Paradoxical relationships between active transport and global protein distributions in neurons

Abstract

Neural function depends on continual synthesis and targeted trafficking of intracellular components, including ion channel proteins. Many kinds of ion channels are trafficked over long distances to specific cellular compartments. This raises the question of whether cargo is directed with high specificity during transit or whether cargo is distributed widely and sequestered at specific sites. We addressed this question by experimentally measuring transport and expression densities of Kv4.2, a voltage-gated transient potassium channel that exhibits a specific dendritic expression that increases with distance from the soma and little or no functional expression in axons. In over 500 h of quantitative live imaging, we found substantially higher densities of actively transported Kv4.2 subunits in axons as opposed to dendrites. This paradoxical relationship between functional expression and traffic density supports a model-commonly known as the sushi belt model-in which trafficking specificity is relatively low and active sequestration occurs in compartments where cargo is expressed. In further support of this model, we find that kinetics of active transport differs qualitatively between axons and dendrites, with axons exhibiting strong superdiffusivity, whereas dendritic transport resembles a weakly directed random walk, promoting mixing and opportunity for sequestration. Finally, we use our data to constrain a compartmental reaction-diffusion model that can recapitulate the known Kv4.2 density profile. Together, our results show how nontrivial expression patterns can be maintained over long distances with a relatively simple trafficking mechanism and how the hallmarks of a global trafficking mechanism can be revealed in the kinetics and density of cargo.

Figure 1

Kv4.2 preferentially localizes to dendrites in both endogenous and transfected expression systems, but axonal density is not negligible. (A) Immunogold localization (arrows) of Kv4.2 in the CA1 stratum radiatum of the hippocampus of WT mice. Synapse profiles show the presynaptic terminal (pre) contacting one or two postsynaptic spines. In (i) and (ii), the axon (ax) can be traced from the presynaptic terminal. Examples of gold labeling associated with the plasma membrane of the synapse and counted in the accompanying graph include those at the axon synaptic membrane shown in (iv), (v), and (vi); the axon extrasynaptic membrane shown in (iii) and (v); the dendrite synaptic membrane shown in (i) and (vi); and the dendrite extrasynaptic membrane shown in (ii). (B) Quantification of (A), in which presynaptic (axonal) and postsynaptic (dendritic) compartments yielded concentrations of 0.149 and 0.327 gold particles per synapse, respectively. Note that the bar “postsynaptic (dendrites)” was published previously in another form in Sun et al., 2011 (30) and is included here for comparison with axons. (C) Histogram of the relative prebleach fluorescence intensities of neurons transfected with Kv4.2-SGFP2, showing total subunit count. (D) E18 cultured rat hippocampal neurons at DIV5 were immunostained with Kv4.2 antibodies (i, green) to visualize the endogenous Kv4.2 and MAP2 antibodies (ii, red) to mark the dendritic arbor. The arrow indicates a representative axon with less Kv4.2 than the surrounding dendrites. To see this figure in color, go online.

Figure 2

Kv4.2 microtubule-based trafficking is observed more frequently in axons than in dendrites. (A) Hour-long recordings of 46 axons are depicted, with highlighted sections indicating periods of puncta mobility. (B) Hour-long recordings of 213 dendrites are depicted, with highlighted sections indicating periods of puncta mobility. This subset of 478 dendrites has ≥1 mobile puncta. (C) Puncta frequency (mt) in axons and dendrites is standardized by total neurite length visualized and time recorded (units: number of puncta/mm/h). (D) Histogram depicting puncta frequency by neurite recording. (E) Three extended recordings that substantiate the puncta frequency discrepancy between axons and dendrites over extended periods of observation. (F) Puncta frequency (mt) decreases with distance from soma in dendrites, consistent with analytical solutions to the drift-diffusion equation. (G) Axons and dendrites originating from the same soma (same neuron) are depicted, demonstrating similar trends as those observed in isolated recordings. The central column of numbers indicates an arbitrary recording index for individual neurons. (H) Number of mobile puncta per neurite from concurrent recordings in (G). (I) Number of mobile puncta per neurite standardized by length and time for concurrent recordings from (G). To see this figure in color, go online.

