Evaluating the Combined Neurotoxicity of Amyloid Beta and Tau Oligomers in Alzheimer's Disease: A Novel Cellular-Level Criterion

Abstract

A criterion characterizing the combined neurotoxicity of amyloid beta and tau oligomers is suggested. A mathematical model for calculating the value of this criterion during senile plaque and neurofibrillary tangle (NFT) formation is proposed. Computations show that for physiologically relevant parameter values, the value of the criterion increases approximately linearly with time. Once neurofibrillary tangles begin forming in addition to senile plaques, there is an increase in the slope characterizing the rate at which the criterion increases. The critical value of the criterion at which a neuron dies is estimated. Unless the production rates of amyloid beta and tau monomers are very large, computations predict that for the accumulated toxicity to reach the critical value, the neural machinery responsible for the degradation of amyloid beta and tau monomers and aggregates must become dysfunctional. The value of the criterion after 20 years of the aggregation process is strongly influenced by the deposition rates of amyloid beta and tau oligomers into senile plaques and NFTs. This suggests that deposition of amyloid beta and tau oligomers into senile plaques and NFTs may reduce accumulated toxicity by sequestering more toxic oligomeric species into less toxic insoluble aggregates.