## 2 Materials and Methods
The FTIR spectra were obtained in the attenuated total reflectance (ATR) mode on a diamond/ZnSe crystal plate (MIRacle ATR, Pike Technologies, Madison, WI, USA, 2015). Experiments with energy dispersive X-ray spectroscopy (EDX) were performed using a QUANTAX EDS system (Bruker Nano GmbH, Berlin, Germany, 2012). Transmission electron microscopy (TEM) images were taken with a Zeiss EM 900 TE microscope (Carl Zeiss GmbH, Oberkochen, Germany, 2010). This TE microscope has a nominal point resolution of 5.0 A at Scherzer defocus and was operated at an acceleration voltage of 80 kV. High resolution transmission electron microscopy (HRTEM) was applied using a Phillips CM 300 UltraTWIN TE microscope (Philips, Eindhoven, The Netherlands, 2000) at an acceleration voltage of 300 kV with a nominal point resolution of 1.7 A at Scherzer defocus. The EDX spectra were acquired using a Super-X detector. The samples for the TEM und HRTEM investigations were obtained by drop-casting the Fe\({}_{3}\)O\({}_{4}\)@Au pNPs solution on amorphous holey carbon film coated copper TEM grids. The XRD scans were measured in the Bragg-Brentano geometry by means of a Bruker AXS Advance D8 (Bruker Nano GmbH, Berlin, Germany, 2015) X-ray diffractometer using Cu K\({}_{\alpha}\) radiation (\(\lambda_{\mathrm{K\alpha}}\) = 1.54 A) at an acceleration voltage of 30 kV. The magnetization curves and ZFC/FC _vs._ temperature plots of the Fe\({}_{3}\)O\({}_{4}\)@Au pNPs and Fe\({}_{3}\)O\({}_{4}\) NPs were recorded on a Quantum Design MPMS-XL5 SQUID magnetometer (Quantum Design Inc., San Diego, CA, USA, 2015). _Cell experiments._ The biocompatibility and the diverse ROS assays were executed by means of a Synergy HT microplate reader (BioTek Inc., Winooski, VT, USA, 2016). TEM images of MCF-7 cells incorporating Fe\({}_{3}\)O\({}_{4}\)@Au pNPs were obtained with a Zeiss EM 906 (Carl Zeiss GmbH, Oberkochen, Germany, 1993). The diverse kinds of cell lines (i.e., MCF-7, MCF-10A and A459) were exposed to X-radiation generated by a 120 kV X-ray tube equipped with a tungsten anode (Comet MXR 160/0.4-3.0, Comet, Flamatt, Switzerland, 2011). The X-radiation has an on average energy value of 34 keV and a maximum energy value of 120 keV. _Cell culture._ The MCF-7, MCF-10A and A459 cells were cultured in DMEM containing 4500 mg glucose/L, enriched with 10% fetal calf serum (FCS), 1 mM sodium pyruvate, 100 U/mL penicillin, 100 ug/mL streptomycin, 2 mM L-glutamine and 1% MEM nonessential amino acids. The cells were incubated in a humidified environment of 5% CO\({}_{2}\) at 37 \({}^{\circ}\)C and sub-cultivated twice a week. _Neutral red assay._ The MCF-7, MCF-10A and A459 cells were seeded in 96-well plates at a cell per well density of 2-3 \(\times\) 10\({}^{4}\) and were incubated overnight. The cell culture medium was replaced by a medium containing the Fe\({}_{3}\)O\({}_{4}\)@Au pNPs, Fe\({}_{3}\)O\({}_{4}\) NPs or gold nanocluster (AuNC) at a concentration of 10 ug/mL. Subsequently to 24 h incubation, the cell medium was substituted by an FCS-free medium containing 40 ug/mL neutral red (NR). After 2 h incubation at 37 \({}^{\circ}\)C, the NR-enriched medium was aspirated off, and the cells were rinsed with PBS. NR molecules trapped inside the lysosomes were released by the addition of 100 uL/well dye-destaining solution (50% ethanol, 49% water, 1% glacial acetic acid). The absorbance of the NR solution was measured at 540 nm. _Cell preparation for TEM examinations._ MCF-7 cells were incubated overnight with culture medium containing the Fe\({}_{3}\)O\({}_{4}\)@Au pNPs at a concentration of 10 ug/mL. The cells were washed with ice-cold PBS (pH 7.4), were subsequently fixed with 2.5% glutaraldehyde electrode at 4 \({}^{\circ}\)C (overnight) and then post-fixed in 1% OsO\({}_{4}\) and 3% K\({}_{3}\)Fe(CN)\({}_{6}\) at room temperature. Thereafter, the cells were dehydrated in ethanol and encapsulated in Epon. 60-70-nm-thick slices were obtained with an ultramicrotome and mounted on Epon blocks. Non-contracted silver-grey ultrathin slices were imaged.