Transport-Based Biophysical System Models of Cells for Quantitatively Describing Responses to Electric Fields

Abstract

In this paper, we review computational methods based on spatially distributed transport models that we have used to describe biological cell system responses to electric fields. Application to electroporation (EP) is emphasized, as it is increasingly used experimentally, but is not well understood quantitatively. We argue that Cartesian transport lattices (CTLs) and meshed transport networks (MTNs) are appropriate for describing transport in cellular systems generally. The approach is based on mathematical descriptions of transport in 1-D, which are then assigned to intranodal regions in 1-D, 2-D, and 3-D cell system geometries. Electrical behavior is based on nonspecific charge movement. Descriptions of heat transfer and both molecular and ionic transport have also been examined. This approach allows both traditional, idealized geometries [e.g., cylindrical, spherical plasma membrane (PM)] and also more realistic, irregular cell shapes and sizes to be used approximately, with little difference in computational difficulty. The more complex (active) local membrane models are similar to “agents” in agent-based modeling, in the sense that it is the individual responses of interactions within local regions that yield overall system behavior, which can be emergent and nonintuitive. Cell system models may be useful for screening of EP candidate combinations of pulse parameters, cell characteristics, and molecular transport properties with the goal of optimizing existing experimental protocols and possibly discovering new effects and applications.