We consider exact solutions for static black holes localized on a three-brane in five-dimensional gravity in the Randall-Sundrum scenario. We show that the Reissner-Nördstrom metric is an exact solution of the effective Einstein equations on the brane, re-interpreted as a black hole without electric charge, but with instead a tidal 'charge' arising via gravitational effects from the fifth dimension. The tidal correction to the Schwarzschild potential is negative, which is impossible in general relativity, and in this case only one horizon is admitted, located outside the Schwarzschild horizon. The solution satisfies a closed system of equations on the brane, and describes the stronggravity regime. Current observations do not strongly constrain the tidal charge, and significant tidal corrections could in principle arise in the strong-gravity regime and for primordial black holes.

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 when an external potential is 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 a net current to be pumped across the microtubule wall and propagate down the microtubule through the lumen. This effect is demonstrated to enhance and add directly to the longitudinal current through the lumen resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment or as a nano-bioelectronic device.

Microtubules (MTs), which are cylindrical protein filaments that play crucial roles in eukaryotic cell functions, have been implicated in electrical signalling as biological nanowires. We report on the small-signal AC (“alternating current”) conductance of electrolytic solutions containing MTs and tubulin dimers, using a microelectrode system. We find that MTs (212 nM tubulin) in a 20-fold diluted BRB80 electrolyte increase solution conductance by 23% at 100 kHz, and this effect is directly proportional to the concentration of MTs in solution. The frequency response of MT-containing electrolytes exhibits a concentration-independent peak in the conductance spectrum at 111 kHz (503 kHz FWHM that decreases linearly with MT concentration), which appears to be an intrinsic property of MT ensembles in aqueous environments. Conversely, tubulin dimers (42 nM) decrease solution conductance by 5% at 100 kHz under similar conditions. We attribute these effects primarily to changes in the mobility of ionic species due to counter-ion condensation effects, and changes in the solvent structure and solvation dynamics. These results provide insight into MTs’ ability to modulate the conductance of aqueous electrolytes, which in turn, has significant implications for biological information processing, especially in neurons, and for intracellular electrical communication in general.