# 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
#### 3.6.4 5 ms Pulses
As electrophoresis continues to act, the probability of pDNA overcoming the free energy barrier and of pDNA being absorbed by the cell membrane increases, reducing the peak of narrow band \(P(X,t)\) (Figure 19C at \(t~{}\sim\) 0.495 ms and \(t~{}\sim\) 0.5 ms and inset). Eventually, electrophoresis acts long enough to ensure that the pDNA molecule is absorbed by the cell membrane. Similar inferences can be made from the evolution of \(PSC(t)\) for the case with the free energy barrier (Figure 19D). \(PSC(t)\) remains negligibly small until \(t~{}\sim\) 40 us and then begins to rise. Compared to the case without the free energy barrier (Figure 19B), the rise in \(PSC(t)\) is slower, owing to the competing effect of electrophoresis and free energy barrier. Eventually, electrophoresis is able to overcome the free energy barrier, and \(PSC(t)\) reaches a final value of 1 before the end of the pulse. \(PSC(t)\) is also evaluated for \((B_{L},B_{R})\) ranging from 77 nm to 433 nm (representing 2500 ug/mL to 15 ug/mL pDNA solution concentration, respectively) and is shown in Figure 20A for the case without the free energy barrier. For all ranges of \((B_{L},B_{R})\) tested, \(PSC(t)\) rises steeply and attains a final value of 1 before pulse termination through electrophoresis. The time at which \(PSC(t)\) begins to rise depends on \((B_{L},B_{R})\), and \(PSC(t)\) starts to rise earlier for lower \((B_{L},B_{R})\) (i.e., higher concentrations). These observations are similar to the case without the free energy barrier for a 100 us pulse (Figure 18A) and unlike for nanosecond pulses and HF-BP pulses, where \(PSC(t)\) rises post-pulse/burst termination through the diffusive process (Figure 13A,C, Figures 15A and 16A). For the case with the free energy barrier, \(PSC(t)\) begins to rise before pulse termination at \(t\) = 5 ms for \((B_{L},B_{R})\) ranging from 77 nm to 433 nm (representing 2500 ug/mL to 15 ug/mL pDNA solution concentration, respectively) (Figure 20B). The time at which \(PSC(t)\) begins to rise depends on \((B_{L},B_{R})\), and the rate of the rise in \(PSC(t)\) is slower compared the case without the free energy barrier. For a 5 ms pulse at an electric field intensity of 0.6 kV/cm, the electrophoresis acts for a sufficient amount of time to ensure that \(PSC(t)\) reaches a final  
Figure 20: Evolution of \(PSC(t)\) for different \((B_{L},B_{R})\) ranging from 77 nm to 433 nm (corresponding to concentrations ranging from 2500 ug/mL to 15 ug/mL) for a 5 ms pulse at an electric field intensity of 0.6 kV/cm (Table 1 for C2C12 cells): (**A**) without free energy barrier and (**B**) with free energy barrier. Dashed lines represent the time at which the 5 ms pulse ends. value of 1 before pulse termination for all \((B_{L},B_{R})\) tested. This is unlike the case for a 100 us pulse with the free energy barrier, where \(PSC(t)\) could not attain a final value of 1 for the range of \((B_{L},B_{R})\) tested, even though twice as strong of an electric field, with an intensity of 1.25 kV/cm, was applied. The results in Figure 20 indicate that irrespective of the presence of free energy barrier, \(PSC(t)\) reaches a final value of 1 before the 5 ms pulse termination for all \((B_{L},B_{R})\) tested, indicating that GET should not depend on the concentration for these pulse parameters. We can further calculate the Peclet number as \(Pe=\frac{\mu E_{p}}{\sqrt{2D_{bp}}}=7.95\); considering \(t_{p}=5\) ms, time between pulses \(t_{bp}=1\) s, and \(E=0.6\) kV/cm. \(Pe=7.95\) indicates that electrophoresis dominates diffusion during the phase (pulse + post pulse), and individual pulses cannot be inferred in isolation. However, the pulse duration is long enough to ensure that \(PSC(t)\) reaches a final value of 1 before pulse termination for both - with and without the free energy barrier. So, even though the model does not account for multiple pulses since \(P(X,t)=0\) in \(X\in[B_{L},B_{R}]\) before the onset of the next pulse, subsequent pulses can be thought to add more pDNA molecules to the cell membrane.