What tau distribution maximizes fast axonal transport toward the axonal synapse?

This theoretical research is aimed at investigating the question of why tau protein concentration exhibits a proximal-distal increase in healthy axons and a proximal-distal decrease in degenerating axons in Alzheimer's disease. We developed a model of fast axonal transport toward the axon synapse. The model is based on recently published experimental results by Dixit et al. (2008) [1] who reported that the attachment rate of kinesin-1 to MTs is reduced by tau. Cytoplasmic dynein is affected less by tau (dynein is affected at much higher tau concentrations than those that affect kinesin-1). We used the model to investigate the effect of various tau distributions along the axon length on organelle flux toward the axon synapse. We found that a proximal-distal increase in tau concentration leads to a higher organelle flux while a proximal-distal decrease in tau concentration leads to a smaller organelle flux than a uniform tau concentration. We also computed what tau distribution would give the largest organelle flux toward the synapse. We found that in order to maximize organelle flux, the tau concentration has to be at its minimum level in the proximal axon and its maximum level at the distal axon, which is in agreement with the bang-bang principle in optimal control theory.