Biomedical Engineering Reference
In-Depth Information
30 CHAPTER 3. ACTIVEMEMBRANES
3.2 THEHODGKIN-HUXLEY ACTION POTENTIAL
When stimulated, the Hodgkin-Huxley model generates a rapid depolarization followed by a slower
depolarization back to rest. This cycle is known as an
action potential
and is the basic functional measure
of all excitable cells. Below we discuss the four phases of the action potential as summarized in Fig. 3.7.
3.2.1 Phase 0 - Rest
When
V
m
0
.
6 and therefore
g
na
m
3
h
is small. On the other
hand,
V
m
is close to
E
K
, so the driving force for
I
K
is small. For these different reasons, both
I
Na
and
I
K
are small. The result is that at rest the linear leakage current,
I
L
, will dominate and the membrane
behaves linearly.
is at rest,
m
=
m
∞
≈
0
.
05 and
h
=
h
∞
≈
3.2.2 Phase 1 - Activation
If a stimulus is applied,
V
m
will depolarize. As
V
m
changes, the
α
,
β
, time constants and steady-state
values will also change. Consider the following:
1. The driving force for
I
Na
(e.g.,
V
m
−
E
Na
) at rest is large and negative because
V
m
is much smaller
than
E
Na
. If given the chance,
Na
+
ions would therefore move
into
the cell.
2.
Na
+
ions are prevented from crossing the membrane because
m
is small.
curve is flat at
V
rest
m
3. Although the
m
∞
, if the membrane is depolarized slightly,
m
∞
will become
relatively large. This is because of the steep slope of the
m
curve.
∞
4.
τ
m
is small so any change to
m
will result in a fast change in
m
.
∞
5. The driving force for
I
K
at rest is small because
V
m
is close to
E
K
.
, and
therefore
m
, to increase quickly. The result is that
g
Na
m
3
h
and thus
I
Na
increase and
Na
+
will rush into
the cell. As
Na
+
rushes into the small volume of the cell, the intracellular potential,
φ
i
, will increase.
The extracellular space, however, is large and so
φ
e
will change only slightly. The result is that the cell
membrane will become more depolarized.
The fast rise in the membrane potential is called
activation
or
upstroke
and the
m
gate is therefore
called the
activation
gate. The origin of a threshold voltage can now be understood. Below
V
t
m
Given these properties, consider that a small depolarizing change in
V
m
would cause
m
∞
,
m
∞
and
m
are not large enough to create a large
I
Na
. But, when
V
m
reaches
V
t
m
,
m
is on the steep part the
m
∞
curve. So, a small depolarizing
I
Na
current pushes
V
m
and
m
to larger and larger values. This runaway
effect is counterbalanced by
repolarization
.
3.2.3 Phase 2 - Repolarization
As the
I
Na
current attempts to drive
V
m
→
E
Na
, two other players become important. First, during
the upstroke
h
∞
0, but does so slowly, i.e.,
τ
h
is relatively large compared to
τ
m
). Over time, however,
h
becomes small enough that the
m
3
h
term, and therefore
I
Na
, is reduced.
The
h
gating variable is therefore called the
inactivation
gate because it turns the Sodium current off
after activation. Second, after depolarization,
V
m
is no longer close to
E
K
and the driving force for
I
K
is increased. Due to the sign of
E
K
,
I
K
will be a positive current, i.e.,
K
+
flows
out
of the cell). Positive
charge exiting the cell causes
V
m
to decrease or
repolarize
.
changes from
≈
0
.
6 to
≈
