-free filtrates were measured throughout the growth curve of each species cultivated in replete (+P) or P-deficient (−P) media. Differences in hydrolysis rates among the three P sources under each growth condition were assessed using repeated measures analysis of variance (ANOVA) and post hoc testing with Tukey's honest significant difference (HSD) method. Average ratios of ATP and 3polyP hydrolysis were compared using a one-sample T-test. To test whether the degradation of each P source was P-regulated, cell-normalized rates of P hydrolysis were compared in +P and −P cultures using repeated measured ANOVA. Average P hydrolysis rates measured in whole cultures and in cell-free filtrates with different quantification methods were compared using Tukey's HSD test. MUF-P hydrolysis rates determined by the SRP vs. fluorescence methods were assessed using simple linear regression. Field-based rates of polyphosphate and MUF-P hydrolysis were compared at each site using an independent two-sample T-test assuming equal variance. Potential relationships between P hydrolysis rates and in situ chlorophyll concentrations were explored with simple linear regression. All statistical analyses were performed in Microsoft Excel R or JMP R Pro (V13.0).

# RESULTS

### Degradation of Model P Sources by Diatom Cultures

#### Relative Lability of P Sources in Cell-Free Filtrates

In order to explore the DOP nutritional preferences of Thalassiosira spp., the labilities of model P sources representing the major P(V) DOP bond classes (**Figure 1**) were tested in whole cultures and cell-free filtrates grown in P-replete (+P) and P-deficient (−P) media. Because P hydrolysis rates were quantified based on the production of SRP, cell-free filtrates were primarily utilized instead of whole cultures in order to avoid technical challenges associated with the analysis of SRP at high cell densities (see Discussion). All model P sources were degraded in diatom filtrates (**Figures 2**–**4**) and showed negligible hydrolysis (below detection) in boiled controls, consistent with enzymatic P-hydrolysis. In −P cultures, P hydrolysis rates were substantial within 1 week (T. oceanica and T. pseudonana CCMP1014) (**Figures 2B,F**) or after 2 weeks (T. pseudonana CCMP1335) (**Figure 2D**). In +P cultures, DOP degradation increased dramatically after about ∼2 weeks (**Figure 2**). Hydrolysis rates increased in all cultures over time, consistent with the depletion of SRP and the eventual onset of stationary phase (**Figures 2A,C,E**). Degradation rates among the three P sources were significantly different in each diatom culture and media condition throughout the growth curves (**Figure 2**). In every case, regardless of the diatom strain and the initial level of P availability, the rate of inorganic 3poly-P hydrolysis was significantly highest, followed by ATP, and finally AMP (**Figure 2**). Over the entire growth curve, ATP and AMP hydrolysis rates were statistically similar for both strains

of T. pseudonana (**Figures 2C–E**), except for T. pseudonana CCMP1014 cultivated in −P media (**Figure 2F**). On the other hand, T. oceanica always hydrolyzed ATP significantly more than AMP, regardless of prevailing P availability (**Figures 2A,B**).

A maximum of three orthophosphate molecules can be released from ATP and 3poly-P. However, the complete degradation of phosphoanhydride bonds would produce three orthophosphate groups from 3poly-P but only two from ATP, since the final orthophosphate is bound to the adenosine moiety by a P-monoester linkage (**Figure 1**). Therefore, if the P-anhydride bonds of ATP are degraded, and the P-monoester bond remains intact, the ratio of ATP:3polyP hydrolysis should be 2/3 (or ∼66.7%). However, ratios of ATP:3poly-P hydrolysis over the last 1–2 weeks of growth were significantly less than 2/3 (**Table 1** and **Figures 2A,C–F**), except in the case of T. oceanica (−P) (**Table 1** and **Figure 2B**), in which ATP degradation was statistically similar to 66.7% of 3poly-P degradation.

#### The Effect of Overall P Availability on Substrate-Specific DOP Hydrolysis in Cell-Free Filtrates

The lability of 3poly-P, ATP, and AMP was assessed in the cell-free filtrates of diatoms cultivated in P-replete and P-deficient media. To account for differences in biomass, P hydrolysis rates were normalized to total cell counts in cultures at the respective sampling time. ATP hydrolysis was significantly upregulated under −P conditions in all diatom cultures (**Figures 3G–I**). On the other hand, P availability did not significantly affect

cell-free filtrates of T. oceanica CCMP1005 (A,D,G,J), T. pseudonana CCMP1335 (B,E,H,K), and T. pseudonana CCMP1014 (C,F,I,L) cultivated under P-replete (+P) and P-deficient (–P) conditions. Error bars represent one standard deviation of the mean of three biological replicates. Statistical results from repeated measures ANOVA are provided above each plot and indicate the overall effect of P availability on hydrolysis rates.

AMP hydrolysis in any culture (**Figures 3J–L**). P-deficient conditions induced significant upregulation of 3poly-P hydrolysis by T. oceanica CCMP1005, significant downregulation by T. pseudonana CCMP1014, and no change by T. pseudonana CCMP1335 (**Figures 3D–F**).

#### Comparison to Fluorescence-Based MUF-P Hydrolysis Measurements

For all diatoms, 3poly-P hydrolysis in cell-free filtrates was significantly higher than MUF-P hydrolysis in whole cultures (**Figure 4**). ATP degradation by T. oceanica CCMP1005 cell-free filtrates was also significantly higher than whole culture MUF-P hydrolysis (**Figure 4A**). Rates of P-ester hydrolysis in the cell-free filtrates of all diatoms reflected strong methodological agreement. For example, AMP and MUF-P (fluorescence and SRP methods) were degraded at similar rates (**Figure 4**). In fact, SRP-based estimates of MUF-P hydrolysis systematically underestimated fluorescence-based measurements of MUF-P degradation by about ∼17% (p = 0.0008) in culture filtrates (**Figure 5**).

FIGURE 4 | P hydrolysis rates of model DOP compounds in the presence (whole culture) and absence (filtrate) of cells and using different detection methods. (A) T. oceanica CCMP1005, (B) T. pseudonana CCMP1335, and (C) T. pseudonana CCMP1014. All rates were quantified by measuring the accumulation of phosphate over time (SRP method), except where MUF-P degradation was quantified via the standard fluorometric method (Fl.). Cultures were analyzed after 30 days of growth. Error bars represent one standard deviation of the mean of three (A,B) or two (C) biological replicates. P hydrolysis rates lacking a shared letter are significantly different (p < 0.05; Tukey's honest significant difference).

# Substrate-Specific P Hydrolysis Rates in the Coastal Western North Atlantic

Maximum hydrolysis rates of inorganic poly-P were measured in whole seawater samples from the coastal North Atlantic (**Figure 6A**) using the SRP method with two substrates: 3poly-P and 45poly-P. Poly-P chain length had no effect on P-hydrolysis rates, and the results from both poly-P sources were therefore combined into single average rates of inorganic poly-P hydrolysis. These rates were compared to maximum MUF-P hydrolysis rates determined via fluorescent detection. Average volume-normalized P hydrolysis rates ranged from 3.8–19.3 nmol P L−1 hr−1 and 1.4–50.6 nmol P L −1 hr−1 for inorganic poly-P and MUF-P, respectively (**Figure 6B**). Chlorophyll-normalized rates ranged from 5.6– 7.7 nmol P µg chl−1 hr−1 and 2.5–20.1 nmol P µg chl−1 hr−1 for inorganic poly-P and MUF-P, respectively (**Supplementary Table S1**). SRP levels were above ∼700 nmol L−1 , except in a phytoplankton bloom along the New Jersey Coast, where SRP was 150 ± 15 nmol L−1 (avg ± SD, n = 3; **Supplementary Table S1**).

Inorganic poly-P hydrolysis rates were significantly higher than rates of MUF-P hydrolysis (p < 0.05) in four out of the five field sites sampled, by a factor of ∼1.5 to ∼2.7 (**Figure 6B** and **Table 2**). However, in one field site (Buzzard's Bay), MUF-P hydrolysis was ∼2.5-fold higher than inorganic poly-P hydrolysis (p < 0.05; **Figure 6B** and **Table 2**). Inorganic poly-P hydrolysis rates exhibited a significant linear correlation with chlorophyll levels (p = 0.01; **Figure 6C**), which was also evident for rates of MUF-P hydrolysis when the Buzzard's Bay outlier was excluded (p = 0.04; **Figure 6C**). However, P hydrolysis rates did not exhibit a significant relationship with bacterial abundance counts (**Figure 6D**). Bacteria cell counts (cells mL−1 ) were ∼125 times higher than phytoplankton counts at the Buzzard's Bay site, yet only ∼17 to ∼45 times higher at all other locations (**Supplementary Table S1**).

SRP uptake/adsorption by whole seawater samples can potentially lead to the underestimation of P hydrolysis rates made by the SRP method. The degree of SRP uptake/adsorption was therefore assessed with standard additions of Na2HPO4 (P = 2–20 µM). Phosphate levels in these amended samples did not change over the course of the 24–65 h incubations.

