## 4 Rationale of Proton Beam Therapy
Band fitting was performed in the spectral region of 800-1800 cm\({}^{-1}\), because the authors were interested in the detection of changes in the DNA backbone spectral range (950-1240 cm\({}^{-1}\)). The results of the band fitting procedure were similar to the ones reported in Table 1 of the present paper (see Table 2 of Reference [44] for further details). All modifications observed in the spectra of cells irradiated by 1000 and 2000 protons per cell were not statistically significant. Instead, changes observed when higher doses were used were significant, with those observed after 8000 protons-per-cell irradiation being higher than those observed after 4000 protons-per-cell irradiation. The area of the O-P-O symmetric stretching band increased with the number of protons, while the area of the P-O-C symmetric stretching band decreased with the number of protons. It could mean that the probability of DNA strand breaks by destroying the C-O bond is higher than the O-P one. An increase with the number of protons in the area under the band corresponding to the motion bond in phosphate-DNA backbones may be ascribed to the destroyed chromosomal structure. Fragmentation of chromosomes could cause an increase in the number of molecule freedom degrees. The emergence of a new peak at approximately 830 cm\({}^{-1}\) in the spectra of cells irradiated with 8000 protons per cell was observed. Simulations show that this peak could be correlated with single-stranded breaks [44]. The PC3 cells exposed to proton beams were also investigated using SR-\(\upmu\)FTIR spectroscopy, and the spectral region related to nucleic acids, proteins, and lipids were analyzed separately [46]. In this case, cells were irradiated with protons and examined with \(\upmu\)FTIR spectroscopy using the same support for minimizing the loss of treated cells. The substrate had to be transparent for both protons and infrared radiation. To this purpose, silicon nitride membranes were used, and cells were irradiated with 50-4000 protons (corresponding to energy ranging from 3.2 to 260 MeV). Treated and untreated cells were washed in PBS and then fixed in 3.7% paraformaldehyde(20 \({}^{\circ}\)C, 10 min) immediately or 24 h after irradiation. The early fixed cell can allow for the study of DNA damage, while the later fixed cells enable for the investigation of the cellular response and repairing mechanisms. The SR-\(\mu\)FTIR spectra were acquired in the transmission mode at the IRENI beamline (SRC, University of Wisconsin-Madison) [47]. An FTIR Vertex 70 spectrometer equipped with a Hyperion FTIR microscope with a focal plane array 64 \(\times\) 64 element detector was used. The SR-FTIR images were collected using a 74\(\times\) objective (Ealing Inc., Rocklin, CA, USA). One hundred and twenty-eight scans were co-added for obtaining a good signal-to-noise ratio. In order to detect DNA damage, infrared spectra from cells fixed immediately after proton irradiation were examined using a second derivative and principal component analysis (PCA). Derivative analysis and PCA are two approaches largely used in the analysis of infrared spectra. By inspecting first or higher derivatives of absorbance with respect to wavelength, qualitative and quantitative information are obtained from infrared spectra. The technique was first introduced in the 1950s, and it is useful for more specific identification of small and nearby lying absorption peaks which are not well-resolved in the original spectrum, thus improving the specificity of absorption peaks. Another important advantage in the use of the second derivatives is that constant and linear components of baseline errors are removed. In the beginning, this technique did not receive much attention due to the complexity of generating derivative spectra. The availability of modern calculation tools allows for the use of mathematical methods to generate derivative spectra quickly, easily, and reproducibly. This significantly increased the use of the derivative technique (see [48; 49] for further details).