# Multivariate Analysis as a Tool for Quantification of Conformational Transitions in DNA Thin Films
## 3 Results
### Principal Component Regression  
In this section, we present the final multivariate method, PCR, utilized to validate the correlation of spectral signatures in the 1800-935 cm\({}^{-1}\) region and DNA conformation as indicated from calculations. Two models build, PCR1 and PCR2, were trained on the 3-, 5-, 10-, and 40-min spectra and validated by introducing an unknown spectra of 15-, 20-, and 25-min films and performed in four distinct regions: (a) the base and phosphate region from 1800 to 935 cm\({}^{-1}\), (b) base region from 1800 to 1550 cm\({}^{-1}\), (c) asymmetric PO\({}_{2}\) region from 1320 to 1155 cm\({}^{-1}\) and (d) symmetric PO\({}_{2}\) region from 1155 to 990 cm\({}^{-1}\). The first model, PCR1, was intended mostly to see whether %B-form can be correctly predicted for DNA thin films of different desiccation times from the vibrational signatures of the base and phosphate regions, (a)-(d). The calibration dataset in the PCR1 model was trained against an estimate of %B-form, calculated for each desiccation time as described previously. The results for the regression model PCR1 calculated for the region (a), 1800-935 cm\({}^{-1}\), are presented in Figure 4, while the results of the PCR1 model for regions (b)-(d) are presented in Table 2. As indicated from Figure 4, %B-form in 15-, 20-, and 25-min films is correctly determined by the PCR1 (a) model and a high \(R^{2}\) value of 0.922 indicates a very good correlation of vibrational signatures in the base and phosphate region to %B-form. The PCR1 (b)-(d) models proved inferior compared to the PCR1 (a) model with \(R^{2}\) values of 0.875, 0.838, and 0.847, respectively. The second model, PCR2, was intended to determine the correlation of spectra with respect to three classes representing different levels of %B-form: class 1 (40%, 3 min film), class 2 (60%, 5 min film) and class 3 (75%, 10-40 min films). The results of the PCR2 model for the region (a), 1800-935 cm\({}^{-1}\), are presented in Figure 5, while the details of the PCR2 (b)-(d) models can be found in Table 2. In the PCR2 (a) model, the class of 15-, 20-, and 25-min films was correctly determined as class 3 with a high \(R^{2}\) value of 0.929, while the PCR2 (b)-(d) models proved inferior with \(R^{2}\) values of 0.882, 0.848, and 0.856, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PCR1** & & **1800–935** & **1800–1550** & **1320–1155** & **1155–990** \\ \hline Calibration ds: 3, 5, 10, 40 min & \(R^{2}\) & 0.922 & 0.875 & 0.838 & 0.847 \\ Validation ds: 15, 20, 25 min & RMSEC & 2.88 & 3.76 & 4.25 & 4.19 \\ classes: 7 & RMSECV & 3.61 & 4.03 & 4.38 & 4.39 \\
3 PCs & RMSEP & 2.99 & 2.46 & 3.33 & 2.36 \\ \hline
**PCR2** & & **1800–935** & **1800–1550** & **1320–1155** & **1155–990** \\ \hline Calibration ds: 3, 5, 10, 40 min & \(R^{2}\) & 0.929 & 0.882 & 0.848 & 0.856 \\ Validation ds: 15, 20, 25 min & RMSEC & 0.18 & 0.24 & 0.27 & 0.27 \\ classes: 3 & RMSECV & 0.23 & 0.26 & 0.28 & 0.28 \\
2 PCs & RMSEP & 0.16 & 0.14 & 0.20 & 0.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The summary of the PCR models and obtained values for goodness-of-fit parameters which include \(R^{2}\) values and errors, the root-mean-square error of calibration (RMSEC), cross-validation (RMSECV), and validation (RMSEP). The abbreviation used for datasets is ds. The PCR1 model was trained with respect to seven distinct desiccation times (seven classes), from 3 to 40 min, while PCR2 was trained with respect to the level of B-form: class 1 (40%, 3 min film), class 2 (60%, 5 min film) and class 3 (75%, 10–40 min films). The respective spectral regions (in cm\({}^{-1}\)) included in the model are indicated in the columns. Figure 4: Results for the regression model PCR1 calculated for the 1800–935 cm\({}^{-1}\) region. Data were trained against calculated %B-form on the 3-, 5-, 10-, and 40-min spectra and then validated by the 15-, 20-, and 25-min spectra.