**3.1 Collection of spectral data set**

The Raman spectra of the bacterial samples before and after the interaction with metal ions were measured by placing them onto an aluminum substrate and then under a Leica microscope (DMLM) integrated to a Renishaw micro-Raman system model 1000B. In order

Application of Principal Component Analysis

and after the removal of outliers.

With outliers, (b) without outliers.

**II**

**III I**

**-22500 -15000 -7500 0 7500 15000**

**PC2 (19%)**

**-30000 -15000 0 15000 30000 45000 60000**

**Outlier?**

**PC1 (77%)**

**Outliers**

separated along this PC).

**3.3.2 Loadings interpretation** 

to Elucidate Experimental and Theoretical Information 33

After the removal of outliers, the three groups identified in Fig. 6 (a), became much better defined in the PC-space. However, a different cluster distribution in the PC-space was observed [Fig. 6 (b)]. Table 1 describes these changes in terms of their PC- coordinates before

Fig. 6. PCA-Scores plots obtained from pre-treated Raman spectra corresponding to three concentrations of bacteria/Cd+2 samples: (■) 0.059 mM, (●) 0.133 mM, (▲) 0.172 mM. (a)

**a**

**bacteria/Cd2+**

**Outliers**

**PC2 (38%)**

**II**

Additionally, a different distribution of the individual percentage of explained variances was observed in both PCs (PC1, 77% to 59%, and PC2 19% to 38%). However, the total percentage of explained variances before and after the removal of outliers was similar (96%before and 97% after the removal of outliers). This indicates that the removal of outliers

> (*PC1i ,PC2j*) coordinates after outlier removal

**-20000 -10000 0 10000 20000 30000**

**PC1 (59%)**

**I**

**bacteria/Cd2+**

**b**

**III**

did not reduce the information about the data structure provided by both PCs.

(*PC1i ,PC2j*) coordinates before outlier removal

Cluster I (*+i, +j*) (*+i, -j*) Cluster II (*-i, -j*) (*-i, +j*) Cluster III (*-i,+j*) (*-i, -j*) Table 1. Cluster coordinates in the PC-space before and after the removal of outliers.

According to Fig 6 (b), a good discrimination between the lowest (group I) and the medium/highest cadmium concentrations (groups II and III) was observed along PC1-axis. In summary, it can be concluded that PC1 allows a gross discrimination (due to the huge difference in the concentration of samples clustered in I and samples clusters in II and III). Lower differences in Cd+2 concentrations are modelled by PC2 (clusters II and III are well

Once that distribution of objects in the scores plot was interpreted and correlated with the cadmium concentration attached to the bacterial biomass, the one-dimensional loadings

to retain the most important spectral information from each sample, multiple scans were conducted in different points of the bacterial sample moving the substrate on an X-Y stage.

The Raman system was calibrated with a silicon semiconductor using the Raman peak at 520 cm-1, and further improved using samples of chloroform (CHCl3) and cyclohexane (C6H12). The wavelength of excitation was 830 nm and the laser beam was focused on the surface of the sample with a 50X objective.

The laser power irradiation over the samples was 45 mW. Each spectrum was registered with an exposure of 30 seconds, two accumulations, and collected in the 1800-200 cm-1 region with a spectral resolution of 2 cm-1.
