## 3 Results
Even if no increase was observed for \(\theta\) equal to 0\({}^{\circ}\) and 180\({}^{\circ}\), the variation in the conductivity along the cell arc length indicated that a large portion of the membrane, corresponding to \(\theta\) rising from 27\({}^{\circ}\) to 153\({}^{\circ}\) and from 207\({}^{\circ}\) to 333\({}^{\circ}\) for \(E^{99\text{th}}_{\text{MAX}}\) (gray lines), and to \(\theta\) rising from 41\({}^{\circ}\) to 139\({}^{\circ}\) and from 229\({}^{\circ}\) to 311\({}^{\circ}\) for \(E^{99\text{th}}_{\text{AllBox}}\) (red lines), was interested by pores opening. When the amplitude of the external applied electric field was set equal to \(E^{99\text{th}}_{\text{MIN}}\), no pore opening was enabled at any point along the cell membrane. For the spherical Au NPs grouped in clusters (Figure 4j-l), results were similar to those obtained for the spherical NPs (Figure 4d-f), with a similar time evolution of \(V_{m}\) for \(E^{99\text{th}}_{\text{AllBox}}\) to \(E^{99\text{th}}_{\text{MAX}}\): in both cases, \(V_{m}\) was high enough to enable pore opening both for \(\theta\) equal to 45\({}^{\circ}\) (dashed lines) and 90\({}^{\circ}\) (continuous lines), with higher pore density values for \(E^{99\text{th}}_{\text{MAX}}\) than for \(E^{99\text{th}}_{\text{AllBox}}\) (Figure 4k), and a corresponding decrease in the time evolution of \(V_{m}\) (enlarged detail of Figure 4j), with a sharper shape for \(\theta\) equal to 90\({}^{\circ}\) (continuous lines) than for \(\theta\) equal to 45\({}^{\circ}\) (dashed lines). The membrane conductivity (Figure 4l) showed an increase from the starting value of 1.26 \(\times\) 10\({}^{-7}\) to the maximum values equal to 0.64 \(\times\) 10\({}^{-3}\) S/m and 0.89 \(\times\) 10\({}^{-3}\) S/m for \(E^{99\text{th}}_{\text{AllBox}}\) (red lines) and \(E^{99\text{th}}_{\text{MAX}}\) (gray lines), respectively, in correspondence of \(\theta\) equal to 90\({}^{\circ}\) and 270\({}^{\circ}\). Even if no increase was observed for \(\theta\) equal to 0\({}^{\circ}\) and 180\({}^{\circ}\), the variation in the conductivity along the cell arc length indicated that a large portion of the membrane, corresponding to \(\theta\) rising from 36\({}^{\circ}\) to 144\({}^{\circ}\) and from 224\({}^{\circ}\) to 316\({}^{\circ}\) for \(E^{99\text{th}}_{\text{MAX}}\) (gray lines), and to \(\theta\) rising from 45\({}^{\circ}\) to 135\({}^{\circ}\) and from 225\({}^{\circ}\) to 315\({}^{\circ}\) for \(E^{99\text{th}}_{\text{AllBox}}\) (red lines), was interested by pores opening. When the amplitude of the external applied electric field was set equal to \(E^{99\text{th}}_{\text{MIN}}\), no pore opening was enabled at any point along the cell membrane. Analogously to Figures 4 and 5 shows the time evolution of the transmembrane voltage \(V_{m}\), the pore density \(N\), and the variation in the conductivity along the cell membrane for \(t\) equal to 15 \(\upmu\)s when considering the amplitude of the external applied electric field equal to \(E^{99\text{th}}_{\text{AllBox}}\), \(E^{99\text{th}}_{\text{MAX}}\), and \(E^{99\text{th}}_{\text{MIN}}\) for all the Au NP configurations when the distance between the cell and the coil was equal to \(d_{2}\). An enlarged detail of the time evolution of the transmembrane voltage \(V_{m}\) is reported in Figure 5d,g,j, to highlight the possible effect of the pore dynamics on \(V_{m}\). Similarly to previous findings about \(d_{1}\), also for \(d_{2}\), when no Au NP was considered (Figure 5a-c), the transmembrane voltage \(V_{m}\) was not high enough to allow the pore opening at any point on the cell membrane.