Electroporation, in which strong electric pulses create transient pores in the cell membrane, is commonly used as a method for delivering molecules into cells. One of the pulsing protocols used in practice, a two-pulse protocol, creates a certain number of pores (Num) with a short, large electric pulse, and then controls the pore size with a second, smaller electric pulse of strength V0. This study uses nonlinear analysis of an electroporation model to determine guidelines for the magnitude of V0 and Num that will produce pores of a desired radius (r). Analysis reveals that for Num between 85 and 3190, number and type of fixed points (FPs) depend on Num and V0. For this range of Num, there exist two stable FPs and one unstable FP, and increasing V0 beyond a certain threshold (V0th) drives the system to the FP with larger r. V0th can be fit to a function that is linearly dependent on Num. This study shows that for a given Num created by the first pulse, choice of V0 will allow the experimenter to optimize pore size for a specific application.
The topological degree and fixed points of DC-mappings