Open Access

ARTICLE

Microtubular Protofilament Analysis Based on Molecular Level Tubulin Interaction

by JongWon Kim¹, Ning Li², Ramana Pidaparti², Xianqiao Wang²

1 Radiation Oncology, Medical College of Wisconsin, Wauwatosa, WI, 53327, USA.
2 College of Engineering, University of Georgia, Athens, GA, 30605, USA.

* Corresponding Author: Ramana Pidaparti. Email: ;
   Xianqiao Wang . Email: .

Molecular & Cellular Biomechanics 2018, 15(3), 127-141. https://doi.org/10.3970/mcb.2018.02669

Abstract

Nonlinear microstructure of the microtubules (MTs) plays an important role in their mechanical properties. Despite the extensive efforts into the development of continuum models for microtubules, a mesoscale finite element model that can link the molecular level information to the overall performance of microtubules is still missing. The aim of this study is to develop a molecular dynamics model (MDM), finite element model (FEM) and structural mechanics beam model (SMBM) for tubulins of protofilament (PF). In MDM, the backbone atoms of α-tubulin were fixed while the backbone atoms of β-tubulin were attached to a molecular dynamics (MD) atom through a virtual spring. In FEM, both α and β tubulins are modeled as spherical shells and adjacent tubulins are connected by linear springs. The spherical shells were framed as beams in SMBM. Corresponding parameters such as the elasticity of tubulin-tubulin interaction (TTI) and the stiffness of springs and beam are derived from MD simulation. Marginal differences in the force-deflection curve among the FEM, the MDM and SMBM indicate the good accuracy in describing the mechanical properties of microtubules. Simulation results show that the protofilament behaves non-linearly under tension and torsion but linearly under bending. Deformation pattern of a PF from the SMBM frame bending can be well captured by the classical Euler-Bernouli beam theory and the flexural rigidity derived from FEM is in good agreement with SMBM. These findings lend compelling credence in our developed models of PF to deepen our understanding of the underlying mechanism of statics and dynamics of MTs. In perspective our approach provides a tool for the analysis of MTs mechanical behavior under different conditions.

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