Finding the Ion Current Density of Microtubules by defining a potential function for the same and Solving the time independent Schrodinger Equation

TL;DR

This paper models microtubules to determine ion current density by defining a potential function, solving the Schrödinger Equation, and analyzing quantum tunneling effects for ion transmission.

Contribution

It introduces a quantum mechanical approach to model ion flow in microtubules by deriving a potential function and solving the Schrödinger Equation for the first time.

Findings

Calculated ion current density using quantum tunneling effects.

Derived a double well potential model for microtubules.

Quantified transmission efficiency of ions through microtubule potential barriers.

Abstract

In this paper, we model a microtubule based on its dimer resolution structure. First, the fundamental structural components were studied and then electrostatic potential function for a single monomer was calculated. Subsequently, the potential function inside a single monomer due to a ring of dimers was obtained. Considering the potential due to protofilament-protofilament interaction with a monomer in a B crystal structure of a microtubule, we obtain a double well potential wall. Quantum mechanically the ions can pass through this wall because of the Tunnelling effect. We solve the time independent Schrodinger Equation, calculate the transmission efficiency of ion flow and use the latter in the calculation of ion current density.