# Efficient Gene Transfection by Electroporation--In Vitro and In Silico Study of Pulse Parameters
## Materials and Methods
### Modeling the Probability of pDNA and Cell Membrane Contact during GET  
To determine the probability of pDNA and cell membrane contact, the distance of a pDNA molecule from the cell membrane needs to be determined. This pDNA-cell membrane distance depends on the concentration of pDNA. To determine the pDNA-cell membrane distance, we followed [16; 55]. The radius of the cell is \(R_{cell}\), and there is a total of \(N_{cells}\) in the suspension. The total volume occupied by the cells in suspension is thus \(V_{cells}=N_{cells}\cdot\left(\frac{4}{3}\pi R_{cell}^{3}\right)\). For a solution volume (\(V_{sol}\)), the volume space left to be occupied by pDNA molecules is:  
\[V_{DNA}=V_{sol}-N_{cells}\cdot\left(\frac{4}{3}\pi R_{cell}^{3}\right) \tag{1}\]  
For pDNA molecules at a concentration (\(c_{DNA}\)) and with molecular weight (\(M_{w}\)), the total number of pDNA molecules in the solution is \(N_{DNA}=\frac{c_{DNA}\cdot V_{sol}\cdot N_{A}}{M_{w}}\), where \(N_{A}\) is the Avogadro's number. Assuming the space available to a single pDNA molecule is defined by a sphere of radius of \(R_{DNA}\) (Figure 1), the volume occupied by pDNA molecules in the solution is \(V_{DNA}=N_{DNA}\cdot\frac{4}{3}\pi R_{DNA}^{3}\) or:  
\[V_{DNA}=\left(\frac{c_{DNA}\cdot V_{sol}\cdot N_{A}}{M_{w}}\right)\cdot\frac {4}{3}\pi R_{DNA}^{3} \tag{2}\]  
Thus, equating (1) and (2), we obtain \(\left(\frac{c_{DNA}\cdot V_{sol}\cdot N_{A}}{M_{w}}\right)\cdot\frac{4}{3}\pi R _{DNA}^{3}=V_{sol}-N_{cells}\cdot\left(\frac{4}{3}\pi R_{cell}^{3}\right)\), or the space available to a single pDNA molecule in a sphere, is defined by radius \(R_{DNA}\) as follows:  
\[R_{DNA}=\left(\frac{1-\rho_{cell}\cdot\left(\frac{4}{3}\pi R_{cell}^{3}\right) }{\frac{4}{3}\pi\cdot\left(\frac{c_{DNA}\cdot N_{A}}{M_{w}}\right)}\right)^{ 1/3} \tag{3}\]  
where \(\rho_{cell}=\frac{N_{cells}}{V_{sol}}\). \(R_{DNA}\) was then calculated using Equation (3) for different values of \(c_{DNA}\) and is shown in Supplementary Table S1. The following set of parameters were used--cell density (\(\rho_{cell}\)) = 2 \(\times\) 10\({}^{6}\) cells/mL, molecular weight of pDNA (\(M_{w}\)) = 660 g/mol/bp \(\times\)\(R_{DNA}\) can be considered as an estimate for the distance between a pDNA molecule and the nearest cell membrane. Furthermore, the boundaries within which a pDNA molecule can move needs to be defined for the model which determines the probability of pDNA molecule coming in contact with the cell membrane. Based on Figure 1, a natural choice for the right boundary (\(B_{R}\)), which constitutes the cell membrane, is \(R_{DNA}\). Since \(R_{DNA}\) is the radius of spherical space available to the pDNA in the solution, the left boundary (\(B_{L}\)) is also considered as \(R_{DNA}\). Other estimates of \(B_{L}\) and \(B_{R}\) can be considered, such as \(R_{DNA}\), \(R_{DNA}-R_{g}\) and \(2R_{DNA}-2R_{g}\), where \(R_{g}\) is the radius of gyration of the pDNA molecule. These are explained in the Supplementary Figure S1. Figure 1: Schematic of distribution of pDNA molecules and cells in suspension. \(R_{cell}\) represents the radius of the cell, \(R_{DNA}\) represents the radius of the (nominal/free) spherical space available to the pDNA molecule. Subset in figure shows the boundaries within which a pDNA molecule close the cell membrane is allowed to move. To determine the probability that a pDNA molecule reaches the permeabilized cell membrane, we assume a 1D case where a pDNA molecule can only move along the one axis (direction of applied electric field) bounded by the left and the right boundaries (Figure 2). The fundamental contribution of electrophoresis and diffusion to the probability of a pDNA molecule reaching the permeabilized cell membrane can be captured in 1D (in the direction of the electric field). We expect that the addition of extra dimensions will not contribute significantly to a more detailed picture of the process with the probabilistic framework described below.