Microtubules as Sub-Cellular Memristors

Abstract

Memristors represent the fourth electrical circuit element complementing resistors, capacitors and inductors. Hallmarks of memristive behavior include pinched and frequency-dependent I-V hysteresis loops and most importantly a functional dependence of the magnetic flux passing through an ideal memristor on its electrical charge. Microtubules (MTs), cylindrical protein polymers composed of tubulin dimers are key components of the cytoskeleton. They have been shown to increase solution's ionic conductance and re-orient in the presence of electric fields. It has been hypothesized that MTs also possess intrinsic capacitive and inductive properties, leading to transistor-like behavior. Here, we show a theoretical basis and experimental support for the assertion that MTs under specific circumstances behave consistently with the definition of a memristor. Their biophysical properties lead to pinched hysteretic current-voltage dependence as well a classic dependence of magnetic flux on electric charge. Based on the information about the structure of MTs we provide an estimate of their memristance. We discuss its significance for biology, especially neuroscience, and potential for nanotechnology applications.

Figure 1

Schematics displaying ionic movement along an MT. Conformational changes in C-termini on the MT surface both alter ionic flows and respond to them, creating a non-linear transmission line. (A–C) display charge transport along the MT length and outside it. (D) displays charge transport across the MT surface into its lumen.

Figure 2

Diagrams showing the effects of nanopores in the current–voltage characteristics of microtubules resulting from the calculations based on the simulations in ref. . Blue asterisks depict the same dependence as red asterisks but with inverted currents and voltages. Fitted pinched hysteresis loops are shown with green asterisks. (A) Current-voltage relation from GCMC/BD simulation for conductance of anions through the type I pore. (B) Current-voltage relation from GCMC/BD simulation for conductance of cations through the type II pore. (C) Current-voltage relation from GCMC/BD simulation for conductance of anions through the type II pore.

Figure 3

A characteristic pinched hysteresis loop for memristors. The purple data points show the observed behavior of MTs in the buffer solution. The red data points show the same data but with the contribution of the buffer subtracted. Grey arrows indicate the direction of the voltage sweep. For details regarding the protocol used, see the Methods section.

Figure 4

(A) A schematic displaying the top view (left) and the side view (right) of the parallel-plate device used to determine the electrical properties of MT solutions in the presence of BRB80 buffer with paclitaxel (BRB80T). (B) MTs imaged at 22 µM tubulin concentration using an epi-fluorescence microscope. Scale bar represents 100 μm. (C) Examples of current-voltage sweeps performed at 100 mV/s for BRB80T and BRB80T containing MTs at a 22 µM tubulin concentration. Error-bars represent standard deviations. Data were collected and averaged from three to five experimental sweeps. In spite of the large amount of noise, which is expected in such complex and irregular MT meshworks, (C) is indicative of a superposition of numerous pinched hysteresis loops providing support for the theoretical predictions in the previous sections of this paper.

Figure 5

Comparison of the TiO₂ memristor and the MT memristor shown from the plus end and from the minus end, respectively: (A) positive charged oxygen vacancies play a role of memory carriers; (B) like role is played by counterions within the Bjerrum region adjoining to the MT from the outer and inner surfaces.

Figure 6

MTs form a complex ionic circuit within a neuron. A schematic displaying the role of MTs as individual circuit elements that transfer signals along a neuron. MAPs link MTs, enhancing long-range ionic transport across the neuronal cytoskeleton.