Viscoelastic Response of Microtubule—Tau Proteins Assembly During Axonal Stretch: Combined Atomistic and Continuum Predictions

Abstract

It is believed that damage during traumatic brain injury is a multiscale process that begins from the axonal substructures. The axonal cytoskeleton can be viewed as a nanofiber reinforced composite structure where nanoscale microtubules are arranged in staggered arrays and cross-linked by tau proteins. The unique viscoelastic nature of axons is thought to govern the damage during traumatic brain injury. Recent studies suggest that dynamic loading of axons may lead to microtubule or tau protein failure, depending on the rate of loading. In particular, it has been found that the viscoelastic behavior of tau proteins leads to mechanical breaking of microtubules at high strain rates. At small strain rates, large extension of tau without failure allows for reversible sliding of microtubules without any damage. Despite experimental and computational evidences suggesting that microtubule and tau protein are both viscoelastic, microtubules have been considered as elastic material in these studies for simplicity. Here, inspired by the earlier works, we have developed a modified shear-lag model to predict axonal damage under dynamic loading conditions. In our model, we have considered both microtubule and tau protein as viscoelastic materials. We have assumed that the viscoelastic response of these two materials can be described by the two-parameter Kelvin model. We have employed full atomistic computations to determine the stiffness and viscosity of microtubules and tau proteins. We have then studied the effect of strain rate on the viscoelastic response of microstubule-tau protein assembly. We have attempted to determine a phase diagram in terms of loading rate and microtubule length to isolate the two possible axonal deformation modes, namely microtubule failure due to excessive stretch and reversible microtubule sliding due to tau protein stretch.