# Efficient Gene Transfection by Electroporation--In Vitro and In Silico Study of Pulse Parameters
## 3 Results
### Modeling the Probability of pDNA and Cell Membrane Contact during GET
#### 3.6.3 100 us Pulses
Figure 17: The 100 us pulses: Evolution of \(P(X,t)\) and the corresponding Probability of Successful Contact \(PSC(t)=1-\int_{-B_{L}}^{+B_{R}}P(X,t)dX\) for \(B_{L},B_{R}\) = 134 nm (500 ug/mL) for a 100 us pulse at an electric field intensity of 1.25 kV/cm (Table 1 for C2C12 cells). (**A**,**B**) represent cases without free energy barrier and (**C**,**D**) represent cases with free energy barrier. The dashed lines in (**B**,**D**) represent the time at which the 100 us pulse ends. For (A), \(P(X,t)=0\) in \(X\in[B_{L},B_{R}]\) for legends in \(t\geq 50\) us, as a result of which \(P(X,t)\) is not visible in (A) for these values of \(t\). For (**C**), \(P(X,t)\sim 0\) in \(X\in[B_{L},B_{R}]\) for legends in \(t\geq 1\) ms, as a result of which \(P(X,t)\) is not visible in (**C**) for these values of \(t\). For the case with the free energy barrier (Figure 18B), \(PSC(t)\) begins to rise before \(t=100\)\(\upmu\)s and continues to rise until \(t=100\)\(\upmu\)s (due to electrophoresis) for all \((B_{L},B_{R})\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL, respectively. The rise is not as steep as it is for the case without the free energy barrier. Moreover, \(PSC(t)\) does not attain a value of 1 at \(t=100\)\(\upmu\)s, and the value of \(PSC(t)\) at \(t=100\)\(\upmu\)s depends on \((B_{L},B_{R})\). After \(t=100\)\(\upmu\)s (pulse termination), \(PSC(t)\) increases slowly through the diffusive process. However, the post-pulse diffusive rise is small since diffusion is not strong enough to efficiently overcome the high free energy barrier. These results indicate that even though the electrophoresis provided by the 100 \(\upmu\)s pulse aids in overcoming the free energy barrier (as indicated by the higher \(PSC(t)\) observed compared to the nanosecond and HF-BP pulses), they are not entirely sufficient to completely ensure that the pDNA molecule comes in contact with the cell membrane during pulse. It is interesting to note that the final \(PSC(t)\) before the onset of the second pulse, i.e., \(PSC(t=1\) s) does not depend upon \((B_{L},B_{R})/\)concentration for no free energy barrier (Figure 18A), whereas it depends on the \((B_{L},B_{R})/\)concentration with the free energy barrier (Figure 18B). Therefore, similar to HF-BP pulses, depending on the presence of a free energy barrier and its strength/height, the results for the 100 \(\upmu\)s pulse at an electric field strength of 1.25 kV/cm may depend on the concentration. Furthermore, the Peclet number during a single phase (pulse + post-pulse) is \(Pe=\frac{\mu Et_{p}}{\sqrt{2 Dt_{bp}}}=0.33\), considering \(t_{p}=100\)\(\upmu\)s, time between pulses \(t_{bp}=1\) s, and \(E=1.25\) kV/cm. Such a value of Peclet number, although \(<1\), does not convince us entirely of either electrophoresis or of diffusion dominating the process during the single phase (pulse + post-pulse). Therefore, there could be a confounding role of subsequent pulses, and individual pulses cannot be inferred in isolation. For the case with the free energy barrier, we expect the additional pulses to increase the probability of pDNA reaching the cell membrane and contribute to the further rise in \(PSC(t)\). For the case without the free energy barrier, \(PSC(t)\) already reaches \(1\) before 100 \(\upmu\)s pulse termination, and \(P(X,t)=0\) in \(X\in[-B_{L},B_{R}]\) before the onset of the second pulse. As mentioned previously, the model does not account for the second (or additional) pulse. Therefore, additional pulses can be thought to add additional pDNA molecules to the cell membrane.