#### Phosphatase Diversity in Diatom Cultures

The full genome data of two model diatom strains utilized in this study, T. oceanica CCMP1005 and T. pseudonana CCMP1335, are publicly available, enabling the analysis of phosphatase diversity in these two species. First, the genomes were searched for putative homologs of three bacterial alkaline phosphatase isoforms (PhoA, PhoD, and PhoX) using BLASTP analysis. In T. oceanica CCMP1005, results revealed the presence of two putative PhoD homologs, one putative PhoX homolog, but no homologous PhoA sequences (**Table 3**). On the other hand, T. pseudonana CCMP1335 possesses one putative homolog each of PhoA and PhoD, but no homologous sequences to PhoX (**Table 3**).

Since cell-free filtrates were the primary focus of substratespecific P hydrolysis measurements, the diversity of phosphatases was investigated in cell-free filtrates of T. oceanica CCMP1005 and T. pseudonana CCMP1335 (under +P conditions for each culture only). Excluding contaminant sequences (i.e., keratin),

TABLE 1 | Comparison of ATP and 3poly-P hydrolysis rates in diatom cell-free filtrates from Figure 2.

T-scores (T; reported as absolute values) are calculated by subtracting from average experimental ATP:3polyP hydrolysis ratios (Avg) the proportion of ATP:3polyP hydrolysis expected from the complete degradation of phosphoanhydride bonds (66.7%), according to the following equation:

$$\mathcal{T} = \frac{\mathcal{A}\mathcal{W} - \mathcal{G}\mathcal{G}\mathcal{Z}}{\mathcal{S}\mathcal{E}}$$

where SE is the standard error of the average ATP:3poly-P hydrolysis ratio, and df is the degrees of freedom. Two-tailed p-values are reported.

a total of 309 and 133 proteins were identified in extracellular proteomes of T. oceanica CCMP1005 and T. pseudonana CCMP1335, respectively (**Supplementary Tables S2**, **S3**). Among these hits, 24 from T. oceanica CCMP1005 and 9 from T. pseudonana CCMP1335 possess conservative domains consistent with phosphatase activity. The majority of these hits were shared among biological triplicates of each diatom (**Figure 7**). None of the putative bacterial alkaline phosphatase homologs identified through genome searches (**Table 3**) were detected in the cell-free culture filtrates, however. Rather, results indicated a diversity of other putative phosphatases, including P-anhydride- and P-ester-degrading enzymes. In fact, P-anhydride-degrading enzymes dominated the phosphatase diversity in the cell-free filtrates of both microorganisms, including inorganic pyrophosphatase and nucleoside triphosphates (**Figure 7**).

#### DISCUSSION

The goal of this study was to assess the relative lability of model P sources that represent the major marine DOP bond classes. The focus here was on the P(V) DOP bond classes – P-esters and P-anhydrides – because of the potential role that these compound classes have in P utilization by the bulk phytoplankton community. Maximum potential hydrolysis rates of model P-esters and P-anhydrides were assessed in the cell-free filtrates of representative diatom cultures and coastal field sites, while phosphatase diversity was also investigated in model diatom filtrates. Overall, results revealed that an innate capacity for the preferential utilization of P-anhydrides was prevalent across all of these sample types.

#### Degradation of Model P Sources by Diatom Cultures

In model diatoms, maximum rates of P hydrolysis were examined in cell-free filtrates that were prepared via syringe filtration of culture samples. Cell-surface and intracellular phosphatases may have been adventitiously released through the potential disruption and lysis of some cells during this process. Thus, P hydrolysis rates in these cell-free filtrates may overestimate truly dissolved rates of P hydrolysis. However, the aim here was not to quantify cell-free P hydrolysis rates per se, but to avoid technical barriers associated with analyzing the degradation of unlabeled P sources in the presence of cells. In particular, tracking P hydrolysis through the production of SRP becomes difficult at high cell densities because microorganisms have a strong ability to adsorb (Sanudo-Wilhelmy et al., 2004) and assimilate dissolved P.

Cell-free filtrates can only provide a glimpse into the overall DOP preferences of a culture because most DOP degradation takes place in the presence of cells. Thus, MUF-P hydrolysis in whole cultures was measured with a standard fluorometric protocol in order to help contextualize the P dynamics observed in cell-free filtrates. Surprisingly, inorganic 3poly-P degradation in the filtrates vastly exceeded MUF-P hydrolysis levels in whole cultures (p < 0.05), by at least ∼3-fold (T. pseudonana

FIGURE 6 | Inorganic poly-P hydrolysis (SRP method) and MUF-P hydrolysis (fluorometric method) in the coastal western North Atlantic. (A) Samples were collected from the New Jersey coast (green; 39◦24043.5000N, 73◦14056.6400W), offshore Long Island (orange; 40◦53043.9800N, 71◦22049.9200W), Narragansett Bay (yellow; 41◦17012.1200N, 71◦30011.6400W), Woods Hole harbor (blue; 41◦31024.6000N, 70◦40040.8000W), and Buzzard's Bay (red; 41◦32038.2800N, 70◦4008.4600W). (B) Substrate-specific P hydrolysis comparison. The diagonal line depicts the 1:1 ratio of P hydrolysis rates. (C) Relationship of P hydrolysis rates to chlorophyll levels. For inorganic poly-P hydrolysis, the regression analysis was performed on the entire dataset (note the two overlapping data points at ∼3 µg L−1 ). For MUF-P hydrolysis, the Buzzard's Bay outlier (note broken axis) was excluded from the regression analysis. Chlorophyll correlated significantly with inorganic poly-P degradation (p = 0.01) and MUF-P hydrolysis (p = 0.04). (D) P hydrolysis rates and bacterial abundance. In all panels, error bars represent the standard error of the mean of replicate samples (MUF-P hydrolysis: n = 3; inorganic poly-P hydrolysis: n = 8; chlorophyll: n = 3; bacterial abundance: n = 3).

TABLE 2 | Comparison of inorganic poly-P and MUF-P hydrolysis rates in field samples from Figure 6.

T-scores (T; reported as absolute values) are calculated using an independent two-sample T-test assuming equal variance, according to the following equation:

$$T = \frac{\mathcal{P}\#\_{\text{pro}(\rho,\rho)} - \mathcal{P}\#\_{\text{MJ}(\rho,\rho)}}{\text{SE}\_{\text{pro\text{totort}}}}$$

where PHpoly-P is the average P hydrolysis rate for inorganic polyhosphate, PHMUF−P is the average P hydrolysis rate for MUF-P, and SEpooled is the pooled standard error of PHpoly-P and PHMUF-P. Two-tailed p-values are reported.

CCMP1014) and up to ∼9-fold (T. oceanica CCMP1005; **Figure 4**). This finding is probably not a result of artificially elevated 3poly-P hydrolysis due to a filtration artifact, because most extracellular DOP-degrading enzymes localize on the cell surface and thus, most of the DOP degradation capacity is removed by filtering the cells out. Indeed, MUF-P hydrolysis was significantly lower in cell-free filtrates than in whole cultures (p < 0.05; **Figure 4**). Nor are the large differences between whole-culture MUF-P hydrolysis and filtrate-based 3poly-P degradation rates a consequence of the different detection TABLE 3 | Putative homologs of bacterial alkaline phosphatase in the genomes of T. oceanica CCMP1005 and T. pseudonana CCMP1335.

Hits are listed by the GenBank accession number.

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methods used. In fact, the SRP method is the more conservative approach (**Figure 5**) yet still shows remarkable correspondence with the MUF-P fluorescence method (**Figure 4**), especially given the large difference in sensitivity between these two techniques.

Relatively low levels of P hydrolysis were detected in the cell-free filtrates of actively growing and late log-phase cultures (**Figure 2A**, days 6–18; **Figure 2C**, days 6–15; **Figure 2E**, days 9, 17; **Figures 3D–I**). However, P hydrolysis rates were highest during the later stages of cultivation, including stationary phase and crash (**Figures 2**, **3**). In fact, the hydrolysis of 3poly-P and ATP increased as the cultures matured, even after accounting for increases in biomass through the growth curve (**Figures 3D–I**). These results may be a consequence of differences in the release, stability, or activity of cell-free P hydrolases over the life of the culture. For example, one interpretation is that active P-hydrolyzing enzymes can be released from healthy, growing cells, but these enzymes may be more extensively released from aging and senescent cells. This release could be actively driven by the diatoms themselves and/or mediated by physical mechanisms such as turbulence (e.g., daily culture mixing) or filtering. Like natural seawater, the cell-free filtrates examined in this study likely contain a mixture of actively and passively released proteins. If cell-free P hydrolysis is indeed linked to cell aging and senescence, as our data suggest, then the dissolved P hydrolase activity of seawater may be highest under certain environmental conditions, such as the collapse of phytoplankton blooms.

All P substrates examined (MUF-P, AMP, ATP, and 3poly-P) were actively degraded in diatom filtrates, but inorganic 3-polyP, followed by ATP, were the most rapidly transformed, regardless of overall P availability (**Figures 2**, **3**). Rates of ATP hydrolysis were lower (most cases) or approximately equal (one case) to that expected from the complete degradation of P-anhydride bonds (**Table 1**). Thus, P-ester hydrolysis may not have played a role in ATP degradation, even though P-ester hydrolysis lead to a relatively small level of AMP degradation in the same samples. Assuming that only terminal phosphate groups are enzymatically labile (Huang et al., 2018), we speculate that P-anhydrides may block P-esterases from accessing the P-O-C bond of ATP. Overall, these findings suggest that Thalassiosira spp. may preferentially hydrolyze inorganic poly-P compared to other DOP sources under a wide range of prevailing P availability. A variety of potential mechanisms may underlie the preferential degradation of P-anhydrides in diatom cell-free filtrates, including differences

in the amount, substrate versatility, stability, and diversity of P-hydrolyzing enzymes.

