## 2 Materials and Methods
### Biomass Characterisation
#### 2.4.1 EA-IRMS Analysis  
Due to differences in mass number, isotopes of the same element exhibit different physical properties, leading to fluctuations in their relative abundances in nature through chemical, physical or biological processes (fractionation phenomena). For example, processes such as metabolic activity in organisms can lead to enrichment or depletion of specific isotopes, a mechanism that is also influenced by the specific isotopic signal of the matrices with which they come into contact [28]. The isotopic composition of elements in  
Figure 2: _G. phlegrea_ ACUF 784.3: personal shot captured using an optical microscope at 100\(\times\) magnification (**A**); test discs usually prepared for the start of cultivation experiments (**B**); discs of biomass on polycarbonate micromembranes (substrate layer), adhered to the fibreglass panel (source layer), and ready for the start of cultivation experiments (**C**); personal shot captured using an optical microscope with 40\(\times\) magnification and 10 \(\upmu\)m sensitivity graduated slide (**D**); an example of dense algal biofilm developed during some preliminary TL-PBR trials (**E**,**F**). environmental matrices is typically expressed in delta notation (8), which indicates the deviation in parts per thousand (%o) of the isotopic ratio of interest relative to that of a reference material of known isotopic composition [29]. A \(\delta\) value greater than 0 indicates that the analysed matrix has a higher content of heavier isotopes compared to the standard. From another perspective, by analysing the isotopic signal of a given matrix over time and observing how it deviates from its original signal (whether it increases or decreases), information about ongoing interactions with surrounding matrices can be obtained. Here, the application of EA-IRMS aims to quantify carbon and nitrogen isotopic ratios and concentrations in the biomass, assessing temporal variations and identifying interaction pathways with the W and A matrices in contact with the microalgae, as reported by [15]. To achieve this, it was also necessary to characterise the initial isotopic signature of W and A, in addition to the EA-IRMS analysis of the algal biomass over time. To prepare the biomass for EA-IRMS measurements, a sample disc removed from the reactor was placed in an Eppendorf tube containing 2 mL of distilled water, exposed to an ultrasonic bath for 5 min, and finally vortexed for a few seconds to recover all the biomass from the disc. The tubes were then centrifuged at 10,000 rpm for 10 min, after which the supernatant was removed, and the biomass was frozen at \(-80\)\({}^{\circ}\)C and lyophilised without further pre-treatment. To obtain the solid matrices necessary to characterise the initial isotopic signal of C and N in the W and A culture media, the following procedure was followed. A volume of 100 mL of acidified and sterilised medium was frozen at \(-80\)\({}^{\circ}\)C without further treatment and lyophilised, thus obtaining residual solid material ready for analysis. To carry out the analyses on the solid matrices thus obtained, a quantity of each sample was weighed in triplicate in the following ranges using a high sensitivity analytical balance (AT20, Mettler Toledo, Milano, Italy, \(\pm 2\) ug): biomass in the range 0.4-0.8 mg, solid residue of A in the range 1.5-2.0 mg, solid residue of W in the range 3.0-5.0 mg. The weighed material was encapsulated in 4 \(\times\) 6 mm tin capsules (Tin capsules for solids, Santis Analytical Italia, Gerenzano, Varese, Italy). These samples were then analysed using an integrated system consisting of an IRMS apparatus (Delta V Advantage-Thermo Fisher, Waltham, MA, USA) coupled to an Elemental Analyzer (1112 Series-Thermo Fisher, Waltham, MA, USA) for the simultaneous measurement of total C and N (%) and their relative isotopic ratios \(\delta^{13}\)C and \(\delta^{15}\)N (%o).