Biomedical Engineering Reference
In-Depth Information
where
K
is the maximum amplitude of
O
(usually 1),
τ
s
is the time of the presynaptic spike,
τ
1
is the
rising time constant, and
τ
2
is the falling time constant.
6.4.4 Multiple Gating Mechanism
It is possible for a synaptic current to be gated by a more complex combination of neurotransmitters,
V
pos
m
, ionic concentrations and secondary chemicals. As an example, the model below is for the NMDA
synaptic current that is dependent upon
Mg
2
+
]
0
),
[
T
]
, the extracellular concentration of magnesium (
[
and
V
post
:
m
B
V
post
Mg
2
+
]
o
V
post
I
NMDA
=
g
NMDA
·
,
[
·
O(t)
[
−
E
NMDA
]
(6.9)
m
m
where
O(t)
has a similar formulation, and dependence on
[
T
]
, as Eq. (6.4) and
B
V
post
,
[
Mg
2
+
]
o
1
=
exp
−
(
0
.
062
V
pos
m
)
[
Mg
2
+
]
o
3
.
57
.
(6.10)
m
1
+
6.4.5 SecondMessenger Gating
Although we will not show the differential equations, the follow reaction illustrates how a G-protein
second messenger is used in the gating of the
GABA
b
receptor
R
o
+
T
R
D
R
+
G
0
RG
R
+
G
G
G
o
R
R
o
K
+
+
nG
O.
First,
binds to a free receptor
R
o
, which becomes active (
R
). At some later time,
R
can become
deactivated (
D
). An inactive g-protein (
G
o
) can bind with
R
to become active (
G
) through a two step
process.
n
activated g-proteins can then bind with a single
K
+
ion to open the channel. In the background,
the active
R
and
G
are inactivated (reset) and ready for another reaction.
[
T
]
6.5 SYNAPTIC SUMMATION
Above, we modeled
I
syn
as a single generic synaptic current. In reality, a single post synapse may have more
than one type of receptor, even mixing excitatory and inhibitory receptors. Likewise, the pre-synapse may
