Modeling tau transport in the axon initial segment

Cellular and pathological functions of tau

Tau protein is involved in various cellular processes, including having a canonical role in binding and stabilization of microtubules in neurons. Tauopathies are neurodegenerative diseases marked by the abnormal accumulation of tau protein aggregates in neurons, as seen, for example, in conditions such as frontotemporal dementia and Alzheimer disease. Mutations in tau coding regions or that disrupt tau mRNA splicing, tau post-translational modifications and cellular stress factors (such as oxidative stress and inflammation) increase the tendency of tau to aggregate and interfere with its clearance. Pathological tau is strongly implicated in the progression of neurodegenerative diseases, and the propagation of tau aggregates is associated with disease severity. Recent technological advancements, including cryo-electron microscopy and disease models derived from human induced pluripotent stem cells, have increased our understanding of tau-related pathology in neurodegenerative conditions. Substantial progress has been made in deciphering tau aggregate structures and the molecular mechanisms that underlie protein aggregation and toxicity. In this Review, we discuss recent insights into the diverse cellular functions of tau and the pathology of tau inclusions and explore the potential for therapeutic interventions.

Why slow axonal transport is bidirectional - can axonal transport of tau protein rely only on motor-driven anterograde transport?

Slow axonal transport (SAT) moves multiple proteins from the soma, where they are synthesized, to the axon terminal. Due to the great lengths of axons, SAT almost exclusively relies on active transport, which is driven by molecular motors. The puzzling feature of slow axonal transport is its bidirectionality. Although the net direction of SAT is anterograde, from the soma to the terminal, experiments show that it also contains a retrograde component. One of the proteins transported by SAT is the microtubule-associated protein tau. To better understand why the retrograde component in tau transport is needed, we used the perturbation technique to analyze how the full tau SAT model can be simplified for the specific case when retrograde motor-driven transport and diffusion-driven transport of tau are negligible and tau is driven only by anterograde (kinesin) motors. The solution of the simplified equations shows that without retrograde transport the tau concentration along the axon length stays almost uniform (decreases very slightly), which is inconsistent with the experimenal tau concentration at the outlet boundary (at the axon tip). Thus kinesin-driven transport alone is not enough to explain the empirically observed distribution of tau, and the retrograde motor-driven component in SAT is needed.

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines

We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the vesicle transport model in [Park and Fai, The Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141 (2020)]. The stochastic version, which may be considered as an agent-based model, relies mostly on the action of individual myosin motors to produce vesicle motion. To aid in our analysis, we coarse-grain this agent-based model using a master equation combined with a partial differential equation describing the probability of local motor positions. We confirm through convergence studies that the coarse-graining captures the essential features of bistability in velocity (observed in experiments) and waiting-time distributions to switch between steady-state velocities. Interestingly, these results allow us to reformulate the translocation problem in terms of conditional mean first passage times for a run-and-tumble particle moving on a finite domain with absorbing boundaries at the two ends. We conclude by presenting numerical and analytical calculations of vesicle translocation.