Paradoxical relationships between active transport and global protein distributions in neurons

Neural function depends on continual synthesis and targeted trafficking of intracellular components, including ion channel proteins. The detailed biophysics active ion channel transport are increasingly well understood, along with the steady-state distribution of functional channels in the membrane. However we lack a quantitative understanding of how transport mechanisms give rise to stable expression patterns, and how live measurements of active transport relate to static estimates of channel density in neurites. We experimentally measured neuronal transport and expression densities of Kv4.2, a voltage-gated transient potassium channel. Kv4.2 is known to have a highly specific dendritic expression and little or no reported functional expression in axons. Surprisingly, in over 500 hours of quantitative live imaging, we found substantially higher microtubule-based transport of Kv4.2 subunits in axons compared to dendrites. We show that this paradoxical result is expected using a mass action trafficking model of intracellular transport that we calibrate to experimental measurements. Furthermore, we find qualitative differences in axonal and dendritic active transport that are captured in a stochastic model of puncta transport. This reveals that active transport is tuned to efficiently move cargo through axons while promoting mixing in dendrites. Finally, our data reveals trends in transport parameters that can explain the functional density profile of Kv4.2. Puncta velocity bias is directed distally and the magnitude of this bias increases with distance from the soma. These trends are consistent with an analytical solution of a linear transport PDE, corroborating previously unexplained distributions of Kv4.2 subunit localization and A-type current density. Together, our results provide new quantitative data on ion channel trafficking and reveal counterintuitive but mathematically consistent relationships between the distribution of cargo that is in transit and its functional expression. SIGNIFICANCE This study of ion channel transport reveals a seemingly counterintuitive result: the majority of subunit transport occurs in axons for a cargo whose static distribution is concentrated in dendrites. This disparity is reconciled by a simple mathematical model of transport, which reveals that the local density of actively transported intracellular cargo can show an inverse relationship with its static expression density. Mass action models also reconcile the previously unexplained, highly asymmetric, increasing distribution of Kv4.2 with its measured trafficking density that resembles diffusion with minimal drift. The generality of our analysis prompts caution in how static snapshots of intracellular cargo distributions should be interpreted for any type of intracellular cargo.