Biomedical Engineering Reference
In-Depth Information
be represented as in Fig. 3.2. The resistors have been replace by
G
-terms that represent
conductances
.
Conductance is simply the inverse of resistance (
G
1
=
R
) and is measured in units of
siemens
, abbreviated
with a capital 'S'.Therefore, as resistance is increased, conductance is decreased. For biological membranes
the most commonly used unit for conductance is
mS/cm
2
.
F
L
,
6WLP
*
.
*
1D
*
/
&
P
,
.
,
1D
,
/
,
&P
(
.
(
1D
(
/
F
H
Figure 3.2:
Hodgkin-Huxley circuit analog.
3.1.2 The Leakage Current
The leakage current is linear and so can be formulated in the same way as the linear current in Eq. (2.36).
I
L
=
G
L
[
V
m
−
E
L
]
(3.2)
where
G
L
is the
leakage conductance
and
E
L
is the leakage Nernst potential. The nature of the leakage
current was not fully known to Hodgkin and Huxley but they guessed (again correctly) that it was some
combination of other ionic currents.
3.1.3 Nonlinear Currents and the Voltage Clamp
Characterization of the two nonlinear currents (
I
Na
and
I
K
) is nontrivial because there is a natural
feedback loop between
I
ion
and
V
m
. Consider the following generic nonlinear current
I
nl
=
G
nl
(V
m
)
[
V
m
−
E
nl
]
.
(3.3)
Notice that the conductance,
G
nl
, is a function of
V
m
. Therefore, a change in
V
m
causes a change in
G
nl
which has an impact on
I
nl
.As
I
nl
is a component of
I
ion
, any nonzero value for
I
nl
may in fact lead to
a further change in
V
m
. Untangling this interdependence in an experiment was a monumental step first
taken by Cole and later used by Hodgkin and Huxley.
The
voltage clamp
is a method of forcing
V
m
to be constant at any desired holding voltage,
V
h
,
using an external circuit (Fig. 3.3). In this way, the feedback loop between
V
m
and
I
m
is effectively cut.
