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In-Depth Information
Fig. 1.4
Electric circuit consisting of ion channels in cell's membrane
V
M
E
k
r
k
I
k
D
(1.20)
By applying Kirchhoff's law in the loop, in the transient stage, one gets [
16
,
65
]
I
capac
C I
k
)c
M
dV
M
dt
.V
M
E
k
/
r
k
C
D 0
(1.21)
that is
c
M
dV
M
dt
V
M
E
k
r
k
D
Dg
k
.V
M
E
k
/
(1.22)
For example, in the case of N D 3 ion channels of the Cl, K and Na type it holds
that the aggregate ions current is
V
M
E
Cl
R
Cl
V
M
E
K
R
K
V
M
E
Na
R
Na
I
ion
D
(1.23)
or using the normalized conductance coefficients g
Cl
, g
K
, and g
Na
and the normal-
ized capacitance c
M
one has
I
ion
Dg
Cl
.V
M
E
Cl
/ g
K
.V
M
E
K
/ g
Na
.V
M
E
Na
/
(1.24)
Equivalently, assuming an external input current I (normalized per surface of the
membrane), it holds that [
16
,
65
]
I.t/
A
c
M
dV
M
dt
Dg
Cl
.V
M
E
Cl
/ g
K
.V
M
E
K
/ g
Na
.V
M
E
Na
/ C
(1.25)
where A denoted membrane's surface (Fig.
1.4
). Using the notation
