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.
MemristorsThe term memristor is the contraction of memory and resistor and it was first proposed in 1971 as the fourth element of the electric circuits 1 . A memristor is defined as a two-terminal passive circuit element that provides a functional relation between electric charge and magnetic flux 1,2 . The first physical realization of a memristor was achieved in 2008 2,3 and it has held a promise of nanoelectronics beyond Moore's law 4 , although this realization has been both difficult and controversial 5 . One of the possible breakthrough applications of memristors is neuromorphic computing 6 . Memristance refers to a property of the memristor that is analogous to resistance but it also depends on the history of applied voltage or injected current, unlike in other electrical circuit elements. When the electrical charge flows in one direction, the resistance of some memristors increases while it decreases when the charge flows in the opposite direction or vice versa. If the applied voltage is turned off, the memristor retains the last resistance value that it exhibited. This history dependence of memristance is expressed via a self-crossing or pinched I-V loop, which is frequency dependent 3,6 , and whose lobe area tends to zero as the frequency tends to infinity.A memristor is said to be charge-controlled if the relation between flux ϕ and charge q is: ϕ = ϕ (q). Conversely, it is said to be flux-controlled if q = q(ϕ). The voltage v of a charge-controlled memristor obeys a linear relationship with the current i(t) representing a charge-dependent Ohm's law such that:
v(t) M(q) i(t)(1) = where memristance is defined as: