Simulated Cytoskeletal Collapse via Tau Degradation

TL;DR

This paper models how tau protein removal causes microtubule bundle collapse in neurons, revealing a potential mechanism for neurodegenerative diseases and predicting collapse conditions that can be tested experimentally.

Contribution

It introduces a coarse-grained mechanical model linking tau degradation to microtubule bundle collapse, incorporating depletion forces and percolation theory insights.

Findings

Collapse occurs at ~60% tau occupancy without depletion force.

Depletion force induces a first-order collapse over a wide tau range.

Microtubule instability likely occurs at low tau occupancy (0.06-0.30).

Abstract

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimer's disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundle falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06-0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse.