Abstract 3209: Numerical modeling of intracellular mechanisms in tumor-treating fields

Abstract

Abstract Tumor Treating Fields (TTFields) are 100-500 kHz electric fields with intensities of about 1-4 V/cm. They are known to exert an antimitotic effect on cancer cells, most likely by exerting forces on highly polar tubulin dimers, thereby disrupting spindle formation. Calculations show that TTFields-tubulin interaction energy is negligible compared to the thermal energy in the cell (1). Therefore, this interaction is unlikely to disrupt cellular function. Conductivity of polymerized tubulin, microtubules (MTs), was measured to be 20 S/m, which is 400 times higher than that of the ambient cytosol (0.05 S/m) (2). Thus when TTFields penetrate the cytosol, they may induce electric currents along MTs that are strong enough to disrupt key cellular functions. In particular, if the power (energy per unit time) deposited by these currents is on par with that the power consumed by the molecular motor kinesin, then TTFields may disrupt the forces needed for cell division, thereby disrupting mitosis. To test this hypothesis, we performed numerical simulations evaluating the magnitude of the electric current along MTs exposed to TTFields at 200 kHz. Based on studies of MTs and their microenvironment, we model the MT as a layered cylindrical structure (1): Innermost is the lumen (15 nm in thickness), surrounded by 13 strands of alpha-beta tubulin dimers linked in a helix (4.5 nm). C-termini extend out from the helix with a thickness of 3.5 nm. MTs carry net negative charge; thus they are surrounded by a counter-ion layer (2 nm), and an outer nonconductive Bjerrum layer (3 nm). We built a finite element model in COMSOL Multiphysics (tm) incorporating these layers and examined the current density induced in each layer by TTFields for MTs varying in length from 1-10 µm within an ambient 200 kHz AC electric field of 1-4 V/cm. Our model shows that MTs act as electrical "shunts" that conduct electric current within them. The highest current flows through the counter-ion layer surrounding the C-termini. The current density in this layer exceeds the level likely to disrupt the motor protein kinesin "walk" along the C-termini. The current density is highest when both the field and the MTs are aligned with the cell axis, in accord with in vitro experiments (3). Our model is consistent with the hypothesis that when cells are exposed to TTFields, MTs act as cables carrying high-density electric currents strong enough to disrupt the function of molecular motors, ultimately disrupting mitosis.