Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the nnicrotubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22-44 s(-1), in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.