Biomedical Engineering Reference
In-Depth Information
permeable to Na
+
ions, which rush into the cell. This results in a reversal of polari-
zation at the points where Na
+
ions entered the cell [Figure 3.5(b)]. The activation
of the ion channels in turn accelerates the depolarization process, producing the
rising phase of the action potential. The rise of the membrane potential ultimately
triggers the process of ion channel inactivation, which prevents further membrane
depolarization. At the same time, the voltage-dependent K
+
ion channels are acti-
vated, repolarizing the cell and producing the falling phase of the action potential.
During depolarization, K
+
ion channels become permeable to K
+
ions, which rush
outside through potassium channels. Because the K
+
ions move from the inside to
outside of the cell, the polarization at the surface of the cell is again reversed, and is
now below the polarization of the resting cell. Since the pumps are slow, the excess
Na
+
ion concentration inside the cell can diffuse along the length of the axon. This
build up of positive charge inside the next node causes the potential at that node
to rise. K
+
ions also diffuse in the opposite direction, partially canceling the effect
of the Na
+
ion diffusion. However, as a K atom is nearly twice as heavy as an Na
atom, the Na diffusion is faster, producing a net current. When the potential at
the next node exceeds the threshold (somewhere between
70 mV and zero), the
Na
+
ion channel is stimulated to open. At this point, the process described above
repeats itself at the next node. Thus the electrochemical nerve impulse jumps from
node to node.
An RC circuit model with single ionic species [Figure 3.4(b)] is insufficient
to describe all the changes in the membrane potential. To develop a model for
the action potential, British biophysicist Alan L. Hodgkin and British physiologist
Andrew F. Huxley studied the changes in the membrane potentials of a squid gi-
ant axon. They extended the RC equivalent circuit to include gated conductances
for Na
+
and K
+
ion species and all other conductances lumped as leakage [Figure
3.5(c)]. Each of these conductances is associated with an equilibrium potential,
represented by a battery in series with the conductance. The net current, which
flows into the cell through these channels, has the effect of charging the membrane
capacitance, giving the interior of the cell a membrane potential
−
ΔΦ
m
relative to the
exterior. When a current
I
inj
is injected into the system, the equivalent circuit of the
cell is written using Kirchoff's law as
d
ΔΦ
C
m
+++ −=
I
I
I
I
0
m
Na
K
Leak
inj
dt
where
I
Leak
is the leakage current required to maintain the constant resting poten-
tial in the absence of any depolarization. Substituting Ohm's law for currents due
to individual ions, we get
d
ΔΦ
(3.24)
C
m
=
I
− ΔΦ
(
− ΔΦ
)
g
− ΔΦ
(
− ΔΦ
)
g
− ΔΦ
(
− ΔΦ
)
g
m
inj
m
Na
Na
m
K
K
m
leak
leak
dt
Hodgkin and Huxley measured potassium and sodium conductance [Figure
3.5(d)] using a voltage clamp and space clamp techniques (described in Section
