Bioelectricity/ biopotentials II
• Malmivuo, Plonsey (MP)
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Ch 2: Nerve and muscle cells
Ch 3: Subthreshold membrane phenomena
Ch 4: Active behavior of the membrane (4.1-4.4)
Ch 5: Synapse (5.1-5.3)
1
The action potential
• The resting state of the cell can be altered by
chemical, electrical or mechanical stimulation.
• The stimulation causes a rapid increase in Na+
conductance and a delayed increase in the K+
conductance.
• The membrane potential increases from its resting
value of about –90 mV towards the Nernst potential
for Na+ (+60 mV). When the K+ conductance
increases the potential decreases towards the resting
potential.
2
1
3
4
2
The Hodgkin-Huxley cell
membrane model
• General cable equation for cell membrane
• Voltage clamping experiments
• Kinetics of ion conductances
5
6
3
7
• The cable equation:
1  2V
V

I

c
 I ion
m
m
ri  re x 2
t
Iion can be obtained from a HH model of the cell
membrane.
8
4
• If the conductances are constant, the cable equation
is linear.
• In general, the conductances are a function of V and
time.
1  2V
V
 cm
 g K (V , t )(V  EK )  g Na (V , t )(V  E Na )  g L (V  EL )
2
ri  re x
t
9
• Ionic current composition?
Squid giant axon potential
when diluting Na+ with
isotonic dextrose.
A.33% sea water (curve 2)
B.50% sea water (curve 2)
10
5
Fig. 4.4. Realistic voltage clamp measurement circuit.
Current is applied through electrodes (a) and (e), while
the transmembrane voltage, Vm, is measured with
electrodes (b) and (c). The current source is controlled to
maintain the membrane voltage at some preselected
value Vc.
11
12
6
13
14
7
Kinetics of Na + and K+ conductances
15
Model for Na/ K conductance
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•
•
•
•
•
gNa= m3hGNa
GNa = maximal conductance
m = probability for open Na-activation gate
h = probability for open Na-inactivation gate
gK = n4GK
n = probability for opening a K-gate
16
8
HH model of voltage clamped axon
• General cable eq:
1  2V
V

c
 I ion
m
ri  re x 2
t
V
V
 0, gives 0  cm
 I K  I Na  I L
x
t
17
0  cm
dV
 GK n 4 (Vm  EK )  GNa m3h(Vm  ENa )  GL (Vm  VL )
dt
• Differential equation for m:
dm
  m (1  m)   m m,
dt
 m  0.1(V  25) /(e 0.1V  2.5  1),
 m  4eV /18
• Full set of equations are given in the guidelines for
the simulations
18
9
A constant current of
50 uA/cm2
19
Subthreshold stimulus
20
10
Stimulus just above threshold
21
Stronger stimulus
22
11
Comparison
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12