**Read the full paper here: Aggregation–fragmentation model of vesicular transport in neurons**

Paul Bressloff extends his work on a mathematical model for the motor-based transport and delivery of vesicles to synaptic targets of an axon.

Motor transport and irreversible delivery of vesicles to presynaptic targets along an axon. Bidirectional transport is modeled in terms of an advection–diffusion equation

**Background:** A major challenge for a neuron is to ensure an even distribution of synaptic material among neighbouring synapses. It has been indicated through experimental studies in drosophila and C elegans that a mechanism for achieving ‘synaptic democracy’ and to prevent excessive aggregation at any particular synapse, is to combine bidirectional transport with inefficient (reversible) capture of mobile vesicles by synapses.

Recently, Bressloff and Levien developed a mathematical model of motor-driven vesicular transport and showed quantitatively that a combination of ‘stop-and-go’ transport and reversible interactions between motors and targets can provide a mechanism for democratic distribution among synapses.

A simplification was made in the model: to assume that each motor-complex could only carry at most one vesicle.

Each motor-complex can reversibly exchange a vesicle with a synaptic target, and there is clustering of vesicles bound to motors and bound to targets.

**In this paper:** Bressloff extends the model to allow motor-complexes to carry an arbitrary number of vesicles. They showed the kinetic part of the equations becomes a modified version of the Becker–Doring (BD) equations for aggregation–fragmentation processes and exploit this to analyse the existence of steady-state solutions and conditions for the uniform distribution of synaptic resources along an axon.

**Extensions**: The authors note the range of extensions to be explored in future works around simplifications made in their current model. These include further investigation into models of association and dissociation of vesicles at synaptic targets, the nature of the distribution of synaptic targets and a more detailed look into the advection-diffusion model given here.

Paul C Bressloff is based at the Department of Mathematics, University of Utah. He has a background in applied mathematics and theoretical physics, and now works broadly within the interdisciplinary field of mathematical biology with his most recent focus being on stochastic processes in cell biology.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Image: Paul C Bressloff 2016 *J. Phys. A: Math. Theor.* **49** 145601 Copyright IOP Publishing 2016.

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Categories: Journal of Physics A: Mathematical and Theoretical, JPhys+

Tags: Biological physics, BioPhysics, Mathematical Biology, Mathematical Model, Mathematical physics, Neurons, Vesicular Transport