Pore disappearance in a cell after electroporation: theoretical simulation and comparison with experiments

Abstract

The process of pore disappearance after cell electroporation is analyzed theoretically. On the basis of the kinetic model, in which the formation and annihilation of a metastable hydrophilic pore are considered as random one-step processes, a distribution function of cell resealing times, Fr(t), is derived. Two cases are studied: 1) the rate of pore resealing, k(r), is significantly greater than the rate of pore formation, k(f); and 2) the rate of pore formation, k(f), is comparable with k(r). It is determined that the shape of the distribution function depends on the initial number of pores in a cell, n(i). If in the absence of an external electric field the rate of pore formation, k(f), is significantly less than the rate of pore resealing, k(r) (case 1), pores disappear completely, whereas when k(f) approximately k(r) (case 2), the cell achieves a steady state in which the number of pores is equal to k(f)/k(r). In case 1, when n(i) = 1, the distribution function Fr(t) is exponential. The developed theory is compared with experimental data available in the literature. Increasing the time of incubation at elevated temperature increases the fraction of resealed cells. This indicates that the time necessary for the resealing varies from cell to cell. Although the shape of experimental relationships depends on the electroporation conditions they can be described by theoretical curves quite well. Thus it can be concluded that the disappearance of pores in the cell membrane after electroporation is a random process. It is shown that from the comparison of presented theory with experiments, the following parameters can be estimated: the average number of pores, n(i), that appeared in a cell during an electric pulse; the rate of pore disappearance, k(r); the ratio k(f)/k(r); and the energy barrier to pore disappearance deltaWr(0). Estimated numerical values of the parameters show that increasing the amplitude of an electric pulse increases either the apparent number of pores created during the pulse (the rate of pore resealing remains the same) or the rate of pore resealing (the average number of pores remains the same).