Thalassiosira oceanica exhibited the most versatile response to P amendments, consistent with a diverse nutrient utilization profile expected in this isolate from the P-limited Sargasso Sea. For example, T. oceanica had the broadest potential to utilize both 3poly-P and ATP, regardless of overall P status (**Figure 2**). Furthermore, every culture upregulated the degradation of ATP under P-deplete conditions, but T. oceanica was the only one that also increased its capacity to degrade 3poly-P in response to P scarcity (**Figure 3**). These results suggest that while enhanced ATP utilization may be a widespread adaptation to low P availability among Thalassiosira spp., elevated 3poly-P utilization may not be. Rather, in T. pseudonana, active P-anhydride degradation may be constitutive. Overall, the P utilization potential of T. pseudonana CCMP1014, an oceanic isolate from the NPSG, exhibited more similarity toward T. pseudonana CCMP1335 than T. oceanica. This finding may indicate that species- rather than habitat-level factors may be a more prevalent control over DOP cycling by these diatoms, although each of these strains has been in culture for over 40 years and some genetic drift has likely occurred.

#### P Hydrolysis of Model DOP Sources in the Coastal Western North Atlantic

Although some SRP uptake probably occurred in our field incubations, the results suggest that it was too slow to decrease SRP concentrations by more than the detection limit of 800 nmol L−1 . This outcome is consistent with SRP uptake rates observed in other coastal systems with similar chlorophyll concentrations as our field sites (Harrison et al., 1977). SRP uptake therefore did not affect measured rates of inorganic poly-P hydrolysis.

Degradation rates of inorganic 3poly-P and 45poly-P were similar in field samples, which is consistent with the chain length-independent utilization of poly-P by some eukaryotic phytoplankton observed in a previous study (Diaz et al., 2016). Maximum rates of inorganic poly-P hydrolysis determined by the SRP method were significantly higher than fluorescence-based measurements of MUF-P hydrolysis in four out of five field sites examined in the coastal North Atlantic (**Figure 6B** and **Table 2**). These differences may be even more extreme, based on the finding that the SRP method for P hydrolysis is systematically conservative relative to the fluorescence-based approach (**Figure 5**).

The majority of studies on marine DOP hydrolysis have focused on P-monoester degradation in oligotrophic waters, where DOP hydrolysis is thought to function primarily as a phosphate-inhibitable phytoplankton response to P depletion (Duhamel et al., 2010; Lin et al., 2016). Above the threshold SRP level of ∼30 nmol L−1 , P-monoester hydrolysis is typically less than ∼1 nmol L−1 hr−1 (∼20 nmol µg chl−1 hr−1 ) in these systems (Mahaffey et al., 2014). Consistent with this finding, chlorophyll-normalized rates of MUF-P and inorganic poly-P hydrolysis are less than ∼20 nmol µg chl−1 hr−1 in the relatively high-P coastal sites examined here (SRP > ∼150 nmol L−1 ). However, because total chlorophyll levels are much higher in the waters examined in this study, the volume-normalized rates are much higher (∼4- to ∼20-fold) than in the oligotrophic ocean. Similar rates of volume-normalized P-ester hydrolysis have been previously reported from coastal systems and deep waters (Li et al., 1998; Dyhrman and Ruttenberg, 2006; Nicholson et al., 2006; Davis et al., 2014).

The strong correlation of P hydrolysis rates with chlorophyll levels (**Figure 6C**), and the lack of correlation with bacterial abundance (**Figure 6D**), suggests that the observed P dynamics were driven by phytoplankton. MUF-P hydrolysis (but not inorganic poly-P degradation) at the Buzzard's Bay site was inconsistent with the overall relationship to chlorophyll, which suggests additional, non-phytoplankton associated mechanisms of P-monoester degradation, such as contributions from heterotrophic bacteria. Heterotrophic bacteria utilize phosphatases to remineralize and acquire the carbon and nitrogen contained in DOP (Wilkins, 1972; Wanner and McSharry, 1982; Hoppe and Ullrich, 1999). Because the degradation of inorganic poly-P yields no carbon or nitrogen, heterotrophic bacteria may not contribute extensively to the degradation of inorganic poly-P sources. Thus, in a system dominated by bacterially driven DOP hydrolysis, the inorganic poly-P and P-ester dynamics may be decoupled, such that P-ester hydrolysis rates are substantially higher than inorganic poly-P degradation, consistent with results from the Buzzard's Bay site. In agreement with this hypothesis, the ratio of bacteria to phytoplankton cells was ∼3 fold higher in Buzzard's Bay than at any other location (**Supplementary Table S1**). Furthermore, White et al. (2012) found that 3poly-P was less extensively degraded than P-esters like AMP and glucose-6-phosphate in seawater incubations that had been pre-conditioned to favor bacterial growth.

#### Phosphatase Diversity in Diatom Cultures

Enzymes modulating the P-hydrolysis reactions observed in diatom cultures and coastal Atlantic field samples may include phosphatases such as AP, inorganic pyrophosphatase, and nucleoside triphosphatases. AP's are the best-known group of enzymes involved in DOP utilization by phytoplankton (Lin et al., 2016). These P-esterases are widely distributed in prokaryotic and eukaryotic microorganisms yet show only limited homology across these two groups (Lin et al., 2012). Furthermore, AP's are much better characterized in prokaryotes than microbial eukaryotes (Shaked et al., 2006; Xu et al., 2006, 2010; Lin et al., 2011, 2013, 2015, 2016). For example, major prokaryotic AP isoforms include PhoA, PhoX, and PhoD (Luo et al., 2009, 2011). All of these have been detected in seawater, with PhoD being the most prevalent, followed by PhoX (Luo et al., 2009; Sebastian and Ammerman, 2009; Kathuria and Martiny, 2010; Luo et al., 2011). Substrate specificities of the AP isoforms are not completely characterized, but they may exhibit a wide degree of flexibility. For example, E. coli PhoA is also a polyphosphatase (Lorenz and Schroder, 2001; Huang et al., 2018).

Multiple putative AP's have been recognized in the genome, transcriptome, and proteome of T. pseudonana CCMP1335 (Armbrust et al., 2004; Dyhrman et al., 2012), and at least one of these has been recognized for its resemblance to bacterial PhoA (Lin et al., 2016). Using BLASTP translated genome searches of T. pseudonana CCMP1335 and T. oceanica CCMP1005 with bacterial PhoA, PhoD, and PhoX queries, additional putative AP homologs were identified herein (**Table 3**). However, none of these sequences were apparent in the exoproteome data of either diatom species (**Figure 7**), suggesting that these enzymes may be exclusively cell-associated and ruling them out from participating in the P-hydrolysis dynamics observed in culture filtrates. Exoproteome samples revealed a number of other putative phosphatases, the diversity of which was biased in favor of P-anhydride degradation (**Figure 7**), consistent with the observed preferential hydrolysis of P-anhydrides in culture filtrates (**Figures 2–4**). The mechanisms leading to the appearance of these phosphatases in the exoproteome remain unclear, but may potentially include active secretion, passive dislodging of cell surface-associated enzymes during cultivation, and/or adventitious release during filtrate preparation.

Nearly all of the phosphatase hits present in the T. pseudonana CCMP1335 exoproteome (**Figure 7**) were also detected in its cell-associated transcriptome and proteome, which were reported in a previous study (Dyhrman et al., 2012). The only exception was the P-diesterase (GenBank EED94265). However, this sequence also could not be found in the JGI translated genome assemblies for T. pseudonana CCMP1335 utilized by Dyhrman et al. (2012). The absence of a protein sequence from the reference database precludes its identification in the experimental data. Thus, the absence of EED94265 in the proteome data from this previous study is at least partially a result of the different methods employed. As for the other putative phosphatases detected in the present study, none were upregulated in the T. pseudonana CCMP1335 transcriptome or proteome under P-deplete conditions (Dyhrman et al., 2012). In fact, three hits were upregulated under P-replete conditions: two GTPases (EED91276 in the proteome only; EED90008 in the transcriptome only) and one ATPase (transcriptome and proteome: EED92744). These results are consistent with the lack of upregulation of 3poly-P hydrolysis in the cell-free filtrate of this species under -P conditions (**Figure 3E**). On the other hand, ATP degradation was enhanced (∼2.5-fold) under low P availability in T. pseudonana CCMP1335 cell-free filtrates (**Figure 3H**), but this activity may not be regulated or sufficiently resolved at the transcriptional or translational levels.

