It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores, both with and without an external potential applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes cations to be pumped across the microtubule wall and propagate in both directions down the microtubule through the lumen, returning to the bulk solution through its open ends. This effect is demonstrated to add directly to the longitudinal current through the lumen resulting from an external voltage source applied across the two ends of the microtubule. The predicted persistent currents directed through the microtubule wall and along the lumen could be significant in directing the dissipation of weak, endogenous potential gradients toward one end of the microtubule within the cellular environment.