Simulated Cytoskeletal Collapse via Tau Degradation in Late State Alzheimer's Disease

Abstract

Amyloid-beta aggregates initiate Alzheimer's disease, and downstream trigger degradation of tau proteins that act as microtubule bundle stabilizers and mechanical spacers. Currently it is unclear which of tau cutting by proteases, tau phosphorylation, or tau aggregation are responsible for cytoskeleton degradation. We present a coarse grained two-dimensional mechanical model for the microtubule-tau bundles in neuronal axons which includes (i) taus modeled as entropic springs between microtubules, (ii) a possible depletion force due to phosphorylated taus between microtubules, and (iii) removal of taus from the bundles due to phosphorylation. We equilibrate upon tau removal using active damped molecular dynamics and measure the bundle's radius of gyration as tau occupation probability falls to zero. In the absence of the depletion force, the microtubule bundles lose rigidity at about 60% tau occupancy, in agreement with standard percolation theory results. With the attractive depletion force, spring removal leads to first order collapse of the bundles at 60% tau occupancy for physiologically realizable conditions. This collapse may be reflected in reduced white matter volume observed via MRI studies of Alzheimer's progression, and suggest mechanical measurements on cultured neurons to test our results. Future work will seek to explore the effects of alternate mechanisms on the bundle radius and expand the model into three dimensions. Supported by NSF grant DMR-1207624.