A viscoelastic model for axonal microtubule rupture

Abstract

Axon is an important part of the neuronal cells and axonal microtubules are bundles in axons. In axons, microtubules are coated with microtubule-associated protein tau, a natively unfolded filamentous protein in the central nervous system. These proteins are responsible for cross-linking axonal microtubule bundles. Through complimentary dimerization with other tau proteins, bridges are formed between nearby microtubules creating bundles. Formation of bundles of microtubules causes their transverse reinforcement and has been shown to enhance their ability to bear compressive loads. Though microtubules are conventionally regarded as bearing compressive loads, in certain circumstances during traumatic brain injuries, they are placed in tension. In our model, microtubule bundles were formed from a large number of discrete masses. We employed Standard Linear Solid model (SLS), a viscoelastic model, to computationally simulate microtubules. In this study, we investigated the dynamic responses of two dimensional axonal microtubules under suddenly applied end forces by implementing discrete masses connected to their neighboring masses with a Standard Linear Solid unit. We also investigated the effect of the applied force rate and magnitude on the deformation of bundles. Under tension, a microtubule fiber may rupture as a result of a sudden force. Using the developed model, we could predict the critical regions of the axonal microtubule bundles in the presence of varying end forces. We finally analyzed the nature of microtubular failure under varying mechanical stresses.