# 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  
From results of modeling the probability of pDNA cell membrane contact during GET, it can be inferred that the process of a pDNA molecule reaching the cell membrane and being absorbed by it is mediated by diffusion for 200 ns, 500 ns pulse and HF-BP pulses, whereas for the 100 \(\upmu\)s and 5 ms pulse, the process is mediated by electrophoresis. As done in the results section, one can define a Peclet number as: \(Pe=\frac{\mu E_{fp}}{\sqrt{2 Dt_{bp}}}\), where \(t_{p}\) is the pulse duration, \(t_{bp}\) is the duration between pulses, \(E\) is the electric field intensity, \(\mu\) is the electrophoretic mobility and \(D\) is the diffusion coefficient. Alternatively, the time between pulses can be inferred as the frequency (\(f\), Hz), in which case \(Pe=\frac{\mu E_{fp}}{\sqrt{2D/f}}\). The values of \(Pe\) used in experiments, and mentioned in the results, are given below again in Table 2. Such a \(Pe\) gives the relative contributions of electrophoresis and diffusion during the single phase of pulse/burst. Inferring the role of electrophoresis for different types of pulses used (ns, HF-BP, \(\upmu\)s, and ms) using this parameter helps to correctly identify the role electrophoresis and diffusion as inferred from the model results. \(Pe\ \ll\ 1\) for the 200 ns, 500 ns, and HF-BP pulses indicates the dominant role of diffusion in bringing the pDNA molecule to the cell membrane. For the 100 \(\upmu\)s pulse, \(Pe\ =\ 0.33\) or \(Pe\ \sim\ 1\), indicating that neither diffusion nor electrophoresis dominates the process of pDNA coming in contact with the cell membrane. From the model results of the 100 \(\upmu\)s pulse, we saw that \(PSC(t)\) begins to rise sharply before \(t=100\)\(\upmu\)s, for both-with and without the free energy barrier. It could be possible that for the range of \((B_{L},\ B_{R})\) tested from 77 nm to 433 nm corresponding to concentrations from 2500 \(\upmu\)g/mL \begin{table}
\begin{tabular}{c c c c c c} \hline  & **200 ns** & **500 ns** & **HF-BP** & **100 \(\upmu\)s** & **5 ms** \\ \hline Frequency,\(f\) (Hz) & 10.00 & 10.00 & 1.00 & 1.00 & 1.00 \\ \hline \(t_{bp}\) (s) & 0.10 & 0.10 & 1.00 & 1.00 & 1.00 \\ \hline \(t_{p}\) (s) & \(2\times 10^{-7}\) & \(5\times 10^{-7}\) & \(2\times 10^{-6}\) & \(1\times 10^{-4}\) & \(5\times 10^{-3}\) \\ \hline \(E\) (kV/cm) & 15.80 & 4.10 & 1.25 & 1.25 & 0.60 \\ \hline \(Pe\) & **0.03** & **0.02** & **0.01** & **0.33** & **7.95** \\ \hline \end{tabular}
\end{table} 
Table 2: Values of \(Pe\) for various experimental conditions for C2C12 cells. to 15 \(\upmu\)g/mL, the pDNA molecule was close to the cell membrane, and electrophoresis played the dominant role in bringing the pDNA molecules to the cell membrane On further reducing the concentration to \(<\)15 \(\upmu\)g/mL, one might find that electrophoresis is insufficient to bring the pDNA molecule close to the cell membrane. As already seen for \((B_{L},\ B_{R})=\) 433 nm, corresponding to 15 \(\upmu\)g/mL (Figure 18A,B), \(PSC(t)\) begins to rise very close to pulse termination (dotted line in Figure 18A,B). Therefore, one can argue that for \((B_{L},\ B_{R})>\) 433 nm (or concentrations \(<\) 15 \(\upmu\)g/mL), electrophoresis will be insufficient to bring the pDNA molecule to the cell membrane, and the process will have to partly rely on diffusion, indicating the dominance of neither. For the 5 ms pulse, \(Pe=\) 7.95 indicates the dominant role of electrophoresis in bringing the pDNA molecule close to the cell membrane. This is also seen from Figure 20A,B, where \(PSC(t)\) begins to rise and attains a value of 1 much before pulse termination for both--with and without the free energy barrier, indicating electrophoresis as the dominant mechanism. For 200 ns, 500 ns, and HF-BP, the electric field acts for a short duration, which is not sufficient to drive the pDNA molecule to the cell membrane through electrophoresis.