Modeling Microtubule Counterion Distributions and Conductivity Using the Poisson-Boltzmann Equation

Microtubules are highly negatively charged proteins which have been shown to behave as bio-nanowires capable of conducting ionic currents. The electrical characteristics of microtubules are highly complicated and have been the subject of previous work; however, the impact of the ionic concentration of the buffer solution on microtubule electrical properties has often been overlooked. In this work we use the non-linear Poisson Boltzmann equation, modified to account for a variable permittivity and a Stern Layer, to calculate counterion concentration profiles as a function of the ionic concentration of the buffer. We find that for low-concentration buffers ([KCl] from 10 μM to 10 mM) the counterion concentration is largely independent of the buffer's ionic concentration, but for physiological-concentration buffers ([KCl] from 100 to 500 mM) the counterion concentration varies dramatically with changes in the buffer's ionic concentration. We then calculate the conductivity of microtubule-counterion complexes, which are found to be more conductive than the buffer when the buffer's ionic concentrations is less than ≈100 mM and less conductive otherwise. These results demonstrate the importance of accounting for the ionic concentration of the buffer when analyzing microtubule electrical properties both under laboratory and physiological conditions. We conclude by calculating the basic electrical parameters of microtubules over a range of ionic buffer concentrations applicable to nanodevice and medical applications.