# 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  
Equations (4) and (5) were solved using \(B_{L},B_{R}=134\) nm (representing 500 \(\upmu\)g/mL pDNA solution concentration) for a 5 ms pulse at an electric field intensity of 0.6 kV/cm  
Figure 18: Evolution of \(PSC(t)\) for different \((B_{L},B_{R})\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 \(\upmu\)g/mL to 15 \(\upmu\)g/mL, for a 100 \(\upmu\)s pulse at an electric field intensity of 1.25 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 100 \(\upmu\)s pulse ends. corresponding to experimental conditions for C2C12 cells (Table 1), and the results are shown in Figure 19A,B for the case without the free energy barrier and in Figure 19C,D for the case with the free energy barrier. For the case in which no free energy barrier is present, the evolution of \(P(X,t)\) is shown in Figure 19A. Similar to a 100 us pulse without a free energy barrier, electrophoresis with a 5 ms pulse drives the peak of \(P(X,t)\) towards the cell membrane. The 5 ms pulse is long enough to ensure that the pDNA molecule is able to reach the cell membrane. This is also evident from the evolution of \(PSC(t)\) in Figure 19B. \(PSC(t)\) remains negligibly small until \(t\sim 40\) us and then suddenly rises to attain a final value of 1 well before the 5 ms pulse ends. For a 100 us pulse without free energy barrier Figure 17B, \(PSC(t)\) remains negligibly small until \(t\sim 20\) us, then rising suddenly to reach a final of 1. The difference in the time when \(PSC(t)\) begins to rise can be explained by the difference in the electric field intensities used. For the 100 us pulse, the electric field was 1.25 kV/cm, whereas for the 5 ms pulse, the electric field was 0.6 kV/cm. As a result, it takes approximately twice the amount of time for \(PSC(t)\) to become non-negligible and then rise suddenly (steeply) for the 5 ms pulse conditions. \(P(X,t)=0\) in \(X\in[B_{L},B_{R}]\) for times \(t>50\) us in Figure 19A, indicating that the pDNA has been absorbed by the cell membrane by this time. When a free energy barrier is present between the pDNA molecule and the cell membrane, similar to the 100 us pulse, electrophoresis from the 5 ms pulses drives the  
Figure 19: The 5 ms 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 5 ms pulse at an electric field intensity of 0.6 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 5 ms pulse ends. For (**A**), \(P(X,t)=0\) in \(X\in[B_{L},B_{R}]\) for legends in \(t\geq 0.495\) ms, as a result of which \(P(X,t)\) is not visible in (**A**) for these values of \(t\). For (**C**), \(P(X,t)=0\) in \(X\in[B_{L},B_{R}]\) for legends in \(t\geq 2.5\) ms, as a result of which \(P(X,t)\) is not visible in (**C**) for these values of \(t\). peak towards the cell membrane (Figure 19C). However, in the presence of the free energy barrier, when the \(P(X,t)\) distribution reaches the cell membrane, electrophoresis is driving the probability for the pDNA to be absorbed at the cell membrane and, at the same time, the free energy barrier is preventing pDNA from being absorbed. This competition between electrophoresis and the free energy barrier leads to another peak of \(P(X,t)\) being formed close to the cell membrane, which rises with time (Figure 19C at \(t~{}\sim\) 0.045 ms and \(t~{}\sim\) 0.05 ms, also note the difference in the scale of the \(Y\)-axis between Figure 19A,C). Eventually, the distribution of \(P(X,t)\) becomes concentrated to a single peak with a narrow distribution (Figure 19C at \(t~{}\sim\) 0.495 ms and inset).