Numerical study of the electroporation pulse shape effect on molecular uptake of biological cells

Abstract

BackgroundIn order to reduce the side-effects of chemotherapy, combined chemotherapy-electroporation (electrochemotherapy) has been suggested. Electroporation, application of appropriate electric pulses to biological cells, can significantly enhance molecular uptake of cells due to formation of transient pores in the cell membrane. It was experimentally demonstrated that the efficiency of electroporation is under the control of electric pulse parameters. However, the theoretical basis for these experimental results is not fully explained. In order to predict the outcome of experiments and optimize the efficiency of electroporation before each treatment, we developed a model to investigate the effect of pulse shape on efficiency of electroporation.ResultsOur model is based on a developed chemical-kinetics scheme and trapezium barrier model, while self-consistency was taken into account. This model is further supplemented with a molecular transport model to acquire the molecular uptake of cells. The investigated pulse shapes in this study were unipolar rectangular pulses with different rise and fall times, triangular, sinusoidal and bipolar rectangular pulses and also sinusoidal modulated unipolar pulses with different percentages of modulation. The obtained results from our modelling and simulations are in good agreement with previously published experimental results.ConclusionsWe therefore conclude that this model can be used to predict the effects of arbitrarily shaped electroporation pulses on cell membrane conductivity and molecular transport across the cell membrane.

Microfluidics cell electroporation

“…Different pulse shapes can generate various effects on the cell (Fox et al 2006). Some studies investigated the effect of different pulse shapes (Sinusoidal, step, and triangular) on the transmembrane potential and number of pores (Talele et al 2010;Miklavcic and Towhidi 2010). Talele et al (2010) developed a numerical model for a single cell electroporated by application of arbitrary external electric field pulses.…”

Comparison between direct and reverse electroporation of cells in situ: a simulation study

“…After the molecules move into the cell, transfection efficiency can be estimated based on the total number of molecules that have moved inside the cell, referred to as the cell “uptake.” The uptake is denoted by n and can be computed by integrating the number of molecules that have transported through the cell membrane over time and cell surface, according to equation (A8) in Appendix 1, where j is the total flux, S is the surface of the cell membrane, τ is the time at which that uptake is to be calculated, and N A is Avogadro's number given in Appendix 2 (Towhidi and Miklavcic 2010). …”

“…2013)Pore conductivity σ p 0.0745 S m −1 (Rems et al. 2013)Free diffusion coefficient D 0 5 × 10 −10  m −2 sec −1 (Towhidi and Miklavcic 2010)Diffusion coefficients for the interactive transport D p D 0 /5(Towhidi and Miklavcic 2010)Effective charge number (with sign) for DNA Z eff −1(Neumann et al. 1999)Elementary charge e 0 1.60 × 10 −19  C(Neumann et al.…”

“…1999)Temperature T 298 K(Neumann et al. 1999)Avogadro's number N A 6.022 × 10 23  mol −1 (Towhidi and Miklavcic 2010)Circular cell radius R 10 × 10 −6  m(Kotnik et al. 1997)Cell membrane thickness d m 5 × 10 −9  m(Pucihar et al.…”

“…2013)Cell membrane electric conductivity (passive) σ m0 5 × 10 −7  S m −1 (Pucihar et al. 2009; Towhidi and Miklavcic 2010; Rems et al. 2013)Cell membrane relative permittivity ε m 5(Pucihar et al.…”