Synaptic Democracy and Vesicular Transport in Axons

Synaptic democracy concerns the general problem of how regions of an axon or dendrite far from the cell body (soma) of a neuron can play an effective role in neuronal function. For example, stimulated synapses far from the soma are unlikely to influence the firing of a neuron unless some sort of active dendritic processing occurs. Analogously, the motor-driven transport of newly synthesized proteins from the soma to presynaptic targets along the axon tends to favor the delivery of resources to proximal synapses. Both of these phenomena reflect fundamental limitations of transport processes based on a localized source. In this Letter, we show that a more democratic distribution of proteins along an axon can be achieved by making the transport process less efficient. This involves two components: bidirectional or “stop-and-go” motor transport (which can be modeled in terms of advection-diffusion), and reversible interactions between motor-cargo complexes and synaptic targets. Both of these features have recently been observed experimentally. Our model suggests that, just as in human societies, there needs to be a balance between “efficiency” and “equality”.

Figure 1

Three-state model of the bidirectional transport of a single motor-cargo complex. The particle switches between an anterograde state $(n=+)$ of speed $v_{+}$, a stationary or slowly diffusing state ($n=0$), and a retrograde state $(n=-)$ of speed $v_{-}$. The motor complex can only deliver a SVP to a presynaptic target in the state $n=0$.

Figure 2

Schematic diagram of the reversible exchange of vesicles between motor-cargo complexes and presynaptic targets. Each motor is modeled according to an advection-diffusion equation with average speed $v$ and diffusivity $D$.

Figure 3

Numerical solutions for steady state vesicle concentration as a function of axonal distance for different values of $\varphi =k_{-}/{\gamma }_c$ and $J_0=1.5$. For comparison, the corresponding concentration profile when $J_0=0$ (which is insensitive to $\varphi$) is shown by the thick line (red line). We have also set ${\gamma }_u=10^{-2}{\mathrm{s}}^{-1}$, $J_1=1.5$, $k_{+}=0.5{\mathrm{s}}^{-1}$, $k_{-}=1.0\mu \mathrm{m}{\mathrm{s}}^{-1}$, $v_0=v_1=1\mu \mathrm{m}{\mathrm{s}}^{-1}$ and $D=0.1\mu \mathrm{m}{\mathrm{s}}^{-2}$.

Figure 4

The dashed line shows the total number of vesicles delivered, while the solid line shows the half-length $l_{1/2}$ of the concentration profile. The norm of $(k_{-}/L,k_{+})$ is fixed at 0.5, but we find that the results are qualitatively independent of this quantity. Other parameter values as Fig. 3 with ${\gamma }_c={10}^{-3}$.