Some of the exoproteome hits identified in this study may exhibit phosphatase activities by operating in the reverse direction of their annotated functions (e.g., ATP synthase components). Sequence information can identify candidate enzymes for a given biochemical function, however, these hits must be purified and assessed in vitro to verify their actual enzymatic reactivity. Furthermore, the presence of some protein hits in the exoproteomes may be unexpected. For example, an abundance of proteins affiliated with the ATP synthase complex were found in the exoproteomes of both diatom species. However, in some microorganisms, ATP synthase localizes in the cell membrane, utilizing the proton-motive force produced by the light activated proton-pump proteorhodopsin to generate ATP (Lin et al., 2016). In fact, proteorhodopsin expression may be an active aspect of diatom physiology (Marchetti et al., 2012; Marchetti et al., 2015). The potential localization of ATP synthase on the plasma membrane suggests that it could potentially become adventitiously dislodged without substantial cellular disruption or lysis (e.g., through daily physical mixing of cultures). Indeed, the release of cell-associated material was likely minimal during the preparation of diatom cell-free filtrates, as only 133 protein hits were detected in T. pseudonana CCMP1335 exoprotomes out of 1264 total protein hits reported in a prior study (Dyhrman et al., 2012).

#### Synthesis and Perspectives

The P-anhydride bond is essential to life. It serves as the universal basis of cellular energy transduction through the formation and hydrolysis of ATP and also plays diverse regulatory roles in the form of inorganic polyphosphates that are made by every cell in nature. As a widespread and labile constituent of marine DOP, P-anhydrides may also represent a bioavailable P source capable of supporting phytoplankton growth and productivity in the ocean. This P-anhydride pool has largely been overshadowed by the prevailing assumption that the much more abundant standing stock of marine P-esters is the most important DOP source. Based on results from this study, however, the possibility that P-anhydrides support a high degree, maybe even a majority, of DOP turnover and assimilation in diverse marine environments should be considered.

If P-esters are less preferred than P-anhydrides, then APA measurements may underestimate levels of P stress in oligotrophic systems, where phosphatase activity primarily functions in the acquisition of P by P-starved phytoplankton. In high-nutrient coastal systems, P-anhydrase activity may be constitutively expressed regardless of prevailing orthophosphate availability (Ammerman and Azam, 1991), suggesting that P-anhydrides may be a part of the highly labile DOP pool that is rapidly cycled in these environments (Benitez-Nelson and Buesseler, 1999). For example, in T. pseudonana, degradation of inorganic 3poly-P was just as high or higher under replete P conditions (**Figures 3E,F**). Furthermore, in T. pseudonana CCMP1335, this trend was consistent at the protein level, where each of the potential enzymes involved in 3poly-P degradation (**Figure 7**) were just as prevalent or more prevalent under P-rich conditions examined in a previous study (Dyhrman et al., 2012).

The degradation of dissolved P-anhydrides may be cryptic, with the relatively low abundance of this pool (Young and Ingall, 2010) masking rapid recycling rates. In situ P-anhydride degradation rates are dependent on the inherent degradation kinetics of the bulk P-anhydrase pool, as well as the in situ concentration of P-anhydride substrates. The maximum

hydrolysis rates reported herein do not necessarily reflect in situ degradation rates, because actual P-anhydride levels may not be rate-saturating. In situ DOP utilization rates have been estimated based on standing stock DOP concentrations (Duhamel et al., 2011), but cryptic cycling commonly evades detection by concentration-based approaches (Canfield et al., 2010; Hansel et al., 2015; Berg et al., 2016). Rather, cryptic transformation rates may be more readily quantified by using high-sensitivity radiotracers amended at levels similar to in situ substrate concentrations. Biologically mediated cryptic pathways can also be illuminated by investigating the community-level metabolic potential, as manifest in environmental genome, transcriptome, and proteome sequence data. As a step toward this goal, the present study has identified a diversity of diatom-derived phosphatases that may drive P-anhydrase reactions in the marine environment.

In addition to radiotracers and bioinformatics approaches, the study of P-anhydride degradation in marine systems would also be advanced by the availability of representative labeled substrates. For example, P-ester degradation (conventionally referred to as APA) is routinely assessed using sensitive fluorogenic and chromogenic substrates (Hoppe, 2003; Dyhrman and Ruttenberg, 2006; Mahaffey et al., 2014; Davis and Mahaffey, 2017). By quantifying the inert, signal-bearing probe that is released during P hydrolysis, these substrates can be used to track P-hydrolysis rates independently of P dynamics, which is especially important at high cell densities. Synthesis of labeled inorganic poly-P has been described (Choi et al., 2010; Hebbard et al., 2014), but these substrates were unreactive in positive controls tested in this study (data not shown).

Future work should focus on methods to assess the P hydrolysis of diverse DOP compounds by whole cells. The application of such methods should confirm whether the DOP dynamics observed here in diatom cell-free filtrates reflect broader DOP nutritional preferences. For example, the P hydrolytic potential of diatom cell-free filtrates implies that these microorganisms have a capacity, and potentially a preference in the case of 3poly-P, to utilize a diversity of P sources for growth. If cultures had been amended with 3poly-P during stationary phase, the elevated potential for 3polyP hydrolysis (**Figure 2**) may have helped the cultures avoid crashing, although this was not tested. The P-hydrolysis of DOP sources is not necessarily coupled to the biological assimilation of enzymatically released P, however (Ammerman and Azam, 1985; Duhamel et al., 2017). For instance, heterotrophic bacteria are thought to degrade organic P sources as a carbon and/or nitrogen utilization strategy, and phosphate may accumulate in seawater as a result (Hoppe and Ullrich, 1999; Hoppe, 2003). Furthermore, if phosphatases are not actively degraded, then their activity can lead to the accumulation of dissolved inorganic P when other factors besides P availability limit plankton growth. In such a case, the accumulation of enzymatically released P may have other implications for marine ecosystem functioning. For example, the primary pathway for long-term P removal is the authigenic (or in situ) formation of marine calcium phosphate minerals (Ruttenberg, 2014). The direct precipitation of these minerals is kinetically inhibited in most marine environments but may involve inorganic poly-P as a reactive intermediate (Schulz and Schulz, 2005; Diaz et al., 2008). In fact, the inherently high capacity for P-anhydride degradation documented in diatom cultures and natural samples in this study suggests that pulsed or spatially-heterogeneous poly-P inputs could lead to the formation of transient, submicron-scale "hotspots," which may be kinetically conducive to the formation of authigenic calcium phosphate minerals.

#### DATA AVAILABILITY STATEMENT

The raw data supporting the conclusions of this manuscript are deposited at the Biological and Chemical Oceanography Data Management Office (http://bco-dmo.org) under project number 747715.

#### AUTHOR CONTRIBUTIONS

JD, SD, and YT conceived the experiments and overall study design. JD, AH, JS, KB, DM, C-WC, and DP generated results and conducted the data analysis. All authors contributed to manuscript preparation.

# FUNDING

This work was supported by the National Science Foundation under grants 1559124 (JD), 1736967 (JD), 1737083 (SD), and 1559087 (YT), as well as a Junior Faculty Seed Grant from the University of Georgia Research Foundation (JD). The Thermo-Fisher LTQ Orbitrap Elite Mass Spectrometer was purchased with funding from National Institutes of Health under grant S10RR028859.

# ACKNOWLEDGMENTS

We thank Colleen Hansel, Carl Lamborg and the science party and crew of the R/V Endeavor during the TORCH I cruise. We thank James Morrissey for his generosity in providing fluorogenic polyphosphate for our research, and Catherine Baker for synthesizing these substrates. We also thank Lee Ann DeLeo for her help with the preparation of graphics for this paper, and we acknowledge Mohit Jain for technical assistance with proteomics data analysis.

# SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmars. 2018.00380/full#supplementary-material

# REFERENCES

fmars-05-00380 October 23, 2018 Time: 14:30 # 15

trace metal addition experiments. Front. Mar. Sci. 1:73. doi: 10.3389/fmars.2014. 00073

fmars-05-00380 October 23, 2018 Time: 14:30 # 16

influence of the Pearl River. Deep Sea Res. I Oceanogr. Res. Pap. 55, 1330–1342. doi: 10.1016/j.dsr.2008.05.007

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Diaz, Holland, Sanders, Bulski, Mollett, Chou, Phillips, Tang and Duhamel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

, Fabrizio D'Ortenzio2

,

# Sensitive Determination of the Dissolved Phosphate Pool for an Improved Resolution of Its Vertical Variability in the Surface Layer: New Views in the P-Depleted Mediterranean Sea

#### Edited by:

Kahina Djaoudi 1

Christian Lønborg, Australian Institute of Marine Science (AIMS), Australia

#### Reviewed by:

Masahiro Suzumura, National Institute of Advanced Industrial Science and Technology (AIST), Japan LeAnn Whitney, University of Rhode Island, United States

#### \*Correspondence:

Kahina Djaoudi<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Marine Biogeochemistry, a section of the journal Frontiers in Marine Science

Received: 01 February 2018 Accepted: 18 June 2018 Published: 10 July 2018

#### Citation:

Djaoudi K, Van Wambeke F, Coppola L, D'Ortenzio F, Helias-Nunige S, Raimbault P, Taillandier V, Testor P, Wagener T and Pulido-Villena E (2018) Sensitive Determination of the Dissolved Phosphate Pool for an Improved Resolution of Its Vertical Variability in the Surface Layer: New Views in the P-Depleted Mediterranean Sea. Front. Mar. Sci. 5:234. doi: 10.3389/fmars.2018.00234 Sandra Helias-Nunige1 , Patrick Raimbault 1 , Vincent Taillandier 2 , Pierre Testor 3 , Thibaut Wagener 1 and Elvira Pulido-Villena1 1 Aix-Marseille Univ., Université de Toulon, Centre National de la Recherche Scientifique, IRD, MIO UM 110, Marseille, France,

