## 2 Materials and Methods
### Analytical Methods
#### 2.2.5 Fourier-Transform Infrared Spectroscopy (FTIR) Spectra  
FTIR spectra were collected using ZnSe 45\({}^{\circ}\) attenuated total reflectance (ATR) through plate crystal, with a HATR sampling accessory on a PerkinElmer Frontier FTIR Spectrometer equipped with a DLaTGS detector with a KBr beam splitter (PerkinElmer Inc., Seer Green, UK). The spectrometer collected spectra over the wavenumber range 4000-650 cm\({}^{-1}\) and was programmed with PerkinElmer Spectrum v10.4.2 software (Seer Green, UK). Ten scans per measurement were used with a resolution of 4 cm\({}^{-1}\). The dried samples were placed on the ZnSe 45\({}^{\circ}\) ATR crystal and pressed with a gripper to have the best possible contact with the crystal surface. Reference spectra were obtained by collecting an air background (spectrum from the cleaned blank crystal) prior to each sample measurement. At the end of each sampling, the crystal surface was first cleaned with detergent, washed with distilled water, cleaned with ethanol and dried with lift-free tissue. Three (3) replicate FTIR spectra were collected from each of the 3 different batches (biological replicates) of each treatment.  
The statistical analysis of the main effects of phosphorus limitation on biomass composition was based on analysis of variance (ANOVA, one-way comparisons), conducted using SigmaPlot 12.0 software (Systat Software, Inc.). Regarding the FTIR model, data analysis was performed using Unscrambler software (version 9.7, CAMO, Norway). The collected FTIR spectral data were background corrected using the standard normal variate (SNV) transformation. Subsequently, spectral data in the range of 1800-650 cm\({}^{-1}\) were used to build the partial least squares regression (PLS-R) models. The database was partitioned into a training and an external validation dataset. The measurements from the two first batches (biological replicates) of samples were included in the training dataset and measurements from the third batch were included in the external validation set (test set). The normalized FTIR data were subjected to partial least squares (PLS) analysis for the estimation of the main quality parameters of Spirulina content (% DW), i.e., proteins, carbohydrates, lipids, \(\beta\)-glucans, \(\alpha\)-glucans, dietary fiber, and glucose. The PLS-R model was evaluated by using a leave-one-out cross validation procedure on the training set only. The number of latent components needed to yield the lowest root mean square error (RMSE) of the cross-validation was evaluated for the modelling and the plot of cross-validation residual variance against the number of latent components was examined in parallel, with up to 20 components included. In the case that the residual variance no longer decreased with additional components, the number of latent components of the first minimum value of residual variance was selected to avoid overfitting. Then, the developed models were validated by applying the test data set. The performance indices for evaluating and comparing the models were the coefficient of determination (R\({}^{2}\)), the RMSE and the residual prediction deviation (RPD) for the known (observed) values versus validation estimations (predictions) for each parameter.