Surface conductance in seamless microtubules

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present a theoretical analysis of the surface conductance of a single seamless MT by representing each tubulin dimer as a resistor. Periodic boundary conditions were utilised both lengthwise (so the MT is pictured as a very large toroidal structure) and around its circumference. Firstly we have investigated the conductance matrix and found the eigenvalues and eigenvectors exactly. Then Wu’s formula has been used to calculate the conductance in terms of them numerically. To check our results we have performed a series of computer simulations of random walks on the lattice of monomers utilising the widely known relationship between such a stochastic process and the theory of electrical networks. We obtain very good agreement between the two approaches.