# 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
Furthermore, adding a free energy barrier between the pDNA and the cell membrane shifts the rise in \(PSC(t)\) vs. \(t/l^{2}\) or \(t/l\) to the right, indicating that it is harder for the pDNA molecule to be absorbed by the cell membrane in the presence of free energy. One can then argue that the cell membrane needs to be competent for a longer amount of time in the presence of a free energy barrier to absorb the incoming pDNA molecule. As a result, larger \(t_{competent}\) was observed for the cases with free energy barrier (Figure 21B,D,F,H,J) compared to the cases without free energy barrier (Figure 21A,C,E,G,I). To determine the time it takes for the pDNA molecule to reach the cell membrane by diffusion or by electrophoresis, some estimates can be considered. The time it takes for the pDNA molecule to reach the cell membrane at a distance \(l\) by diffusion is given by \(t=l^{2}/2D\) (for 200 ns, 500 ns, and HF-BP pulses), whereas time it takes for the pDNA molecule to reach the cell membrane at distance \(l\) by electrophoresis is given by \(t=l/\mu E\) (for 100 \(\upmu\)s and 5 ms pulse). These estimates are given in Figure 22 for \(l\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL. \(E\) is taken as 0.6 kV/cm for the 5 ms pulse and 1.25 kV/cm for the 100 \(\upmu\)s pulse. One can observe that the time it takes for pDNA to reach the cell membrane by diffusion varies from around \(O\)(1) ms (for \(l\) = 77 nm, 2500 \(\upmu\)g/mL) to around \(O\)(100) ms (for \(l\) = 433 nm, 15 \(\upmu\)g/mL). For electrophoresis, the time it takes to reach the cell membrane varies from around \(O\)(0.01) ms (for \(l\) = 77 nm, 2500 \(\upmu\)g/mL) to \(O\)(0.1) ms (for \(l\) = 433 nm, 15 \(\upmu\)g/mL). It can be inferred that the cell membrane should be competent for at least \(O\)(100) ms, i.e., \(t_{competent}~{}\sim\) 100 ms, for transfection by 200 ns, 500 ns, and HF-BP pulses, whereas the cell membrane should be competent for at least \(O\)(0.1) ms, i.e., \(t_{competent}~{}\sim\) 100 \(\upmu\)s, for transfection by 100 \(\upmu\)s and 5 ms pulses. There is a 2-3 orders of magnitude difference in \(t_{competent}\) for 200 ns, 500 ns, and HF-BP and \(t_{competent}\) for 100 \(\upmu\)s and 5 ms pulses, as also inferred from the fitting parameters in Figure 21.  
One can also observe from Figure 21 that for very large values of \(t/l\) or \(t/l^{2}\), \(PSC(t)\) reaches a final value of 1, and the results should not depend on \(l\) (or concentration). That is, if the cell membrane is able to absorb the pDNA molecule for a very large amount of time, then irrespective of \(l\) (or concentration), the pDNA molecule will have an equally high probability of reaching the cell membrane. Since we see a concentration dependence  
Figure 22: Time it takes for a pDNA molecule to cover a distance by diffusion and by electrophoresis. \(l\) ranges from 77 nm too 433 nm, corresponding to concentrations ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL. for 200 ns, 500 ns, and HF-BP pulses, one can argue that \(t_{competent}\) is around \(O\)(1-100) ms, since this the amount of time it takes for the pDNA to reach the cell membrane by diffusion (Figure 22). The time it takes for the pDNA to reach the cell membrane by electrophoresis is \(O\)(0.01-0.1) ms (Figure 22). For a large \(t_{competent}\) of around \(O\)(1-100) ms, we should not observe a concentration dependence for 100 us and 5 ms pulses. However, since we do observe a concentration dependence for Overall GET and GET for 100 us and 5 ms pulses, it could be that the \(t_{competent}\) is different--and shorter (around \(O\)(0.01-0.1) ms)--for these pulses. It has been observed experimentally that the cell membrane remains permeable for a longer amount of time with ns pulses compared to us and ms pulses [48]. Recently, 300 ns pulses have been successfully used for GET [106]. However, 100 pulses were used at a pulse repetition frequency of 1 MHz.