**3.3.2 Loadings interpretation**

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

Application of Principal Component Analysis

**A** 

**PC2 (10%)**

**B** 

**PC2 (25%)**

to Elucidate Experimental and Theoretical Information 35

**-0.08**

**-0.06 -0.03 0.00 0.03 0.06 0.09 0.12**

**0.20 Bacteria/Ni2+**

**PC- loadings** **-0.04**

**0.00**

**PC- loadings**

**0.04**

**0.08**

**0.12**

**Bacteria/Pb2+**

**Bacteria/Zn2+**

**1800 1500 1200 900 600 300**

**II <sup>I</sup>**

**1800 1500 1200 900 600 300**

**1800 1500 1200 900 600 300**

**Raman Shift / cm-1**

**Raman Shift / cm-1**

**III I**

**Raman Shift / cm-1**

**II**

**III**

**I**

Fig. 8. Scores and loadings plots corresponding to different bacteria/metal concentrations. a) lead: (■) 0.028 mM, (●) 0.181 mM, (▲) 0.217 mM, b) zinc: (■) 0.114 mM, (●) 0.307 mM, (▲) 0.350 mM and c) nickel: (■) 0.022 mM, (●) 0.109 mM, (▲) 0.181 mM. Solid line corresponds

**-0.08 -0.04 0.00 0.04 0.08 0.12 0.16**

**PC-loadings**

**Bacteria/Ni2+**

**II**

**II**

These two regions provide vibrational information about the phosphate groups and superficial polysaccharides related with certain bacteria superficial structures that have been previously reported as responsible for the bacteria/metal interaction (Mobili et al., 2010;

to PC1-loadings and dashed line to PC2-loadings.

**-16000 -12000 -8000 -4000 0 4000 8000**

**PC1 (69%)**

**II & III <sup>I</sup>**

**-9000 -6000 -3000 0 3000 6000 9000**

**PC1 (71%)**

**<sup>4000</sup> Bacteria/Zn2+**

**III**

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

**PC1 (86%)**

**I Bacteria/Pb2+**

Sara & Sleytr, 2000).

**-6000**

**-4000**

**-2000**

**PC2 (12%)**

**C** 

**0**

**2000**

**4000**

**-6000**

**-4000**

**I**

**-2000**

**0**

**2000**

**-12000**

**-8000**

**III**

**-4000**

**0**

**4000**

**8000**

before and after the removal of outliers were analysed to correlate Cd+2 concentrations with changes in the original spectra (*i.e.* Raman shift, wavenumber, wavelength, etc.).

Fig. 7. One-dimensional loadings plots obtained from the PCA corresponding to different bacteria/Cd+2 concentrations; (a) before and (b) after the removal of outliers. Solid line corresponds to PC1-loadings and dashed line to PC2-loadings.

Considering that PCs can be represented as a linear combination of the original unit vectors, where the loadings are the coefficients in these linear combinations, distribution and/or localization of each object in the PC-space has a direct relation with their respective PCloadings values (Esbensen, 2005).

Fig. 7 (a) depicts the one-dimensional loadings plots corresponding to PC1 and PC2 before the removal of outliers. The influent spectral regions for the distribution of objects in the PCspace were underlined using dashed frames. The main spectral differences between objects of cluster I and objects of clusters II and III were found in the 1800-1500 cm-1 spectral region. This region was selected taking into account the loadings values and the PC-coordinates for each cluster.

For instance, cluster I has PC-coordinates (*+i, +j*), then we selected the region where both loadings, PC1 and PC2 have positive values (in this case, the 1800-1500 cm-1 region). For cluster II, whose coordinates are *-i, -j*, we selected the region with negative loadings values for both PCs (1000-600 cm-1). Finally, for cluster III, we selected the region with negative and positive loadings values for PC1 and the PC2, respectively (1500-1100 cm-1) whose coordinates are *-i, +j*. The same strategy was adopted for the loading analysis after the removal of outliers [Figure 7 (b)]. Even when the loading values are different, the spectral regions representing each cluster are the same.

In summary, it can be concluded that the main spectral differences between objects of cluster I and objects of clusters II and III, can be observed in the 1800-1500 cm-1 region. Very interestingly, the carboxylate (COO-) groups absorb in this region. In our previous work we have reported that metal ions can be attached to the bacterial surface through the COOgroups (Gerbino et al., 2011). Spectral differences between clusters II and III were found in the 1000-600 cm-1 and 1500-1100 cm-1 regions, respectively.

