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Center for Nonlinear Studies |
In the late stages of Alzheimer’s disease, the tau proteins that serve to nucleate, stabilize, and crosslink microtubules in the axons of nerve cells are degraded. The customary view is that the removal of taus can allow for the catastrophic dynamical instability of microtubules in which depolymerization of tubulin monomers overwhelms polymerization and the microtubules vanish. We offer an alternative perspective, that removal of taus essentially corresponds to a problem of rigidity percolation with the added feature of a depletion force induced by the taus themselves. We show with a combination of 2D projected simulations and analytic arguments that there is an irreversible first order collapse when too many taus are removed, driven by the attractive depletion force, loosely analogous to gravitational collapse. The values of tau density and entropic spring constants are such to make this likely dominate over the dynamic instability for a wide range of tau occupancies. If correct, these arguments point to kinase phosphorylation as the main mechanism of tau degradation. We discuss possible experimental tests of this on cultured neurons and whether “white matter” volume loss observed by functional MRI in afflicted patients can be attributed to this phenomenon. Clearly this collapse represents a “Point of No Return” signpost in disease progression and therapeutic intervention.
*Work supported by US NSF Grants DMR-1207624 and DMR-0844115 in collaboration with A. Sendek, H.R. Fuller, N.E. Hall, and R.R.P. Singh.
Host: Lena Lopatina