# Measuring vesicular release from neurons

A problem presented at the UK MMSG Imperial College 2009.

### Categories

- Presented by:
- Department of Bioengineering, Imperial College London) (
- Participants:

## Problem Description

The human brain contains billions of neurons, which form connections involving chemical signals. The chemical concentrations can be measured experimentally and undergo significant changes as a result of the aging process, which are not fully understood. The chemical is known to be released from vesicles on the cell surface and then reabsorbed at other sites on the cell. In this problem, participants are asked to develop a model to predict the concentration profile, and this may be used to test theories about the aging process.

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## Study Group Report

We have derived a simple model for the process, by assuming that the release of the neurotransmitter is instantaneous and
from a point. The other key assumptions are firstly that the re-uptake takes place uniformly across the membrane and may be represented by a constant mass transfer coefficient `k`; secondly, that the rate of oxidation at the electrode is so fast that the concentration of neurotransmitter is zero there; and thirdly, that the gap between the electrode and the membrane surface is much smaller than the diameter of the electrode so that the membrane and the electrode can be modelled as two planes.

In reality the re-uptake takes place at discrete sites. If there are a large number of perfectly absorbing sites, whose size and separation is small compared to the distance between the electrode and the membrane and distributed periodically across the membrane, then all the non-uniformity caused by their distribution is contained in a small boundary layer near the membrane and by solving the problem in this boundary layer we have shown how to deduce the effective mass transfer coefficient due to these sites.

In addition to this analytical approach, we have done some preliminary numerical investigations into the effect of a single re-uptake site on the current experienced by the electrode, assuming that the re-uptake site and the vesicle release site are of similar size. In particular we have investigated the effect of changing the distance of separation of the two sites, and also changing the mass transfer coefficient in the re-uptake site. The effects are as would be expected, but further work is needed to quantify precisely the effects over the whole parameter space.

## Follow-Up Activities

The following follow-up meetings have occured to continue work on aspects of this problem:

- 2010 Neurons Follow-up Meeting
- Monday 10th May 2010, Imperial College

The following student projects have been inspired by this problem:

- Neurotransmitter release in the brain
- Modelling problem, VI Modelling Week for the Masters in Mathematical Engineering at Universidad Complutense de Madrid, July 2012.
- Supervised by .