# Efficient Gene Transfection by Electroporation--In Vitro and In Silico Study of Pulse Parameters
## 4 Discussion
### Modeling the Probability of pDNA Cell Membrane Contact during GET
The pDNA molecule thus diffuses to the cell membrane, and the distance (\(l\)) that the pDNA molecule travels by diffusion varies with time as \(l^{2}\sim Dt\). Therefore, normalizing the time in Figure 13A,C for nanosecond pulses and in Figure 15A for HF-BP pulses with \(l^{2}\) should collapse the curves for different domain lengths \(l=(B_{L},B_{R})\) ranging from 77 nm to 433 nm (corresponding concentration ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL). The normalization (and the corresponding collapse) is shown in Figure 21A for the 200 ns pulse, in Figure 21C for the 500 ns pulse, and in Figure 21E for the HF-BP pulses for the case without the free energy barrier. This collapse further indicates that the process for pDNA reaching the cell membrane in the absence of a free energy barrier is purely diffusive for 200 ns, 500 ns, and HF-BP pulses. For the case with the free energy barrier for 200 ns, 500 ns, and HF-BP pulses (Figures 13B,D and 15B), normalizing the time with \(l^{2}\) does not produce a good collapse. Rather, normalizing with \(l\) collapses all the curves onto a single master curve (Figure 21B,D,F). Such a collapse with \(l\) indicates that the process for 200 ns, 500 ns, and HF-BP pulses with the free energy barrier is not entirely diffusive. For 100 \(\upmu\)s and 5 ms pulses without the free energy barrier, the process of pDNA reaching the cell membrane is electrophoretic for \((B_{L},B_{R})\) ranging from 77 nm to 433 nm (corresponding concentration ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL). The electrophoretic distance traveled by the pDNA molecule in the presence of an electric field is given by \(l=\mu Et\); therefore, normalizing the curves with \(l\) in Figures 18A and 20A should collapse them into a single master curve. The collapse is shown as \(PSC(t)\) vs. \(t/l\) in Figure 21G for the 100 \(\upmu\)s pulse and in Figure 21I for the 5 ms pulse. This indicates that the process by which the pDNA molecule establishes contact with the cell membrane in the absence of the free energy barrier is driven by electrophoresis for 100 \(\upmu\)s and 5 ms pulses. For 100 \(\upmu\)s and 5 ms pulses, in the case when the free energy barrier is present, we can follow the same process of normalizing the curves in Figures 18B and 20B by \(l\) and check the collapse. This is shown in Figure 21H,J for the 100 \(\upmu\)s and 5 ms pulse, respectively. As can be seen from these figures, the collapse for times \(t\) when \(PSC(t)\) begins to rise is good; however, for later times or far larger \(PSC(t)\), the collapse is not satisfactory. This indicates that in the presence of free energy barrier, the process by which the pDNA molecule moves close to the cell membrane (since that is when \(PSC(t)\) begins to rise) is driven by electrophoresis. However, the process of a pDNA molecule coming into contact with the cell membrane by overcoming the free energy barrier is not entirely electrophoretic. It is observed from Figure 20B that \(PSC(t)\) is already collapsed for late times (i.e., for \(PSC(t)\) close to 1) without normalizing, implying that \(PSC(t)\) is independent of \(l=(B_{L},B_{R})\) for the range of \(l\) tested between 77 nm and 433 nm. Figure 21: (**A**) Results for 200 ns pulse in Figure 13A plotted as \(PSC(t)\) vs. \(t/l^{2}\), (**B**) Results for 200 ns pulse in Figure 13B plotted as \(PSC(t)\) vs. \(t/l^{2}\); (**C**) Results for 500 ns pulse in Figure 13C plotted as \(PSC(t)\) vs. \(t/l^{2}\); (**D**) Results for 500 ns pulse in Figure 13D plotted as \(PSC(t)\) vs. \(t/l\); (**E**) Results for HF-BP pulses in Figure 15A plotted as \(PSC(t)\) vs. \(t/l^{2}\); (**F**) Results for HF-BP pulses in Figure 15B  
plotted as \(PSC(t)\) vs. \(t/l\); (**G**) Results for 100 us pulse in Figure 18A plotted as \(PSC(t)\) vs. \(t/l\); (**H**) Results for 100 us pulse in Figure 18B plotted as \(PSC(t)\) vs. \(t/l\); (**I**) Results for 5 ms pulse in Figure 20A plotted as \(PSC(t)\) vs. \(t/l\); (**J**) Results for 5 ms pulse in Figure 20B plotted as \(PSC(t)\) vs. \(t/l\).