Introduction

In the previous chapter we showed that acetylcholine (Ach) is released in discrete packets (quanta) in an all-or-none way from the presynaptic nerve terminal. In this chapter we derive a statistical model of quantal release that occurs in synaptic transmission. Since the release of transmitter is probabilistic, the postsynaptic membrane potential randomly fluctuates around a mean value. These fluctuations, or membrane noise, will be analysed in some detail in the latter part of the chapter and used as an example of the way in which membrane noise can be studied more generally.

A probabilistic model of quantal release

It was seen in the last chapter that the actual number of quanta released is not an exact constant and, in fact, the number changes in a random way with every action potential that invades the nerve terminal. (The average number of released quanta per action potential depends on factors such as the calcium or the magnesium concentrations in the bathing fluid. Under normal conditions the average number of quanta released is around 1000. If the calcium is replaced by magnesium the average number of quanta released per action potential may be quite small. It is this situation that we shall be analysing.) Since the exact number of quanta released is not constant, this means that it is possible (although unlikely) that some action potentials may not release any quanta, while others will release one, or two, or more, quanta.