## 2 Materials and Methods
### Simulation Method and Geometry  
The programing of simulation involved building a main application with different classes, namely, action initialization, primary generator, detector constructor, run and run action ([[https://indico.cern.ch/event/865808/page/19021-geant4-virtual-machine](https://indico.cern.ch/event/865808/page/19021-geant4-virtual-machine)]([https://indico.cern.ch/event/865808/page/19021-geant4-virtual-machine](https://indico.cern.ch/event/865808/page/19021-geant4-virtual-machine)), assessed date: 2 November 2021). The action initialization class contained a class header (.hh files) and source (.cc files), and the class was used to instantiate and register to the Geant4 kernel. The primary generator class used a script to specify how a primary event is generated. The generator class defined the beam type (proton), beam direction (particle gun), beam energy, beam field size and distance between the beam source and gold nanoparticle. The detector constructor class defined the geometry environment of the MC simulation. The detector constructor source included the gold nanoparticle size and shape, as well as the distance between the gold nanoparticle and DNA. The material of the gold nanoparticle could be changed to gold (G4_Au) or water (G4_WATER) to investigate the effectiveness of adding a gold nanoparticle as a radiosensitizer in the medium. Moreover, detectors were set in this class. The Livermore low-energy physics models were used to simulate the interactions between protons and the gold nanoparticle, while the de-excitation cascade model was used for the secondary electrons produced by the gold nanoparticle [33]. In this study, the DNA base pair was defined as a dose detector to observe the total dose absorbed by the DNA. The cellular medium is assumed water equivalent. The run class managed the run procedure of the simulation. The dose absorptions were measured for each radiation history and passed to the run action class. There were 500 million histories in each simulation. The run action class was the user's action for each running procedure. This class was designed to obtain the deposited dose from the run action which was then added to the previous results. After finishing all simulations, the total dose was shown as the result. The main function script of the simulation was used to create the G4 RunManager instance to control the program's flow and manage the event loop. Through the creation of the run manager, the information to build and run the simulation was provided. This information included how the detector should be created, how all the particles and all the physics processes were to be simulated, how the primary particle in an event should be created, and any additional simulation requirements. In this study, the hadron therapy physics list was used for the simulation [34]. The physics list included many necessary processes for proton interactions with matter, such as the Bremsstrahlung effect, elastic scattering and inelastic scattering. The hadron therapy physics list was provided with the pre-packaged virtual machine Geant4 files. The simulation geometry is shown in Figure 1.  
In the simulation geometry, the DNA model as per [PERSON] et al. was used [35] and defined with a single gold nanoparticle inside a spherical water phantom with a radius of 0.5 \(\upmu\)m [36]. The nanoparticle was positioned at the center of the phantom with the proton beam source on the left and the DNA on the right as shown in Figure 1. The proton source field (proton beam diameter) was a circular plane with a diameter of twice the diameter of the nanoparticle. It was positioned 200 nm away from the nanoparticle. The proton flux was irradiated as parallel beams onto the gold nanoparticle with different distances (30, 80 and 130 nm) from the DNA molecule. Different nanoparticle radii of 15, 25 and 50 nm and different proton beam energies of 0.5, 5, 15 and 25 MeV were used.