\*, France Van Wambeke1

2 Sorbonne Université, CNRS, Laboratoire d'Océanographie de Villefanche, LOV, Villefranche-sur-mer, France, 3 Sorbonne Université, UPMC, Université Paris 06, Centre National de la Recherche Scientifique, IRD, MNH, Laboratoire d'Océanographie et de Climatologie, IPSL, Paris, France

, Laurent Coppola2

An accurate understanding of the biogeochemistry of dissolved phosphate pool in the upper waters of P-depleted oceanic regions is constrained by the low sensitivity of routine phosphate measurements. In this study, by using the sensitive Liquid Waveguide Capillary Cell method, we report the first extensive cross-basin survey of nanomolar dissolved inorganic phosphate (DIP) and dissolved organic phosphate (DOP) concentration in P-depleted surface waters of the Mediterranean Sea during the stratification period. In the north western Mediterranean Sea (NWMS), DIP above the mixed layer depth (MLD) ranged between 4.9 and 26.5 nM. Along an E-W transect crossing Ionian and Tyrrhenian Seas (E-W transect), DIP above the MLD was lower, ranging between 0.9 and 11.4 nM. Contrarily to the traditional view of a depleted and invariant surface dissolved phosphate pool, a significant vertical variability of DIP and DOP was revealed in upper waters. A positive gradient of DIP was observed above the phosphacline, between the MLD and the deep chlorophyll maximum (DCM) depth, suggesting a potential diffusion of new phosphate to near-surface waters, even under stratified conditions. Interestingly, despite this apparent DIP availability, a significant negative gradient of DOP concentration was observed in the same layer. Finally, the positive gradient in DIP coincided with a significant increase in N:P ratio, suggesting a higher rate of increase of N than of P. The results obtained in this study indicate that acquiring nanomolar DIP data is a sine qua non condition for the comprehension and prediction of the biogeochemical functioning of P-depleted oceanic regions, such as the Mediterranean Sea.

Keywords: the Mediterranean Sea, dissolved inorganic phosphate, dissolved organic phosphate, N:P ratios, liquid waveguide capillary cell

#### Djaoudi et al. Nanomolar Phosphate in Mediterranean Sea

# INTRODUCTION

Nitrogen (N) and phosphorus (P) are essential macronutrients for sustaining marine organisms (Redfield, 1958). By controlling the efficiency of the biological pump, N and P determine the strength of the oceanic carbon uptake (Balino et al., 2001). Over the vast oligotrophic ocean, upper waters are often subjected to N and P exhaustion due to a strong vertical stratification and an active drawdown by biological activity (Tyrrell, 1999). N has traditionally been viewed as the limiting nutrient of primary production in marine waters (Ryther and Dunstan, 1971). However, with an increased understanding of the N cycling in the ocean, there is a growing awareness that P has also the potential to limit primary production in certain regions of the oligotrophic ocean (i.e., Wu et al., 2000; Moutin et al., 2008; Lomas et al., 2010). The Redfield N:P ratio of 16:1 has been considered as a fundamental tenet in marine biogeochemistry. Deviations from this canonical ratio have been used to provide insights, for instance, on the efficiency of carbon sequestration in the ocean (Sigman and Boyle, 2000), or on nutrient limitation of primary production (i.e., Falkowski and Raven, 1997; Moore et al., 2013). In some oligotrophic regions, such as the North Atlantic subtropical gyre, N:P ratios in near-surface waters are higher than 16:1, suggesting a depletion of P before that of N (Wu et al., 2000; Ammerman et al., 2003).

In such P-depleted oligotrophic regions, the quantification of dissolved inorganic phosphate (DIP) is a challenging task because concentrations drop to nanomolar (nM) levels, so unquantifiable using the conventional automated colorimetric procedure (CACP) which presents a limit of detection (LOD) of 20 nM, at best cases. Alternative analytical procedures have been introduced to improve the LOD and precision of DIP analysis (see review by Patey et al., 2008). The pre-concentration by magnesium-induced co-precipitation (MAGIC) method substantially improved the amount of DIP data at nM levels (Karl and Tien, 1992; Rimmelin and Moutin, 2005). During the last decade, the Liquid Waveguide Capillary Cell (LWCC) method, have gained a foothold as a reliable method for nM DIP measurements (i.e., Zhang and Chi, 2002; Patey et al., 2008). By using these high sensitive methods, studies in both the North Pacific (Karl et al., 2001 and references therein; Suzumura et al., 2012; Hashihama et al., 2013) and North Atlantic (Ammerman et al., 2003; Lomas et al., 2010) subtropical gyres have revealed DIP concentrations as low as 0.2 nM (Wu et al., 2000). Moreover, since the determination of dissolved organic phosphate (DOP) relies upon DIP measurements, some of the above cited studies have also provided accurate DOP data (i.e., Mather et al., 2008; Suzumura et al., 2012), crucially enhancing our knowledge on the biogeochemical functioning of P-depleted oceanic regions, where DOP represents a P source for sustaining community productivity (Karl and Björkman, 2015 and references therein; Sato et al., 2013).

The Mediterranean Sea is one of the world's most oligotrophic oceanic regions. It is divided into two sub-basins, western and eastern, exhibiting distinct hydrodynamics and biogeochemical features. The Mediterranean Sea exhibits low nutrient concentrations, with a west to east decreasing gradient (Krom et al., 1991; Moutin and Raimbault, 2002; De Madron et al., 2011), partly linked to its anti-estuarine thermohaline circulation (Crispi et al., 2001). Available nutrients in the Atlantic surface inflow entering the Mediterranean Sea are consumed along the way to the eastern basin and exported to deep waters (Crise et al., 1999; Lazzari et al., 2012). Consequently, the western Mediterranean basin is oligotrophic while the eastern basin is ultraoligotrophic (Moutin and Raimbault, 2002).

In the Mediterranean surface waters, DIP concentration has been shown to limit primary production, nitrogen fixation and heterotrophic bacterial activity (Van Wambeke et al., 2002; Thingstad et al., 2005). These findings are supported by low DIP concentrations measured in upper waters and a deep N:P ratio which diverges greatly from the canonical Redfield ratio, with values ranging between 21 and 23 in the Western basin (Bethoux et al., 1992) and even higher in the Eastern basin (Krom et al., 1991). Surface DIP concentration in surface waters is systematically below 20 nM (LOD of the CACP) during the stratification period, dramatically constraining data coverage in this oceanic region (i.e., Pujo-Pay et al., 2011; Céa et al., 2015). The depth at which DIP concentration becomes measurable by the CACP is usually used to define the phosphacline and it has been reported to be between 45 m and 120 m, during the stratified period, in the western and eastern Mediterranean Sea, respectively (Moutin and Raimbault, 2002). To date, lack of DIP data above this phosphacline has precluded resolving vertical variability in this key layer as has led to the traditional view of an entirely depleted and invariant dissolved phosphate surface pool. Few studies, however, by using sensitive determination of DIP, have reported low but detectable increases in nanomolar DIP concentration above the phosphacline adding evidence against this traditional view (Van Wambeke et al., 2002; Krom et al., 2005; Djaoudi et al., 2017). Nevertheless, the scarcity and the sparse nature of available nM DIP data in the Mediterranean Sea still precludes a complete assessment of DIP dynamics in the upper waters at the basin scale.

As for DIP, a critical gap in accurate DOP data (i.e., based on nanomolar DIP measurements) persists in the upper waters of the Mediterranean Sea (Moutin and Raimbault, 2002; Pujo-Pay et al., 2011). Indeed, only two studies have reported nanomolar DIP and DOP data simultaneously (Krom et al., 2005; Djaoudi et al., 2017). In the Mediterranean Sea, when DIP is exhausted, DOP becomes a possible alternative source of P as confirmed by high activities of alkaline phosphatase suggesting an active utilization of the DOP pool in upper waters (Van Wambeke et al., 2002, 2009; Thingstad and Mantoura, 2005). How and to which extent such biogeochemical dynamics induce changes in DOP concentration above the phosphacline remains unknown.

In this study, we conducted cross-basin observations of nM DIP and DOP concentration in the Mediterranean Sea with emphasis on upper waters. The main goals of this work are: (1) to extend the nM dataset of accurate paired DIP/DOP data in the upper Mediterranean Sea under stratification conditions, (2) to examine the vertical variability of both DIP and DOP above the phosphacline, under stratification conditions and, (3) to better resolve the DIN:DIP and DON:DOP ratios in the upper waters of this P-depleted oceanic region.

### MATERIALS AND METHODS

#### Study Area and Sampling

This study was performed in the framework of two research cruises carried out in 2015 in the Mediterranean Sea, during the stratification period, MOOSE-GE (doi.org/10.18142/235) and BioArgomed (doi.org/10.17882/51678) (**Figure 1**).

