Cellular Neuroscience (207) Ian Parker

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Cellular Neuroscience (207)Ian Parker

• Lecture 5 - Action potential propagation

http//parkerlab.bio.uci.edu
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The problem axons are not a very good
electrical wire
RM
CM
IN
OUT
RA
The axoplasmic resistance RA is high (axons are a
very long, thin tube), and the membrane
resistance RM forms a series of potential
dividers, so a voltage at one end steadily
decrements along the length of the axon. AND,
for fast changing signals charging of the
membrane capacitance CM further causes the signal
to diminish.
So, injection of a square pulse of current at one
end of an axon induces a passive voltage change
whose amplitude declines exponentially (space
constant) with distance. And, the voltage change
becomes progressively more rounded as the axon
membrane acts like a low-pass filter. Space
constant is typically 1 mm not nearly enough
to get a signal to your big toe!
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Solution the action potential serves as an
amplifier to boost the signal as it travels along
the axon. If an axon membrane is depolarized to
threshold ( -35 mV) it will trigger an
all-or-none action potential, that depolarizes to
50 mV
Local circuits
Depolarization here has no effect as membrane is
refractory
Action potential
Passive current flow depolarizes membrane ahead
of action potential
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Excited region of axon at instant of time
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What limits the propagation velocity of an action
potential?
The excited region of membrane at an action
potential must depolarize the membrane ahead past
threshold. This involves charging the membrane
capacitance. So, back to RC circuits.
E (voltage at peak of action potential
CM
membrane
RA
Voltage at membrane ahead of the action potential
will rise exponentially with time constant t RA
CM (Resistance of extracellular fluid is low
compared to RA, so we ignore it)

• Thus, an axon will transmit faster if either or
  both
• RA is smaller,
• CM is smaller

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How to make a faster axon
1. The brute force ignorance method (like a
squid)
Relationship between axon diameter and conduction
velocity
Membrane area per unit length proportional to 2 p
r i.e. membrane capacitance increases linearly
with radius.
Cross section of an axon
Cross sectional area proportional to p r2 i.e.
longitudinal axonal resistance decreases as the
square of the radius
Thus, the net effect is that the time constant
for charging the membrane capacitance shortens
about linearly with increasing radius. So,
doubling the diameter of an axon will speed
action potential propagation about 2x, tripling
the diameter will speed about 3x and so on. The
squid takes this to an extreme. But, you cant
fit many giant axons into a sciatic nerve!
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How to make a faster axon
2. The intelligent way myelinating the axon to
increase effective membrane thickness and thereby
decrease membrane capacitance without much
increasing the diameter of the axon
Cross section of myelinated axon
Cross section of an unmyelinated axon
Membrane thickness many-fold increased
Overall diameter not much increased
Capacitance decreases linearly with increasing
thickness of dielectric (membrane). Because a
cell membrane is so thin to begin with ( 7nm),
capacitance can be reduced gt50-fold with only a
modest increase of diameter of the axon as a
whole. Myelination achieved by oligodendrocytes
wrapping themselves around and around the axon
(like a Swiss roll), leaving behind double-layers
of cell membrane.
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Problem if all the axon were myelinated, no
space left to put Na channels.
Solution leave gaps of exposed axon membrane
Nodes of Ranvier
Propagation of the action potential is saltatory
jumps from node to node. The delay in triggering
an action potential at the next node is small
(i,.e propagation speed is fast), because time
constant for charging the intervening myelinated
segment is fast. A safety margin is built in
passive electrotonic spread allows the action
potential to skip over 2 or 3 damaged nerves
before it is attenuated below threshold.