Synapses - Quantitative Neurophysiology - page 72

be capable of generating different types of neurotransmitters. To model a synapse with multiple types of
receptors we can sum up the effects as in the parallel conductance model.

I Dop I GABA

syn

I Ser
syn

I silent
syn

I syn (t) = + + + (6.11)

syn

, I Dop where I GABA

syn

syn , I Ser

syn , and I silent

syn are formulated using some form of Eq. (6.3). In this way, one synapse
can respond to many different molecules.
Given this summation we can now understand the role of the silent synaptic current. Since a
silent synapse has a reversal potential at the resting potential, it will try to depolarize the membrane if
V post <V m and hyperpolarize the membrane if V post <V m . In other words, the direction of I silent

syn will
be such as to bring the post synaptic potential back to rest. This is a very important feedback mechanism
since it prevents the potential from deviating far from rest. You can also think of the silent synapse as a
type of inertia that the excitatory and inhibitory receptors must overcome to be effective.
Three additional properties of synapses are important. First, it is also possible for a post-synapse
to form directly on the soma in which case there will be no attenuation due to the dendrites. Second, the
left-hand side of the reactions in Sec. 6.4.4 reveal how dependent an open channel is on all of the reactions.
For example, if there are not enough inactive g-proteins ( G o ), then no more channels can open. This is
a problem called availability and is a rate-limiting step in any step-wise opening of the post-synaptic
channels. Third, the opposite problem may occur if O

m m

1, meaning that all the post-synaptic channels
are open. When this is the case the post-synapse has become saturated and additional neurotransmitter
will not have any effect.

→

6.6 SIMPLIFIEDMODELS OFTHE SYNAPSE
There are many ways to simplify the action of the synapse. Typically, the simplification is to remove
any dynamics of the neurotransmitter and create a direct electrical connection between the pre and post
synapse. One simplification is to model the conductance in Eq. (6.3) as an alpha function (top panel of
Fig. 6.2).

g max t

τ e 1 − t/τ

=

G(t) (6.12)

G(t) V post E syn I syn = − (6.13)

m

where t is the time after the action potential reaches the axon terminal, τ is a time constant, and g max is
the maximum possible conductance. A slightly more complex model is a bi-exponential (bottom panel
of Fig. 6.2)

τ 2 e − t/τ 1

e − t/τ 2 .

Ag max
τ 1 −

G(t) = − (6.14)

An even more simple model would be to skip the conductance term all together and simply model the
synaptic current, I syn , as a pulse that follows the arrival of a pre-synaptic action potential. In any of these
simple synapse models it is possible to control the onset time and therefore easy to introduce any delays
that may occur.