A comparison between the diffusion-reaction and slow axonal transport models for predicting tau distribution along an axon

This paper developed equations describing steady-state tau distributions for three versions of the diffusion-reaction model of tau transport: a model with constant kinetic rates, a model that additionally accounts for tau diffusion along microtubules (MTs) and a model with a modulated rate of tau attachment to MTs. We demonstrated that, for the model with constant kinetic rates, the concentration of free tau in the cytoplasm was determined by a single dimensionless parameter that represents the ratio of the diffusion time (the time it takes tau to diffuse from the axon hillock to the axon tip) to the half-life of tau. We also developed a model based on the hypothesis that tau is actively transported. Analytical solutions for some special situations were obtained. The model predictions were compared with experimentally measured tau distributions in axons reported in Black et al. (1996, J. Neurosc., 16, 3601-3619), and based on these comparisons, we discussed the performance of various models. We demonstrated the significance of modulation of the tau attachment rate to MTs in the diffusion-reaction model. On the other hand, the active transport model predictions were consistent with experimental data even with constant kinetic rates. For short axons (up to 600 mu m in length) the predicted average transport velocity of tau was in the experimentally reported range for both the diffusion-reaction and active transport models, but for the active transport model the average tau velocity was larger.