What is it about?
This publication explores how the tau protein is transported along the axon of a neuron using a simplified mathematical model. We calculate sensitivity coefficients to determine how different variables affect three main outcomes: the total concentration of tau, its average velocity, and the percentage of tau bound to microtubules. The model accounts for tau transitioning between seven distinct kinetic states, including being actively carried by molecular motors, diffusing freely, or pausing. Specifically, we investigate how the model's outputs respond to changes in eight fundamental parameters. By observing these mathematical reactions, we can isolate exactly which transport mechanisms—such as the transition from retrograde to anterograde motion, or passive diffusion—control the distribution and speed of tau throughout the nerve cell.
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Why is it important?
Understanding tau transport is critical because the abnormal accumulation of tau into neurofibrillary tangles is a primary hallmark of Alzheimer's disease and other tauopathies. Abnormalities in how tau moves along the axon often precede the formation of these tangles and any clinical symptoms, making the mechanics of tau transport a highly promising therapeutic target for halting neurodegeneration. Our model uniquely demonstrates that motor-driven transport dominates tau's movement over long distances, whereas passive diffusion only plays a role in the proximal axon near the cell body. Additionally, our sensitivity analysis pinpoints the exact locations in the axon where tau's behavior is most responsive to parameter changes, providing experimental biologists with specific targets for designing future physical experiments.
Perspectives
Collaborating with Ivan on this research has been a highly rewarding continuation of our ongoing mission to apply rigorous mechanical engineering principles to intricate biological systems. We have spent several years refining mathematical models of axonal transport, and utilizing multi-objective optimization to narrow a complex 24-parameter system down to 8 critical variables feels like a significant leap forward in making our theoretical work practically useful. I hope this article demonstrates that abstract mathematical concepts, like sensitivity coefficients, hold real-world power for medical research. It is my greatest ambition that our calculations will guide future laboratory experiments, helping researchers know exactly where and what to measure to accelerate the development of therapies for devastating diseases like Alzheimer's.
Andrey V Kuznetsov
North Carolina State University
Read the Original
This page is a summary of: Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters, Computer Methods in Biomechanics & Biomedical Engineering, December 2018, Taylor & Francis,
DOI: 10.1080/10255842.2018.1534233.
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