*4.5. DIC Concentration and Bulk Carbon Isotopic Composition*

Samples for dissolved inorganic carbon (DIC) concentration and stable isotopic composition were collected from the filtrate of POC samples and processed as described in Remize et al. (2020) [34]. Analyses were conducted in a gas bench coupled to a Delta Plus mass spectrometer from Thermo Fisher Scientific, Bremen, Germany (GB-IRMS).

#### *4.6. Isotopic Data Processing*

We used the atomic proportion of 13C in percent (%atom of 13C) to express the results instead of the δ notation due to 13C-labelling. Conversion between δ notation and%atom13C notation can be done as follow [65]:

$$\% \text{atom}^{13}\text{C} = 100 \times \frac{(\frac{\ $^{13}\text{C}}{1000} + 1) \times (\frac{^{13}\text{C}}{^{12}\text{C}})\_{\text{VPDB}}}{1 + (\frac{\$ ^{13}\text{C}}{1000} + 1) \times (\frac{^{13}\text{C}}{^{12}\text{C}})\_{\text{VPDB}}} \tag{1}$$

where (13C/12C)PDB = 0.0112372, the ratio of 13C to 12C in the international reference VPDB standard.

Atomic enrichment (AE) of POC and DIC is then calculated from atom%13C-POC correction by POCcontrol values (i.e., corrected by 1.08%) and from atom%13C DIC corrected by control values (DICcontrol = 1.12%), respectively, according to the following equations:

$$\text{AE}\_{\text{POC}} = \% \text{atom}^{13} \text{C} - \text{POC}\_{\text{control}} \tag{2}$$

$$\text{AE}\_{\text{DIC}} = \% \text{atom}^{13} \text{C} - \text{DIC}\_{\text{control}} \tag{3}$$

#### *4.7. Fatty Acids Analysis*

4.7.1. Fatty Acids Analysis by Gas Chromatography Flame Ionisation Detector (GC-FID)

Lipid extraction, separation of neutral and polar lipid fractions, and transesterification processes are described elsewhere [34]. Fatty acids methyl esters (FAME) samples were analyzed by gas chromatography on a Varian CP8400 gas chromatograph (Agilent, Santa Clara, CA, USA) and separated concomitantly on two columns: one polar (ZB-WAX: 30 mm × 0.25 mm ID × 0.2 μm, Phenomenex, Torrance CA, USA) and the other apolar (ZB-5HT: 30 m × 0.25 mm ID × 0.2 μm, Phenomenex, Torrance CA, USA). The FAME of *T. lutea* were quantified using C23:0 as an internal standard (2.3 μg in each lipid fraction prior transmethylation) and were identified by comparison of their retention times with commercial standards (Supelco 37 component FAME mix, the PUFA No. 1 and No. 3 and the Bacterial Acid Methyl Esther Mix from Sigma-Aldrich, Darmstadt, Germany) and in-house standards mixtures. FA concentrations were reported as <sup>μ</sup>g C·L−<sup>1</sup> and as % of total fatty acids from each lipid fraction. Thirty two fatty acids (FA) were thus identified and quantified: iso15:0, anteiso15:0, 14:0, 15:0, 16:0, 18:0, 22:0, 24:0, 14:1n-5, 16:1n-9, 16:1n-7, 17:1n-1, 18:1n-9, 18:1n-7, 16:2n-7, 16:2n-4, 16:4n-3, 18:2n-6, 18:3n-6, 18:3n-3, 18:4n-3, 18:5n-3, 20:2n-6, 20:3n-6, 20:4n-6, 20:4n-3, 20:5n-3, 22:2n-6, 22:4n-6, 22:5n-6, 22:5n-3, and 22:6n-3. Individual fatty acid and total fatty acid concentrations (as the sum of both fractions, named thereafter TFA) obtained in <sup>μ</sup>g·L−<sup>1</sup> by GC-FID were also expressed in <sup>μ</sup>molC·L−<sup>1</sup>

(μg·L−1/molecular weight of individual fatty acid × carbon number of individual fatty acid) to ease the comparison with POC concentrations expressed in <sup>μ</sup>molC·L−<sup>1</sup> as well.

#### 4.7.2. Fatty Acid Compound-Specific Isotope Analysis and Processing

Samples for compound-specific isotope analyses (CSIA) of FAME were performed on a Thermo Fisher Scientific GC ISOLINK TRACE ULTRA (Bremen, Germany) using the same apolar column as mentioned above for FAME analysis. Only the fatty acids with the highest concentrations, as measured by GC-FID analyses, were considered for CSIA (namely 14:0, 16:0, 18:0, 18:1n-9, 18:2n-6, 18:3n-3, 18:4n-3, 18:5n-3, 20:5n-3, 22:5n-6, 22:5n-3, and 22:6n-3). The other FA presenting a too low signal amplitude (<800 mV) on the GC-c-IRMS did not allow precise isotope ratio analysis. Additionally, 18:1n-9 and 18:3n-3 co-eluted for GC-c-IRMS on the apolar column, but most of the isotopic signature for neutral lipids (NL) is attributed to 18:1n-9. However, in the polar fraction (PL), 18:1n-9 and 18:3n-3 are in relatively similar proportion and so were considered together. Additionally, 13C enrichment of 18:5n-3 could only be measured in the polar lipid fraction, but its concentration was too low in neutral lipid fraction to measure its isotope composition.

To evidence FA conversion of fatty acid A into fatty acid B in *T. lutea*, we calculated the AEFA ratio (R) of product B over expected precursor A. R was defined with a confidence interval calculated at α = 0.1 (defined arbitrarily) as follows:

$$\mathcal{R} = \frac{\text{AE}\_{\text{FA}(\mathcal{B})}}{\text{AE}\_{\text{FA}(\mathcal{A})}} \tag{4}$$

where A is the fatty acid hypothesized to be a precursor to fatty acid B, and AEFA(A) and AEFA(B) are their respective atomic enrichments at each sampling time.

If the AE of the product (B) exceeds the AE of the reactant (A), ratio > 1, then it is necessary to consider another formation process for B, since any molecule formed from A would have the same AE as A or below. If the ratio is <1, transformation of A into B is considered possible. If the ratio is close to 1, the fatty acids A and B are at equilibrium in terms of label incorporated, implying B is then synthesized simultaneously or very rapidly from A.
