Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

• Published in: Computer methods in biomechanics and biomedical engineering 2019-01, Vol.22 (1), p.71-83
• Main Authors: Kuznetsov, Ivan A., Kuznetsov, Andrey V.
• Format: Article
• Language: English
• Subjects: Alzheimer's disease; Axonal transport; Basal ganglia; Biological models (mathematics); Central nervous system diseases; Coefficients; Computer simulation; Diffusion; Diffusion effects; Diffusivity; mathematical modeling; Microtubules; Movement disorders; Neurodegenerative diseases; Neuron; Parameter sensitivity; Protein transport; Proteins; Sensitivity; Sensitivity analysis; sensitivity coefficients; Simulation; Tau protein; Velocity
• ISSN: 1025-5842; 1476-8259
• DOI: 10.1080/10255842.2018.1534233

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer's disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.