Oscillatory Dynamics in Biological Neurons - Advanced Models of Neural Networks - page 78

Fig. 4.3 Neurotransmitter
for neurons connected
through a synapse

the post-synaptic neuron it is attached to various receptors (usually on the so-called
protuberances, which are part of dendrites known as spines).
In their turn, these receptors open channels which either hyperpolarize or
depolarize the neuron according to the type of the neurotransmitter. The presence
of other chemical substances in the presynaptic channel may facilitate or inhibit
the binding of ions by the vesicle. Moreover, the binding or release of ions by
the vesicle can be performed in a stochastic manner. Additionally, the presynaptic
excitation can lead to activation of more proteins-transmitters which means that a
larger quantity of ions will be transferred and released at the post-synaptic neuron.
This increase of ion transfer is called potentiation or facilitation. There is also the
inverse phenomenon, in which after several presynaptic spikes, the transfer and
release of ions at the post-synaptic neuron decreases. This is known as depression
(Fig. 4.3 ).

4.3 Dynamics of the Synapses

The following cases of synapses dynamics are examined: (1) the glutamate: it
stimulates the post-synaptic cell and open channels [ 16 , 65 ], (2) the aminobutyric
acid, also known as GABA: it inhibits the postsynaptic cell and closes channels.
The synaptic currents which are developed in such a case depend on a conduc-
tivity parameter and on the difference between the membrane's voltage and voltage
threshold value.

I syn D g.t/.V post V rev / (4.2)

A common assumption made is that conductivity is a sum of constant functions
which depend only on the time instances in which the presynaptic cell has given a
spike.