Oscillatory Dynamics in Biological Neurons - Advanced Models of Neural Networks - page 81

The NMDA current is modelled as

I NMDA Dg NMDA sB.V/.V V NMDA / (4.14)

where s is given by the previous relation

ds
dt

D a r ŒT.1 s/ a d s (4.15)

and

1
1Ce 0:062V ŒMg 2 C =3:57

B.V/ D

(4.16)

4.5 Study of the GABA Neurotransmitter

GABA is the main inhibitory neurotransmitter in the cortex and can be distinguished
into two types, i.e. GABA A and GABA B [ 16 , 65 ].
(a) GABA A
The neurotransmitter GABA A is responsible for inhibiting the stimulation
of the post-synaptic neuron and as in the case of AMPA and NMDA this
neurotransmitter is activated by a spike.
The associated current equation is

I GABA A D G GABA A s.V V GABA A / (4.17)

(b) GABA B
At the postsynaptic neuron a receptor protein binds the neurotransmitter and
activates an intracellular circuit (G-protein). Next a K C channel is activated
which polarizes the membrane of the post-synaptic neuron. The equations of
current associated with the GABA B neurotransmitter are as follows:

s n

I GABA B Dg GABA B

Kd Cs n .V E k /

dr
dt

(4.18)

D a r ŒT.1 r/ b r r
ds
dt

D k 3 r k d s

(c) Permanent connections between neurons (Gap or electrical junctions)
There are connections between neurons which do not depend on a neurotrans-
mitter (vesicle). The associated current is

I gap Dg gap .V post V pre / (4.19)

where g gap denotes conductivity. This model is usually met in neurons of the
cerebral cortex.