The MOOSE-GE (Mediterranean Ocean Observing System for the Environment– Grande Échelle) cruise took place on board the R/V Le Suroit between 10 and 26 July in the oligotrophic North Western Mediterranean Sea (NWMS). The BioArgoMed cruise took place on board the R/V Tethys II between 13 May and 03 June along an east to west transect (E-W transect) crossing the ultraoligotrophic Ionian and Tyrrhenian Seas. Therefore, these cruises covered the two Mediterranean sub-basins, western and eastern, which exhibit distinct hydrological and biogeochemical features (i.e., De Madron et al., 2011).

During the two cruises, oceanographic casts were acquired using a conductivity-temperature-depth profiling system (SBE911 + CTD unit). The density profiles were calculated from temperature and salinity profiles, and linearly interpolated at 1 m depth intervals. Fluorescence profiles were provided by a Chelsea Aquatracka 3 fluorimeter interfaced with the CTD unit.

Seawater samples were collected during up casts with a carousel of Niskin bottles for analyses of dissolved phosphate (dissolved inorganic phosphate, DIP; total dissolved phosphate, TDP) and dissolved nitrogen (dissolved inorganic nitrogen, DIN; total dissolved nitrogen, TDN). In the present study, DIN includes nitrate + nitrite concentration and does not include ammonium. Pujo-Pay et al. (2011) reported NH+ 4 concentrations in the Mediterranean Sea between 0 and 10 nM, indicating that DIN data reported in this study can suffer from up to 10 nM underestimation.

Samples were collected in duplicate and filtered on board through a pre-cleaned (500 mL of ultrapure water) 0.2µm syringe filter. Samples were then disposed into acid washed HDPE-60 mL bottles and were stored frozen (−20◦C) until analysis. To check for potential N and P contamination through filtration, DIP and DIN concentration were analyzed on ultrapure water filtered the same way as samples. DIN concentration in such blanks was below the limit of detection. DIP concentrations in the blanks was 2.8 ± 0.6 nM (n = 5), not significantly different from the reagent blanks (2.2 ± 0.3 nM, n = 5).

During the MOOSE-GE cruise, seawater samples were collected at 25 stations (**Figure 1**), between the surface and 100 m at 4 different depths. Sampling depths were chosen according to the density and fluorescence depth profiles. Density profiles were used to determine the depth of the mixed layer, in which a sampling point was defined (depth 1, **Figure 2**). From the fluorescence depth profiles, which exhibited the characteristic subsurface maximum (deep chlorophyll maximum, DCM) reported for the western Mediterranean Sea during the stratification period (Lavigne et al., 2015), 3 sampling points were defined: one point at the DCM (depth 3, **Figure 2**) and two points above and below the DCM (depths 2 and 4, **Figure 2**). During the BioArgoMed cruise, seawater samples were collected from 6 stations (**Figure 1**) at 6 different depths between the surface and 120 m.

### Dissolved Nutrient Analysis

DIP concentration was determined by using both the CACP (Aminot and Kérouel, 2007) and the LWCC method (Zhang and Chi, 2002). Both spectrophotometric methods are based on the molybdenum blue reaction, described by Murphy and Riley (1962). In the LWCC method, according to the Beer-Lambert law, the sensitivity of the spectrophotometric measurement is improved by increasing the optical path length of the measurement cell from 1 cm (CACP) to 2.5 m (LWCC). The LOD, estimated as three times the standard deviation of ten measurements of the blank, was 20 and 0.8 nM for the CACP and the LWCC method, respectively. For the LWCC method, the linearity of absorbance vs. DIP concentration was assessed, and the dynamic range was determined to be between 0.8 and 143 nM. Therefore, for DIP concentrations above such range, the DIP value provided by the CACP was used. Between 20 and 143 nM (range of concentrations for which both methods are comparable), the relationship between the two methods followed a linear model (r = 0.96; n = 80) with a slope of 1.14 ± 0.04, not significantly different from 1 (p > 0.05).

Total dissolved phosphate (TDP) concentration was analyzed by using the CACP after sample processing by the wet oxidation method (Valderrama, 1981). DOP concentrations were then estimated by subtracting nM LWCC-DIP from TDP concentrations, with an analytical precision of 7%.

Dissolved inorganic nitrogen (DIN) and total dissolved nitrogen (TDN) concentrations were measured by using the CACP with a LOD of 50 nM. As for TDP, samples for TDN were processed according to the wet oxidation method (Valderrama, 1981). Dissolved organic nitrogen (DON) concentrations were then estimated by subtracting DIN from TDN concentrations.

#### Data Treatment and Calculations

The mixed layer depth (MLD) was estimated from the density profiles as the depth where the difference of density from the surface reference (i.e., density at 10 m depth) was 0.03 kg m−3 (De Boyer Montégut, 2004).

The depth of the phosphacline was calculated as the average of 4 phosphacline depth values determined based on 4 different reported criteria following Van Wambeke et al. (2009). Phosphacline1 and phosphacline2 were calculated as the shallowest depths in which DIP concentrations exceeded the mixed layer value by 10 and 50 nM, respectively (Van Wambeke et al., 2009); phosphacline3 and Phosphacline4 were calculated as the depths in which DIP concentrations exceeded the concentration at the immediate previous depths by 20 and 100 nM, respectively (Van Wambeke et al., 2009; Pujo-Pay et al., 2011).

The Wilcoxon signed-rank test was used to assess the overall significance of the vertical differences in DIP and DOP concentration for each cruise. For each individual profile, vertical differences in DIP and DOP concentration where considered significant when they were higher than the LOD and precision of the analytical methods.

stations, see Table 1 for references).

#### RESULTS

Over the study area and for both cruises, a stratification of the water column was observed. The MLD ranged between 6 and 30 m with an average of 13 ± 5 m (n = 25) during the MOOSE-GE cruise (hereafter, NWMS: for NW Mediterranean Sea) and between 14 and 20 m with an average of 17 ± 3 m (n = 6) during the BioArgoMed cruise (hereafter, E-W transect) (**Figure 3**). The phosphacline depth in the NWMS ranged between 30 and 89 m with an average of 56 ± 14 m for 21 stations and was higher than 100 m for the remaining 4 stations (**Figure 3**). Along the E-W transect, the phosphacline depths were higher than 120 m (maximum sampled depth) except for one value at 70 m (**Figure 3**).

#### Dissolved Phosphate Pools

By using the LWCC, all DIP concentrations in the upper waters of the Mediterranean Sea obtained in this study were above the LOD of 0.8 nM. Compared to the CACP, the sensitive LWCC method resulted in a 75% increase of valid DIP data and therefore of DOP data in the study area.

Surface (0–100 m) DIP concentration in the NWMS ranged over two orders of magnitude, between 3.6 and 251 nM (**Figure 3A**). Surface (0–120 m) DIP concentrations along the E-W transect were lower, ranging between 0.9 and 14.6 nM except for one single value at 127.5 nM (**Figure 3B**). DIP concentrations above the MLD ranged between 4.9 and 26.5 with an average of 12.8 ± 6.8 (n = 28) in the NWMS (**Figure 3A**) and between 0.9 and 11.4 nM with an average of 5.5 ± 3.6 nM (n = 11) along the E-W transect (**Figure 3B**).

Concerning vertical variability, DIP concentration in the NWMS exhibited a first significant increase between the MLD and the DCM depth (Wilcoxon signed-ranks test, Z = 3.2, p < 0.01, n = 25) (**Figure 4**). It then increased more sharply between the DCM depth and 100 m (Wilcoxon signed-ranked test, Z = 4.0, p < 0.001, n = 25) (**Figure 4**). In order to get a deeper insight on the observed DIP vertical variability, a gradient of DIP was calculated by dividing the difference in DIP concentration by the corresponding difference in depth. In the NWMS, the first DIP positive gradient (between the MLD and the DCM depth) was recorded in 21 out of 25 of the sampling stations (Figure S1) and ranged between 0.04 and 3.2 nM m−1 with an average of 0.4 ± 0.7 nM m−1 . The second positive gradient

FIGURE 3 | Vertical section of dissolved inorganic phosphate concentrations (DIP) in the North Western Mediterranean Sea (between the surface and 100 m, A) and along the E-W transect crossing Ionian and Tyrrhenian seas (between the surface and 120 m, B). The red plot represents the mixed layer depth. The orange plot represents the phosphacline depth. Note that the scale of the color bar has been tightened to point out the positive gradient of DIP in the North Western Mediterranean Sea.

bounded line the standard deviation from the mean. The blue dashed line corresponds to the limit of detection (LOD) of the conventional automated colorimetric

procedure (20 nM). The green plot represents the fluorescence profile (mean ± standard of deviation).

(between the DCM depth and 100 m) was recorded in 21 out of 25 of the sampling stations (Figure S1) and ranged between 0.03 and 5.7 nM m−1 with an average of 2.6 ± 1.6 nM m−1 .

Likewise, along the E-W transect, a significant increase in DIP concentration was observed between the MLD and the DCM depth (Wilcoxon signed-ranks test, Z = 2.2, p < 0.05, n = 6) (**Figure 4**). This DIP positive gradient was recorded for all stations and ranged between 0.01 and 0.08 nM m−1 with an average of 0.04 ± 0.03 nM m−1 (Figure S1). Because in the E-W transect the maximum sampling depth was above the phosphacline, the second increase in DIP concentration below the DCM was not observed.