Figure 3

Kinetic differences between axons and dendrites are attributable to varying propensities for cargo offloading and unidirectional runs. (A) Representative histograms in axon (i) and dendrite (ii) show typical puncta trajectories and kinetics. Untraced histograms are depicted in Fig. S7. (B) Histograms for various transport parameters, normalized as probability density functions. On average, axonal puncta have greater net displacement (i), faster speed (ii), deceased stall time (iii), and increased unidirectional runs (iv). Model fits to these results using p_off alone (second column) as well as using p_off and p_mem (third column) are depicted. (C) Setup of stochastic simulations along linear multicompartment model (axon-soma-dendrite), with left and right jump and offloading rates depicted. Complete model is depicted in Fig. S9. To see this figure in color, go online.

Figure 4

Mathematical model of intracellular transport. (A) Kv4.2 subunits are divided into microtubule-bound (mt) and delivered (del) cargo populations. (B) Individual vesicles containing cargo (puncta) have microscopic dynamics modeled as a directed random walk (i and ii). At the population level, the density of cargo (iv) behaves as a deterministic process, described by a drift-diffusion equation with decay (iii), which can be discretized into a compartmental model (v). Compartmental models can represent neurites of a full neuron morphology (vi). (C) Steady-state cargo densities depend on the relative rates of delivery and transport. Delivered (del) Kv4.2 density is low in axons and high in dendrites and increases with dendritic distance (i). Microtubule-bound (mt) trafficking densities are high in axons and low in dendrites (ii). To see this figure in color, go online.

Figure 5

Disparity between delivered Kv4.2 (del) subunit density and puncta frequency (mt) in lumped neurites is explained by a mass-action model. (A) Box diagram of mass-action model of axon and dendrite transport. In a full morphology (i), the central soma is surrounded by microtubule (mt) and delivered (del) cargo compartments for axons a and dendrites d. Arrows denote rates of cargo transfer between compartments. A lumped variant (ii) can accommodate experimental constraints to simulate disparities in subunit density between axons and dendrites. (B) Result of simulation with experimentally constrained rates, corroborating mt and del densities observed experimentally. (C) Analytical result demonstrating negative correlation between a_del and a_mt or d_del and d_mt when restricted to a constant total (tot) density. To see this figure in color, go online.

Figure 6

Opposing gradients in del and mt along somatodendritic axis are reconciled with mass-action kinetics. (A) The mean instantaneous velocities for all dendritic puncta are standardized by puncta frequency along the length of the dendrite. A linear tread line is plotted through the data with 90% confidence intervals, indicating a positive (distal) velocity bias that increases with distance from soma. (B) Box diagram of a mass-action model of dendritic transport and delivery with feedback. The dendrite is spatially discretized, with each discretization i comprising a microtubule-bound $d_{\text{mt}}^i$ and delivered $d_{\text{del}}^i$ compartment. f_i-values, b_i-values, and $d_{\text{off}}^i$-values denote rates between compartments. Degradation rates for all compartments are simulated but not depicted. (C) Simulation results for $d_{\text{mt}}^i$ (i) and $d_{\text{del}}^i$ (ii). (D) Steady-state concentrations of all compartments. (E) Steady-state concentrations of $d_{\text{del}}^i$-values standardized by $d_{\text{del}}^2$ at 50 μm overlaid on equivalently standardized experimental data of Kv4.2 localization (17). To see this figure in color, go online.

Figure 7

A summary of the relationships between microtubule-bound (mt) and delivered (del) cargo densities. The negative correlation between mt and del holds in lumped neurites (A) and along intraneurite gradients (B). (C) The kinetic properties of individual puncta trajectories in mt also reflects cargo demand in del. To see this figure in color, go online.