## 2 Materials and Methods  
### Monte Carlo (MC) Codes: MCNP and MCDS  
Our calculations have been based on the Model Carlo simulation technique. MC codes have been widely used to simulate damage induction to a cell exposed to any type of the IR spectrum [37]. Theoretical studies, together with MC Track Structure codes (MCTS), have contributed remarkably to the understanding of the DNA damage dynamics and to the simulation of particle tracks in biological matter, leading scientific research to the estimation of the radiation effect parameters and, therefore, providing important information applied in radiation protection and radiotherapy [35; 36]. In this way, MCTS simulations have proved to be the most sophisticated tool for studying and understanding the interactions of IR with biological matter and for determining the damage induced by it to the major target of the cell: its DNA macromolecule [31].  
In our study, we have used two different MC codes for obtaining our calculations. The first one, MCNP, being one of the most accurate in its category, is a multipurpose code used widely in nuclear and medical applications, utilizing a large spectrum of particles. The simulation of particle interactions with living matter are based on databases that are embedded in the software and include internationally recognized libraries of cross sections [38]. The MCNP6.1 version of the code used by us, especially, has the ability to accurately describe the electron transport down to 10 eV [39]. Via this code, we have estimated the absorbed dose by our target and the spectrum of secondary electrons produced in it. As aforementioned, one part of the damage induced to a cell is due to secondary electrons ejected as a result of the ionizations in the medium.  
The second MC code used in our study, in combination with MCNP, is the Monte Carlo damage simulation (MCDS) algorithm, which has been selected among the other MC codes of the bibliography because of its simplicity and its results production swiftness. It does not have the accuracy of other codes in its category, but it can yield major trends in the spectrum of DNA damage predicted by other detailed MCTS simulations. This code has been developed in order to predict the initial yield and types of DNA damage formed by IR and is much faster compared to conventional track structure simulations (it can give results within seconds to minutes), in addition to its easy-to-use algorithm [34]. MCDS algorithm is characterized as a quasi-phenomenological model, which can predict the full spectrum of DNA damage induced by electrons, protons, \(\alpha\)-particles and ions up to \({}^{56}\)Fe. Although this code does not possess the ability to directly simulate the damage in irradiated cellsfor photons or other neutral particles, secondary electron spectra for \({}^{137}\)Cs in a monolayer cell geometry were used to produce DNA damage yields [40]. The estimates of the code parameters are based on the interpolated damage yields, derived mainly from the track structure simulations of [PERSON] et al. [41; 42; 43; 44] and [PERSON] et al. [45; 46]. MCDS [47] uses only four adjustable parameters, three of which are the same for electrons, protons and \(\alpha\)-particles. In brief, simulations are performed in two steps: (1) random distribution of the expected number of lesions produced in a cell per Gy of radiation in a DNA segment and (2) subdivision of the lesions in the former segment into clusters [34].