Surface DOP concentration in the NWMS ranged between 4 and 149 nM with an average of 44 ± 25 nM (n = 100) (**Figure 5A**). As for DIP, DOP concentrations were lower along the E-W transect, ranging between 15 and 64 nM with an average of 33 ± 12 nM (n = 36) (**Figure 5B**). DOP concentration above the MLD ranged between 17 and 139 nM with an average of 47 ± 36 (n = 28) in the NWMS (**Figure 5A**) and between 20 and 62 nM with an average of 35 ± 11 nM (n = 11) along the E-W transect (**Figure 5B**).

Concerning the vertical variability, DOP concentration in the NWMS exhibited a significant decrease between the MLD and the DCM (Wilcoxon signed-ranks test, Z = 2.1, p < 0.05,

FIGURE 5 | Vertical section of dissolved organic phosphate concentrations (DOP) in the North Western Mediterranean Sea (between the surface and 100 m, A) and along the E-W transect crossing Ionian and Tyrrhenian seas (between the surface and 120 m, B). The red plot represents the mixed layer depth. The orange plot represents the phosphacline depth. Note that the scale of the color bar has been tightened to point out the negative gradient of DOP in the North Western Mediterranean Sea.

n = 25) (**Figure 6**). As for DIP, a DOP gradient between the MLD and the DCM was calculated by dividing the difference in DOP concentration by the corresponding difference in depth. The negative gradient of DOP in this layer was recorded in 15 out of 25 of the sampling stations (Figure S2) and ranged between 0.05 and 2.7 nM m−1 with an average value of 0.6 ± 0.7 nM m−1 .

Along the E-W transect, no significant difference in DOP concentration was observed between the MLD and the DCM depth (Wilcoxon signed-ranks test, Z = 0.94, p > 0.05, n = 6).

# N:P Molar Ratios in the Upper Mediterranean Sea

In the NWMS, surface (0–100 m) DIN:DIP ratios ranged between 2 and 165 (**Figure 7**) and DON:DOP ratios ranged between 55 and 525 (**Figure 8**). Above the mixed layer depth, DIN:DIP ratios ranged between 1 and 65 with an average of 20 ± 19 and DON:DOP ratios between 113 and 312 with an average of 182 ± 55. Along the E-W transect, 50% of DIN data were below the LOD of the CACP. When DIN data were available, the surface (0–120 m) DIN:DIP ratios in this area ranged between 10 and 289 (**Figure 7**) and DON:DOP ratios ranged between 67 and 252 (**Figure 8**). Along the E-W transect, DIN:DIP and DON:DOP molar ratios have not been calculated above the MLD due to insufficient valid DIN data.

Regarding vertical profiles, in the NWMS, there was a significant increase of DIN:DIP (Wilcoxon signed-ranks test, z = 3.4, p < 0.001, n = 19) and of DON:DOP ratios (Wilcoxon signed-ranks test, z = 2.4, p < 0.05, n = 17), between the MLD

Redfield molar ratio of 16:1.

and the DCM (**Figures 7**, **8**). The increase in the DIN:DIP ratio was observed for 15 out of 19 stations (Figure S3) and ranged between 0.2 and 5.7 m−1 . The increase in the DON:DOP ratio within this layer was observed for 12 out of 17 stations (Figure S4) and ranged between 0.2 and 9.3 m−1 . Along the E-W transect, no assessment of the vertical variability of N:P ratios was made due to insufficient valid DIN data.

#### DISCUSSION

In the Mediterranean Sea, the existent dataset of nM measurements of DIP at both spatial and temporal scales is severely scarce. The few reported nM concentrations of DIP are limited to two cross-basin cruises (PROSOPE cruise in 1999, Moutin et al., 2002: 7 values reported; Van Wambeke et al., 2002: 2 profiles reported and BOUM cruise in 2008: Talarmin et al., 2015, 5 profiles reported) and data acquired as part of the CYCLOPS project in the eastern basin of the Mediterranean Sea (Krom et al., 2005, 3 profiles reported). Two additional studies reported 1-year time series of surface nM DIP in the NW Mediterranean Sea at fixed observation stations: DYFAMED (Pulido-Villena et al., 2010) and ANTARES (Djaoudi et al., 2017). By reporting an important amount of vertical profiles along a longitudinal gradient, the present study is the first to extensively address the distribution of nM DIP in the P-depleted Mediterranean surface waters.

The nM DIP data obtained in this study are within the range reported in the above cited few previous studies, despite the use of different methods of analysis (**Table 1**). Regarding the longitudinal pattern of nM DIP, as previously reported by Moutin et al. (2002) for bioavailable DIP concentration in the upper layer (between 10 and 15 m), the present study shows a decreasing trend toward the East within the mixed layer with lower concentrations along the E-W transect (5.5 ± 3.6 nM) compared to the NWMS (12.8 ± 6.8 nM). This longitudinal gradient extends below the mixed layer (between the surface and 100 m), in contrast to Talarmin et al. (2015) study in which DIP concentrations (between the surface and 130 m) did not show any clear longitudinal trend crossing a W-E transect.

Regarding the vertical variability of surface DIP, the few existing data revealed a low but detectable increase of DIP concentration in the layer encompassing the DCM depth (Van Wambeke et al., 2002; Krom et al., 2005). In the present study, a significant vertical gradient of DIP but also of DOP was observed in both the NWMS and the E-W transect, allowing the generalization of this vertical pattern to the whole Mediterranean Sea. The positive gradient of DIP occurred above the phosphacline depth (Figure S1), suggesting that the phosphacline may be shallower than previously thought in both the NWMS and along the E-W transect. This result confirms that DIP in surface waters is not just a depleted invariant pool, highlighting the need to refine the criteria of the phosphacline determination.

The observed positive gradient of DIP, both in the NWMS and along the E-W transect, was higher than the bioavailable orthophosphate (<1–3 nM) reported by Moutin et al. (2002) in the upper waters (10–15 m). This means that the positive gradient of DIP observed in this study may be sufficient to sustain a biological activity in the surface waters, particularly by promoting microbial assemblages with very high-affinity transport systems and living very close to the theoretical diffusion limit for uptake. Indeed, the success of Synechococcus in the oligotrophic Mediterranean Sea has been linked to its ability to acquire phosphate even at low (<5 nM) concentrations (Moutin et al., 2002). However, the lack of biological data in this study precludes any deeper interpretation of the observed DIP gradient in a biological context.

The DIP concentration in surface waters would be the net resultant between biological and physical sources and sinks. The appearance of a positive gradient in upper waters suggests a balance in favor of DIP supply. This positive gradient of DIP could indeed arise from vertical phosphate diffusion from deep layers, suggesting the potential ability of new DIP to reach the upper waters even under stratification conditions in spite of an active biological uptake. The positive gradient of DIP above the phosphacline was, on average, higher in the NWMS than along the E-W transect, in agreement with reported differences in oligotrophy degree between the two sub-basins. Differences in DIP diffusion from deep layers, but also in rates of DOP hydrolysis could explain the observed differences in DIP gradient between the two cruises.

DOP data reported in this study are within the range of previous studies (**Table 1**), despite using different digestion methods (wet persulfate oxidation vs. UV digestion). Regarding the vertical profiles, this study revealed an important variability of DOP concentration in surface waters. Indeed, in the NWMS, a significant negative gradient of DOP was observed between the MLD and the DCM depth (av. 0.6 ± 0.7 nM m−1 ), which could be the result of its potential bioavailability. High alkaline phosphatase activities have been reported in the NW Mediterranean basin (Van Wambeke et al., 2002; Thingstad and Mantoura, 2005), suggesting an active DOP hydrolysis of phospho-ester bonds which could explain the DOP decrease observed in our study. Interestingly, the negative DOP gradient coincided with the DIP positive gradient, suggesting a DOP utilization even under available DIP conditions. These findings could suggest a possible simultaneous biological uptake of both DIP and DOP in this layer. In a cross-basin cruise in the Mediterranean Sea, Van Wambeke et al. (2002) showed that heterotrophic prokaryotes switched from P to labile carbon limitation at depths where DIP was still undetectable by the conventional technique. Thus, another explanation for the observed DOP decreasing gradient at the DCM depth coincident with sufficiently available DIP is a possible limitation by organic carbon, based on the hypothesis that another role of alkaline phosphatase is to decompose dissolved organic matter (Nausch and Nausch, 2004; Luo et al., 2011). Therefore, if the diffusion is enough to maintain a DIP gradient in the nanomolar range and, thus, remove P limitation, then the observed DOP decrease may be a consequence of the shift from P to C limitation. Again, further studies combining nanomolar DIP and DOP measurements with biological data are needed to confirm the biological meaning of the observed gradients.

