Microtubule as nanobioelectronic nonlinear circuit

Abstract

In recent years, the use of biological molecules has offered exciting alternatives to conventional synthetic methods. Specific methods use various biological templates to direct the deposition and patterning of inorganic materials. Here we have established a new electrical model of microtubules as a biological nanoscale circuit based on polyelectrolyte features of cylindrical biopolymers. Our working hypothesis is that microtubules play an active role in sub-cellular computation and signaling via electronic and protonic conductivity and can thus be made useful in hybrid materials that offer novel electronic characteristics. We verify these hypotheses both computationally and analytically through a quantitative model based on the atomic resolution structures of the key functional proteins

An improved nanoscale transmission line model of microtubule: The effect of nonlinearity on the propagation of electrical signals

“…In order to estimate the conductance of nano-pores, we rely on the detailed atomicscale in silico calculations using 3D Brownian dynamics [14]. In accordance with these numerical results, the conductance of both nano-pores is estimated to be G = 10.7 nS, which is determined as a sum of pretty different components reflecting difference in two types of nano-pores [7,13]. Using the same numerical calculation, the resistance of the parallel flow of ions along elementary electric unit is R = 6.2×10 7 Ω, neglecting the ionic current which leaks through the depleted layer.…”

“…where l eff = l CT -λ TD = 1.54 nm is the corresponding effective length of the part of Cterminal not plunged in λ TD . Since each tubulin heterodimer has two C-terminal tails, and keeping in mind that the capacitances of tubulin dimer and C-terminal tails are in parallel arrangement [13], it implies that total maximal static capacitance of the elementary electric unit is readily estimated as the simple sum of above determined components:…”

Investigation of the Electrical Properties of Microtubule Ensembles under Cell-Like Conditions

“…As they stretch outwards into the solution in a pH and ionic strengthdependant manner, they increase the effective area of the tubulin dimer and significantly contribute to the overall MT capacitance [7,8]. Coherent oscillations of these C-terminal tails are modelled to generate solitonic pulses of mobile charge along the outer surface of an MT, creating ionic currents along its length [7,44,50]. Ions from the bulk solution are also modelled to be pumped into the hollow MT lumen through nanopores in its wall, resulting in charge accumulation inside the cylindrical MT over time [45].…”

Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation

“…In particular, in presenting the questions to be solved, for comparison purposes, we follow the initial set up established by Zayed and Alurrfi [56], solving the extended Riccatti equations (see Equations (1) and (2)). We then depart generically from their development by using an entirely distinct method, albeit we compare our final results with theirs in [56], keeping in focus the developments in [57][58][59], as well.…”

“…In [57], authors have used the simple equation method to find the exact solutions of Equation (2), after relating physical aspects and equation derivation being omitted here. This paper is organized as follows: In Section 2, we give the description of the expp´Φpξqq-Expansion Method, while in Section 3, we apply the said method to solve the given NPDEs, Equations (1) and (2).…”