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where parameter
T
is usually called temperature and regulates the inclination
of the curve. The usual procedure for generating an “o=1” with probability
O
,
is generating a random number between
o
and 1. If the random number is lower
than
O
a binary “o=1” is produced. Parameter
s
is the shift of the sigmoid. In
the following sections we arbitrarily set
T
to 0.066 and
s
to 0.5.
3Rsus
At molecular levels, plasticity is related to the amount of
Ca
2+
entering postsy-
naptic NMDA channels (Artola [1]). When calcium is above a certain threshold,
metabolic events lead to synaptic potentiation. Conversely, lower calcium levels
yield synaptic depression. Without calcium, neither potentiation nor depression
takes place. Notice that calcium entrance depends on the presence of presynap-
tic action potentials. Therefore, presynaptic action potentials are necessary for
homosynaptic plasticity. The need of a presynaptic action potential for allowing
homosynaptic plasticity will be called “synaptic directionality”.
Several facts related to NMDA channel operation should be taken into ac-
count in order to perform a realistic model of plasticity in NMDA channels. We
consider two cases: the case in which plasticity is restricted to a single synapse
(homosynaptic plasticity) and the case in which there is some influence from
other synapses over the one under study (heterosynaptic plasticity).
A0.
Homosynaptic plasticity. We will take into account the three following facts:
A1.
Synaptic directionality. A presynaptic action potential is necessary to pro-
duce any positive or negative change in synaptic plasticity.
A2.
Metaplasticity of the LTP threshold. The greater the synaptic weight, the
higher the LTP threshold.
A3.
Magnesium leakage in NMDA channels: When neurotransmitters are bound
in AMPA and NMDA channels, ions like
Na
+
and
Mg
2+
enter through the
channels, and produce the postsynaptic voltage. The greater the number of chan-
nels, the higher is this postsynaptic voltage. However, once NMDA channels are
opened, there is not only an entrance of
Ca
2+
ions, but also an outward leakage
of
Mg
2+
and
K
+
ions, that diminishes the expected postsynaptic voltage.
B0.
Heterosynaptic plasticity. Two or more nearby synapses are involved, and
we consider the following additional facts that are not present in homosynaptic
plasticity:
B1.
The postsynaptic potential in the synapse under study is incremented by
the postsynaptic potential of nearby synapses.
B2.
Metaplasticity of the LTD threshold. The higher the weight, the lower the
LTD threshold (Mockett et al [3].
B3.
The ABS rule.
3.1 Biological Plausibility of Presynaptic Rule Incremental Version
Let us recall the incremental version of the pre-synaptic rule:
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