What is it about?
Alzheimer’s disease is a widespread neurodegenerative disorder that currently lacks curative treatments. The disease is characterized by two main physical hallmarks in the brain: extracellular plaques formed by amyloid-β (Aβ) peptides and intracellular neurofibrillary tangles (NFTs) made of misfolded tau proteins. In this publication, we developed a mathematical model to investigate how amyloid precursor protein (APP) and tau protein are produced and transported within a single neuron. Specifically, our model explores the "amyloid cascade hypothesis," which suggests that the buildup of Aβ initiates a chain of negative events inside the neuron, including tau pathology. We used a minimalistic mathematical framework to simulate how Aβ and tau proteins misfold and clump together. By mathematically linking these two aggregation processes, we sought to understand how the accumulation of Aβ might influence the transport and aggregation of tau proteins in both the main cell body (soma) and the long neuronal extension (axon).
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Why is it important?
This work is uniquely timely because the scientific community urgently needs new ways to test hypotheses about Alzheimer's disease, especially given the failure of several recent drug trials that attempted to target Aβ levels. Mathematical modeling is a powerful tool that allows us to uncover the physical consequences of the amyloid cascade hypothesis. Instead of relying solely on difficult direct experimental testing, our mathematical framework provides a way to verify if this biological hypothesis leads to realistic, biologically sound predictions about neuron breakdown. Our approach is important because it yields several unique and testable predictions regarding how these proteins behave in different parts of the cell: APP that is present in the axon is uniformly distributed along the axon length. The concentration of tau monomers first decreases, goes through a minimum, and then increases towards the synapse. A much larger number of Aβ polymers are produced at the soma membrane than at the axon membrane. A much larger number of tau polymers are produced in the soma than in the axon. The tau polymers produced in the axon are mostly produced in the proximal axon.
Perspectives
Writing this article was a deeply fulfilling step in my ongoing research journey. Having previously investigated the tau hypothesis—which assumes tau agglomeration precedes Aβ—turning our attention to the amyloid cascade hypothesis allowed us to look at the disease from a completely different, yet equally critical, mathematical angle. Developing these equations to represent how motor proteins transport vital cargo through the neuron felt like piecing together a tragic but fascinating puzzle. I hope this article demonstrates that mathematical modelling is an essential, albeit sometimes overlooked, weapon in the fight against neurodegenerative diseases. Our simulation results suggest that the transport processes in neurons might not be significantly affected at the very onset of the disease, which personally gives me tremendous hope. It suggests that if we can develop diagnostics to catch Alzheimer's early enough, future therapeutic interventions could still successfully halt the progression of this devastating condition before the neuronal transport system completely breaks down.
Andrey V Kuznetsov
North Carolina State University
Read the Original
This page is a summary of: Simulating the effect of formation of amyloid plaques on aggregation of tau protein, Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, December 2018, Royal Society Publishing,
DOI: 10.1098/rspa.2018.0511.
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