34 Principal Component Analysis

before and after the removal of outliers were analysed to correlate Cd+2 concentrations with

Fig. 7. One-dimensional loadings plots obtained from the PCA corresponding to different bacteria/Cd+2 concentrations; (a) before and (b) after the removal of outliers. Solid line

**-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14**

**I**

**PC- loadings**

**1800 1600 1400 1200 1000 800 600 400**

**Raman spectra Bacteria/Cd2+**

**III**

**Raman Shift / cm-1**

**II**

**b**

**a**

Considering that PCs can be represented as a linear combination of the original unit vectors, where the loadings are the coefficients in these linear combinations, distribution and/or localization of each object in the PC-space has a direct relation with their respective PC-

Fig. 7 (a) depicts the one-dimensional loadings plots corresponding to PC1 and PC2 before the removal of outliers. The influent spectral regions for the distribution of objects in the PCspace were underlined using dashed frames. The main spectral differences between objects of cluster I and objects of clusters II and III were found in the 1800-1500 cm-1 spectral region. This region was selected taking into account the loadings values and the PC-coordinates for

For instance, cluster I has PC-coordinates (*+i, +j*), then we selected the region where both loadings, PC1 and PC2 have positive values (in this case, the 1800-1500 cm-1 region). For cluster II, whose coordinates are *-i, -j*, we selected the region with negative loadings values for both PCs (1000-600 cm-1). Finally, for cluster III, we selected the region with negative and positive loadings values for PC1 and the PC2, respectively (1500-1100 cm-1) whose coordinates are *-i, +j*. The same strategy was adopted for the loading analysis after the removal of outliers [Figure 7 (b)]. Even when the loading values are different, the spectral

In summary, it can be concluded that the main spectral differences between objects of cluster I and objects of clusters II and III, can be observed in the 1800-1500 cm-1 region. Very interestingly, the carboxylate (COO-) groups absorb in this region. In our previous work we have reported that metal ions can be attached to the bacterial surface through the COOgroups (Gerbino et al., 2011). Spectral differences between clusters II and III were found in

corresponds to PC1-loadings and dashed line to PC2-loadings.

**Bacteria/Cd2+**

**II**

**1800 1600 1400 1200 1000 800 600 400**

**Raman Shift / cm-1**

loadings values (Esbensen, 2005).

regions representing each cluster are the same.

the 1000-600 cm-1 and 1500-1100 cm-1 regions, respectively.

each cluster.

**-0.05**

**0.00**

**PC-** 

**loadings**

**0.05**

**0.10**

**0.15**

**Raman spectra**

**<sup>I</sup> III**

changes in the original spectra (*i.e.* Raman shift, wavenumber, wavelength, etc.).

Fig. 8. Scores and loadings plots corresponding to different bacteria/metal concentrations. a) lead: (■) 0.028 mM, (●) 0.181 mM, (▲) 0.217 mM, b) zinc: (■) 0.114 mM, (●) 0.307 mM, (▲) 0.350 mM and c) nickel: (■) 0.022 mM, (●) 0.109 mM, (▲) 0.181 mM. Solid line corresponds to PC1-loadings and dashed line to PC2-loadings.

These two regions provide vibrational information about the phosphate groups and superficial polysaccharides related with certain bacteria superficial structures that have been previously reported as responsible for the bacteria/metal interaction (Mobili et al., 2010; Sara & Sleytr, 2000).

Application of Principal Component Analysis

inhibits melanin synthesis by inhibition of tyrosinase activity.

and the remaining three taking part in the skeletal of the molecule.

analysis of quantum chemical information were reported.

O H

11 15

5

H 20

3

H 18

7

H22 H21

4

H 19

OH

13 9

**4.1 Quantum chemical calculations** 

2002; Saunders, 1987, 1990).

OH

et al., 2010)

14 10

to Elucidate Experimental and Theoretical Information 37

(Witting et al., 2001). It is also used as a depigmenting agent (skin whitening agent) as it

From a chemical point of view, arbutin is a flexible molecule composed by a glucopyranoside moiety bound to a phenol ring (Fig. 9). It has eight conformationally relevant dihedral angles, five of them related with the orientation of the hydroxyl groups

Up to our knowledge, no attempts to use of a PCA based methodology for the structural

1

H 16

Fig. 9. Arbutin molecule, with atom numbering scheme. (copyrighted from Araujo-Andrade

The semi-empirical PM3 method (Stewart, 1989) was used to perform a systematic preliminary conformational search on the arbutin potential energies surface (PES), which were later on taken into account in the subsequent, more reliable analysis performed at higher level of theory. This preliminary conformational search was carried out using the HyperChem Conformational Search module (Howard & Kollman, 1988; HyperChem, Inc. ©

The eight dihedral angles defining the conformational isomers of arbutin (Fig. 9) were considered in the random search: C2C1O23C24, C1O23C24C25, O6C5C7O11, C5C7O11H15, C3C4O10H14, C2C3O9H13, C1C2O8H12 and C26C27O34H35. Conformations with energies lower than 50 kJ mol-1 were stored while higher-energy conformations or duplicate structures were discarded. The structures obtained from this conformational search were used as start points for the construction of the input files later used in the higher level quantum chemical calculations. These latter were performed with Gaussian 03 (Gaussian, 2003) at the DFT level of theory, using the 6-311++G(d,p) basis set (Frisch et al, 1990) and the three-parameter density hybrid functional abbreviated as B3LYP, which includes Becke's gradient exchange correction (Becke, 1988) and the Lee, Yang and Parr (Lee et al, 1988) and Vosko, Wilk and Nusair correlation functionals (Vosko et al., 1980). Conformations were optimized using the Geometry Direct Inversion of the Invariant Subspace (GDIIS) method (Csaszar & Pulay,

2 O

O 6

H17

O H

8 12

28

H 32

O H

34 35

29

H 33

24

23

H 30 25

26

H 31 27
