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. 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:

Biomolecular Basis of Cellular Consciousness via Subcellular Nanobrains

“…As microtubules act as memristors, as combinations of memory and electromagnetic resistance [ 49 ], they are well suited to faithfully decode the cellular senomic fields and to act accordingly. Furthermore, microtubules are structurally linked to both the actin filaments as well as the plasma membrane; they are perfectly suited to generate subcellular bioelectric circuits [ 49 , 50 ].…”

Revealing and Attenuating the Electrostatic Properties of Tubulin and Its Polymers

“…[ 28,29 ] When exposed to a.c. electric fields (in the kHz regime), these condensed counterions are modelled to contribute to imaginary impedance of the system, leading to experimentally observable frequency‐specific changes in solution conductance. [ 30–32 ] The high negative charge of tubulin also leads to a large protein dipole moment because ≈40% of the total negative charge is accumulated on the filamentous C‐termini “tails” ( Figure a), which contributes to the dipole moment of the dimer when a counter ionic double layer is formed around these charges. Depending on the tubulin isotype, the value of the dimer's dipole moment ranges between 1500 and 3500 D. [ 33 ] Upon exposure to electrical nanosecond pulses, C‐termini tails are modeled to undergo conformational changes that can attenuate microtubule assembly.…”

Fractal, Scale Free Electromagnetic Resonance of a Single Brain Extracted Microtubule Nanowire, a Single Tubulin Protein and a Single Neuron

“…In most of the dielectric measurements of proteins or biomaterials, the material is dissolved into the solution and the electrodes are dipped to make a contact with many elements since the background response of solution and biomaterial + solution are identical, the minimum differences are subtracted and the resultant signal is claimed as the pure material property. Consequently, the researchers derive non-physical results e.g., a metal-like ampere level current flow in tubulin (1 A current in tubulin solution at 0.2 V, 0.2 Ω resistance, like a superconductor, 15 µA at 1V for microtubule solution [15] and a massive microfarad capacitance in microtubule [16], quantum-like near-ballistic resistance without any electromagnetic resonance (97.4 kΩ). Collisionless quantum transport of electrons under massive noise in water along the microtubule surface at ambient atmosphere is non-physical.…”