# 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  
Equations (4) and (5) were solved using \(B_{L},B_{R}=134\) nm (representing 500 \(\upmu\)g/mL pDNA solution concentration) for a 100 \(\upmu\)s (monopolar) pulse at an electric field intensity of 1.25 kV/cm, corresponding to experimental conditions for C2C12 cells (Table 1). The evolution of \(P(X,t)\) is shown in Figure 17A for the case without the free energy barrier and in Figure 17C for the case with free energy barrier. For the case without the free energy barrier, electophoresis shifts the peak of \(P(X,t)\) towards the cell membrane and acts for a sufficient amount of time to ensure that the pDNA molecule reaches the cell membrane during the pulse. This is further evident from the evolution of \(PSC(t)\) in Figure 17B, where \(PSC(t)\) remains negligibly small until around \(t\ \sim 20\) us and then suddenly increases to a final value of 1 well before the pulse terminates at \(t=100\) us. This is further evident from \(P(X,t)=0\) in \(X\ \in\ [B_{L},B_{R}]\) for times \(t>20\) us in Figure 17A, indicating that the pDNA has been absorbed by the cell membrane by this time. For the case with the free energy barrier, similar to the case without the free energy barrier, electrophoresis drives the peak of \(P(X,t)\) towards the cell membrane during the pulse (Figure 17C). When nearing the cell membrane, and while electrophoresis is still present, electrophoresis is driving the pDNA molecule to establish a contact with the cell membrane, and at the same time, it is facing the free energy barrier preventing the pDNA molecule from being absorbed at the cell membrane. As a result of this, there is a high probability of finding the pDNA molecule close to the cell membrane (see the peak at \(t\sim 50\) us in Figure 17C, also notice the change in scale of the \(Y\)-axis between Figure 17A,C) Eventually, with electophoresis acting on the pDNA molecule, the probability of pDNA overcoming the free energy barrier and establishing a contact with the cell membrane increases. Simultaneously, the probability of the pDNA molecule being located close to the cell membrane decreases, as is evident in the decrease in the peak of \(P(X,t)\) from \(t\sim 50\) us to \(t\ \sim\)100 us (Figure 17C). Similar inferences can be made from the evolution of \(PSC(t)\) in Figure 17D. Similar to the case without the free energy barrier (Figure 17B), \(PSC(t)\) begins to rise at \(t\ \sim 20\) us in Figure 17D; however, the rise is not as steep as was with the case without the free energy barrier. The free energy barrier slows down the rise in \(PSC(t)\). Furthermore, it also prevents \(PSC(t)\) from attaining a vlue of 1 during the pulse. Once the pulse is terminated, \(PSC(t)\) begins to rise by diffusion. However, the rise is negligibly small since the free energy barrier is too strong/high to be overcome by diffusion. \(PSC(t)\) is evaluated for \((B_{L},B_{R})\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 ug/mL to 15 ug/mL, respectively, and is shown in Figure 18A for the case without the free energy barrier. For most ranges of \((B_{L},B_{R})\) tested, \(PSC(t)\) rises steeply through electrophoresis and attains a final value of 1 before the 100 us pulse. For \((B_{L},B_{R})\) = 433 nm (corresponding to the lowest concentration of 15 ug/mL), \(PSC(t)\) just falls short of reaching a value of 1 before the 100 us pulse's termination; however, \(PSC(t)\) reaches a value of 1 post-pulse termination. 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., for higher concentrations. For the 100 us pulse, the rise in \(PSC(t)\) happens before the termination of the pulse, unlike nanosecond and HF-BP pulses, where \(PSC(t)\) rises post-pulse/burst termination through the diffusive process.