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Electroporation has been widely used to manipulate cells and tissues, but quantitative understanding of electrical behavior in cell membranes has not been achieved. According to the transient aqueous pore hypothesis, pore creation and expansion is a nonlinear, hysteretic process. Different membrane sites respond locally to their own transmembrane voltage history, so that a self-consistent description should involve the interaction of many different regions of a cell membrane model and its aqueous electrolytes. A transport lattice system model of a cell allows active and passive interaction models for local transport and storage of charge to be combined, yielding approximate solutions for this highly interacting system. Here, we use an asymptotic model for local membrane electroporation, which involves solving an ordinary differential equation for each local membrane area of the system model, subject to constraints imposed by self-consistency throughout the system model of the cell. To illustrate this approach, we first treat a model for a space- and voltage-clamped skeletal muscle cell. We then create and analyze models of a circular cell and of a budding yeast cell pair, both of which exhibit electroporation when exposed to pulsed electric fields.