#### N:P Ratios

N:P ratios in the upper waters reported in this study showed a high variability in both inorganic and organic pools. This contrasts with the deep waters of the Mediterranean Sea in which N:P ratios are constrained to a narrow range of values, between 21 and 22 in the western basin, and somewhat higher in the eastern basin (Krom et al., 1991; Bethoux et al., 1992). The vertical profiles of DIN:DIP ratio exhibited the classical shape reported for the Mediterranean Sea surface waters, during the stratification period, with a marked increase of the DIN:DIP ratio in subsurface water (Diaz et al., 2001; Moutin and Raimbault, 2002; Van Wambeke et al., 2009). Based on the conventional definition of nutriclines, this increase would be due to a nitracline shallower than the phosphacline, as previously reported (Moutin and Raimbault, 2002; Van Wambeke et al., 2009; Pujo-Pay et al., 2011). In this study, the use of the sensitive LWCC technique for DIP analysis revealed that this increase of the N:P ratio occurred between the MLD and the DCM depth. As said previously, a positive gradient of nM DIP was recorded in this layer, indicating the existence of a higher gradient of DIN compared to DIP. This observation stresses the need to extend nanomolar measurements to DIN concentration for a better understanding of the controlling factors of DIN:DIP ratios variability as on other oceans, DIN also can be the first limiting nutrient (i.e., Gruber, 2008)

The DON:DOP molar ratios in the surface waters of both NWMS and along the E-W transect were higher than the corresponding DIN:DIP ratios pointing to a DOP depletion TABLE 1 | Summary of published data on nanomolar dissolved inorganic phosphate (DIP) and dissolved organic phosphate (DOP) concentration in the Mediterranean Sea.

Depth of the corresponding measurements as well as the methods used for both DIP analysis and DOP hydrolysis are presented. MAGIC and LWCC relate to the magnesium induced co-precipitation and the liquid waveguide capillary cell methods, respectively.

relative to DON. This could be the result of a preferential remineralization of DOP with depth as reported by Aminot and Kérouel (2004) in the Mediterranean Sea and by Letscher and Moore (2015) at the scale of the global ocean. Similarly to the DIN:DIP molar ratios, an increase of the DON:DOP was observed at the DCM depth. This finding could be related to a biological utilization of DOP, since in this layer a negative gradient of DOP was observed. Nevertheless, accurate measurement of DON, implying nM measurements of nitrogen, would help to a better constraining of the DON:DOP variability in upper waters.

#### CONCLUSION

This study reports the first cross-basin distribution of nM DIP and DOP in the P-depleted Mediterranean surface waters. Surface DIP and DOP concentration showed an important variability on both longitudinal and vertical axis. Vertical profiles of DIP exhibited a significant positive gradient above the phosphacline, suggesting the potential of new phosphate to reach the near-surface waters by diffusion even under stratified conditions, and giving evidence against the traditional view of a depleted invariant DIP pool in the surface Mediterranean Sea. Despite this evidence of sufficient P availability, a significant negative gradient of DOP concentration was observed between the mixed layer depth and the DCM. Finally, the positive gradient in DIP was accompanied by a concomitant increase in N:P ratios, suggesting the existence of a higher gradient in DIN compared to DIP. The results obtained in this study indicate that acquiring nanomolar DIP data is a sine qua non condition for the comprehension and prediction of the biogeochemical functioning of the P-depleted Mediterranean Sea.

# AUTHOR CONTRIBUTIONS

KD, EP-V, and FV contributed to the conception and design of the study. KD and TW did seawater sampling and sample conditioning during the MOOSE-GE and BioArgoMed cruises, respectively. KD and SH-N analyzed nutrient concentrations. VT, LC, and PT acquired hydrological data (CTD). KD organized the database and wrote the first draft of the manuscript. EP-V and FV wrote sections in the manuscript. LC and PT were chief scientists during the MOOSE-GE cruise. VT and FD were chief scientists during the BioArgoMed cruise. PR is the principal investigator of the MOOSE project. FD is the coordinator of the Mediterranean work package of the NAOS project. All authors contributed to the manuscript revision, read and approved the submitted version.

#### ACKNOWLEDGMENTS

The authors would like to thank the MOOSE project and the NAOS project (ANR J11R107-F, funded by the French Equipement d'Avenir) in the framework of which this study was performed. Captains and crews of the R/V le Suroit and the R/V le Tethys II are warmly acknowledged for their cooperative work at sea. The work leading to this publication has received funding from European FEDER Fund under project 1166-39417. This work is a contribution to the Labex OT-Med (n◦ ANR-11-LABX-0061) funded by the French Government

#### REFERENCES

Investissements d'Avenir program of the French National Research Agency (ANR) through the A∗MIDEX project (n◦ ANR-11-IDEX-0001-02). Two reviewers are acknowledged for their relevant comments and suggestions on the manuscript.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmars. 2018.00234/full#supplementary-material

predominance of the cyanobacterium Synechococcus? Limnol. Oceanogr. 47, 1562–1567. doi: 10.4319/lo.2<IP_ADDRESS>2

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Djaoudi, Van Wambeke, Coppola, D'Ortenzio, Helias-Nunige, Raimbault, Taillandier, Testor, Wagener and Pulido-Villena. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.


**5.4 Dispersion of dissolved CO2 due to flow through a porous medium**

In addition to diffusion, dispersion occurs when a solute flows through a porous medium. This can essentially be understood as an unsteady irreversible mixing process of two miscible fluids which have different solute concentrations (e.g. brine saturated with CO2 = fluid 1, and brine undersaturated with CO2 = fluid 2). Dispersion can therefore influence CO2 mass transfer as it changes the CO2 concentration gradient. Dispersion is caused by several effects (Bear 1972, Özgür 2006, 2010):

Bear (1972) distinguishes between mechanical dispersion and hydrodynamic dispersion. He defined hydrodynamical dispersion as the sum of mechanical dispersion plus molecular diffusion. The dispersion described above - and all dispersion mentioned in this text – is the same as Bear's mechanical dispersion.

At reservoir scale dispersion can be described by equation (21) where Ddis is the dispersion coefficient, u is the average pore flow velocity and α the dispersivity (Bear, 1972; Özgür, 2006).

$$D\_{dis} = \mu \alpha \tag{21}$$

The dispersivity α is a property of the reservoir and it depends on the heterogeneity of the porous medium and the length of flow. Schulze-Makuch (2005) reviewed 307 datasets and suggested αL = c 0.5 L (where αL is the longitudinal dispersivity, L is flow distance and c varies between 0.01 m for sandstones and unconsolidated material and 0.8 m for carbonates). A detailed discussion of dispersion and dispersivities is given by Bear (1972).


*3.1. Temperature and Humidity Variation*

In order to ascertain a proper fixing of the FBG to the lithium-ion cell surface and to gain information about the influence of the cell temperature as well as of the relative air humidity on the reflected wavelength, first, the cell is exposed to temperature variations. For this purpose, the temperature chamber 1 is set to 20 ◦C for a sufficiently long time, followed by a step to 25 ◦C, and after a rest time of 4 h, the temperature is increased by a step of 5 K again. The temperature is held at 30 ◦C for 4 h and afterwards the temperature is decreased to 20 ◦C again, by means of 5 K steps, with the same resting periods as during temperature raise. These steps are conducted two times, followed by 40 h with constant temperature. The results can be seen in Figure 5.

During the experiment, relative humidity of the surrounding air in the temperature chamber 2 is additionally recorded with a digital sensor (HYT 939, Innovative Sensor Technology, Ebnat-Kappel, Switzerland). As a result of the regional weather changes, the values for the relative air humidity vary between 45%–55% inside the non-air-conditioned laboratory. For the isothermal period starting from experiment hour 30, no change of the reflected wavelength is expected and almost none is measured by the OSA. Nevertheless, the variation of the reflected wavelength measured by the AWG is 110 pm, as shown in Figure 5.

It is well known that polymeric plastics in general and the EpoClad/EpoCore photoresists used within this research work in particular are hygroscopic [38], and the absorption of water molecules, in turn, changes the optical properties of the AWG. In Figure 6, it can be seen, that for the herein presented humidity range, a linear relationship, including a hysteresis, exists.

**Figure 5.** FBG wavelength measured by the OSA and the AWG, respectively, during the temperature experiment together with the relative air humidity in the surrounding of the AWG. The humidity strongly influences the optical properties of the AWG. The corrected AWG values (blue course) are calculated by using Equation (2).

**Figure 6.** FBG wavelength measured by the AWG during the isothermal period of the temperature experiment shown in Figure 5. In the relevant humidity range there is a linear correlation between the optical output of the AWG and the relative humidity.

To minimize the variation of the AWG output due to the change of relative humidity, a multiple linear regression fit is done, expressed by Equation (2), where ξ is the relative air humidity in percent and ξ the change of the relative humidity in %/min. Λ is the regression constant determined to 853.1 nm, α and β are coefficients determined to −0.0128 nm/% and 0.9077 nm·min/%, respectively. Λc, as the result of Equation (2), represents the corrected wavelength, shown as the blue course in Figure 5.

$$
\Lambda\_{\mathfrak{C}}(\xi, \dot{\xi}) = \Lambda + \mathfrak{a}\,\xi + \,\mathfrak{F}\dot{\xi} \tag{2}
$$

The disturbance-related variation of the AWG values can be decreased to 20 pm during the isothermal period by applying Equation (2). The deviation from the values measured by the OSA during change of the temperature is also improved.