## 2 Material and Methods
### Experimental Set-Up  
The clinical SOBP beam configuration was used for the radiobiological and microdosimetric measures. The SOBP penetration range, measured as the depth corresponding to the 80% of the SOBP maximum and measured in the distal part, was 29.5 mm in water. The measured dose distribution as well as the LET and dose simulated by using the Geant4 _Hadrontherapy_ advanced example that reproduce the entire beamline [28], is reported in Figure 1). The algorithms adopted to compute the LET take into account both primary and secondary particles interacting in a voxel, more details are reported in [27].  
Absolute absorbed dose was measured in water, by means of a plane-parallel PTW 34045 advanced-type Markus ionisation chamber, according to the International Atomic Energy Agency Technical Report Series 398 Code of practice [29]. The absorbed dose in water per monitor unit (cGy/M.U.) for the specific SOBP adopted in cell irradiations, was measured at the isocenter at 24 mm depth in water, corresponding to the middle of the SOBP. A reference 25-mm diameter circular collimator was used to determine the beam spot size at the irradiation point. The absolute dose dosimetry was performed just before each irradiation session; the variation of beam calibration on the various experiments amounted to a total of 3%. The overall uncertainty in absolute dose measurement was kept within 1.5%. Details on the irradiation beamlines, dosimetric procedures and related uncertainties for irradiation conditions can be found elsewhere [28]. As regards cell line irradiation, the experimental procedure was described previously [30]. Briefly, cells were seeded in T25 tissue culture flasks with a density of 3-5 \(\times 10^{5}\) cells per flask 24 h before irradiation. T25 were irradiated in the upright position in front of the proton beam exit and hit with separate shots to ensure a complete dose distribution on the flask area. An automatic system for sample positioning and movement was used to move the flasks after each shot in order to cover its entire surface. Cell sample irradiations were carried out positioning each flask at 24 mm, the mid-position of the spread-out Bragg peak, to mimic a clinical condition, with dose values ranging from 1 to 4 Gy and a dose rate of 6 Gy min\({}^{-1}\). Finally, the microdosimetric spectra were acquired positioning the mini-TEPC and MicroPlus-Bridge detectors at the entrance and mid position along the same SOBP, while the depths were varied by placing a stack of calibrated PMMA layers between the detectors and the beam collimator [27]. The mini-TEPC is a miniaturized, tissue-equivalent, proportional counter developed at the Legnaro National Laboratories of the Italian National Institute for Nuclear Physics (INFN-LNL) to work in a sealed mode, without gas flow [25]. The sensitive volume (SV) is a cylinder with both diameter and height of 0.9 mm; the cathode is made of a 0.35 mm-thick A-150 wall, surrounded by a 0.35 mm-thick Rexolite insulator and a 0.2 mm-thick titanium sleeve; the total external diameter is 2.7 mm. The anode is a 10-\(\upmu\)m gold plated tungsten wire. The detector was filled with propane gas, at the pressure of 45.4 kPa at 21.8 \({}^{\circ}\)C; these conditions simulate a water volume of 1 \(\upmu\)m in diameter.  
The silicon detector adopted was the MicroPlus-Bridge, designed by the Centre for Medical Radiation Physics (CMRP), University of Wollongong, Australia. It consists of an array of 3D right parallelepiped (RPP) shape SVs with an area of 30 \(\upmu\)m \(\times\) 30 \(\upmu\)m each and a thickness of 10 \(\upmu\)m, constructed on a silicon-on-insulator wafer. The water equivalent thickness of this microdosimeter is 17.24 \(\upmu\)m. Additional details and microdosimetric results on the MicroPlus-Bridge microdosimeter technology can be found elsewhere [26]. It has already been shown that the dose mean lineal energy measured with these two detectors reproduces the variation with depth of the dose-averaged LET [23].