Cellular Neuroscience (207) Ian Parker

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Cellular Neuroscience (207)Ian Parker

• Lecture 4 - The Hodgkin-Huxley Axon

http//parkerlab.bio.uci.edu
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The Action Potential
An electrical depolarization that propagates
rapidly (up to 10s of m per sec) along nerve
axons
record
stimulate
50 mV
overshoot
0 mV
depolarization
Rising phase
Falling phase
repolarization
- 70 mV
hyperpolarization
Afterpotential (undershoot)
Stimulus artifact
Conduction delay
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Basic mechanisms of the action potential
The action potential is a brief time when
the membrane potential is flipped positive
rather than negative inside. This arises because
the cell membrane becomes transiently permeable
to Na ions, which rush into the cell down their
concentration gradient, depolarizing it toward
ENa.
RISING PHASE FALLING PHASE

1. Na channels inactivate, so depolarizing, inward
   Na current stops.
2. Voltage-gated K channels open
3. Efflux of K ions down their electrochemical
   gradient repolarizes the cell toward Ek
4. Repolarization causes K channels to shut, but
   slow gating may cause undershoot below normal
   resting potential.

1. Depolarization (e.g. excitatory synaptic
input) opens voltage-dependent Na channels. 2.
Na ions enter cell causing 3. Depolarization
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Some properties of the action potential

• 1. Action potentials are all-or-none events.
  Once a stimulus exceeds threshold (ca. -45 mV) an
  action potential is triggered. Size of the
  action potential (peak 50 mV) is fixed, and
  does not depend on stimulus strength.
• 2. Action potentials propagate without decrement
  at a finite speed. Speed is fast by biological
  standards (several m per sec vs. um per sec for
  chemical signals), but much (million-fold)
  slower than an electrical signal along a wire.
• 3. Refractory period. After one action potential
  there is a short time (ms) when an axon cannot be
  stimulated to give another action potential.
  Primarily due to the time for Na channels to
  recover from inactivation. This is important
  because it
• a. Stops action potentials from traveling
  backwards
• b. Sets a limit to the maximum frequency of
  action potentials an axon can transmit.

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Hodgkin - Huxley analysis of the action
potential (early 1950s)
Voltage-clamp Technique that allows the voltage
across an axon membrane to be held at any desired
level, while measuring the resulting current flow
across the membrane. Used with giant (1 mm
diameter) squid axon, that allows easy insertion
of intracellular electrodes.
Feedback circuit compares the actual membrane
potential with the desired command voltage. Any
difference (error) is amplified and inverted,
and fed back into the axon as a current to bring
the potential to the desired level (like cruise
control on a car). Current flowing from the
circuit thus gives a direct measure of current
flowing acros the axon membrane.
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Currents flowing across a squid axon in response
to voltage steps
Depolarization to voltages more positive than
about -25 mV evokes a complex series of currents.
A transient current usually inward-, followed by
a slower developing , maintained outward current.
The initial transient current at first becomes
larger (more inward current) with increasing
depolarization, then reduces to zero at 60 mV,
and inverts to become outward at yet more
positive voltages. The slower current is always
outward, and becomes increasingly large at more
positive potentials.
Depolarization to -35 mV evokes only passive
responses
Hyperpolarization evokes only passive, leakage
currents
depolarize or hyperpolarize
Resting potential
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How to make sense of this pharmacologically
dissect the transient and maintained currents
into their ionic components
Total currents evoked by a range of depolarizing
stimuli
Blocking Na channels with tetrodotoxin abolishes
the initial transient current, leaving only the
slower, maintained outward K current.
Blocking K channels with TEA abolishes the slow
outward current, leaving just the fast, inward Na
currrent
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Current/voltage relationships for the initial and
maintained current components
Current amplitudes measured at their peaks
The delayed, outward current increases
progressively at increasingly positive voltages
Both currents begin to activate at about -35 mV.
The initial transient current increases with
voltages up to about 20 mV, then declines to
zero at about 50 - 60 mV, and becomes outward
at voltages gt 60 mV
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Currents through Na and K channels reflect both
the Ohmic dependence of current flow through
single channels, and the voltage-dependence of
channel open probability
We can separate these two effects by calculating
whole-cell conductance as a function of voltage
e.g. for transient Na current
IM
ENa 50 mV
Sigmoid relationship reflecting voltage-dependent
activation of Na channels
Current across the axon membrane is the product
of the single-channel Na current and the number
of Na channels open at a given voltage. We can
estimate the latter by calculating Na
conductance gNa IM/VM-ENa
VM
0 mV
g Na
Ichannel
VM
VM
0
50 mV
-50 mV
The conductance/voltage relationship for K
channels looks very similar, except that the
initial turn-on is a little less steep
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Equivalent circuit diagram for an axon membrane
The Na and K channels can be thought of as
variable resistors, whose values depend on
voltage, and which determine the importance of
their respective batteries (Na and K
equilibrium potentials) in setting the final
voltage across the cell membrane. Changing the
membrane potential involves charging the membrane
capacitance, so the voltage changes during an
action potential depend on the time course
(kinetics) of the Na and K conductance changes as
well as their peak values.
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So, what are the kinetics of gNa and gK?
0 mV
VM
-60 mV
gNa
gK
During depolarization, gNa shows both
time-dependent activation and inactivation. gK
shows only activation. During the falling phase
of an action potential, gK declines because the
membrane potential repolarizes, NOT because K
channels inactivate
The kinetics of Na channel activation and
inactivation, and the kinetics of K channel
activation all become faster at more positive
potentials
- 20 mV
20 mV
gK
gNa
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Time course of K channel activation and closing
H-H expained the openinng of a K channel as being
controlled by movement of several independent
particles (voltage sensors). The channel is
open only if all are in the ON
position. Suppose 4 particles, each with
probability n of being in the ON
position. Probability of channel opening is then
given by n4 Further suppose that probability n
changes exponentially with time following a
voltage step
VM
gK (varies as n)
n
gK (varies as n4)
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More about gating particles
The K channel molecule has 4 charged particles
that move according to the voltage across the
membrane. In the 1950s these particles were
merely postulates we now know they correspond
to the S4 regions of the channel molecule
- - - - - - - - - - - - -
Out




ON position
OFF position





In - - - - - - - - - - - - -
n varies with voltage and with time. H-H
characterized it by two parameters ninfinity
probability of being in the ON state after
holding at a given voltage for a very long
time tn the rate at which n changes following a
step to a new voltage. From their experimental
data H-H could derive empirical values for these
parameters.
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What about Na channels?

• H-H described Na channel activation in the same
  way as for K channels, by movement of gating
  particles.
• For the Na channel, these are referred to as m
  (not n), and movement of only 3 (not 4) was
  required to give the best fit to the data.
• Also, another gating particle (h only one per
  channel) was introduced to account for the
  inactivation of the Na channel

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The Hodgkin Huxley Equation
Ionic currents across the axon membrane can be
described in terms of three components
IM m3hgNa(E-ENa) n4gK(E-EK) gL(E-EL)
Na current K current leak
current
Dont worry you wont be asked to remember this
in an exam!
All of the electrical excitability of the
membrane is embodied in the time- and
voltage-dependence of n, m and h. The model
accurately predicts observed action potentials in
many species, and is one of the few cases where
we can reduce biology to an equation. But, like
any other model it cannot prove the existence of
underlying mechanisms.