Aggregation–fragmentation model of vesicular transport in neurons

We develop a mathematical model of the motor-based transport and delivery of vesicles to synaptic targets of an axon. Our model incorporates the 'stop-and-go' nature of bidirectional motor transport (which can be modeled in terms of advection–diffusion) and the reversible exchange of vesicles between motors and targets, both of which have been observed experimentally. Since motor-target interactions are reversible, it is necessary to keep track of the cluster size of vesicles bound to each motor-complex. This naturally leads to a modified version of the Becker–Doring model of aggregation–fragmentation processes. We analyze steady-state solutions of the transport model and obtain an explicit solution that supports a uniform distribution of synaptic resources along an axon. We thus establish a possible mechanism for the democratic distribution of synaptic resources along the length of an axon, based on reversible motor-target interactions. In the irreversible case, one finds that 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 more proximal synapses